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Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation

Data publikacji: 15 Dec 2021
Tom & Zeszyt: AHEAD OF PRINT
Zakres stron: -
Otrzymano: 16 Jun 2021
Przyjęty: 24 Sep 2021
Informacje o czasopiśmie
License
Format
Czasopismo
eISSN
2444-8656
Pierwsze wydanie
01 Jan 2016
Częstotliwość wydawania
2 razy w roku
Języki
Angielski
Abstract

This paper, based on the numerical simulation research, has come out with findings, such as the sluggish interregional industrial transformation in China and the factors responsible for that, the need to define the new economic geography from the angle of geographic view, the need to have a theoretical model based on implementing development centre periphery, the use of element resources endowment system reference analysis, and the need for implementation of the numerical simulation of the model, and finally the need to clear the factors that influence the sluggish industrial transfer. The final results show that the factor resource endowment, transportation cost, and labour price are still impediments affecting industrial transfer. Since the development level of the manufacturing industry in eastern China has not reached the critical point of industrial transfer, it is necessary to to find out a pragmatic solution to achieve development.

Keywords

MSC 2010

Theoretical model of industrial transfer stagnation

According to the analysis of the current stagnating situation of the inter-regional industrial transfer in China, there are many reasons for this phenomenon, such as the increasing liquidity of factors, the changes in the market system and the advantages of market share and labour efficiency. This paper mainly starts with the relationship between industrial agglomeration and transfer, builds a model from the two aspects of labour distribution and manufacturer location, and studies the obstacles caused by industrial agglomeration efficiency on transfer [1].

Distribution model of the skilled labour force

It is assumed to be an economy composed of two regions r = A and B. In this case, if the overall economic level of region A exceeds that of region B, then in the model, the number of skilled workers in the initial distribution of region A is greater than that of region B, and region A has more externalities of production than region B. It should be noted that the products within the region are fully competitive and have no transportation costs, so the prices of the two are consistent, which can be regarded as 1.

Definition 1

Similarly, the regional factor market has a competitive relationship, so the regional wages of all factors will be affected by marginal productivity, and the externality E (Ha) is clear, and the formula can be obtained as follows: waH=E(Ha)f'(Ha);wbH=f'(Hb) w_a^H = E\left( {{H_a}} \right){f'}\left( {{H_a}} \right);w_b^H = {f'}\left( {{H_b}} \right)

Theorem 1

Where, HA and HB represent the number of skilled labour within a region, while LA and LB represent the number of unskilled labour within a region.

Workers have the same preferences. The utility formula for skilled workers living in the region (R = A, B) is as follows: u(wrH)=log(wrH)r=A,B u\left( {w_r^H} \right) = \log \left( {w_r^H} \right)r = A,B

Proposition 2

Since the above formula does not take into account the externalities of consumption, it is proved that the implicit assumption that the migration of skilled workers in and out of the country does not have much impact on the welfare of local residents is limited by wage differences: Ha*=u(waH)u(wbH) H_a^* = u\left( {w_a^H} \right) - u\left( {w_b^H} \right)

In Ha*>0 H_a^* > 0 Under the condition of, it is proved that the skilled labour force has the motivation to move to A area, otherwise, it will move to B area.

Lemma 3

Due to the Ha + Hb = H, and Hb*=Ha* \mathop {{H_b}}\limits^* = - \mathop {{H_a}}\limits^* . Then you can limit the process of moving to the H*a {\mathop H\limits^* _a} . In the study of, the following equation can be obtained by combining the above formula: H*a=u[E(Ha)f'(Ha)]u[f'(HHa)]ϕ(Ha) {\mathop H\limits^* _a} = u\left[ {E\left( {{H_a}} \right){f'}\left( {{H_a}} \right)} \right] - u\left[ {{f'}\left( {H - {H_a}} \right)} \right] \equiv \phi \left( {{H_a}} \right)

Due to the f′ (0) = ∞ and U belongs to the monotonically increasing development trend, so in Under the condition of, Ