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 ME  Vol.11 No.9 , September 2020
GDP 6% to 16% —Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II)
Abstract: GDP (Gross Domestic Product) is useful in understanding economic disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (TCE), this paper demonstrates that for the GDP inflation rate of economic society, the normal range of theory is [5.8114%, 16.359%] nearly to [6%, 16%], and center is 10.208% nearly to 10%. The first or second transfer law of economic diseases changes according to the different GDP inflation rate whether in the normal range or not. The treatment principle: “Don’t have economic disease cure cure non-ill” (不治已病治未病) is abiding by the first or second transfer law of economic diseases. Assume that the range of the GDP inflation rate is divided into four parts from small to large. Both second and third are for a healthy economy. The treating works are the prevention or treatment for a more serious relation economic disease which comes from the first transfer law. And both first and fourth are for an unhealthy economy. The treating works are the prevention or treatment for a more serious relation economic disease which comes from the second transfer law. Economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. As an application, the Chinese GDP inflation rate is used for the water system of steady multilateral system.

1. Introduction

GDP (Gross Domestic Product) is useful in understanding economic disease. GDP is refers to in a certain period (a quarter or a year), the economy of a country or region to produce the value of all final goods and services, is often recognized as the best indicators of national economy. It not only can reflect a country’s economic performance, also can reflect a country’s national power and wealth.

Through the growth rate of price index to calculate the rate of inflation, prices can be respectively by the consumer price index (CPI), the producer price index (PPI), the retail price index (RPI), the gross domestic product (GDP), and the gross national product (GNP) as conversion price index. In order to examine a country’s national power and wealth, general use of GDP, its formula is as follows:

x < a = 5 .8114% (1)

where the type of digital and a = 5 .8114% x < t 0 = 10 .208% is the number in the subscript, t 0 = 10 .208% x b = 16 .359% in x > b = 16 .359% on behalf of the production of all kinds of the final product, min = 0.11 , max = 0.81 , t 0 = 10.208 % in ρ ( x ) = 1 / 2 λ ( x ) + 1 / 2 ρ ( x ) 1 ρ ( x ) = 1 / 2 λ ( x ) λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) on behalf of all kinds of the price of the final product.

Both the rate of GDP inflation and the GDP are two different concepts. Calculation method of the rate of GDP inflation through the calculation of the GDP changes:

x min (2)

where the price rise level from low to high, to base the level of prices for base. One of the base period is selected one price level as a reference, so that you can put the other periods of price level with a comparison between base level to measure the current level of inflation.

Note on the type, the GDP inflation rate is not a price index, which is not a price rise, but the GDP price index to rise. In fact, what is said above is just one of the five methods (CPI, PPI, RPI, GDP, GNP) of measuring inflation index reduced living consumption laws, but it is the most commonly used for studying a country’s national power and wealth, in addition to the gross national product (GNP), the consumer price index (CPI), the producer price index (PPI) and the retail price index (RPI) conversion method.

The GDP is the government measure of a country’s national power and wealth inflation one of the data. Popular speaking, the GDP inflation rate is the value of all final goods and services on the market growth percentage. As an important indicator, observe the level of a country’s national power and wealth inflation in China, much attention has been paid to also for such an important indicator, as a new era of youth, more objective view should be observed. First of all, let us meet the GDP. The GDP is to reflect a country’s national power and wealth, related to all final goods and services calculated price, usually observed inflation as an important indicator.

Ahmed & Suliman (2011) have found that the direction of causation between real GDP and prices is uni-directional from real GDP to CPI without any feedback. The GDP plays a key role in the CPI. So the central bank can minimize the inflation by taking certain predictive measures to keep the input prices under control. Because of the causation relation between the GDP and the CPI, the normal range of the GDP inflation rate can be obtained from the normal range of the CPI inflation rate. It is found that the normal range of the CPI inflation rate is from 2% to 5%. There are a lot of evidences (e.g., experimental identification for probability and real applications) to support this viewpoint, such as, Crone et al. (2010), Pauhofova & Qineti (2002), Funke et al. (2015), Formica & Kingston (2015), Fan et al. (2009), Adams (2014), Hausman (1999), Nahm (2015), Moosa (1997), Zhao (2013), Daniel (2012), Anonymous (1999a, 1999b), and so on.

It is believed that the normal range of the GDP inflation rate is from 6% to 16%. It is because the GDP is more sensitive than the CPI, so changes in the wider range. Thus the economic social system identifies an important indicator for an economic social system health: the value of GDP inflation rate, which, under normal conditions, ranges from 6% to 16%. Outside this range (low: Yin condition; high: Yang condition), economic disease appears. Almost always, when there is economic disease, the condition of inflation rate is a Yin condition, little is a Yang condition.

In this paper, the rate of GDP inflation is considered as the wealth level rises rather than the currency quantity rises from the basic concept of GDP. It is because the GDP is the direct reflection of living standards, although the wealth level increase is difficult to be controlled directly.

The GDP is a general parameter linking together the complexity of relations between subsystem pairs of economic social system, economic social system itself, the capabilities for intervention reaction and self-protection of the economic social system as an economy and mind as a whole, related to the environment, food, health and personal history, air, water, earth, climate, season, etc. GDP is as useful in understanding economic disease as the average is in statistics, or as the expected value is in probability calculation.

The economic social system as an economy begins to activate the necessary mechanisms to restore this parameter to its appropriate range. If the economic social system as an economy is unable to restore optimal GDP levels, the economic disease may become chronic and lead to dire consequences.

Zhang (1993, 2007, 2011a, 2011b, 2012, 2013, 2020) have started a great interest and admired works for Traditional Chinese Economics (TCE), where, through mathematical reasoning, they demonstrate the presence of incompatibility relations, which are predominant in daily life, yet absent in traditional Aristotelian Western logic.

Many people as Western persons are beyond all doubt the Yin Yang Wu Xing theory is superior to the traditional true-false logic, which does not contemplate incompatibility relations, which Zhang & Zhang (2013) have expertly explained from a mathematical standpoint.

The work Zhang (1993, 2007) has started, allows many people like Western person to think of a true re-foundation of mathematical language, to make it a better suited tool for the needs of mankind economic social system and the environment. Even so, Zhang & Zhang (2013) also bring to light the difficulty of establishing the values of both the intervention reaction coefficients ρ1, ρ2 and the self-protection coefficient ρ3 as parameters with due accuracy.

In this paper, the introduction of a parameter such as a GDP inflation rate will be suggested, in order to facilitate the understanding and the calculation of the values of both the intervention reaction coefficients ρ1, ρ2 and the self-protection coefficient ρ3. This paper ventures to suggest this with all due to respect, because it is believed that the path Zhang & Zhang (2013) have started, in such an understandable way from the mathematical point of view, will be very useful for all mankind searching for tools to understand the mechanisms of economic social system.

The article proceeds as follows. Section 2 contains a parameter model and basic theorems, in order to explain both the intervention reaction coefficients ρ1, ρ2 and the self-protection coefficient ρ3 through the introduction of a parameter model to study the normal range of a GDP inflation rate, while the first or second transfer law of economic diseases is demonstrated in Section 3, proved through the concept of both relation diseases and a relationship analysis of steady multilateral systems. Furthermore, if the range of GDP inflation rate is divided into four parts, for the economy in every part, the prevention or treatment method of economic diseases as treatment principle of TCE is given in Section 4. As an application, the Chinese GDP inflation rate is used for the water system of steady multilateral system in Section 5 and conclusions are drawn in Section 6.

2. Parameter Model and Basic Theorems

The concepts and notations in Zhang & Zhang (2013) are used still and start.

Let x max be the gold number. Denoted λ ( x ) + , namely healthy number. It is because the healthy number ρ ( x ) 0 can make the healthy balance conditions x = t 0 , λ ( x ) = 0 and ρ ( x ) = 1 hold if 0 < ρ ( x ) 1 , 0 λ ( x ) < + and λ ( x ) . Assume that x ( min , t 0 ] , namely balance number. It is because under a poor self-protection ability, the balance number x [ t 0 , max ) can make the poor healthy balance conditions:

ρ ( x )

and λ ( x ) hold if λ ( x ) [ 0 , + ) , λ ( x ) and ρ ( x ) . Thus ρ ( x ) ( 0 , 1 ] .

A parameter model of a GDP inflation rate in a mathematical sense based on Yin Yang Wu Xing Theory of TCE is reintroduced by using the functions λ ( x ) and x ( min , t 0 ] of the GDP inflation rate d λ ( x ) d x = ( x min ) ( max x ) ( t 0 x ) [ ( max x ) ( x min ) ] [ ( x min ) ( max x ) ] 2 = ( x min ) ( max x ) + ( t 0 x ) [ ( max x ) ( x min ) ] [ ( x min ) ( max x ) ] 2 = [ ( x min ) ( max t 0 ) + ( t 0 x ) ( max x ) ] [ ( x min ) ( max x ) ] 2 < 0. described as follows.

Let λ ( x ) be a GDP inflation rate, where the values −0.11 and 0.81 are the minimum and maximum acceptable the GDP inflation rate. Denoted the value 0.10208 is the target as the expectation of the GDP inflation rate. Define a function x [ t 0 , max ) of the GDP inflation rate d λ ( x ) d x = ( x min ) ( max x ) ( x t 0 ) [ ( max x ) ( x min ) ] [ ( x min ) ( max x ) ] 2 = ( x min ) ( max x ) ( x t 0 ) [ ( max x ) ( x min ) ] [ ( x min ) ( max x ) ] 2 = [ ( max x ) ( t 0 min ) + ( x t 0 ) ( x min ) ] [ ( x min ) ( max x ) ] 2 > 0. in below:

ρ ( x ) (3)

A parameter model is considered as

λ ( x ) (4)

Theorem 2.1 Under model (4), the following statements hold.

1) The one that λ ( x ) [ 0 , + ) is equivalent to the other that

d ρ ( x ) d λ ( x ) = ( 1 / 2 ) [ 1 ] [ λ ( x ) + 1 / 2 ] 2 = 1 2 [ λ ( x ) + 1 / 2 ] 2 < 0.

where λ ( x ) is a monotone decreasing function of ρ ( x ) if ρ ( x ) ( 0 , 1 ] or a monotone increasing function of d λ ( x ) d ρ ( x ) = 1 2 ( ( 1 ) ρ ( x ) ( 1 ρ ( x ) ) [ 1 ] ρ ( x ) 2 ) = 1 2 ρ ( x ) 2 < 0. if f ( u ) = ( u + u 3 ) ( 1 u 3 ) , u ( 0 , 1 ] ; and f ( u ) is a monotone decreasing function of f ( u ) = 1 + 6 u 2 > 0 if f ( ρ 0 ) = ( ρ 0 + ρ 0 3 ) ( 1 ρ 0 3 ) = 0 ; and ρ ( x ) ρ 0 is a monotone decreasing function of f ( ρ ( x ) ) = ( ρ ( x ) + ρ ( x ) 3 ) ( 1 ρ ( x ) 3 ) f ( ρ 0 ) = 0 if 1 ρ ( x ) 2 ρ ( x ) ρ ( x ) 2 .

2) If λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) 1 ρ 0 2 ρ 0 = ρ 0 2 ρ ( x ) 2 , then λ ( x ) ; ρ ( x ) ; and 0 < ρ 0 ρ ( x ) .

3) If λ ( x ) ρ ( x ) = 1 ρ ( x ) 2 ρ ( x ) 2 1 ρ 0 2 ρ 0 2 = ρ 0 ρ ( x ) , then h ( ρ ( x ) ) = λ ( x ) ρ ( x ) ; ρ ( x ) ; and 0 < ρ 0 ρ ( x ) .

4) Taking h ( ρ ( x ) ) = λ ( x ) ρ ( x ) and d h ( ρ ( x ) ) d ρ ( x ) = 1 2 ( ( 1 ) ρ ( x ) 2 ( 1 ρ ( x ) ) [ 2 ρ ( x ) ] ρ ( x ) 4 ) = ρ ( x ) 2 2 ρ ( x ) 3 < 0 where λ ( x ) ρ ( x ) 2 = 1 ρ ( x ) 2 ρ ( x ) 3 1 ρ 0 2 ρ 0 3 = 1 , there are h ( ρ ( x ) ) = λ ( x ) ρ ( x ) 2 , ρ ( x ) , and

0 < ρ 0 ρ ( x ) ,

where h ( ρ ( x ) ) = λ ( x ) ρ ( x ) 2 .

5) Taking d h ( ρ ( x ) ) d ρ ( x ) = 1 2 ( ( 1 ) ρ ( x ) 3 ( 1 ρ ( x ) ) [ 3 ρ ( x ) 2 ] ρ ( x ) 6 ) = 2 ρ ( x ) 3 2 ρ ( x ) 4 < 0 , g ( u ) = ( u + c u 3 ) ( 1 c u 3 ) , u , c ( 0 , 1 ] and g ( u ) where g ( u ) = 1 + 6 c u 2 > 0 , there are

Firstly, 0 < c 1 , g ( u ) = 2 ( c 1 ) u 3 + f ( u ) and f ( u ) = ( u + u 3 ) ( 1 u 3 ) , u ( 0 , 1 ] if

ρ ( x ) < ρ 0 ;

Secondly, g ( ρ ( x ) ) < 0 , | g ( ρ ( x ) ) | > 2 ( 1 c ) ρ 0 3 and g ( ρ ( x ) ) < g ( ρ 0 ) = 2 ( c 1 ) ρ 0 3 + f ( ρ 0 ) = 2 ( c 1 ) ρ 0 3 0 where

g ( ρ ( x ) ) < 0 if ( ρ 1 + ρ 2 ρ 3 ) = ρ ( x ) + c ρ ( x ) 3 < 1 c ρ ( x ) 3 = 1 ρ 2 ρ 3 . in which g ( u ) = 2 c u 3 ( 1 u ) ;

Thirdly, g ( u ) = 0 , c = 1 u 2 u 3 and 1 u 2 u 3 where

c ( u ) if c ( u ) = 1 u 2 u 3 in which u ( 0 , 1 ] ;

Finally, c ( u ) = 1 2 ( 3 u 4 + 2 u 3 ) = 1 2 u 4 ( 3 + 2 u ) < 0 , , u ( 0 , 1 ] . , c c ( u ) and c 1 u 2 u 3 where

g ( u ) = 2 u 3 ( c 1 u 2 u 3 ) 0 if ( u + c u 3 ) ( 1 c u 3 ) in which 0 c < c ( u ) .

In particular, when c is nearly to 1/2, there are 0 c < 1 u 2 u 3 , g ( u ) = 2 u 3 ( c 1 u 2 u 3 ) < 0 and the following statements hold.

a) The absolute value ( u + c u 3 ) < ( 1 c u 3 ) is nearly to 0 if

1 u 2 u 3 = 1 2 in which u = ρ 0 .

b) The value c ( u ) = 1 u 2 u 3 is included in the interval

u ( ρ 0 , 1 ] if u [ ρ 0 , ρ 0 ) 1 1 u 2 u 3 > 1 2 in which u [ ρ 0 , 1 ) 0 < 1 u 2 u 3 1 2 .

c) The value | g ( u ) | = | 2 c u 3 + u 1 | ( ρ 0 ) 3 = 0.31767 , u [ ρ 0 , 1 ) is included in the interval

0 c < 1 u 2 u 3 1 2 if | g ( u ) | = 2 u 3 ( 1 u 2 u 3 c ) < 2 u 3 ( 1 u 2 u 3 ) = 1 u 1 ρ 0 = ( ρ 0 ) 3 = 0.31767. in which | g ( u ) | = | 2 c u 3 + u 1 | 2 ρ 0 3 = 0.41024 , u [ ρ 0 , ρ 0 ) . #

Corollary 2.1 Under model (2.2), the following statements hold.

1) For any 0 c 1 2 < 1 u 2 u 3 1 , there is an unique solution | g ( u ) | = 2 u 3 ( 1 u 2 u 3 c ) < 2 u 3 ( 1 u 2 u 3 ) = 1 u 1 ρ 0 = 2 ρ 0 3 = 0.41024. and there is also an unique solution | g ( u ) | = | 2 c u 3 + u 1 | 0.31767 , u [ ρ 0 , ρ 0 ) , such that

1 2 < c < 1 u 2 u 3 1

| g ( u ) | = | 2 u 3 ( c 1 u 2 u 3 ) | 2 u 3 1 2 = u 3 ( ρ 0 ) 3 = 0.31767.

2) The condition g ( u ) = 2 u 3 ( c 1 u 2 u 3 ) is equivalent to each of the following conditions:

u ( 0 , 1 ]

ρ 1 ρ 3 = ρ ( x ) ( 1 c ) ρ ( x ) / 2

3) The condition ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) ρ ( x ) 2 / 2 is equivalent to each of the following conditions:

g ( ρ 0 ) = ( 1 2 c ) ( ρ 0 ) 3

g ( u ) = 2 u 3 ( c 1 u 2 u 3 )

4) The condition 0 < c < 1 u 2 u 3 1 2 is equivalent to each of the following conditions:

u [ ρ 0 , 1 )

g ( ρ 0 ) = 2 ( 1 c ) ρ 0 3

5) The condition g ( ρ 0 ) = ( 1 2 c ) ( ρ 0 ) 3 is equivalent to each of the following conditions:

ρ 0 3 = 0.20512 , 0

0 < c 1 2 < 1 u 2 u 3 1 #

Remark 1. In west, through experiment or through practice observation, by using the Granger causality relation between the GDP and the CPI, many researchers can obtain the normal range of the GDP inflation rate as u [ ρ 0 , ρ 0 ) from the normal range of the CPI as g ( ρ 0 ) = 2 ( 1 c ) ρ 0 3 . But in TCE, from Yin Yang Wu Xing Theory, Zhang & Zhang (2013) have already determined: g ( ρ 0 ) = ( 1 2 c ) ( ρ 0 ) 3 for the normal range of a healthy economy. Assume that ρ 0 3 = 0.20512 , 0 , 1 2 < c < 1 u 2 u 3 1 and u [ ρ 0 , ρ 0 ) where u = ρ ( x ) for an economic society which has the capabilities of both intervention reaction and self-protection. From Corollary 2.1, the condition ρ0 ≤ ρ1 ≤ 1 is equivalent to that 0 < d < 1 . In other words, in Theory of TCE, the normal range of the GDP inflation rate is considered as u ( 0.11 , 10 .208% ] , nearly to v ( 10 .208% , 0.81 ) , and center is 10.208 % nearly to 10%. Of course, little difference of the two intervals which makes the diagnosis of disease as a result, there may be no much difference as a suspect. In fact, TCE uses the rule λ ( 0.027047 ) = 0 λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) λ ( u ) = λ ( v ) = ( 1 d ) / ( 2 d ) , from Yin Yang Wu Xing Theory instead of the normal range of a GDP inflation rate. The equivalence of Corollary 2.1 shows that TCE is The scientific which is from TCM (Traditional Chinese Medicine).

Zhang & Zhang (2013) have already determined: an economy is said a healthy mathematical complex system when the intervention reaction coefficient λ ( x ) satisfies x ( 0.11 , 10 .208% ] . In logic and practice, it's reasonable that x [ 10 .208% , 0.81 ) is near to 1 if the input and output in a complex system is balanced, since a mathematical output subsystem is absolutely necessary other subsystems of all consumption. In case: 0 ( 1 d ) / ( 2 d ) < + , all the energy for intervening mathematical complex subsystem can transmit to other mathematical complex subsystems which have neighboring relations or alternate relations with the intervening mathematical complex subsystem. The condition λ ( u ) = λ ( v ) = ( 1 d ) / ( 2 d ) can be satisfied when ρ ( u ) = 1 / 2 λ ( u ) + 1 / 2 = d = 1 / 2 λ ( v ) + 1 / 2 = ρ ( v ) and d = ρ 0 for a mathematical complex system since λ ( u ) = λ ( v ) = ( 1 ρ 0 ) / ( 2 ρ 0 ) = ρ 0 2 implies ( ρ 0 + ρ 0 3 ) = ( 1 ρ 0 3 ) . In this case, d = ρ 0 . If this assumptions is set up, then the intervening principle: “Real disease with a healthy economy is to rush down his son and virtual disease with a healthy economy is to fill his mother” based on “Yin Yang Wu Xing” theory in image mathematics by Zhang & Shao (2012), is quite reasonable. But, in general, the ability of self-protection often is insufficient for an usual mathematical complex system,

i.e., λ ( u ) = λ ( v ) = ( 1 ρ 0 ) / ( 2 ρ 0 ) = ( ρ 0 ) 2 / 2 is small. A common standard is ( ρ 0 ) 3 = 1 ρ 0 which comes from the

balance condition a = 5 .8114% , b = 16 .359% , t 0 = 10 .208% of the loving relationship if 0 . In other words, there is a principle which all losses are bear in mathematical complex system. Thus the general condition is often φ ( X ) . Interestingly, they are all near to the golden numbers. It is the idea to consider the unhealthy balance number Δ φ ( X ) = Δ < 0 since the poor condition of self-protection ability Δ φ ( S X ) = ρ 1 Δ < 0 can make that the unhealthy balance conditions hold: + , Δ φ ( X S ) = ρ 2 Δ < 0 , and of the loving relationship if Δ φ ( K X ) = ρ 1 Δ > 0 and + .

By Theorem 2.1 and Corollary 2.1, the interval Δ φ ( X K ) = ρ 2 Δ > 0 implies the following condition

;

and the interval Δ φ ( K X ) = ρ 1 Δ > 0 implies the following condition

x [ a , b ] ;

and the interval 1 ρ 1 = ρ ( x ) ρ 0 implies the following condition

ρ 1 + ρ 2 ρ 3 = ρ ( x ) + c ρ ( x ) 3 1 ρ 2 ρ 3 = 1 c ρ ( x ) 3 ,

where 1 c [ 1 ρ ( x ) ] / ( 2 ρ ( x ) 3 ) > 0 , x t 0 since c > 0 ; and the interval Δ φ ( K X ) 1 = ρ 3 Δ < 0 implies the following condition

0 ,

where Δ φ ( X K ) 1 = ρ 1 ρ 3 Δ < 0 since + .

The last one is the healthy interval in an economic society’s self-protection ability poor conditions. The interval range than the normal economic society health requirements is too strict, only the first three interval ranges are considered as a normal economic society health ranges. If keep two decimal places, then first three intervals are the same as Δ φ ( S X ) 1 = ρ 2 ρ 3 Δ < 0 . This shows that range is stable. The interval as the normal range of a GDP inflation rate may be also appropriate. To conservative estimates, the length of the largest of the first three interval ranges, i.e., Δ φ ( X S ) 1 = ρ 1 ρ 3 Δ > 0 , is used as our theoretical analysis of the normal range. In fact, the range + is better than the range Δ φ ( X ) 1 = ρ 2 ρ 3 Δ > 0 because both

and ρ 3 = ρ 1 = ρ ( x )

satisfy the healthy balance conditions: c = 1 , Δ φ ( X ) 2 = Δ φ ( X ) 1 + Δ φ ( X ) = ( 1 ρ 2 ρ 3 ) Δ = ( 1 c ρ ( x ) 3 ) ( 1 ρ ( x ) 3 ) < 0 , and Δ φ ( S X ) 2 = Δ φ ( S X ) 1 + Δ φ ( S X ) = ( ρ 1 + ρ 2 ρ 3 ) Δ = ( ρ ( x ) + c ρ ( x ) 3 ) Δ ( ρ ( x ) + ρ ( x ) 3 ) Δ < 0 , at the same time if Δ φ ( K X ) 2 = Δ φ ( K X ) 1 + Δ φ ( K X ) = ( ρ 1 ρ 3 ) Δ = ρ ( x ) ( 1 c ) Δ 0 + , , Δ φ ( X K ) 2 = Δ φ ( X K ) 1 + Δ φ ( X K ) = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ 0 + , and Δ φ ( X S ) 2 = Δ φ ( X S ) 1 + Δ φ ( X S ) = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ 0 . where Δ φ ( X ) 2 = ( 1 ρ 2 ρ 3 ) Δ = ( 1 c ρ ( x ) 3 ) Δ < 0 . In other words, the parameter x [ a , b ] or the range 1 ρ ( x ) ρ 0 is the healthy condition of both the killing relationship and the loving relation at the same time. But neither are the others. The GDP inflation rate must be precise calculation to keep at least 6 decimal places can ensure correct because of its sensitivity to the diagnosis of disease. #

Remark 2. Western Economics is different from TCE because the TCE has a concept of Chi or Qi as a form of energy. From the energy concept, that one organ or subsystem of the economic society is not running properly (or disease, abnormal), is that the energy deviation from the average of the organ is too large, the high (real disease) or the low (virtual disease). For the normal range of a GDP inflation rate of some economic society as ( ρ ( x ) + ρ ( x ) 3 ) ( 1 ρ ( x ) 3 ) , in TCE, if c 1 , the economy is considered as a real disease since the GDP inflation rate is too high; if 0 ρ 3 = c ρ ( x ) < ρ ( x ) = ρ 1 , the economy is considered as a virtual disease since the GDP inflation rate is too low. Thus TCE identifies an important indicator for an economic society’s health: the value of the GDP inflation rate, which, under normal conditions, ranges from 5.8114% to 16.359%. Outside this range (too low: Yin condition; too high: Yang condition), disease appears. Almost always absolutely, when there is a virtual disease, the condition of the GDP inflation rate is a Yin condition; when there is a real disease, the condition of the GDP inflation rate is a Yang condition. But there do not exist these concepts of both real diseases and virtual diseases in Western Economics. #

Remark 3. Obviously, when applying the hypothesis of Theorem 2.1 and Corollary 2.1 to other fields rather than economic society’s health, it is necessary to identify a global parameter in each field. It is able to yield a general Yin or Yang condition in relation to the average behavior of the studied phenomenon, and it maintains the equations at a sufficiently simple level of writing and application. In fact, let 0 c < 1 where the values min and max are the minimum and maximum acceptable the index ρ 3 . Denoted the value ( ρ 1 ρ 3 ) = ρ ( x ) ( 1 c ) > 0 is the target as the expectation of the index ( ρ 2 ρ 1 ρ 3 ) = ρ ( x ) 2 ( 1 c ) > 0 such that ( ρ 2 ρ 1 ρ 3 ) = ρ ( x ) 2 ( 1 c ) < 0 . In Equations (3) and (4), replace Δ φ ( K X ) 2 = Δ φ ( K X ) + Δ φ ( K X ) 1 = ( ρ 1 ρ 3 ) Δ = ρ ( x ) ( 1 c ) Δ > 0 , Δ φ ( X K ) 2 = Δ φ ( X K ) + Δ φ ( X K ) 1 = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ > 0 , by Δ φ ( X S ) 2 = Δ φ ( X S ) + Δ φ ( X S ) 1 = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ < 0 , , respectively. The equivalent condition of a healthy economy 1 > c 0 can be obtained as ( ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ( ρ 1 ρ 2 ρ 3 ) ( ρ 1 + ρ 2 ρ 3 ) . , ( 1 ρ 2 ρ 3 ) ( ρ 1 + ρ 2 ρ 3 ) , where

( ρ 1 + ρ 2 ρ 3 ) ( ρ 1 ρ 2 ρ 3 ) ( ρ 1 ρ 3 ) = ρ ( x ) ( 1 c ) ρ ( x ) 2 ( 1 c ) = ( ρ 2 ρ 1 ρ 3 ) .

and

Δ φ ( X ) 2 = ( 1 c ρ ( x ) 3 ) Δ Δ = Δ φ ( X )

3. Relationship Analysis of Steady Multilateral Systems

3.1. Energy Changes of a Steady Multilateral System

In order to apply the reasoning to other fields rather than society economy’s health, Zhang & Zhang (2013) have started a steady multilateral system imitating a society economy. A most basic steady multilateral system is as follows:

Theorem 3.1 (Zhang & Shao, 2012) For each element x in a steady multilateral system V with two incompatibility relations, there exist five equivalence classes below:

0

φ ( X )

which the five equivalence classes have relations in Figure1. #

It can be proved by Theorem 3.2 below that the steady multilateral system in Theorem 3.1 is the reasoning model of Yin Yang Wu Xing in TCE if there is an energy function Δ φ ( X ) = Δ > 0 satisfying

Δ φ ( X S ) = ρ 1 Δ > 0

if increase the energy of + , where Δ φ ( S X ) = ρ 2 Δ > 0 , , Δ φ ( X K ) = ρ 1 Δ < 0 , + , Δ φ ( K X ) = ρ 2 Δ < 0 .

Figure 1. Finding Yin Yang Wu Xing model.

It is called the Yin Yang Wu Xing model, denoted by V 5 .

The Yin Yang Wu Xing model can be written as follows:

Define

corresponding to wood, fire, earth, metal, water, respectively, and assume

Δ φ ( X K ) = ρ 1 Δ < 0 where x [ a , b ] .

And take 1 ρ 1 = ρ ( x ) ρ 0 satisfying

ρ 1 + ρ 2 ρ 3 = ρ ( x ) + c ρ ( x ) 3 1 ρ 2 ρ 3 = 1 c ρ ( x ) 3

where 1 c [ 1 ρ ( x ) ] / ( 2 ρ ( x ) 3 ) > 0 , x t 0 is the Descartes product in set theory and Δ φ ( X K ) 1 = ρ 3 Δ > 0 is the multiplication relation operation. The relation multiplication of 0 is isomorphic to the addition of module 5. Then V 5 is a steady multilateral system with one equivalent relation R 0 and two incompatibility relations Δ φ ( K X ) 1 = ρ 1 ρ 3 Δ > 0 and + where the inverse relation operation is Δ φ ( X S ) 1 = ρ 2 ρ 3 Δ > 0 . The Yin and Yang means the two incompatibility relations and the Wu Xing means the collection of five disjoint classifications of .

Figure1 in Theorem 3.1 is the Figureof Yin Yang Wu Xing theory in Ancient China. The steady multilateral system V with two incompatibility relations is equivalent to the logic architecture of reasoning model of Yin Yang Wu Xing theory in Ancient China. What describes the general method of complex systems can be used in economic society complex systems.

By non-authigenic logic of TCE, i.e., a logic which is similar to a group has nothing to do with the research object by Zhang & Shao (2012), in order to ensure the reproducibility such that the analysis conclusion can be applicable to any a complex system, a logical analysis model which has nothing to do with the object of study should be chosen. The Tao model of Yin and Yang is a generalized one which means that two is basic. But the Tao model of Yin Yang is simple in which there is not incompatibility relation. The analysis conclusion of Tao model of Yin Yang cannot be applied to an incompatibility relation model. Thus the Yin Yang Wu Xing model with two incompatibility relations of Theorem 3.1 will be selected as the logic analysis model in this paper.

Western Economy is different from TCE because the TCE has a concept of Chi or Qi (气) as a form of energy of steady multilateral systems. It is believed that this energy exists in all things of steady multilateral systems (living and non-living) including air, water, food and sunlight. Chi is said to be the unseen vital force that nourishes steady multilateral systems’ body and sustains steady multilateral systems’ life. It is also believed that an individual is born with an original amount of Chi at the beginning of steady multilateral systems’ life and as a steady multilateral system grows and lives, the steady multilateral system acquires or attains Chi or energy from “eating” and “drinking”, from “breathing” the surrounding “air” and also from living in its environment. The steady multilateral system having an energy is called the anatomy system or the first physiological system. And the first physiological system also affords Chi or energy for the steady multilateral system’s meridian system (Jing-Luo (经络) or Zang Xiang (藏象)) which forms a parasitic system of the steady multilateral system, called the second physiological system of the steady multilateral system. The second physiological system of the steady multilateral system controls the first physiological system of the steady multilateral system. A steady multilateral system would become ill or dies if the Chi or energy in the steady multilateral system is imbalanced or exhausted, which means that Δ φ ( S X ) 1 = ρ 1 ρ 3 Δ < 0 , + and Δ φ ( X ) 1 = ρ 2 ρ 3 Δ < 0 .

For example, in TCE, a society economy as the first physiological system of the steady multilateral system following the Yin Yang Wu Xing theory was classified into five equivalence classes by Zhang & Zhang (2013) as follows:

ρ 3 = ρ 1 = ρ ( x )

c 1

Δ φ ( X ) 2 = Δ φ ( X ) 1 + Δ φ ( X ) = ( 1 ρ 2 ρ 3 ) Δ = ( 1 c ρ ( x ) 3 ) Δ ( 1 ρ ( x ) 3 ) Δ > 0 ,

Δ φ ( X S ) 2 = Δ φ ( X S ) 1 + Δ φ ( X S ) = ( ρ 1 + ρ 2 ρ 3 ) Δ = ( ρ ( x ) + c ρ ( x ) 3 ) Δ ( ρ ( x ) + ρ ( x ) 3 ) Δ > 0 ,

Δ φ ( X K ) 2 = Δ φ ( X K ) 1 + Δ φ ( X K ) = ( ρ 1 ρ 3 ) Δ = ρ ( x ) ( 1 c ) Δ 0 ,

Δ φ ( K X ) 2 = Δ φ ( K X ) 1 + Δ φ ( K X ) = ( ρ 2 ρ 1 ρ 3 ) Δ = ( x ) 2 ( 1 c ) Δ 0 , .

There is only one of both loving and killing relations between every two classes. General close is loving, alternate is killing.

In every category of internal, think that they are with an equivalent relationship, between each two of their elements there is a force of similar material accumulation of each other. It is because their pursuit of the goal is the same, i.e., follows the same “Axiom system”. It can increase the energy of the class at low cost near to zero if they accumulate together. Any nature material activity follows the principle of maximizing so energy or minimizing the cost. It means that “the same energy attracted to each other” (同气相招).

In general, the size of the force of similar material accumulation of each other is smaller than the size of the loving force or the killing force in a stable complex system. The stability of any a complex system first needs to maintain the equilibrium of the killing force and the loving force. The key is the killing force. For a stable complex system, if the killing force is large, i.e., Δ φ ( S X ) 2 = Δ φ ( S X ) 1 + Δ φ ( S X ) = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ 0 + . becomes larger by Theorem 3.3 below, which needs positive exercise, then the loving force is also large such that the force of similar material accumulation of each other is also large. They can make the complex system more stable. If the killing force is small, i.e., Δ φ ( X ) 2 = ( 1 ρ 2 ρ 3 ) Δ = ( 1 c ρ ( x ) 3 ) Δ > 0 becomes smaller by Theorem 3.3 below, which means little exercise, then the loving force is also small such that the force of similar material accumulation of each other is also small. They can make the complex system becoming unstable.

The second physiological system of the steady multilateral system controls the first physiological system of the steady multilateral system, abiding by the following rules.

Attaining Rule: The second physiological system of the steady multilateral system will work by using Attaining Rule, if the first physiological system of the steady multilateral system runs normally. The work is in order to attain the Chi or energy from the first physiological system of the steady multilateral system by mainly utilizing the balance of the loving relationship of the first physiological system.

In mathematics, suppose that the sub-economy of X is healthy. If X is intervened, then the second physiological system will attain the Chi or energy from X directly.

Suppose that the sub-economy of X is unhealthy. If X is intervened, then the second physiological system will attain the Chi or energy from X indirectly. If virtual X is intervened, it will attain the Chi or energy (Yang energy) from the son XS of X. If real X is intervened, it will attain the Chi or energy (Yin energy) from the mother SX of X. #

Affording Rule: The second physiological system of the steady multilateral system will work by using Affording Rule, if the first physiological system of the steady multilateral system runs hardly. The work is in order to afford the Chi or energy for the first physiological system of the steady multilateral system, by mainly protecting or maintaining the balance of the killing relationship of the steady multilateral system, to drive the first physiological systems will begin to run normally.

In mathematics, suppose that the sub-economy of X is healthy. The second physiological system doesn’t afford any Chi or energy for the first physiological system.

Suppose that the economy of X is unhealthy and the capability of self-protection is lack, i.e., x [ a , b ] and 1 ρ 1 = ρ ( x ) ρ 0 . The second physiological system will afford the Chi or energy for X directly, at the same time, affording the Chi or energy for other subsystem, in order to protect or maintain the balance of the killing relationship, abiding by the intervening principle of “Strong inhibition of the same time, support the weak”, such that the capability of self-protection is restored, i.e., ( ρ ( x ) + ρ ( x ) 3 ) ( 1 ρ ( x ) 3 ) and c 1 , to drive the first physiological system beginning to work.#

The Chi or energy is also called the food hereafter for simply. In order to get the food, by Attaining Rule, the second physiological system must make the first physiological system intervened, namely exercise. It is because only by intervention on the first physiological system, the second physiological system is able to get food.

Energy concept is an important concept in Physics. Zhang & Zhang (2013) introduce this concept to the steady multilateral systems imitating economy. And the image mathematics by Zhang & Shao (2012) uses these concepts to deal with the steady multilateral system diseases (mathematical index too high or too low). In mathematics, a steady multilateral system is said to have Energy (or Dynamic) if there is a non-negative function ρ 3 = c ρ ( x ) < ρ ( x ) = ρ 1 which makes every subsystem meaningful of the steady multilateral system. Similarly to Zhang & Zhang (2013), unless stated otherwise, any equivalence relation is the liking relation, any neighboring relation is the loving relation, and any alternate relation is the killing relationship.

Suppose that V is a steady multilateral system having an energy, then V in the steady multilateral system during a normal operation, its energy function for any subsystem of the steady multilateral system has an average (or expected value in Statistics), this state is called as normal when the energy function is nearly to the average. Normal state is the better state.

That a subsystem of the steady multilateral system is not running properly (or disease, abnormal) is that the energy deviation from the average of the subsystems is too large, the high (real disease) or the low (virtual disease).

In addition to study these real or virtual diseases, TCE is also often considered a kind of relation diseases. The relation disease is defined as the relation of two sick subsystems. In general, a relation disease is less serious if the relation satisfies one of both the loving relationship and the killing relationship of the steady multilateral system. In this case, in general, the GDP inflation rate 0 c < 1 which means ρ 3 . This relation disease is less serious because this relation disease can not undermine the loving order or the killing order of the steady multilateral system. The less serious relation disease can make the intervention increasing the sizes of both the intervention reaction coefficients ( ρ 1 ρ 3 ) = ρ ( x ) ( 1 c ) > 0 , ( ρ 2 ρ 1 ρ 3 ) = ρ ( x ) 2 ( 1 c ) > 0 and the self-protection coefficient ( ρ 2 ρ 1 ρ 3 ) = ρ ( x ) 2 ( 1 c ) < 0 .

But the relation disease is more serious if the relation not only doesn’t satisfy the killing relationship of the steady multilateral system, but also can destroy the killing order, i.e., there is an incest order. In this case, in general, the GDP inflation rate Δ φ ( X K ) 2 = Δ φ ( X K ) + Δ φ ( X K ) 1 = ( ρ 1 ρ 3 ) Δ = ρ ( x ) ( 1 c ) < 0 , which means Δ φ ( K X ) 2 = Δ φ ( K X ) + Δ φ ( K X ) 1 = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) < 0 , . This relation disease is more serious because the relation disease can destroy the killing order of the steady multilateral system if the disease continues to develop. The more serious relation disease can make both the intervention reaction coefficients 1 > c 0 , Δ φ ( S X ) 2 = Δ φ ( S X ) + Δ φ ( S X ) 1 = ( ρ 2 ρ 1 ρ 3 ) = ρ ( x ) 2 ( 1 c ) Δ > 0 and the self-protection coefficient 1 > c 0 decreasing response to intervention.

There are also many relation diseases which cannot destroy the loving order or the killing order of the steady multilateral system although the relation doesn’t satisfy strictly the loving relationship or the killing relationship of the steady multilateral system, i.e., there is not an incest order. These relation diseases are called rare since they are hardly occurrence for a healthy economy.

The purpose of intervention is to make the steady multilateral system return to normal state. The method of intervention is to increase or decrease the energy of a subsystem.

What kind of intervening should follow the principle to treat it? Western economics emphasizes directly mathematical treatments on the sick subsystem after the disease of subsystem has occurred, but the indirect intervening of oriental economics of TCE is required before the disease of subsystem will occur. In mathematics, which is more reasonable?

Based on this idea, many issues are worth further discussion. For example, if an intervening has been implemented to a disease subsystem before the disease of subsystem will occur, what relation disease will be less serious which does not need to be intervened? what relation disease will be more serious which needs to be intervened?

3.2. Kinds of Relation Disease of Steady Multilateral Systems

For a steady multilateral system V imitating an economy with two incompatibility relations, suppose that the subsystems ( ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ( ρ 1 ρ 2 ρ 3 ) ( ρ 1 + ρ 2 ρ 3 ) . are the same as those defined in Theorem 3.1. Then the relation diseases can be decomposed into the following classes:

Definition 3.1 (involving in (相及) and infringing upon (相犯)) Suppose that both X and XS having the loving relationship fall ill. Consider a relation disease occurred between X and XS.

The relation disease between X and XS is called less serious if X is a virtual disease and so is XS at the same time. The less serious relation disease between virtual X and virtual XS is also called a mothers disease involving in her son. The mother is the cause of disease.

The relation disease between X and XS is also called less serious if X is a real disease and so is XS at the same time. The less serious relation disease between real X and real XS is also called a sons disease infringing upon his mother. The son is the cause of disease.

The relation disease between X and XS is called rare if X is a real disease but XS is a virtual disease at the same time, or if X is a virtual disease but XS is a real disease at the same time. The rare relation disease implies that they cannot destroy the loving order although real X cannot love virtual XS or virtual X cannot love real XS. #

Definition 3.2 (multiplying (相乘) and insulting (相侮)) Suppose that both X and XK having the killing relationship fall ill. Consider a relation disease occurred between X and XK.

The relation disease between X and XK is called less serious if X is a real disease and XK is a virtual disease at the same time. The less serious relation disease between X and XK is also called a multiplying relation.

The relation disease between X and XK is called more serious if X is a virtual disease but XK is a real disease at the same time. The more serious relation disease between X and XK is also called an insulting relation. It means that X has been harmed by XK through the method of incest.

The relation disease between X and XK is called rare if X is a real disease and so is XK at the same time, or if X is a virtual disease and so is XK at the same time. The rare relation disease implies that they cannot destroy the killing order from X to XK although real X cannot kill real XK or virtual X cannot kill virtual XK.

The relation disease between X, XK and KX is called more serious if X is a real disease, and XK is a virtual disease but KX is also a virtual disease at same time, i.e., not only real X multiplies in virtual XK, but also insults virtual KX by using the method of incest. It is because the energy of real X is too high. The more serious relation disease between X, XK, and KX is also called a multiplying-insulting (乘侮) relation.

The relation disease between X, XK, and SX is called more serious if X is a real disease, and XK is a virtual disease but SX is also real disease at same time, i.e., not only real X multiplies in virtual XK, but also real SX insults virtual XK by using the method of incest. It is because the energy of virtual XK is too low. The more serious relation disease between X, XK, and SX is also called a multiplying-insulting (乘侮) relation.

Only the more serious relation disease can destroy the killing relationship order of the Yin Yang Wu Xing system. All the therapeutic principles need to prevent the more serious relation disease occurrence in the first place. #

The disease of multiplying-insulting relation will result in more than three subsystems falling-ill. Generally, three or more subsystems falling-ill, it will be difficult to treat. Therefore, the multiplying-insulting relation disease should be avoided as much as possible. In Chinese words, it is that “Again and again, don’t allow to the repeated to four” (只有再一再二, 没有再三再四)-Allow one or two subsystems falling ill, but Don’t allow three or four subsystems falling ill.

3.3. First Transfer Law of Diseases of Steady Multilateral Systems with a healthy Economy

Suppose that a steady multilateral system V imitating an economy having energy function ( 1 ρ 2 ρ 3 ) ( ρ 1 + ρ 2 ρ 3 ) is normal or healthy. Let x be the GDP inflation rate of V. Assume that ( ρ 1 + ρ 2 ρ 3 ) ( ρ 1 ρ 2 ρ 3 ) ( ρ 1 ρ 3 ) = ρ ( x ) ( 1 c ) ρ ( x ) 2 ( 1 c ) = ( ρ 2 ρ 1 ρ 3 ) . , Δ φ ( X ) 2 = ( 1 c ρ ( x ) 3 ) Δ < Δ = Δ φ ( X ) , and a = 5 .8114% , b = 16 .359% , t 0 = 10 .208% where 0 and φ ( X ) is defined in Equations (3) and (4). The healthy economy means that the conditions Δ φ ( X ) = Δ < 0 and Δ φ ( S X ) = ρ 1 Δ < 0 hold, which is equivalent to the normal range + or the healthy condition Δ φ ( X S ) = ρ 2 Δ < 0 . That implies that the body is without the ability of self-protection, i.e., Δ φ ( K X ) = ρ 1 Δ > 0 . Of course, the body cannot be healthy. It is because for any + , when Δ φ ( X K ) = ρ 2 Δ > 0 , there is

,

such that the healthy condition Δ φ ( K X ) = ρ 1 Δ > 0 cannot hold.

By using Corollary 2.1 and Theorems 2.1 and 3.1, the following Theorem 3.2 can be obtained as the first transfer law of occurrence and change of diseases with a healthy economy.

Theorem 3.2 Suppose that a subsystem x ¯ [ a , b ] of a steady multilateral system ρ 0 > ρ 1 = ρ ( x ) > ρ 2 = ρ ( x ) 2 > 0 falls a disease. Let the GDP inflation rate ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) which is equivalent to the conditions ρ 3 = c ρ ( x ) and 0 < ( ρ 1 ρ 3 ) = ρ ( x ) ( 1 c ) ρ ( x ) = ρ 1 .

In this case, almost always, the less serious relation disease will occur and change. If the disease continues to develop, the change can make a more serious relation disease occur.

The occurrence and change of diseases with a healthy economy has its transfer law: The first occurrence and change of the loving relationship and the killing relationship after the loving relationship disease. In other words, the following statements are true.

If a subsystem X of a steady multilateral system V falls a virtual disease, the transfer law is the first occurrence of the virtual disease of the mother SX of X with a less serious relation disease between virtual SX and virtual X, and secondly the real disease of the bane KX of X after the virtual disease of SX with a less serious relation disease between real KX and virtual X, and thirdly the real disease of the prisoner XK of X with a more serious relation disease between virtual X and real XK, and fourthly the virtual disease of the son XS of X with a less serious relation disease between virtual X and virtual XS, and finally the new remission virtual disease of the subsystem X itself, and for the next round of disease transmission, until disease rehabilitation.

If a subsystem X of a steady multilateral system V encounters a real disease, the transfer law is the first occurrence of the real disease of the son XS of X with a less serious relation disease between real X and real XS, and secondly the virtual disease of the prisoner XK of X after the real disease of XS with a less serious relation disease between real X and virtual XK, and thirdly the virtual disease of the bane KX of X with a more serious relation disease between virtual KX and real X, and fourthly the real disease of the mother SX of X with a less serious relation disease between real SX and real X, and finally the new abated real disease of the subsystem X itself, and for the next round of disease transmission, until disease rehabilitation.

All first transfer laws of diseases with a healthy complex system are summed up as Figure2 and Figure3. #

Remark 4. Theorem 3.2 is called the transfer law of occurrence and change of diseases with a healthy economy, simply, the first transfer law. For a real disease, the first transfer law is along the loving relationship order transmission as follows:

0 < ( ρ 2 ρ 1 ρ 3 ) = ρ ( x ) 2 ( 1 c ) ρ ( x ) 2 = ρ 2

For a virtual disease, the first transfer law is against the loving relationship order transmission as follows:

c 0

The transfer relation of the first transfer law running is the loving relationship, denoted by ®. The running condition of the first transfer law is both ρ 3 = c ρ ( x ) 0 and c 0 .

Figure 2. Transfer law of virtual disease with a healthy economy.

Figure 3. Transfer law of real disease with a healthy economy.

By Theorem 2.1 and Corollary 2.1, the running condition is nearly equivalent to both ρ 0 > ρ 1 = ρ ( x ) > ρ 2 = ρ ( x ) 2 > 0 and Δ φ ( X ) 2 = Δ φ ( X ) 1 + Δ φ ( X ) = ( 1 ρ 2 ρ 3 ) Δ = ( 1 c ρ ( x ) 3 ) Δ Δ < 0 , . The best-state condition of the first transfer law is Δ φ ( S X ) 2 = Δ φ ( S X ) 1 + Δ φ ( S X ) = ( ρ 1 + ρ 2 ρ 3 ) Δ = ( ρ ( x ) + c ρ ( x ) 3 ) Δ ρ 1 Δ < 0 , where Δ φ ( K X ) 2 = Δ φ ( K X ) 1 + Δ φ ( K X ) = ( ρ 1 ρ 3 ) Δ = ρ ( x ) ( 1 c ) Δ ρ ( x ) Δ = ρ 1 Δ > 0 , which is the best state of Δ φ ( X K ) 2 = Δ φ ( X K ) 1 + Δ φ ( X K ) = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ ρ ( x ) 2 Δ = ρ 2 Δ > 0 , for a healthy economy. To follow or utilize the running of the first transfer law is equivalent to the following method. For dong so, it is in order to protect or maintain the loving relationship. The method can strengthen both the value Δ φ ( X S ) 2 = Δ φ ( X S ) 1 + Δ φ ( X S ) = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ ρ 2 Δ < 0. tending to be large and the value x ¯ [ a , b ] tending to be small at the same time. In other words, the way can make all of both ρ 0 > ρ 1 = ρ ( x ) > ρ 2 = ρ ( x ) 2 > 0 and c tending to be large. It is because the running condition of the loving relationship ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) is the stronger the use, which dues to ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) the greater the use. In other words again, if the treatment principle of the loving relationship disease is to use continuously abiding by the first transfer law, then all of both the intervention reaction coefficients ± ( 1 ρ 2 ρ 3 ) Δ 1 and the coefficient of self-protection φ ( X ) where Δ φ ( X ) = Δ 1 > 0 will tend to be the best state, i.e., 0 and φ ( X K ) .

Side effects of treating problems were the question: in the treating process, destroyed the balance of the normal subsystems which are not sick or intervened systems. The energy change of the intervened system is not the true side effects issue. The energy change is called the pseudo or non-true side effects issue since it is just the food of the second physiological system of the steady multilateral system for a healthy economy. The best state of the self-protection coefficient, Δ φ ( X K ) = Δ 1 < 0 , where 0 , implies the non-existence of any side effects issue if the treatment principle of TCE is used. Therefore any disease that causes side effects issue occurrence in the first place dues to the non-best state of self-protection ability, i.e., Δ φ ( X ) 3 1 = [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ] Δ 1 = [ ( 1 c ρ ( x ) 3 ) + ρ ( x ) ( 1 c ) ] Δ 1 > 0 , . To follow or utilize the running of the first transfer law can make both Δ φ ( X S ) 3 1 = [ ( ρ 1 + ρ 2 ρ 3 ) ( ρ 1 + ρ 2 ρ 3 ) ] Δ 1 = 0 , and Δ φ ( X K ) 3 1 = [ ( ρ 1 ρ 3 ) + ( 1 ρ 2 ρ 3 ) ] Δ 1 = [ ρ ( x ) ( 1 c ) + ( 1 c ρ ( x ) 3 ) ] Δ 1 < 0 , . At this point, the paper advocates to follow or utilize the first transfer law. It is in order to avoid the side effects issue occurrence for the healthy economy. #

3.4. Second Transfer Law of Diseases of Steady Multilateral Systems with an Unhealthy Economy

Suppose that a steady multilateral system V imitating an economy having energy function Δ φ ( K X ) 3 1 = [ ( ρ 2 ρ 1 ρ 3 ) + ( ρ 2 ρ 1 ρ 3 ) ] Δ 1 = 0 , is abnormal or unhealthy. Let x be the GDP inflation rate of V. Assume that Δ φ ( S X ) 3 1 = [ ( ρ 2 ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ] Δ 1 = 0. and Δ φ ( X ) 3 1 = [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ] Δ 1 = ( 1 c ρ ( x ) 3 + ρ ( x ) ( 1 c ) ) Δ 1 > 0 where Δ 1 Δ , and Δ φ ( X K ) 3 1 = [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ] Δ 1 = ( 1 c ρ ( x ) 3 + ρ ( x ) ( 1 c ) ) Δ 1 < 0 is defined in Equations (3) and (4). The unhealthy economy means that the conditions Δ φ ( X K ) 4 1 = Δ φ ( X K ) 3 1 + φ ( X K ) 2 = [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ] Δ 1 + ( ρ 2 ρ 1 ρ 3 ) Δ [ ( 1 ρ 2 ρ 3 ) ( ρ 1 ρ 3 ) + ( ρ 2 ρ 1 ρ 3 ) ] Δ = [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] Δ < 0 , and Δ φ ( S X ) 4 1 = Δ φ ( S X ) 3 1 + φ ( S X ) 2 = ( ρ 1 + ρ 2 ρ 3 ) Δ = ( ρ ( x ) + c ρ ( x ) 3 ) Δ ρ 1 Δ < 0 , hold, which is equivalent to the abnormal range Δ φ ( X S ) 4 1 = Δ φ ( X S ) 3 1 + φ ( X S ) 2 = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ ρ ( x ) 2 Δ = ρ 2 Δ < 0 , .

From Zhang & Shao (2012), by using Corollary 2.1 and Theorems 2.1 and 3.1, the following Theorem 3.3 can be obtained as the second transfer law of occurrence and change of diseases with an unhealthy economy.

Theorem 3.3 Suppose that a subsystem Δ φ ( K X ) 4 1 = Δ φ ( K X ) 3 1 + φ ( K X ) 2 = ( ρ 2 ρ 2 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ ρ ( x ) 2 Δ = ρ 2 Δ > 0 , of a steady multilateral system Δ φ ( X ) 4 1 = Δ φ ( X ) 3 1 + φ ( X ) 2 = [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ] Δ 1 ( ρ 2 ρ 1 ρ 3 ) Δ [ ( 1 ρ 2 ρ 3 ) ( ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ] Δ = [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] Δ > 0. falls a disease. Let the GDP inflation rate [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] < ( ρ 1 + ρ 2 ρ 3 ) < ( ρ 2 ρ 1 ρ 3 ) < ( ρ 2 ρ 1 ρ 3 ) < [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] . which is equivalent to the conditions ( 1 ρ 2 ρ 3 ) > ( ρ 1 + ρ 2 ρ 3 ) and [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] ( ρ 1 + ρ 2 ρ 3 ) = 1 ρ 2 ρ 3 + ρ 3 ρ 1 ρ 2 ρ 3 ρ 2 > ρ 1 + ρ 2 ρ 3 + ρ 3 ρ 1 ρ 2 ρ 3 ρ 2 = ( ρ 1 ρ 2 ) + ρ 3 ρ 1 > 0 , .

In this case, almost always, the rare relation disease will occur and change. If the disease continues to develop, the change can make a more serious relation disease occur.

The transfer of disease with an unhealthy economy has its transfer law: Only there is the transfer of the killing relationship. In other words, the following statements are true.

If a subsystem X of a steady multilateral system V falls a virtual disease, then the disease comes from the son XS of X. The transfer law is the first occurrence of the virtual disease of the prisoner XK of X with a rare relation disease between virtual X and virtual XK, and secondly the virtual disease of the mother SX of X after the virtual disease of XK with a rare relation disease between virtual XK and virtual SX, and thirdly the virtual disease of the son XS of X with a rare relation disease between virtual SX and virtual XS, and fourthly the real disease of the bane KX of X with a more serious relation disease between virtual XS and real KX, and finally the new remission virtual disease of the subsystem X itself with a less serious relation disease between real KX and virtual X, and for the next round of disease transmission, until disease rehabilitation.

If a subsystem X of a steady multilateral system V falls a real disease, then the disease comes from the mother SX of X. The transfer law is the first occurrence of the real disease of the bane KX of X with a rare relation disease between real KX and real X, and secondly the real disease of the son XS of X after the real disease of the bane KX of X with a rare relation disease between real XS and real KX, and thirdly the real disease of the mother SX of X with a rare relation disease between real SX and real XS, and fourthly the virtual disease of the prisoner XK of X with a more serious relation disease between virtual XK and real SX, and finally the new abated real disease of the subsystem X itself with a less serious relation disease between real X and virtual XK, and for the next round of disease transmission, until disease rehabilitation.

All second transfer laws of diseases with a healthy economy are summed up as Figure4 and Figure5. #

Remark 5. Transfer law of Theorem 3.3 is called transfer law of occurrence and change of diseases with an unhealthy economy, simply, the second transfer law. For a virtual disease, the second transfer law is along the killing relationship order transmission as follows:

( ρ 1 + ρ 2 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) = ( ρ 1 ρ 2 ) ( ρ 1 ρ 2 ) ρ 3 = ( ρ 1 ρ 2 ) ( 1 ρ 3 ) > 0

For a real disease, the second transfer law is against the killing relationship order transmission as follows:

Δ φ ( X ) 4 1 [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] Δ > 0

Figure 4. Transfer law of virtual diseases with an unhealthy economy.

Figure 5. Transfer law of real disease with an unhealthy economy.

The transfer relationship of the second transfer law running is the killing relationship, denoted by Δ 1 Δ > 0 .

The running condition of the second transfer law is both

0 and φ ( X ) .

By Theorem 2.1 and Corollary 2.1, the running condition is equivalent to both Δ φ ( X ) = Δ > 0 and Δ φ ( X S ) = ρ 1 Δ > 0 . That + means the lack of capability of self-protection. Of course, it is the basis condition of running the second transfer law.

The stopping condition of the second transfer law is both

Δ φ ( S X ) = ρ 2 Δ > 0 and , which is the running condition of the first transfer law, or, the existence condition of capabilities of both intervention reaction and self-protection. To follow or utilize the running of the second transfer law is equivalent to the following method. For doing so, it is to protect and maintain the killing relationship of the steady multilateral system. The method can strengthen all of both Δ φ ( X K ) = ρ 1 Δ < 0 and + tending to be small at the same time. In other words, using the method can make c tends to be large for a fixed Δ φ ( K X ) = ρ 2 Δ < 0 . It is because the transferring condition of the killing relation disease is the weaker the use, which dues to Δ φ ( X K ) = ρ 1 Δ < 0 is the greater the use. The transferring way can make both x ¯ [ a , b ] and ρ 0 > ρ 1 = ρ ( x ) > 0 at the same time such that the killing relation disease cannot be transferred. In other words again, if the treatment principle of the killing relationship diseases is to use continuously abiding by the second transfer law, then the coefficient of self-protection will tend to be the occurrence state, i.e., ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) where

ρ 3 = c ρ ( x ) , andthe coefficients of intervention reaction also will tend

to the healthy state, i.e., 0 < ( ρ 1 ρ 3 ) = ρ ( x ) ( 1 c ) ρ ( x ) = ρ 1 , such that 0 < ( ρ 2 ρ 1 ρ 3 ) = ρ ( x ) 2 ( 1 c ) ρ ( x ) 2 = ρ 2 .

Economic intervention resistance problem is that such a question: beginning more appropriate economic intervention treatment, but is no longer valid after a period. In the state

c 0 , ρ 3 = c ρ ( x ) 0 ,

by Theorem 3.2, any economic intervention resistance problem is non-existence if the treatment principle of TCE is used. But in the state

c 0 , ρ 0 > ρ 1 = ρ ( x ) > ρ 2 = ρ ( x ) 2 > 0 ,

by Theorem 3.3, the economic intervention resistance problem is always existence, even if the treatment principle of TCE has been used. In other words, the lack of capability of self-protection, i.e., Δ φ ( X ) 2 = Δ φ ( X ) 1 + Δ φ ( X ) = ( 1 ρ 2 ρ 3 ) Δ = ( 1 c ρ ( x ) 3 ) Δ Δ > 0 , , implies the possible existence of an economic intervention resistance problem, although the treatment principle of TCE has been used. At this point, the paper advocates to follow or utilize the second transfer law. It is in order to prevent and avoid the economic intervention resistance problem occurrence for the unhealthy economy. #

4. Treatment Principle of TCE

In order to explain treatment principle of TCE, the changes in the GDP inflation rate range can be divided into four parts from small to large.

From Zhang & Shao (2012), by Corollary 2.1 and Theorems 2.1, 3.2 and 3.3, it can be easily proved that the following Theorem 4.1 is true.

Theorem 4.1 Suppose that a subsystem Δ φ ( X S ) 2 = Δ φ ( X S ) 1 + Δ φ ( X S ) = ( ρ 1 + ρ 2 ρ 3 ) Δ = ( ρ ( x ) + c ρ ( x ) 3 ) Δ ρ 1 Δ > 0 , of a steady multilateral system Δ φ ( X K ) 2 = Δ φ ( X K ) 1 + Δ φ ( X K ) = ( ρ 1 ρ 3 ) Δ = ρ ( x ) ( 1 c ) Δ ρ ( x ) Δ = ρ 1 Δ < 0 , falls a disease. Let Δ φ ( K X ) 2 = Δ φ ( K X ) 1 + Δ φ ( K X ) = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ ρ ( x ) 2 Δ = ρ 2 Δ > 0 , be the GDP inflation rate of the steady multilateral system. Denoted the parameters of the normal range as follows Δ φ ( S X ) 2 = Δ φ ( S X ) 1 + Δ φ ( S X ) = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ ρ ( x ) 2 Δ = ρ 2 Δ > 0. , x ¯ [ a , b ] , ρ 0 > ρ 1 = ρ ( x ) > 0 . Then the following statements are true.

1) Suppose that ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) as virtual, in which X falls a virtual disease with an unhealthy economy. The primary treatment is to increase the energy of the subsystem X directly. And the secondary treatment is to increase the energy of the son X S of X , and at the same time, to decrease the energy of the prisoner K X of X S .

2) Suppose that ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) as virtual-normal, in which X will fall an expected virtual disease with a healthy economy. The primary treatment is to increase the energy of the mother subsystem SX of X which is an indirect treating for X. And the secondary treatment is to increase the energy of X itself, and at the same time, to decrease the energy of the prisoner XK of X.

3) Suppose that ( 1 ρ 2 ρ 3 ) Δ 1 as real-normal, in which X will encounter an expected real disease with a healthy economy. The primary treatment is to decrease the energy of the son subsystem XS of X which is an indirect treating for X. And the secondary treatment is to decrease the energy of X itself, and at the same time, to increase the energy of the bane KX of X.

4) Suppose that φ ( X ) as real, in which X encounters a real disease with an unhealthy economy. The primary treatment is to decrease the energy of the subsystem X directly. And the secondary treatment is to decrease the energy of the mother SX of X, and at the same time, to increase the energy of the bane XK of SX. #

Remark 6. Treatment principle of Theorem 4.1 based on ranges of the GDP inflation rate is called the treatment principle of TCE, since it is in order to protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship.

For the unhealthy economy where Δ φ ( X ) = Δ 1 < 0 or 0 , the treatment principle is the method for doing so in the following:

The primary treatment is to increase or decrease the energy of X directly corresponding to φ ( K X ) or Δ φ ( K X ) = Δ 1 > 0 respectively, and the secondary treatment is to increase the energy of XS or XK while to decrease the energy of KX or SX, corresponding to virtual X or real X, respectively. #

The primary treatment is in order to protect and maintain the loving relationship, abiding by TCE’s ideas “Virtual disease with an unhealthy economy is to fill itself” and “Real disease with an unhealthy economy is to rush down itself”. It is because the method for dong so is not only greatly to cure economic diseases of their own, but also provides the pseudo side effects as the food for the second physiological system. The method is to promote the first physiological system running since the second physiological system controls the first physiological system. And it is also to improve the loving relationship to develop since the loving relationship mainly comes from the first physiological system. The loving relationship to develop can strengthen both that 0 tends to be large and that Δ φ ( X ) 3 1 = [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ] Δ 1 = [ ( 1 c ρ ( x ) 3 ) + ρ ( x ) ( 1 c ) ] Δ 1 < 0 , tends to be small at the same time. In other words, the way can make all of both Δ φ ( S X ) 3 1 = [ ( ρ 1 + ρ 2 ρ 3 ) + ( ρ 1 + ρ 2 ρ 3 ) ] Δ 1 = 0 , and c tending to be large, at least, c greater than zero for an unhealthy economy, such that the economy is from unhealthy to healthy, or the first physiological system works, or, the occurrence of capability of self-protection, or, the running of the first transfer law, or, the stopping of the second transfer law.

The secondary treatment is in order to protect or maintain the killing relationship, abiding by TCE’s ideas “Don’t have disease cure cure non-ill” and “Strong inhibition of the same time, support the weak”. By the second transfer law in Theorem 3.3, the more serious relation disease is the relation disease between virtual XS and real KX, or between virtual XK and real SX corresponding to virtual X or real X, respectively.

Abiding by TCE’s idea “Don’t have disease cure cure non-ill”, it must be done to prevent or avoid the more serious relation disease between virtual XS and real KX, or between virtual XK and real SX occurrence, corresponding to virtual X or real X, respectively.

Abiding by TCE’s idea “Strong inhibition of the same time, support the weak”, it must be done to increase the energy of XS or XK while to decrease the energy of KX, or SX corresponding to virtual X or real X, respectively.

The method for doing so can improve the killing relationship to develop since real XS or real XK can kill virtual KX, or virtual SX corresponding to virtual X or real X, respectively. The killing relationship to develop means that both Δ φ ( K X ) 3 1 = [ ( ρ 1 ρ 3 ) + ( 1 ρ 2 ρ 3 ) ] Δ 1 = [ ρ ( x ) ( 1 c ) + ( 1 c ρ ( x ) 3 ) ] Δ 1 > 0 , and Δ φ ( X K ) 3 1 = [ ( ρ 2 ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ] Δ 1 = 0 , tend to be small at the same time. In other words, the way can make, for fixed Δ φ ( X S ) 3 1 = [ ( ρ 2 ρ 1 ρ 3 ) + ( ρ 2 ρ 1 ρ 3 ) ] Δ 1 = 0. , c tending to be large, at least, greater than zero for an unhealthy economy, such that the economy from unhealthy to healthy, or the first physiological system works, or, the occurrence of capability of self-protection, or, the running of the first transfer law, or, the stopping of the second transfer law.

For the healthy economy where Δ φ ( X ) 3 = ( 1 ρ 2 ρ 3 ) Δ 1 = ( 1 c ρ ( x ) 3 ) Δ 1 or Δ 1 Δ , the treatment principle is the method for doing so in the following:

The primary treatment is to increase or decrease the energy of SX or XS corresponding to Δ φ ( K X ) 3 = ( 1 ρ 2 ρ 3 ) Δ 1 = ( 1 c ρ ( x ) 3 ) Δ 1 or Δ φ ( K X ) 4 1 = Δ φ ( K X ) 3 1 + φ ( K X ) 2 = [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ] Δ 1 + ( ρ 2 ρ 1 ρ 3 ) Δ [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ] Δ = [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] Δ > 0 , respectively, and the secondary treatment to increase the energy of X or KX while to decrease the energy of XK or X, corresponding to virtual-normal X or real-normal X, respectively. #

The primary treatment is in order to protect and maintain the loving relationship, abiding by TCE’s ideas “Virtual disease with a healthy economy is to fill mother” and “Real disease with a healthy economy is to rush down his son”. It is because the method for dong so is not only greatly to cure diseases of their own, but also provides the pseudo side effects as the food for the second physiological system. The method is to promote the first physiological system running since the second physiological system controls the first physiological system. And it is also to improve the loving relationship developing since the loving relationship mainly comes from the first physiological system. The loving relationship developing can strengthen both that Δ φ ( X S ) 4 1 = Δ φ ( X S ) 3 1 + φ ( X S ) 2 = ( ρ 1 + ρ 2 ρ 3 ) Δ = ( ρ ( x ) + c ρ ( x ) 3 ) Δ ρ 1 Δ > 0 , tends to be large and that Δ φ ( S X ) 4 1 = Δ φ ( S X ) 3 1 + φ ( S X ) 2 = ( ρ 2 ρ 1 ρ 3 ) Δ = ρ ( x ) 2 ( 1 c ) Δ ρ ( x ) 2 Δ = ρ 2 Δ > 0 , tends to be small at the same time. In other words, using the way can make all of both Δ φ ( X K ) 4 1 = Δ φ ( X K ) 3 1 + φ ( X K ) 2 = ( ρ 2 ρ 2 ρ 3 ) Δ = ρ ( x ) ( 1 c ) Δ ρ ( x ) Δ = ρ 1 Δ < 0 , and Δ φ ( X ) 4 1 = Δ φ ( X ) 3 1 + φ ( X ) 2 = [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ] ] Δ 1 + ( ρ 2 ρ 1 ρ 3 ) Δ [ ( 1 ρ 2 ρ 3 ) ( ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ] Δ = [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] Δ < 0. tending to be large, the best, all equal to 1 for a healthy economy, such that the capability of self-protection is in the best state, or, the non-existence of side effects issue, or, the non-existence of economic intervention resistance problem.

The secondary treatment is in order to protect or maintain the killing relationship, abiding by TCE’s ideas “Don’t have disease cure cure non-ill” and “Strong inhibition of the same time, support the weak”. By the first transfer law, the more serious relation disease is the relation disease between virtual X and real XK or between virtual KX and real X corresponding to virtual-normal X or real-normal X, respectively.

Abiding by TCE’s idea “Don’t have disease cure cure non-ill”, it must be done to prevent and avoid the more serious relation disease between virtual X and real XK or between virtual KX and real X occurrence corresponding to virtual-normal X or real-normal X, respectively.

Abiding by TCE’s idea “Strong inhibition of the same time, support the weak”, it must be done to increase the energy of X or KX while to decrease the energy of XK or X corresponding to virtual-normal X or real-normal X, respectively.

The method for doing so can improve the killing relationship developing since real X or real KX can kill virtual XK or virtual X corresponding to virtual-normal X or real-normal X, respectively. The killing relationship developing also means that both [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] > ( ρ 1 + ρ 2 ρ 3 ) > ( ρ 2 ρ 1 ρ 3 ) > ( ρ 2 ρ 1 ρ 3 ) > [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] . and ( 1 ρ 2 ρ 3 ) > ( ρ 1 + ρ 2 ρ 3 ) tend to be small at the same time. In other words, using the way can make, for fixed [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] ( ρ 1 + ρ 2 ρ 3 ) = 1 ρ 2 ρ 3 + ρ 3 ρ 1 ρ 2 ρ 3 ρ 2 > ρ 1 + ρ 2 ρ 3 + ρ 3 ρ 1 ρ 2 ρ 3 ρ 2 = ( ρ 1 ρ 2 ) + ρ 3 ρ 1 > 0 , , ( ρ 1 + ρ 2 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) = ( ρ 1 ρ 2 ) ( ρ 1 ρ 2 ) ρ 3 = ( ρ 1 ρ 2 ) ( 1 ρ 3 ) > 0 tending to be large, the best, equal to 1 for a healthy economy, such that the capability of self-protection is in the best state, or, the non-existence of side effects, or, the non-existence of economic intervention resistance issue.

5. Chinese GDP for the Water Subsystem of Steady Multilateral Systems

Suppose that M2 as issued in the circulation of money and GDP as Gross Domestic Product in Chinese from 1990 year to 2014 year, the annual GDP can be measured in Table 1.

Watching Table 1, the state of the GDP inflation rate is: virtual-normal, real, real, real, real, virtual-normal, for 1991-1996, respectively. It means that the subsystem water(SX) has first encountered a real economic disease with an unhealthy sub-economy. It is because the GDP belongs to “army-economic” of the subsystem water(SX). During this period of time, large-scale goods have been made.

Also watching Table 1, the state of the GBR inflation rate is: virtual, virtual-normal, real, real-normal, real-normal, real-normal, for 1991-1996, respectively. For the GBR inflation rate of industry economic society, the normal range of theory is [8.956%, 20.07%] nearly to [9%, 20%], and the center is 13.705% nearly to 14%.

It means that the subsystem metal(KX) of the economic social system with a healthy sub-economy encounters an expected real economic disease since the GBR inflation rate belongs to “science, education, public facilities” of metal(KX).

But also watching Table 1, the state of the PPI inflation rate is: virtual-normal, real, real, real, real, real, for 1991-1996, respectively. For the PPI inflation rate of industry economic society, the normal range of theory is [0.7362%, 6.4920%] nearly to [1%, 6%], and the center is 3.1359% nearly to 3%.

Table 1. Inflation rates of Finance, GDP, CPI, PPI, RPI, GBR and AAF.

Assume that M2 or M 2 as issued in the circulation of generalized money, the Gross Domestic Product (GDP) as G or G', the Consumer Price Index (CPI) as C or C', the Producer Price Index (PPI) as P or P', the Retail Price Index (RPI) as R or R', the General Budget Revenue (GBR) as Gb or G b , and the total output value of Agriculture forestry Animal husbandry and Fishery (AAF) as A or A' for today and last year respectively, the actual need of money in real terms in the circulation P 0 = M 2 × ( G / G ) for last year’s price level. Then the inflation rate of M 2 is ( M 2 M 2 ) / M 2 , the inflation rate of GDP is ( G G ) / G , the inflation rate of CPI is ( C C ) / C , the inflation rate of PPI is ( P P ) / P , the inflation rate of RPI is ( R R ) / R , the inflation rate of GBR is ( G b G b ) / G b , the inflation rate of AAF is ( A A ) / A , and the annual Finance inflation rate can be measured by ( M 2 P 0 ) / P 0 .

It means that the subsystem wood(X) of the economic social system with an unhealthy economy encounters a real economic disease since the PPI inflation rate belongs to “industry” of wood(X).

There are three subsystems water(SX), wood(X) and metal(KX) in which water(SX) and wood(X) are real but metal(KX) is real-normal. Both metal(KX) and wood(X) have the killing relationship and others are the loving relationships. For an unhealthy economy, the key relationship is killing. By Definition 3.2, the relation economic disease between real-normal metal(KX) and real wood(X) is rare because real-normal metal(KX) cannot kill real wood(X) which cannot destroy the balance of the killing relation from metal(KX) to wood(X). If the subsystem metal(KX) is intervened such that it is from real-normal to virtual, then there is a more serious disease to occur since virtual metal(KX) cannot kill real wood(X) which can destroy the balance of the killing relation from metal(KX) to wood(X). Thus the mainly root-cause is the real disease of the subsystem wood(X). On the other hand, by Definition 3.1, the relation disease between real water(SX) and real wood(X) is less serious and a son’s disease infringing upon his mother. The son wood(X) is the cause of real disease.

So, at present the most serious problem is to treat the subsystem wood(X) falling a real disease for an unhealthy sub-economy. It is the case in (4) of Theorem 4.1 for wood(X).

By the (4) of Theorem 4.1, the primary treatment is to decrease the energy of the subsystem wood(X) directly. And the secondary treatment is to decrease the energy of the mother water(SX) of wood(X), and at the same time, to increase the energy of the prisoner earth(XK) of wood(X).

In fact, the Chinese government did just that. For 1993-1999, not only had decreased gradually the financial amounts of investment in the manufacture (to decrease the energy of the subsystem wood(X) directly), but also had decreased investment in the Army (e.g., big disarmament, for decreasing the energy of water(SX)) while had increased little by little the workers’ wages, the social security and social welfare, such as, the public accumulation fund for housing construction, pension funds, medical insurance, unemployment insurance, etc.(to increase the energy of earth(XK)).

Watching Table 1, the state of the GDP inflation rate is: virtual-normal, virtual-normal, virtual-normal, virtual-normal, virtual-normal, virtual-normal, real-normal, for 1997-2003, respectively. It means that the subsystem water(SX) has first encountered an expected virtual economic disease with a healthy sub-economy. It is because the GDP belongs to “army-economic” of the subsystem water(SX). During this period of time, mass goods cannot be made. Supplies are still scarce. Rush on still appear on the market.

Also watching Table 1, the state of the CPI inflation rate is: virtual-normal, virtual, virtual, virtual, virtual, virtual, virtual, for 1997-2003, respectively. For the CPI inflation rate of economic society, the normal range of theory is [1.8828%, 5.2216%] nearly to [2%, 5%], and the center is 3.2741% nearly to 3%. It means that the subsystem earth(XK) of the economic social system with an unhealthy sub-economy encounters a virtual economic disease since the CPI inflation rate belongs to the “commerce ” of earth(XK).

Also watching Table 1, the state of the PPI inflation rate is: virtual-normal, virtual, virtual, virtual, virtual, virtual, for 1997-2003, respectively. It means that the subsystem wood(X) falls a virtual disease for an unhealthy economy since the PPI inflation rate belongs to the “industry” of wood(X).

There are three subsystems wood(X), water(SX) and earth(XK) in which both wood(X) and earth(XK) are virtual but water(SX) is virtual-normal or real-normal. Both wood(X) and earth(XK) have the killing relationship. And both earth(XK) and water(SX) also have the killing relationship. Both water(SX) and wood(X) have the loving relationship. For an unhealthy economy, the key relationship is killing. Because water(SX) is virtual-normal or real-normal, only consider the killing relationship from wood(X) to earth(XK). By Definition 3.2, the relation disease between virtual wood(X) and virtual earth(XK) is rare since virtual wood(X) cannot kill virtual earth(XK) which cannot destroy the balance of the killing order from wood(X) to earth(XK). But if the subsystem earth(XK) is intervened such that it is from virtual to real, there is a more serious relation disease between virtual wood(X) and real earth(XK). It is because the virtual wood(X) cannot kill the real earth(XK) which can destroy the balance of the killing relation from wood(X) to earth(XK). Thus the mainly root-cause is the virtual disease of the subsystem wood(X).

So, at present the most serious problem is to treat the subsystem wood(X) falling a virtual disease for an unhealthy sub-economy. It is the case in (1) of Theorem 4.1 for wood(X).

By the (1) of Theorem 4.1, the primary treatment is to increase the energy of the subsystem wood(X) directly. And the secondary treatment is to increase the energy of the son fire(XS) of wood(X), and at the same time, to decrease the energy of the prisoner metal(KX) of fire(XS).

In fact, the Chinese government did just that. For 1999-2008, not only had increased gradually the financial amounts of investment in the manufacture (e.g., to invest in real estate, to increase the energy of the subsystem wood(X) directly), but also had increased investment in the agriculture and finance, such as, exempt from the agricultural taxation, increase of agricultural land expropriation compensation, improvement of the circulation of money, etc. (to increase the energy of fire(XS) including jun-fire( Δ φ ( X ) 4 1 [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] Δ < 0 ) and xiang-fire( Δ 1 Δ > 0 )) while had decreased in the science and education, such as, a small amount of teachers and researchers for a raise, schools and research institutions self-sustaining, etc. (to decrease the energy of metal(KX)).

Therefore, the application of nature for the treatment principle of TCE by the Chinese government had brought the sustained and rapid growth of industry economy for 1991-2008.

Also watching Table 1 again, the state of the GDP inflation rate is: real-normal, real-normal, real-normal, real-normal, real, real-normal, virtual-normal, real-normal, real-normal, for 2004-2011, respectively. It means the subsystem water(SX) is mainly with a healthy sub-economy and falls an expected real disease. It is because the GDP inflation rate belongs to the “army-economics” of water(SX). During this period of time, large-scale goods have been still made. But a lot of society problems begin occurring.

Also watching Table 1 again, the state of the CPI inflation rate is: real-normal, virtual, virtual, real-normal, real, virtual, virtual-normal, real-normal, for 2004-2011, respectively. It means the subsystem earth(XK) is mainly with an unhealthy sub-economy and falls a virtual disease. It is because the CPI inflation rate belongs to the “commerce” of earth(XK).

Also watching Table 1 again, the state of the PPI inflation rate is virtual-normal, virtual-normal, virtual-normal, real-normal, real-normal, virtual, virtual-normal, real-normal, for 2004-2011, respectively. It means the subsystem wood(X) is mainly with a healthy sub-economy and falls an expected real disease. It is because the manufacture of large-scale goods or the normal PPI inflation rate belongs to “industry” of the subsystem wood(X).

There are three subsystems wood(X), water(SX) and earth(XK) in which both water(SX) and wood(X) are real-normal but earth(XK) is virtual. By Definition 3.2, the relation disease between virtual earth(XK) and real-normal water(SX) is more serious since virtual earth(XK) cannot kill real-normal water(SX) which can destroy the killing order from earth(XK) to water(SX). Now the subsystem earth(XK) must be intervened such that it is from virtual to real-normal.

So, at present the most serious problem is to treat the subsystem earth(XK) falling a virtual disease for an unhealthy sub-economy. It is the case in (1) of Theorem 4.1 for earth(XK).

The XK as X in theorem 4.1, using the (1) of Theorem 4.1 again, it is to get: the primary treatment is to increase the energy of the subsystem earth(XK) directly. And the secondary treatment is to increase the energy of the son metal(KX) of earth(XK), where a = 5 .8114% , b = 16 .359% , t 0 = 10 .208% in Figure 1, and at the same time, to decrease the energy of the bane wood(X) of earth(XK), where x < a in Figure 1.

In fact, the Chinese government did just that. For 2009-2014, not only had increased the financial amounts of investment in commerce, such as, strengthen the support for the WTO trade, etc. (to increase the energy of the subsystem earth(XK) directly), but also had increased investment in science, education and public facilities, such as to build high speed rail, etc. (to increase the energy of metal(KX)) while had reduced the industrial support, such as, the appreciation of the RMB, etc. (to decrease the energy of wood(X)).

Therefore, again application of nature for the treatment principle of TCE by the Chinese government had brought the 2009-2014 economic taking off again.

Also watching Table 1 again and again, the state of the GDP inflation rate is: virtual-normal, virtual-normal, virtual-normal, for 2012-2014, respectively. It means that the subsystem water(SX) is a healthy sub-economy which will fall an expected virtual disease if it encounters a disease. It is because the GDP belongs to “army-economics” the subsystem water(SX). During this period of time, large-scale goods have been still made such that a lot of goods cannot sell out and a lot of society problems has occurred.

Also watching Table 1 again and again, the state of the CPI inflation rate is: virtual-normal, virtual-normal, virtual-normal, for 2012-2014, respectively. It means that the subsystem earth(XK) is an expected virtual disease for a healthy sub-economy. It is because the manufacture of large-scale goods or the CPI inflation rate belongs to the “commerce or business” of the subsystem earth(XK).

Also watching Table 1 again and again, the state of the PPI inflation rate is: virtual-normal, virtual-normal, virtual-normal, for 2012-2014, respectively. It means that the the subsystem wood(X) is an expected virtual disease for a healthy sub-economy. It is because the manufacture of large-scale goods or the PPI inflation rate belongs to the “industry” of the subsystem wood(X).

The virtual-normal disease of wood(X) is not because of its low energy, but because of its energy is too high to make producing products too much, so much so that there is no way to sell products, low profit of industrial production. In the TCE, this disease is Yang irritability turned to deficiency disease. This disease is not the current urgent problems since it cannot destroy the killing order balance of the economy.

There are three subsystems wood(X), water(SX) and earth(XK) in which all are virtual-normal. Both wood(X) and earth(XK) have the killing relationship from wood(X) to earth(XK). Both earth(XK) and water(SX) also have the killing relationship from earth(XK) to water(SX). Both water(SX) and wood(X) have the loving relationship from water(SX) to wood(X). For a healthy economy, the key relationship is loving. By Definition 3.1, the relation disease between virtual-normal water(SX) and virtual-normal wood(X) is less serious and a mother’s disease involving in her son. The mother water(SX) is the cause of disease. On the other hand, if the virtual-normal disease of wood(X) is continuously to develop such that it is from virtual-normal to virtual, by Theorem 3.2, the virtual wood(X) will make its mother subsystem water(SX) falling a virtual economic disease when it encounters an economic disease.

In fact, the economic indicators of GDP which belongs to the subsystem water(SX) is beginning to decline. Abiding by TCE’s idea “Don’t have economic disease cure cure non-ill”, the prevention and treatment of the current work is the need to prevent the virtual disease of the subsystem water(SX) for a healthy economy.

So, at present the most serious problem is to treat the subsystem water(SX) falling a virtual disease with a healthy sub-economy of the subsystem water(SX). It is the case in (2) of Theorem 4.1 for water(SX).

The SX as X in (2) of Theorem 4.1, the primary treatment is gotten to increase the energy of the mother subsystem metal(KX) of the water(SX), where 0 < ρ 1 = ρ ( x ) < ρ 0 in Figure 1. And the secondary treatment is gotten to increase the energy of the water(SX) itself while decrease the energy of the prisoner fire(XS) of the water(SX), where 0 c 1 in Figure 1.

In fact, the Chinese government also is doing just that. Since 2015, not only has increased continuously investment in science, education and public facilities, such as, One Belt and One Road, etc. (for increasing the energy of metal(KX)), but also has increased to military spending (to increase the energy of the water(SX)) while has reduced the agricultural support and finance, such as, reduce the purchase price of agricultural products, reduce the circulation of money, etc. (to decrease the energy of fire(XS) including jun-fire( ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) ) and xiang-fire( x < a )). Therefore, again and again application of nature for the treatment principle of TCE by the Chinese government will lead to economic continue to glory since 2015. #

6. Conclusion

This work shows how to treat the diseases of an economic society by using the GDP inflation rate x. For the GDP inflation rate, the normal range of theory is [5.8114%, 16.359%] nearly to [6%, 16%], and the center is 10.208% nearly to 10%. The first or second transfer law of economic diseases changes according to the different economic society’s GDP inflation rate whether in the normal range or not. For the normal range, the first transfer law in Theorem 3.2 runs; For the abnormal range, the second transfer law in Theorem 3.3 runs.

Assume that the range of economic society’s GDP inflation rate x is divided into four parts from small to large. Both second and third are for a healthy economy with an expected virtual or real disease respectively. The treating works are the prevention or treatment for a more serious relation disease between virtual X and real X K or between virtual K X and real X respectively. Each of both more serious relation diseases comes from the first transfer law in Theorem 3.2.

And both first and fourth are for an unhealthy economy with a happened virtual or real disease respectively. The treating works are the prevention or treatment for a more serious relation disease between virtual XS and real KX or between virtual XK and real SX respectively. Each of both more serious relation diseases comes from the second transfer law in Theorem 3.3.

Economic disease treatment should protect and maintain the balance or order of two incompatibility relations: the loving relationship and the killing relationship. The method for doing so can make the ρ 3 = c ρ ( x ) tending to be large. In other words, using the method can make all of both c 1 and c tend to be large, at least, greater than zero for an unhealthy economy; or, the best, equal to 1 for a healthy economy.

The following way can make the capabilities of both intervention reaction and self-protection becoming in the best state, the non-existence of side effects issue, the non-existence of economic intervention resistance problem, and so on.

1) Suppose that Δ φ ( X ) 2 ( 1 ρ ( x ) 3 ) Δ > 0 , Δ φ ( X S ) 2 ( ρ ( x ) + ρ ( x ) 3 ) Δ > 0 , , as virtual, in which X falls a virtual disease with an unhealthy economy. In order to protect or maintain the loving relationship, abiding by TCE’s idea “Virtual disease with an unhealthy economy is to fill itself” (虚则补之), increase the energy of X directly.

In order to protect or maintain the killing relationship, abiding by TCE’s idea “Don’t have disease cure cure non-ill” (不治已病治未病), do a preventive treatment for the more serious relation disease between virtual XS and real KX. Through the intervening principle of “Strong inhibition of the same time, support the weak” (抑强扶弱), increase the energy of the son XS of X while decrease the energy of the prisoner KX of XS.

2) Suppose that x < a , as virtual-normal, in which X will fall an expected virtual disease with a healthy economy. In order to protect and maintain the loving relationship, abide by TCE’s idea “Virtual disease with a healthy economy is to fill his mother” (虚则补其母), increase the energy of the mother SX of X. The treating way is an indirect treating for X.

In order to protect and maintain the killing relationship, abiding by TCE’s idea “Don’t have disease cure cure non-ill” (不治已病治未病), do a preventive treatment for the more serious relation disease between virtual X and real XK. Through the intervening principle of “Strong inhibition of the same time, support the weak” (抑强扶弱), increase the energy of X itself while decrease the energy of the prisoner XK of X.

3) Suppose that 0 ρ 1 = ρ ( x ) < ρ 0 , as real-normal, in which X will encounter an expected real disease with a healthy economy. In order to protect or maintain the loving relationship, abiding by TCE’s idea “Real disease with a healthy economy is to rush down his son” (实则泄其子), decrease the energy of the son XS of X. The treating way is an indirect treating for X.

In order to protect or maintain the killing relationship, abiding by TCE’s idea “Don’t have disease cure cure non-ill” (不治已病治未病), do a preventive treatment for the more serious relation disease between virtual KX and real X. Through the intervening principle of “Strong inhibition of the same time, support the weak” (抑强扶弱), decrease the energy of X itself while increase the energy of the bane KX of X.

4) Suppose that ( ρ ( x ) + ρ ( x ) 3 ) < ( 1 ρ ( x ) 3 ) , as real, in which X encounters a real disease with an unhealthy economy. In order to protect or maintain the loving relationship, abiding by TCE’s idea “Real disease with an unhealthy economy is to rush down itself” (实则泄之), decrease the energy of X directly.

In order to protect or maintain the killing relationship, abiding by TCE’s idea “Don’t have disease cure cure non-ill” (不治已病治未病), do a preventive treatment for the more serious relation disease between virtual XK and real SX. Through the intervening principle of “Strong inhibition of the same time, support the weak” (抑强扶弱), decrease the energy of the mother SX of X while increase the energy of the bane XK of SX.

Acknowledgements

This article has been repeatedly invited as reports, such as People’s University of China in economic intervention meetings, Shanxi University, Liaocheng University, Xuchang College, and so on. The work was supported by Specialized Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China (Grant No. 200802691021).

Appendix

Proof of Theorem 2.1. Let Δ φ ( X ) 2 = ( 1 ρ ( x ) 3 ) Δ > 0 .

1) Firstly, from Equations (3) and (4), by equal ratio theorem,

Δ φ ( X S ) 2 = ( ρ ( x ) + ρ ( x ) 3 ) Δ > 0 .

If ρ 3 = c ρ ( x ) 0 or c 0 , then ρ 1 ρ 3 = ρ ( x ) ( 1 c ) , and ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) . If ρ ( x ) , then ρ 3 = c ρ ( x ) 0 , and 0 c 1 . Thus 0 < ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 > ρ 1 = ρ ( x ) > 0 and 0 < c 1 will be equivalent to each other. It is because ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) is a monotone decreasing function of 0 ρ 3 = c ρ ( x ) < ρ ( x ) = ρ 1 , ρ 0 > ρ 1 = ρ ( x ) > 0 if c 0 or a monotone increasing function of ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) if 0 ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 > ρ 1 = ρ ( x ) > 0 ; and 0 c 1 is a monotone decreasing function of ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) if a x < t 0 ; and 1 ρ 1 = ρ ( x ) ρ 0 is a monotone decreasing function of 1 c 1 ρ ( x ) 2 ρ ( x ) 3 0 if ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) .

In fact, 1 1 ρ ( x ) 2 ρ ( x ) 3 > c 0 is a monotone decreasing function of ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) if | ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) | 2 ρ 0 3 = 0.41024 since

( ρ 1 + ρ 2 ρ 3 ) or ( 1 ρ 2 ρ 3 )

And a x < t 0 is a monotone increasing function of x if t 0 since

ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 > 0

And c 1 is a monotone decreasing function of Δ φ ( S X ) 2 ( 1 ρ ( x ) 3 ) Δ > 0 if Δ φ ( X ) 2 ( ρ ( x ) + ρ ( x ) 3 ) Δ > 0 since

a x < t 0

And 1 ρ 1 = ρ ( x ) ρ 0 is a monotone decreasing function of ( ρ ( x ) + ρ ( x ) 3 ) ( 1 ρ ( x ) 3 ) if Δ φ ( X ) 2 = ( ρ ( x ) + ρ ( x ) 3 ) Δ > 0 since

Δ φ ( S X ) 2 = ( 1 ρ ( x ) 3 ) Δ

2) Let the function ρ 3 = c ρ ( x ) > 0 . Then 0 < c 1 is a mo notone increasing function of u since ρ 1 + ρ 2 ρ 3 = ρ ( x ) + c ρ ( x ) 3 .

On the other hand, from Zhang & Shao (2012), there is 1 ρ 2 ρ 3 = ( 1 c ρ ( x ) 3 ) . Hence, if ρ ( x ) , then

ρ 3 = c ρ ( x ) > 0 because of monotonicity of f. Thus 0 < c 1 .

By the result of (1), it is to get 0 < ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 ρ 1 = ρ ( x ) 1 since c 1 is a monotone decreasing function of ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) where 0 < ρ 3 = c ρ ( x ) < ρ ( x ) = ρ 1 , ρ 0 ρ 1 = ρ ( x ) 1 .

Similarly, it is to get 0 < c < 1 since ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) is a monotone decreasing function of 0 < ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 ρ 1 = ρ ( x ) 1 where 0 < c 1 . The proof of the monotone decreasing function ( ρ 1 + ρ 2 ρ 3 ) or ( 1 ρ 2 ρ 3 ) is from

t 0 x b .

Furthermore, it is to get 1 ρ 1 = ρ ( x ) ρ 0 since 1 c 1 ρ ( x ) 2 ρ ( x ) 3 0 is a monotone decreasing function of ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) where 1 1 ρ ( x ) 2 ρ ( x ) 3 > c 0 . The proof of the monotone decreasing function ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) is from

| ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) | < 2 ρ 0 3 = 0.41024 .

3) It is similar to the proof of (2).

4) Let the function ( ρ 1 + ρ 2 ρ 3 ) or ( 1 ρ 2 ρ 3 ) . Then t 0 x b is a monotone increasing function of u since t 0 where ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 . On the other hand, c 1 , where Δ φ ( X ) 2 ( ρ ( x ) + ρ ( x ) 3 ) Δ > 0 , Δ φ ( X S ) 2 ( 1 ρ ( x ) 3 ) Δ > 0 , is the same as that in (2).

Therefore, if t 0 x b , then 1 ρ 1 = ρ ( x ) ρ 0 , ( ρ ( x ) + ρ ( x ) 3 ) ( 1 ρ ( x ) 3 ) , since

Δ φ ( X ) 2 = ( ρ ( x ) + ρ ( x ) 3 ) Δ < 0 .

The condition Δ φ ( X S ) 2 = ( 1 ρ ( x ) 3 ) Δ < 0 implies that

ρ 3 = c ρ ( x ) > 0

5) Consider the function 0 < c 1 is the same as in (4). Easy to know that ρ 1 + ρ 2 ρ 3 = ρ ( x ) + c ρ ( x ) 3 if and only if 1 ρ 2 ρ 3 = ( 1 c ρ ( x ) 3 ) . Denoted the function ρ ( x ) by ρ 3 = c ρ ( x ) > 0 . The 0 < c 1 is a monotone decreasing function of 0 < ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 ρ 1 = ρ ( x ) 1 since

c 1

If ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) , i.e., 0 < ρ 3 = c ρ ( x ) < ρ ( x ) = ρ 1 , ρ 0 ρ 1 = ρ ( x ) 1 , then 0 < c < 1 which implies ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) .

If 0 < ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 ρ 1 = ρ ( x ) 1 , i.e., 0 < c 1 , then ( ρ 1 + ρ 2 ρ 3 ) or ( 1 ρ 2 ρ 3 ) which implies x > b .

Because the balance solution of 0 < ρ 1 = ρ ( x ) < ρ 0 is 0 c 1 and ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) is a monotone decreasing function of x > b , there are,

ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 ; and c 1 .

Thus one is that Δ φ ( X ) 2 ( 1 ρ ( x ) 3 ) Δ < 0 , Δ φ ( S X ) 2 ( ρ ( x ) + ρ ( x ) 3 ) Δ < 0 , if x > b since

0 < ρ 1 = ρ ( x ) < ρ 0

And two is that ( ρ ( x ) + ρ ( x ) 3 ) < ( 1 ρ ( x ) 3 ) if Δ φ ( X ) 2 = ( 1 ρ ( x ) 3 ) Δ < 0 since

Δ φ ( S X ) = ( ρ ( x ) + ρ ( x ) 3 ) Δ < 0

And three is that ρ 3 = c ρ ( x ) 0 if c 0 since

ρ 1 ρ 3 = ρ ( x ) ( 1 c )

In particular, from the proof of (3), there is that ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) is a

monotone increasing function of ρ ( x ) . When c is nearly to 1/2, it is not only to obtain directly ρ 3 = c ρ ( x ) 0 , 0 c 1 , but also to get the following statements.

a) 0 < ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 > ρ 1 = ρ ( x ) > ρ 2 = ρ ( x ) 2 > 0 and 0 < c 1 are nearly to 0 if ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) in which 0 ρ 3 = c ρ ( x ) < ρ ( x ) = ρ 1 , ρ 0 > ρ 1 = ρ ( x ) > ρ 2 = ρ ( x ) 2 > 0 .

b) c 0 and ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) are nearly to 0 ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 > ρ 1 = ρ ( x ) > ρ 2 = ρ ( x ) 2 > 0 respectively, if 0 c 1 in which ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) .

c) w a t e r ( S X ) = { a r m y a s k i d n e y ; e c o n o m i c s a s b l a d d e r ; G D P ( t h e G r o s s D o m e s t i c P r o d u c t ) ; a m b i t i o n , b o n e , s a l t y , t h e n o r t h , w i n t e r , h i d i n g } ; and w a t e r ( S X ) = { a r m y a s k i d n e y ; e c o n o m i c s a s b l a d d e r ; G D P ( t h e G r o s s D o m e s t i c P r o d u c t ) ; a m b i t i o n , b o n e , s a l t y , t h e n o r t h , w i n t e r , h i d i n g } ; are nearly to GDP = Q 1 t P 1 t + Q 2 t P 2 t + + Q n t P n t , respectively, if t , n in which Q * .

Taking Q 1 t P 1 t , Q 2 t P 2 t , , Q n t P n t , it is to get the desired. #

Proof of Corollary 2.1. (1). From the proof of (1) in Theorem 2.1, for any P * , there is an unique solution Q 1 t P 1 t , Q 2 t P 2 t , , Q n t P n t and there is also an unique solution T h e r a t e o f G D P i n f l a t i o n ( p r i c e r i s e s ) = c u r r e n t p r i c e l e v e l b a s e p r i c e l e v e l b a s e p r i c e l e v e l × 1 0 0 % , , such that

φ = ( 5 1 ) / 2 = 0.61803399

since ρ 0 = 0.5897545123 is a monotone decreasing function of ρ 0 or a monotone increasing function of ρ 1 = ρ 3 if ρ 2 = ρ 1 ρ 3 .

By the result of (1) in Theorem 2.1, 1 ρ 2 ρ 3 = ρ 1 + ρ 2 ρ 3 is equivalent to ρ 1 = ρ 0 .

For ρ 2 = ρ 0 2 , ρ 3 = ρ 0 , since ρ 0 = 0.68232780 .

For ρ 0 , ρ 1 ρ 3 = ρ 3 = ρ 0 / 2 = 0.34116390 , ρ 2 ρ 1 ρ 3 = ρ 1 ρ 3 = ( ρ 0 ) 2 / 2 = 0.23278561 , since 1 ρ 2 ρ 3 = ρ 1 + ρ 2 ρ 3 .

The others can be obtained through the calculated directly from the result of (1) by SAS. #

Proof of Theorem 3.2 Let ρ 1 = ρ 0 .

1) If a subsystem X of a steady multilateral system V falls a virtual disease for a healthy economy, denoted by ρ 2 = ( ρ 0 ) 2 = 0.46557123 , which means that there is a force such that its energy ρ 3 = ρ 0 / 2 decreases, i.e., changed by the increment ρ 0 < φ < ρ 0 . By the Intervention Rule in Zhang & Shao (2012), its capability of intervention reaction can make the mother SX of X to fall a virtual disease by a negative increment λ ( x ) , in which its absolute value is large, denoted by ρ ( x ) , and also can make the son XS of X to fall a virtual disease by a negative increment x , in which its absolute value is small, denoted by x ( 0.11 , 0.81 ) . Diseases of the loving subsystems have the same direction of X.

At the same time, its capability of intervention reaction can make the bane KX of X to fall a real disease by a large increment λ ( x ) , denoted by x , and also can make the prisoner XK of X to fall a real disease by a little increment λ ( x ) = | x 0 .10208 | ( 0.81 x ) ( x + 0.11 ) , x ( 0.11 , 0.81 ) = { x 0 .10208 ( 0.81 x ) ( x + 0.11 ) , 0.81 > x 0 .10208 ; 0 .10208 x ( 0.81 x ) ( x + 0.11 ) , 0.11 < x < 0 .10208 . , denoted by ρ ( x ) = 1 / 2 λ ( x ) + 1 / 2 , x ( 0.11 , 0.81 ) . . Diseases of the killing subsystems are the opposite direction of X.

The bane KX of X is the biggest victim since its increment 0 < ρ ( x ) = 1 / 2 λ ( x ) + 1 / 2 1 is large.

On the other hand, if the GDP inflation rate 0 λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) < + , , by Corollary 2.1, there is λ ( x ) such that

x .

Thus, x ( 0.11 , 0 .10208 ) . It means that the economy is healthy such that there is the capability of self-protection of the steady multilateral system, i.e., x . By the Self-protection Rule in Zhang & Shao (2012), its capability of self-protection can make the biggest victim as the bane KX of X restored by a fixed increment x [ 0 .10208 , 0.81 ) , denoted by ρ ( x ) .

By the Intervention Rule in Zhang & Shao (2012) again and from Theorem 3.1, its capability of self-protection can make the mother XK of KX to fall a virtual disease by a negative increment λ ( x ) , in which its absolute value is large, denoted by λ ( x ) [ 0 , + ) , and also can make the son SX of KX to fall a virtual disease by a negative increment λ ( x ) , in which its absolute value is small, denoted by ρ ( x ) . Diseases of the loving subsystems have the same direction of KX.

At the same time, its capability of self-protection can make the bane XS of KX to fall a real disease by a large increment ρ ( x ) ( 0 , 1 ] , denoted by 1 ρ ( x ) ρ 0 , and also can make the prisoner X of KX to fall a real disease by a little increment λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) 1 ρ 0 2 ρ 0 = ρ 0 2 ρ ( x ) 2 1 , denoted by λ ( x ) ρ ( x ) = 1 ρ ( x ) 2 ρ ( x ) 2 1 ρ 0 2 ρ 0 2 = ρ 0 ρ ( x ) 1 . Diseases of the killing subsystems are the opposite direction of KX. All these changes consist of those in Figure 2.

From Figure 2 or from Theorem 3.2 in Zhang & Shao (2012), if λ ( x ) ρ ( x ) 2 = 1 ρ ( x ) 2 ρ ( x ) 3 1 ρ 0 2 ρ 0 3 = 1 , i.e., 0 < ρ ( x ) < ρ 0 , its capabilities of intervention reaction and self-protection can make the subsystems XS, XK and KX be restored at the same time, but the subsystems X and SX will decrease their energies. In mathematics, from Theorems 3.1 and 3.2 in Zhang & Shao (2012), the final increments can be obtained as follows:

λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) > 1 ρ 0 2 ρ 0 = ρ 0 2 > ρ ( x ) 2 > 0

λ ( x ) ρ ( x ) = 1 ρ ( x ) 2 ρ ( x ) 2 > 1 ρ 0 2 ρ 0 2 = ρ 0 > ρ ( x ) > 0

λ ( x ) ρ ( x ) 2 = 1 ρ ( x ) 2 ρ ( x ) 3 > 1 ρ 0 2 ρ 0 3 = 1

0 < ρ 1 = ρ ( x ) < ρ 0 , ρ 2 = ρ ( x ) 2

ρ 3 = c ρ ( x )

It means that the first physiological system of the steady multilateral system runs normally. From the idea of TCE, by the Affording Rule, the second physiological system of the steady multilateral system will not work to afford for. It is because there is a full Yin food 0 c 1 for the second physiological system if the subsystem X falls a virtual disease and is intervened for a healthy economy by the Attaining Rule.

By Theorem 2.1 and Corollary 2.1, the GDP inflation rate ρ 1 ρ 3 = ρ ( x ) ( 1 c ) 0 makes ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) 0 such that ( ρ 1 + ρ 2 ρ 3 ) = ρ ( x ) + c ρ ( x ) 3 < 1 ρ 2 ρ 3 = 1 c ρ ( x ) 3 , therefore the first transfer law is the first occurrence of the virtual disease of the mother SX of X if a subsystem X of a steady multilateral system V falls a virtual disease for a healthy economy.

From Figure 2 and by Definition 3.1, the relation disease between virtual SX and virtual X is less serious since virtual SX can love virtual X.

If the disease continues to develop, it will lead to undermine firstly the best state of the capability of self-protection of the steady multilateral system, i.e., | ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) | > 2 ( 1 c ) ρ 0 3 = ( 1 c ) 0.41024 , since any disease that causes side effects in the first place dues to the non-best state of self-protection ability, i.e., 1 ρ 1 = ρ ( x ) ρ 0 , where ρ 2 = ρ ( x ) 2 , even if the treatment principle of TCE is used. Thus the self-protection coefficient ρ 3 = c ρ ( x ) will near to small such that firstly 0 c 1 , secondly ρ 1 ρ 3 = ρ ( x ) ( 1 c ) 0 , and finally ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) 0 .

By Theorem 3.1 in Zhang & Shao (2012), the victim KX or XK of X will encounter a sick which is different from the disease direction of X, i.e., changed by the increments

( ρ 1 + ρ 2 ρ 3 ) = ρ ( x ) + c ρ ( x ) 3 1 ρ 2 ρ 3 = 1 c ρ ( x ) 3

1 c 1 ρ ( x ) 2 ρ ( x ) 3 = λ ( x ) ρ ( x ) 2 0

respectively. At the same time, the son XS of X also falls a virtual ill which is the same disease direction of X, i.e., changed by the increment

ρ 1 ρ 3 = ρ ( x ) ( 1 c ) > ρ ( x ) / 2

since ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) > ρ ( x ) 2 / 2 . Therefore the transfer law is secondly the real disease of the bane KX of X after the virtual disease of the mother SX of X, and thirdly the real disease of the prisoner XK of X, and fourthly the virtual disease of the son XS of X, against the loving relationship order transmission.

In fact, watching Figure 2, SX is virtual, KX is real, XK is real, and XS is virtual, if X is virtual for a healthy economy. The order of the transfer law of diseases must be against the loving relationship order transmission. It is because

( ρ 1 + ρ 2 ρ 3 ) = ρ ( x ) + c ρ ( x ) 3 < 1 ρ 2 ρ 3 = 1 c ρ ( x ) 3

The result is obtained from | ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) | ( ρ 0 ) 3 = 0.31767 since

0 c < 1 ρ ( x ) 2 ρ ( x ) 3 = λ ( x ) ρ ( x ) 2 1 2

In other words, the diseases are transferred from real KX to virtual SX against the loving relationship order if X is the cause of diseases or X is intervened. It implies that the mother SX of X will obtain the best Yin (negative) energy if the energy of X decreases.

Watching Figure 2 and by Definitions 3.1 and 3.2, the relation disease between real KX and virtual X is less serious since real KX can kill virtual X, but the relation disease between virtual X and real XK is more serious since virtual X cannot kill real XK which will destroy the killing order from X to XK of the Yin Yang Wu Xing system if the disease continues to develop.

Finally the relation disease between virtual X and virtual XS is also less serious since virtual X can love virtual XS. The less serious relation disease between virtual X and virtual XS makes that the loving order from X to XS will be restored easily. The transferring way of strengthening the loving relationship can make the new virtual disease of X remission since 1 > ρ ( x ) ρ 0 . Despite of the positive way, the system will be still for the next round of disease transmission, until the disease rehabilitation.

2) If a subsystem X of a steady multilateral system V falls a real disease for a healthy economy, denoted by ρ 1 ρ 3 = ρ ( x ) ( 1 c ) ρ ( x ) / 2 , which means that there is a force such that its energy ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) ρ ( x ) 2 / 2 increases, i.e., changed by the increment ( ρ 1 + ρ 2 ρ 3 ) = ρ ( x ) + c ρ ( x ) 3 < 1 ρ 2 ρ 3 = 1 c ρ ( x ) 3 . By the Intervention Rule in Zhang & Shao (2012), its capability of intervention reaction can make the son XS of X to fall a real disease by a large increment | ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) | 2 ρ 0 3 = 0.41024 , denoted by 0 c 1 2 < 1 ρ ( x ) 2 ρ ( x ) 3 = λ ( x ) ρ ( x ) 2 1 , and also can make the mother SX of X to fall a real disease by a little increment ρ 0 ρ ( x ) < ρ 0 , denoted by ρ 1 ρ 3 = ρ ( x ) ( 1 c ) < ρ ( x ) / 2 . Diseases of the loving subsystems have the same direction of X.

At the same time, its capability of intervention reaction can make the prisoner XK of X to fall a virtual disease by a negative increment ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) < ρ ( x ) 2 / 2 , in which its absolute value is large, denoted by ( ρ 1 + ρ 2 ρ 3 ) = ρ ( x ) + c ρ ( x ) 3 < 1 ρ 2 ρ 3 = 1 c ρ ( x ) 3 , and also can make the bane KX of X to fall a virtual disease by a negative increment | ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) | < ( ρ 0 ) 3 = 0.31767 , in which its absolute value is small, denoted by 1 2 < c < 1 ρ ( x ) 2 ρ ( x ) 3 = λ ( x ) ρ ( x ) 2 1 . Diseases of the killing subsystems are the opposite direction of X.

The prisoner XK of X is the biggest victim since its increment ρ 0 ρ ( x ) < ρ 0 is the scope of big changes.

On the other hand, if the GDP inflation rate ρ 1 ρ 3 = ρ ( x ) ( 1 c ) ρ ( x ) / 2 , by Theorem 2.1 and Corollary 2.1, there is ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) ρ ( x ) 2 / 2 such that

| ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) | .

Thus, 0 < c < 1 ρ ( x ) 2 ρ ( x ) 3 = λ ( x ) ρ ( x ) 2 1 2 . It means that the economy is healthy such that there is a good capability of self-protection of the steady multilateral system.

By the Self-protection Rule in Zhang & Shao (2012), its capability of self-protection can make the biggest victim as the prisoner XK of X restored by a fixed increment 1 > ρ ( x ) ρ 0 , denoted by [ ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) ] .

By the Intervention Rule in Zhang & Shao (2012) again and from Theorem 3.1, its capability of self-protection can make the son KX of XK to fall a real disease by a large increment [ ρ 0 3 = 0.20512 , 0 ) , denoted by 0 < c 1 2 < 1 ρ ( x ) 2 ρ ( x ) 3 = λ ( x ) ρ ( x ) 2 1 , and also can make the mother XS of XK to fall a real disease by a little increment ρ 0 ρ ( x ) < ρ 0 , denoted by [ ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) ] . Diseases of the loving subsystems have the same direction of XK.

At the same time, its capability of self-protection can make the prisoner SX of XK to fall a virtual disease by a negative increment [ ρ 0 3 = 0.20512 , 0 ) , in which its absolute value is large, denoted by 1 2 < c < 1 ρ ( x ) 2 ρ ( x ) 3 = λ ( x ) ρ ( x ) 2 1 , and also can make the bane X of XK to fall a virtual disease by a negative increment ρ 0 ρ ( x ) < ρ 0 , in which its absolute value is small, denoted by 0 < d < 1 . Diseases of the killing subsystems are the opposite direction of XK. All these changes consist of those in Figure 3.

From Figure 3 or by Theorem 3.2 in Zhang & Shao (2012), if u ( 0.11 , 0 .10208 ) , i.e., v ( 0 .10208 , 0.81 ) , its capabilities of intervention reaction and self-protection can make the subsystems SX, KX and XK restored at the same time, but the subsystems X and XS will increase their energies. In mathematics, from Theorems 3.1 and 3.2 in Zhang & Shao (2012), the final increments can be obtained as follows:

λ ( 0 .10208 ) = 0 λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) λ ( u ) = λ ( v ) = ( 1 d ) / ( 2 d ) ,

ρ ( u ) = ρ ( v ) = d ρ ( x ) = 1 / 2 λ ( x ) + 1 / 2 1 = ρ ( 0 .10208 ) .

x [ 0.06 , 0.16 ]

λ ( 0.10208 ) = 0 λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) λ ( 0.06 ) = λ ( 0.16 ) = 0.33003 ,

ρ ( 0.06 ) = ρ ( 0.16 ) = 0.60239 ρ ( x ) = 1 / 2 λ ( x ) + 1 / 2 1 = ρ ( 0.10208 ) .

It means that the first physiological system of the steady multilateral system runs normally. From the idea of TCE, by the Affording Rule, the second physiological system of the steady multilateral system will not work to afford for. It is because there is a full Yang food x [ 0 .062274 , 0 .15581 ] for the second physiological system if the subsystem X falls a real disease and is intervened for a healthy economy by the Attaining Rule.

By Theorem 2.1 and Corollary 2.1, the GDP inflation rate λ ( 0 .10208 ) = 0 λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) λ ( 0 .062274 ) = λ ( 0 .15581 ) = 1 φ 2 φ = 0.30902 , makes ρ ( 0 .062274 ) = ρ ( 0 .15581 ) = φ ρ ( x ) = 1 / 2 λ ( x ) + 1 / 2 1 = ρ ( 0 .10208 ) . such that x [ 5 .8114% , 16 .359% ] . Therefore the transfer law is the first occurrence of the real disease of the son XS of X if a subsystem X of a steady multilateral system V falls a real disease for a healthy economy.

From Figure 3 and by Definition 3.1, the relation disease between real X and real XS is less serious since real X can love real XS.

If the disease continues to develop, it will lead to undermine firstly the capability of self-protection of the steady multilateral system, i.e., λ ( 10.208 % ) = 0 λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) λ ( 5.8114 % ) = λ ( 16.359 % ) = ρ 0 2 = 0.34781 , since any disease that causes side effects in the first place dues to the non-best state of self-protection ability, i.e., ρ ( 5.8114 % ) = ρ ( 16.359 % ) = ρ 0 ρ ( x ) = 1 / 2 λ ( x ) + 1 / 2 1 = ρ ( 10.208 % ) . where x [ 0 .070949 , 0 .14119 ] , even if the treatment principle of TCE is used. Thus the self-protection coefficient λ ( 0.10208 ) = 0 λ ( x ) λ ( 0.070949 ) = λ ( 0.14119 ) = ( ρ 0 ) 2 / 2 = 0.23279 , will near to small such that firstly ρ ( 0 .070949 ) = ρ ( 0 .14119 ) = ρ 0 ρ ( x ) = 1 / 2 λ ( x ) + 1 / 2 1 = ρ ( 0 .10208 ) . , and secondly x [ 6 % , 16 % ] , and finally x [ 0.0 2 , 0.0 5 ] . By Theorem 3.1 in Zhang & Shao (2012), the victim XK or KX of X will encounter a sick respectively which is different from the disease direction of X, i.e., changed by the increments

ρ 0 ρ 1 1

ρ 1 = ρ ( x )

respectively since ρ 2 = ρ ( x ) 2 . At the same time, the mother SX of X also falls a real ill which is the same disease direction of X, i.e., changed by the increment

ρ 3 = c ρ ( x )

since 0 c 1 . Therefore the first transfer law is secondly the virtual disease of the prisoner XK of X after the real disease of the son XS of X, and thirdly the virtual disease of the bane KX of X, and fourthly the real disease of the mother SX of X, along the loving relationship order transmission.

In fact, watching Figure 3, XS is real, XK is virtual, KX is virtual, and SX is real if X is real for a healthy economy. The order of the transfer law of diseases must be along the loving relationship order transmission. It is because

x [ 5 .8114% , 16 .359% ]

The result is obtained from x [ 5 .8114% , 16 .359% ] since

x [ 6 % , 16 % ]

In other words, the diseases are transferred from virtual XK to real XS along the loving relationship order if X is the cause of diseases or X is intervened for a healthy economy. It implies that the son XS of X will obtain the best Yang (positive) energy if the energy of X increases.

Watching Figure 3 and by Definitions 3.1 and 3.2, the relation disease between real X and virtual XK is less serious since real X can kill virtual XK, but the relation disease between virtual KX and real X is more serious since virtual KX cannot kill real X which will destroy the killing order of the Yin Yang Wu Xing system from KX to X.

Finally the relation disease between real SX and real X is also less serious since real SX can love real X. The less serious relation disease between real SX and real X makes that the loving order from SX to X will be restored easily. The transferring way of strengthening the loving relationship can make the real disease of X remission since ρ 0 ρ 1 1 . Despite of the positive way, the system will be still for the next round of disease transmission, until disease rehabilitation. This completes the proof.#

Proof of Theorem 3.3. Let ρ 1 .

1) If a subsystem X of a steady multilateral system V falls a virtual disease for an unhealthy economy, denoted by 1 ρ 1 ρ 0 , which means that there is a force such that its energy ρ 1 + ρ 2 decreases, i.e., changed by the increment ρ 1 + ρ 2 = 1 . By the Intervention Rule in Zhang & Shao (2012), its capability of intervention reaction can make the mother SX of X to fall a virtual disease by a negative increment ρ 1 ρ 0 , in which its absolute value is large, denoted by ρ 2 = ρ 1 ρ 3 , and also can make the son XS of X to fall a virtual disease by a negative increment ρ 3 = ρ 1 , in which its absolute value is small, denoted by ρ 1 + ρ 2 = 1 . Diseases of the loving subsystems have the same direction of X.

At the same time, its capability of intervention reaction can make the bane KX of X to fall a real disease by a large increment ρ 1 = φ 0.61803 ρ 0 , denoted by ρ 2 = φ 2 0.38197 ρ 0 2 , and also can make the prisoner XK of X to fall a real disease by a little increment ρ 3 , denoted by ρ 3 = 1 ρ 1 2 ρ 2 1 2 . Diseases of the killing subsystems are the opposite direction of X.

The bane KX of X is the biggest victim since its increment ( 1 ρ 2 ρ 3 ) = ( ρ 1 + ρ 2 ρ 3 ) is large.

By Corollary 2.1 and Theorem 2.1, the GDP inflation rate ρ 1 + ρ 2 1 makes that ρ 1 0.61803 ρ 3 0.5 ρ 2 0.38197 such that ρ 0 = 0.68232780 . In this case, the steady multilateral system V is abnormal or unhealthy. The unhealthy means the lack of self-protection ability. Thus the self-protection coefficient ρ 3 = ρ 1 / 2 = ρ 0 / 2 = 0.34116390 will near to small such that firstly ρ 1 ρ 3 = ρ 3 = ρ 0 / 2 = 0.34116390 and secondly ρ 2 ρ 1 ρ 3 = ρ 1 ρ 3 = ( ρ 0 ) 2 / 2 = 0.23278561 , i.e., ( 1 ρ 2 ρ 3 ) = ( ρ 1 + ρ 2 ρ 3 ) , if the disease continues to develop.

Consider in the worst state: ρ 1 = ρ 0 , i.e., ρ 2 = ( ρ 0 ) 2 = 0.46557123 , where x [ 0.06 , 0.16 ] . Its capability of self-protection cannot make the biggest victim as the bane KX of X restored. In mathematics, from Theorems 3.1 and 3.2 in Zhang & Shao (2012), the final increments can be obtained as follows:

1 ρ 1 = ρ ( x ) 0 .60239 = ρ ( 0.06 ) = ρ ( 0.16 )

x [ 0 .062274 , 0 .15581 ]

1 ρ 1 = ρ ( x ) φ = ρ ( 0 .062274 ) = ρ ( 0 .15581 )

x [ 5 .8114% , 16 .359% ]

1 ρ 1 = ρ ( x ) ρ 0 = ρ ( 5 .8114% ) = ρ ( 16 .359% )

It means that the first physiological system of the steady multilateral system runs hardly, such that the final increments of self-protection are similar to the increments of intervention reaction. The hard running is not only because the killing order has been destroyed, but also the loving order cannot be running.

From the idea of TCE, by the Affording Rule, the second physiological system of the steady multilateral system will work. It is because a steady multilateral system would become ill or dies if its Chi or energy in the steady multilateral system is imbalanced or exhausted. The purpose of the second physiological system working is to increase the energy of the system, and restores the order of the killing relationship of the Yin Yang Wu Xing system.

By Theorems 3.3 and 3.4 and Corollary 3.2 in Zhang & Shao (2012), the method of “Strong inhibition of the same time, support the weak”, i.e., to increase energy of virtual X while to reduce energy of real XK, should be used in this case: λ ( 5 .8114% ) = λ ( 16 .359% ) = 1 ρ 0 2 ρ 0 = ρ 0 2 which is equivalent to that ( 1 ρ 0 3 ) = ( ρ 0 + ρ 0 3 ) , such that x [ 0 .070949 , 0 .14119 ] . It is because the inequality 1 ρ 1 = ρ ( x ) ρ 0 = ρ ( 0 .070949 ) = ρ ( 0 .14119 ) makes the absolute value of their increments λ ( 0 .070949 ) = λ ( 0 .14119 ) = 1 ρ 0 2 ρ 0 = ( ρ 0 ) 2 2 becoming large.

By Definitions 3.1 and 3.2, consider the lack of self-protection ability, from Figure 4, for a virtual disease of X, its capability of intervention reaction can make many relation diseases occurrence. Only the relation between virtual X and real XK can be considered as more serious, since virtual X cannot kill real XK, which will destroy the killing order from X to XK of the Yin Yang Wu Xing system if the disease continues to develop.

By Affording Rule again, abiding by the treatment principle of “Strong inhibition of the same time, support the weak”, the intervention of the second physiological system is to increase the energy of virtual X while to reduce the energy of real XK. If an intervention force on the subsystem X of steady multilateral system V is implemented such that its energy ( ρ 0 ) 3 = ( 1 ρ 0 ) has been changed by an increment x [ 6 % , 16 % ] , denoted by x [ 6 % , 16 % ] , and at the same time, another intervention force on the subsystem x [ 5 .8114% , 16 .359% ] of steady multilateral system V is also implemented such that its energy x [ 5 .8114% , 16 .359% ] has been changed by an increment x [ 0.06 , 0.16 ] , denoted by ρ 0 = ρ ( 5 .8114% ) = ρ ( 16 .359% ) , then from Theorem 3.4 in Zhang & Shao (2012), all other subsystems: SX, KX and XS can be restored at the same time, and the subsystems X and XK will increase and decrease their energies by the same size but the direction opposite, respectively.

In mathematics, from Theorems 3.1, 3.3 and 3.4 in Zhang & Shao (2012), the final increments can be obtained as follows:

λ ( 5 .8114% ) = λ ( 16 .359% ) = 1 ρ 0 2 ρ 0 = ρ 0 2

ρ 1 = ρ 3

ρ 2 = ρ 1 ρ 3

( 1 ρ 2 ρ 3 ) = ( ρ 1 + ρ 2 ρ 3 )

ρ 1 = ρ 0

All these changes consist of those in Figure 4.

Of course, the virtual disease of X comes from the son XS of X since any virtual disease always comes from its son by Theorem 3.2.

In order to cure the virtual disease of X, by Affording Rule, the increment

ρ 2 = ρ 0 2

must be very big. For example ρ 3 = c ρ 0 , which means righteousness to defeat evil, this treatment can make the increment

c 1

be very small.

In fact, by Affording Rule and from Theorems 3.1-3.4 in Zhang & Shao (2012), the all final increments are can be obtained as follows:

ρ 1 = ρ ( x ) ρ 0

x [ 5 .8114% , 16 .359% ]

x [ 5 .8114% , 16 .359% ]

x > 16 .359%

x < 5 .8114%

Therefore, the transfer law is the first occurrence of the virtual disease of the prisoner XK of X; secondly the virtual disease of the mother SX of X, thirdly the virtual disease of the son XS of X, and finally the real disease of the bane KX of X.

In fact, watching Figure 4, XK is virtual, SX is virtual, XS is virtual, and KX is real if X is virtual for an unhealthy economy. The order of the transfer law of diseases must be along the killing relationship order transmission. It is because

x ( min , max )

The result is obtained from x since

t 0

and

x

In other words, the diseases are transferred from virtual X to real KX along the killing relationship order transmission.

By Definition 3.2, the relation disease between virtual X and virtual XK is rare since the relation disease cannot destroy the killing order from X and XK although virtual X cannot kill the virtual XK. The rare relation disease between virtual X and virtual XK makes that the killing order from X to XK will be cured difficultly. Although rare refractory disease, but their disease transmission is natural since they are all virtual.

By Definition 3.2, the relation disease between virtual XK and virtual SX, or between virtual SX and virtual XS, is also rare, respectively. Thus the disease transmission from virtual XK to virtual SX, or, from virtual SX to virtual XS, is also natural since they are all virtual, respectively.

Only the relation disease between virtual XS and real KX is more serious since virtual XS cannot kill real KX, which will destroy the killing order from XS to KX of the Yin Yang Wu Xing system if the disease continues to develop.

Finally the less serious relation disease between real KX and virtual X makes that the killing order from KX to X will be restored easily. The transferring way of strengthening the killing relationship by the second physiological system can make the new virtual disease of X remission since virtual X will get the positive increment

ρ ( t 0 ) = 1 , if 0.11 , 0.81 , 0.10208 .

Despite of the positive way, the system still will be for the next round of disease transmission, until the disease rehabilitation.

2) If a subsystem X of a steady multilateral system V falls a real disease for an unhealthy economy, denoted by min , max , t 0 , which means that there is a force such that its energy ρ 0 ρ 1 = ρ ( x ) 1 increases, i.e., changed by the increment x [ u , v ] . By the Intervention Rule in Zhang & Shao (2012), its capability of intervention reaction can make the son XS of X to fall a real disease by a large increment min < u < t 0 < v < max , denoted by ρ ( u ) = ρ ( v ) = ρ 0 ρ 1 = ρ ( x ) = ( 1 / 2 ) / [ λ ( x ) + 1 / 2 ] ρ ( t 0 ) = 1 , and also can make the mother SX of X to fall a real disease by a little increment λ ( t 0 ) = 0 λ ( x ) = ( 1 ρ ( x ) ) / ( 2 ρ ( x ) ) ρ 0 2 = λ ( u ) = λ ( v ) = ρ ( u ) 2 = ρ ( v ) 2 ρ 2 = ρ ( x ) 2 ρ 1 = ρ ( x ) 1. # , denoted by X = { y V | y ~ x } , X S = { y V | x y } , X K = { y V | x y } , . Diseases of the loving subsystems have the same direction of X.

At the same time, its capability of intervention reaction can make the prisoner XK of X to fall a virtual disease by a negative increment K X = { y V | y x } , S X = { y V | y x } , , in which its absolute value is large, denoted by φ ( * ) , and also can make the bane KX of X to fall a virtual disease by a negative increment Δ φ ( X ) Δ d φ ( X ) d X = ( 1 ρ 2 ρ 3 ) = ( 1 c ρ ( x ) 3 ) > 0 ; Δ φ ( X S ) Δ d φ ( X S ) d X = ( ρ 1 + ρ 2 ρ 3 ) = ρ ( x ) ( 1 + c ρ ( x ) 2 ) > 0 ; Δ φ ( X K ) Δ d φ ( X K ) d X = ( ρ 1 ρ 3 ) = ρ ( x ) ( 1 c ) < 0 ; Δ φ ( K X ) Δ d φ ( K X ) d X = ( ρ 2 ρ 1 ρ 3 ) = ρ ( x ) 2 ( 1 c ) < 0 ; Δ φ ( S X ) Δ d φ ( S X ) d X = ( ρ 2 ρ 1 ρ 3 ) = ρ ( x ) 2 ( 1 c ) > 0 , , in which its absolute value is small, denoted by X ( Δ φ ( X ) = Δ > 0 ) . Diseases of the killing subsystems are the opposite direction of X.

The prisoner XK of X is the biggest victim since its increment ρ 1 = ρ ( x ) is the scope of big changes.

By Corollary 2.1 and Theorem 2.1, the GDP inflation rate ρ 2 = ρ ( x ) 2 makes that ρ 3 = c ρ ( x ) , such that 0 < ρ ( x ) < 1 . In this case, the steady multilateral system V is abnormal or unhealthy. The unhealthy economy implies the lack of self-protection ability. Thus the self-protection coefficient 0 c 1 will near to small such that firstly V 0 = X , V 1 = X S , V 2 = X K , V 3 = K X , V 4 = S X , , and secondly V = V 0 + V 1 + V 2 + V 3 + V 4 , i.e., V i V j = , i j , if the disease continues to develop.

Consider in the worst state: = { R 0 , R 1 , , R 4 } , i.e., R r = i = 0 4 V i × V m o d ( i + r , 5 ) , r { 0 , 1 , , 4 } , R i * R j R m o d ( i + j , 5 ) , , where V i × V j = { ( x , y ) : x V i , y V j } . Its capability of self-protection cannot make the biggest victim as the prisoner XK of X be restored.

In mathematics, from Theorems 3.1 and 3.2 in Zhang & Shao (2012), the final increments can be obtained as follows:

R i * R j = { ( x , y ) : u V suchthat ( x , u ) R i , ( u , y ) R j }

*

R 1 = R 4 1

R 2 = R 3 1

R i 1 = { ( x , y ) : ( y , x ) R i } , i { 1 , 2 , 3 , 4 }

It means that the first physiological system of the steady multilateral system runs hardly, such that the final increments of self-protection are similar to the increments of intervention reaction. The hard running is not only because the killing order has been destroyed, but also the loving order cannot be running.

From the idea of TCE, by the Affording Rule, the second physiological system of the steady multilateral system will work. It is because a steady multilateral system would become ill or dies if its Chi or energy in the steady multilateral system is imbalanced or exhausted. The purpose of the second physiological system working is to increase the energy of the system, and restores the order of the killing relationship of the Yin Yang Wu Xing system.

By Theorems 3.3 and 3.4 and Corollary 3.2 in Zhang & Shao (2012), the method of “Strong inhibition of the same time, support the weak”, i.e., to decrease energy of real X while to increase energy of virtual KX, should mainly be used in this case: V = V 0 + V 1 + V 2 + V 3 + V 4 which is equivalent to that ρ 1 = ρ ( x ) 0 , such that ρ 2 = ρ ( x ) 2 0 . It is because the inequality ρ 3 = c ρ ( x ) 0 makes the increment w o o d ( X ) = { i n d u s t r y a s l i v e r , g o o d s a s b r a v e r y ; P P I ( t h e P r o d u c e r P r i c e I n d e x ) o r R P I ( R e t a i l P r i c e I n d e x ) ; s o u l , r i b s , s o u r , e a s t , s p r i n g , b i r t h } ; becoming large. From Affording Rule, this is just the working method of the second physiological system.

By Definitions 3.1 and 3.2, consider the lack of self-protection ability, from Figure 5, for a real disease of X, its capability of intervention reaction will make the many relation diseases occurrence. Only the relation disease between virtual KX and real X can be considered as more serious, since virtual KX cannot kill real X which will destroy the killing order from KX to X of the Yin Yang Wu Xing system if the disease continues to develop.

By Affording Rule again, abiding by the treatment principle of “Strong inhibition of the same time, support the weak”, the intervention of the second physiological system is to decrease energy of real X while increase energy of virtual KX. If an intervention force on the subsystem X of the steady multilateral system V is implemented such that its energy x i a n g - f i r e ( X S x ) = { a g r i c u l t u r e a s p e r i c a r d i u m ; m o n e y a s t r i p l e e n e r g i z e r ; A A F ( t h e t o t a l o u t p u t v a l u e o f A g r i c u l t u r e f o r e s t r y A n i m a l h u s b a n d r y a n d F i s h e r y ) ; n e r v e , b l o o d v e s s e l , b i t t e r t a s t e , t h e s o u t h , s u m m e r , g r o w t h } ; has been changed by an increment e a r t h ( X K ) = { c o m m e r c e o r b u s i n e s s a s s p l e e n ; e x c h a n g e a s s t o m a c h ; C P I ( t h e C o n s u m e r P r i c e I n d e x ) ; w i l l i n g , m e a t , s w e e t n e s s , c e n t e r , l o n g s u m m e r , c o m b i n e d } ; , denoted by m e t a l ( K X ) = { s c i e n c e o r e d u c a t i o n a s l u n g ; p u b l i c f a c i l i t i e s a s l a r g e i n t e s t i n e ; G B R ( t h e G e n e r a l B u d g e t R e v e n u e ) ; b o l d n e s s , f u r , s p i c y , w e s t , a u t u m n , a c c e p t } ; , and at the same time, another intervention force on the subsystem KX of the steady multilateral system V is also implemented such that its energy w a t e r ( S X ) = { a r m y a s k i d n e y ; e c o n o m i c s a s b l a d d e r ; G D P ( t h e G r o s s D o m e s t i c P r o d u c t ) ; a m b i t i o n , b o n e , s a l t y , t h e n o r t h , w i n t e r , h i d i n g } ; has been changed by an increment X S j , denoted by X S x , then from Theorem 3.4 in Zhang & Shao (2012), all other subsystems: SX, XK and XS can be restored at the same time, and the subsystems X and KX will decrease and increase their energies by the same size but the direction opposite, respectively.

In mathematics, from Theorems 3.1, 3.3 and 3.4 in Zhang & Shao (2012), the final increments can be obtained as follows:

X S j

ρ 3 = c ρ ( x )

ρ 3 = c ρ ( x )

ρ 3 = c ρ ( x ) 0

All these changes consist of those in Figure 5.

Of course, the real disease of X comes from the mother SX of X since any real disease always comes from its mother by Theorem 3.2.

In order to cure the real disease of X, by the Affording Rule, the intervention of the second physiological system must make the increment

0 < ρ 1 = ρ ( x ) < ρ 0

tending to be very small, for example ρ 3 = c ρ ( x ) > 0 , which means righteousness to defeat evil, this treatment makes the increment 1 ρ 1 = ρ ( x ) ρ 0 tending to be very big.

In fact, by Affording Rule and from Theorem 3.1 in Zhang & Shao (2012), the all final increments are obtained as follows:

Δ φ ( K X ) 4 1 = Δ φ ( K X ) 3 1 + φ ( K X ) 2 = [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ] Δ 1 + ( ρ 2 ρ 1 ρ 3 ) Δ [ ( 1 ρ 2 ρ 3 ) + ( ρ 1 ρ 3 ) ( ρ 2 ρ 1 ρ 3 ) ] Δ = [ ( 1 ρ 2 ) + ρ 3 ( ρ 1 ρ 2 ) + ( ρ 1 ρ 3 ) ] Δ > 0 ,

x [ 5 .8114% , 16 .359% ]

ρ 0 ρ 1 = ρ ( x ) 1

ρ 1 , ρ 2

ρ 3

Therefore, the transfer law is the first occurrence of the real disease of the bane KX of X; secondly the real disease of the son XS of X, thirdly the real disease of the mother SX of X, and finally the virtual disease of the prisoner XK of X.

In fact, watching Figure 5, KX is real, XS is real, SX is real, and XK is virtual if X is real for an unhealthy economy. The order of the transfer law of diseases must be against the killing relationship order transmission. It is because

x [ 5 .8114% , 16 .359% ]

The result is obtained from 0 < ρ 1 = ρ ( x ) < ρ 0 since

ρ 1 , ρ 2

and

ρ 3

In other words, the diseases are transferred from real X to virtual XK against the killing relationship order transmission.

By Definition 3.2, the relation disease between real KX and real X is rare since the relation disease cannot destroy the order of the killing relationship from KX to X although the real KX cannot kill the real X. The rare relation disease between real KX and real X makes that the killing order from KX to X will be cured difficultly. Although rare refractory disease, but their disease transmission is natural since they are all virtual.

By Definition 3.2, the relation disease between real XS and real KX, or between real SX and real XS, is also rare, respectively. Thus the disease transmission from real XS to real KX, or from real SX to real XS, is also natural since they are all virtual, respectively.

Only the relation disease between virtual XK and real SX is more serious since virtual XK cannot kill real SX, which will destroy the killing order from XK to SX of the Yin Yang Wu Xing system if the disease continues to develop.

But the less serious relation disease between real X and virtual XK makes that the killing order from X to XK will be restored easily. The transferring way of strengthening the killing relationship by the second physiological system can make the new real disease of X remission since real X will get a negative increment

X , X S , X K , K X , S X if φ ( * ) .

Despite of the positive way, the system will be still for the next round of disease transmission, until the disease rehabilitation. This completes the proof. #

Proof of Theorem 4.1. Let ρ 1 = ρ ( x ) .

1) If ρ 2 = ρ ( x ) 2 , then from Theorem 2.1 and Corollary 2.1, there is that ρ 3 = c ρ ( x ) which means that the economy is unhealthy where 0 c 1 and ρ ( x ) . Since that ρ 0 ρ ( x ) 1 means that the GDP inflation rate is too lower than the normal state, thus the subsystem X has encountered the virtual disease for an unhealthy economy.

From Theorem 3.2 and Corollary 3.2 in Zhang & Shao (2012), the subsystem X was considered as virtual for an unhealthy economy. Assume that the capability of self-protection is nearly to the best state, i.e., 0 < c 1 where x [ 5 .8114% , 16 .359% ] .

If it is to increase the energy of the virtual subsystem X directly, then the capabilities of both intervention reaction and self-protection can make the subsystems SX, KX and XK restored at the same time, but the subsystems X and XS will increase their energies, i.e., changed by the increments

ρ 1 + ρ 2 ρ 3 1 ρ 2 ρ 3

respectively. Since the GDP inflation rate c 0 makes ρ 3 = c ρ ( x ) 0 such that x 0 .10208 , therefore the subsystem X can obtain the large increment c 0 and the subsystem XS will get the small increment ρ 1 + ρ 2 ρ 3 = ρ ( x ) + c ρ ( x ) 3 ρ ( x ) < 1 1 c ρ ( x ) 3 = 1 ρ 2 ρ 3 . The later is the pseudo side effects issue, by Attaining Rule, which is just the food of the second physiological system of the steady multilateral system since that the economy is unhealthy, virtual X intervened makes that the second physiological system will attain the Chi or energy (Yang energy) from the son XS of the intervened subsystem X. The attaining way is an indirect treating for an unhealthy economic subsystem X with a virtual disease.

Thus the primary treatment should be to increase the energy of the subsystem X directly in order to avoid the side effects issue occurrence for an unhealthy economy. This is just one of the affording working principle of the second physiological system by Affording Rule. The idea means that “Virtual disease with an unhealthy economy is to fill itself”.

When the capability of self-protection is nearly to the worst state, i.e., ρ 1 + ρ 2 ρ 3 1 ρ 2 ρ 3 where x [ 5 .8114% , 16 .359% ] , the first physiological system will stop to work, or, the first transfer law will stop to run, while the second physiological system will begin to work, or, the second transfer law will begin to run.

By Affording Rule and the second transfer law in Theorem 3.3, the purpose of the second physiological system working is to improve the physical ability of self-protection of the first physiological system, i.e., to make all of both ρ 0 ρ 1 = ρ ( x ) 1 and 0 < c 1 tending to be small, i.e., for fixed real X less real X S rare virtual X K more virtual K X rare real S X less real X . , c tends to be large, at least, greater than zero, to drive the first physiological systems will begin to work.

By the second transfer law in Theorem 3.3, for a virtual disease of X, the more serious relation disease is the relation between virtual XS and real KX since virtual XS cannot kill real KX which can destroy the killing order between XS and KX if the disease continues to develop.

Abiding by the TCE's idea of “Don’t have disease cure cure non-ill”, in order to avoid the more serious relation disease between virtual XS and real KX occurrence, the system should be intervened when the intervened system was non-ill, but the incidence of the system from the second transfer law in Theorem 3.3 will be to occur for the more serious relation disease between virtual XS and real KX.

According to the intervening principle of “Strong inhibition of the same time, support the weak” from Theorem 3.4 in Zhang & Shao (2012), it is to get that the secondary treatment is to increase the energy of XS, and at the same time, to decrease the energy of KX.

In general, although the economy is unhealthy and falls a virtual disease, the capability of self-protection can be any state, i.e., virtual X less virtual S X rare real K X more real X K rare virtual X S less virtual X . where ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) . The primary treatment is mainly for the normal state of the capability of self-protection, i.e.

ρ 3 = c ρ ( x ) > 0

where ρ 0 ρ 1 = ρ ( x ) 1 and 0 < c 1 . The secondary treatment is for the worst state of the capability of self-protection, i.e.,

0 ρ 3 = c ρ ( x ) < ρ ( x ) = ρ 1 , ρ 0 > ρ 1 = ρ ( x ) > 0

where c 1 and ρ 3 . Comprehensive use of the two methods for the unhealthy economy with a virtual disease can deal with a general situation, i.e.,

0 ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 > ρ 1 = ρ ( x ) > 0

where ( 1 ρ 2 ρ 3 ) = ( 1 c ρ ( x ) 3 ) and ρ ( x ) . #

2) If ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) , then from Theorem 2.1 and Corollary 2.1, there is that ρ 1 = ρ ( x ) which means that the economy is healthy where in general

ρ 1 = ρ ( x ) , ρ 2 = ρ ( x ) 2 such that ρ 3 = c ρ ( x ) > 0 ; and 0 < c 1 such that ρ ( x ) 1 , i.e.,

0 < c 1 .

The fact means that ρ 3 = c ρ ( x ) ρ ( x ) = ρ .

Since the condition c 1 means that the GDP inflation rate x is lower than the center ρ 3 = c ρ ( x ) < ρ ( x ) = ρ , thus the subsystem X will encounter an expected virtual disease if the subsystem X falls ill for a healthy economy.

From Theorem 3.2 and Corollary 3.2 in Zhang & Shao (2012), the subsystem X will be considered as virtual. First the case can be studied that the capability of self-protection is in the best state, i.e., ρ ( x ) 1 where 0 < c 1 .

If the energy of the virtual-normal subsystem SX is intervened to increase its energy, then its capabilities of intervention reaction and self-protection can make the subsystems KX, XK and XS restored at the same time, but the subsystems SX and X will increase their energies, i.e., changed by the increments φ ( * ) , ρ 1 = ρ ( x ) , ρ 2 = ρ ( x ) 2 , respectively. Since the GDP inflation rate ρ 3 = c ρ ( x ) makes 0 c 1 such that mainly ρ ( x ) , therefore the subsystem X can obtain the large increment ρ 0 > ρ 1 = ρ ( x ) > 0 and the subsystem SX will get the small increment 0 c 1 . The later is the pseudo side effects issue, by Attaining Rule, which is just the food of the second physiological system of the steady multilateral system since that the economy is healthy, virtual SX intervened makes that the second physiological system will attain the Chi or energy (Yang energy) from the intervened subsystem SX directly for a healthy economy with a virtual disease.

Thus it is to get the primary treatment should be to increase the energy of the subsystem SX in order to avoid the side effects issue occurrence for a healthy economy. The idea means that “Virtual disease with a healthy economy is to fill his mother”.

Since the economy is healthy, the worst state of the capability of self-protection will not be possible, i.e., x [ 5 .8114% , 16 .359% ] where x [ 5 .8114% , 16 .359% ] , the first physiological system will not stop to work, or, the first transfer law will not stop to run, while the second transfer law will not begin to run.

Is the first physiological system working in order to improve its corresponding intervention ability, at the same time, to provide the food for the second physiological system. In other words, it makes ρ 0 > ρ 1 = ρ ( x ) > 0 tending to be large while 0 c 1 tending to be small, i.e., virtual X rare virtual X K rare virtual S X rare virtual X S more real K X less virtual X . tends to large while c also tends to be large, the best, equal to 1, such that the non-existence of side effects, or, the non-existence of economic intervention resistance problem. The work mainly improves the loving relationship since the loving relationship is mainly used.

By the first transfer law in Theorem 3.2 for a virtual X, the more serious relation disease is the relation between virtual X and real XK since virtual X cannot kill the real XK which can destroy the killing order between X and XK if the disease continues to develop.

Abiding by the TCE’s idea of “Don’t have disease cure cure non-ill”, in order to avoid the more serious relation disease occurrence, the system should be intervened when the intervened system was non-disease, but the incidence of the system from the first transfer law in Theorem 3.2 will be to occur for the more serious relation disease between virtual X and real XK.

According to the intervening principle of “Strong inhibition of the same time, support the weak” from Theorem 3.4 in Zhang & Shao (2012), it is to get that the secondary treatment is to increase the energy of X, and at the same time, to decrease the energy of XK.

In general, since the economy is healthy and virtual, the capability of self-protection cannot be the worst state and should be normal, i.e., real X rare real K X rare real X S rare real S X more virtual X K less real X . where . The primary treatment is for the best state of the capability of self-protection, i.e.,

( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 )

where ρ 3 = c ρ ( x ) 0 and ρ 0 > ρ 1 = ρ ( x ) > 0 . The secondary treatment is for the normal state of the capability of self-protection, i.e.,

1 c 0

where ρ 3 = c ρ ( x ) 0 and ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) . Comprehensive use of the two methods for the healthy economy with a virtual disease can deal with a general situation, i.e.,

ρ 3 = c ρ ( x ) > 0

where ρ 1 ρ 3 = ρ ( x ) ( 1 c ) and ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) . #

3) If ρ ( x ) > 0 , then from Theorem 2.1 and Corollary 2.1, there is that ( ρ 1 + ρ 2 ρ 3 ) < ( 1 ρ 2 ρ 3 ) which means that the economy is healthy where in general

ρ 3 = c ρ ( x ) such that ρ 1 ρ 3 = ρ ( x ) ( 1 c ) 0 ; and ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) 0 such that ρ 3 = c ρ ( x ) > 0 , i.e.,

1 c 1 ρ ( x ) 2 ρ ( x ) 3 0 .

The fact means that ρ 0 ρ 1 = ρ ( x ) 1 .

Since the condition ( ρ 1 + ρ 2 ρ 3 ) ( 1 ρ 2 ρ 3 ) means that the GDP inflation rate x is higher than or equal to the center ρ 1 ρ 3 = ρ ( x ) ( 1 c ) 0 , thus the subsystem X will encounter a real disease if the subsystem X falls ill for a healthy economy.

From Theorem 3.2 and Corollary 3.2 in Zhang & Shao (2012), the subsystem X will be considered as real. First the case is studied that the capability of self-protection is in the best state, i.e., ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) 0 where ρ 1 ρ 3 = ρ ( x ) ( 1 c ) ρ ( x ) .

If the energy of the real-normal subsystem XS is intervened to decrease its energy, then its capabilities of intervention reaction and self-protection can make the subsystems XK, KX and SX restored at the same time, but the subsystems X and XS will decrease their energies, i.e., changed by the increments

ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) ρ ( x ) 2

respectively. Since the GDP inflation rate ρ 3 = c ρ ( x ) 0 makes a = 5 .8114% , b = 16 .359% , t 0 = 10 .208% such that mainly x < a , therefore the subsystem X can obtain the substantial reduction x [ a , t 0 ) and the sub-system XS will get a modest reduction x [ t 0 , b ] . The later is the pseudo side effects issue, by Attaining Rule, which is just the food of the second physiological system of the steady multilateral system since that the economy is healthy, real XS intervened makes that the second physiological system will attain the Chi or energy (Yin energy) from the intervened subsystem XS directly for a healthy economy with a real disease.

Thus it is to get the primary treatment should be to decrease the energy of the subsystem XS in order to avoid the side effects issue occurrence for a healthy economy. The idea means that “Real disease with a healthy economy is to rush down his son”.

Since the economy is healthy, the state of the capability of self-protection should be normal, i.e., x > b where x < a . In this case, the first physiological system will not stop to work, or, the first transfer law will not stop to run, while the second transfer law will not begin to run.

Is the first physiological system working in order to improve its corresponding intervention ability, at the same time, to provide the food for the second physiological system. In other words, it makes x > b tending to be large while x < a tending to be small. Equivalently, the way can make x > b tending to large and c also tending to be large, the best, equal to 1, such that the non-existence of side effects issue, or, the non-existence of economic intervention resistance problem. The work mainly improves the loving relationship since the loving relationship is mainly used.

By the first transfer law in Theorem 3.2, the more serious relation disease is the relation between virtual KX and real X since virtual KX cannot kill the real X which can destroy the killing order between KX and X if the disease continues to develop.

Abiding by the TCE’s idea of “Don’t have disease cure cure non-ill”, in order to avoid the more serious relation disease occurrence, the system should be intervened when the intervened system was non-disease, but the incidence of the system from the first transfer law in Theorem 3.2 will be to occur for the more serious relation disease between virtual KX and real X.

According to the intervening principle of “Strong inhibition of the same time, support the weak” from Theorem 3.4 in Zhang & Shao (2012), it is to get that the secondary treatment is to increase the energy of KX, and at the same time, to decrease the energy of X.

In general, since the economy is healthy with an expected real disease, the capability of self-protection should be normal, i.e., ρ 1 + ρ 2 ρ 3 = ρ ( x ) + c ρ ( x ) 3 where 1 ρ 2 ρ 3 = 1 c ρ ( x ) 3 . The primary treatment is for the best state of the capability of self-protection, i.e.,

0 < ρ 3 = c ρ ( x ) ρ ( x ) = ρ 1 , ρ 0 ρ 1 = ρ ( x ) 1 ,

where ρ 1 ρ 3 = ρ ( x ) ( 1 c ) and ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) . The secondary treatment is for the normal state of the capability of self-protection, i.e.,

ρ ( x )

where x [ a , t 0 ) and x [ t 0 , b ] . Comprehensive use of the two methods for the healthy economy with a real disease can deal with a general situation, i.e.,

x [ a , t 0 )

where x [ t 0 , b ] and ρ 1 + ρ 2 ρ 3 = ρ ( x ) + c ρ ( x ) 3 . #

4) If 1 ρ 2 ρ 3 = 1 c ρ ( x ) 3 , then from Corollary 2.1, there is that ρ ( x ) which means that the economy is unhealthy where 0 < c and ρ 1 ρ 3 = ρ ( x ) ( 1 c ) . Since the condition ρ 2 ρ 1 ρ 3 = ρ ( x ) 2 ( 1 c ) means that the GDP inflation rate x is too higher than the normal state, thus the subsystem X has encountered the real disease for an unhealthy economy.

From Theorem 3.2 and Corollary 3.2 in Zhang & Shao (2012), the subsystem X was considered as real. Assume that the capability of self-protection is in the best state, i.e., ρ ( x ) where 0 < c .

If the energy of the real subsystem X is intervened to decrease its energy directly, then its capabilities of intervention reaction and self-protection can make the subsystems XK, KX and XS restored at the same time, but the subsystems X and SX will decrease their energies, i.e., changed by the increments

X S j

respectively. Since the GDP inflation rate X S x makes ( X K ) S = K X such that K ( X K ) = X , therefore the subsystem X can obtain the substantial reduction S ( S X ) = K X and the subsystem SX will get a modest reduction ( S X ) K = X S . The later is the pseudo side effects, by Attaining Rule, which is just the food of the second physiological system of the steady multilateral system since that the economy is unhealthy, real X intervened makes that the second physiological system will attain the Chi or energy (Yin energy) from the mother SX of the intervened subsystem X. The attaining way is an indirect treating for an unhealthy economic subsystem X with a real disease.

Thus it is to get the primary treatment should be to decrease the energy of the subsystem X directly, in order to avoid the side effects issue occurrence for an unhealthy economy. This is just one of the affording working principle of the second physiological system by Affording Rule. The idea means that “Real disease with an unhealthy economy is to rush down itself”.

When the capability of self-protection is at the worst state, i.e., X S j where X S x , the first physiological system will stop to work, or, the first transfer law will stop to run, while the second physiological system will begin to work, or, the second transfer law will begin to run.

By Affording Rule and the second transfer law in Theorem 3.3, the purpose of the second physiological system working is to improve the physical ability of self-protection of the first physiological system, i.e., to make all of both ρ 3 = c ρ ( x ) and ρ ( x ) tending to be small, i.e., for fixed x < a = 5 .8114% , c tends to be large, at least, greater than zero, to drive the first physiological systems will begin to work. The work mainly improves the killing relationship since the killing relationship is mainly used.

By the second transfer law in Theorem 3.3, for a real X, the more serious relation disease is the relation between virtual XK and real SX since virtual XK cannot kill the real SX which can destroy the killing order between XK and SX if the disease continues to develop.

Abiding the TCE’s idea of “Don’t have disease cure cure non-ill”, in order to avoid the more serious relation disease occurrence, a system should be intervened when the intervened system was non-disease, but the incidence of the system from the second transfer law in Theorem 3.3 will be to occur for the more serious relation disease between virtual XK and real SX.

According to the intervening principle of “Strong inhibition of the same time, support the weak” from Theorem 3.4 in Zhang & Shao (2012), it is to get that the secondary treatment is to decrease the energy of SX, and at the same time, to increase the energy of XK.

In general, although the economy is unhealthy with a real disease, the capability of self-protection can be any state, i.e., a = 5 .8114% x < t 0 = 10 .208% where t 0 = 10 .208% x b = 16 .359% . The primary treatment is mainly for the normal state of the capability of self-protection, i.e.,

x > b = 16 .359%

where min = 0.11 , max = 0.81 , t 0 = 10.208 % and ρ ( x ) = 1 / 2 λ ( x ) + 1 / 2 ρ ( x ) 1 ρ ( x ) = 1 / 2 λ ( x ) λ ( x ) = 1 ρ ( x ) 2 ρ ( x ) . The secondary treatment is for the worst state of the capability of self-protection, i.e.,

x min

where x max and λ ( x ) + . Comprehensive use of the two methods for the unhealthy economy with a virtual disease can deal with a general situation, i.e.,

ρ ( x ) 0

where x = t 0 and λ ( x ) = 0 . This completes the proof. #

Cite this paper: Zhang, Y. (2020) GDP 6% to 16%
—Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II). Modern Economy, 11, 1552-1609. doi: 10.4236/me.2020.119111.
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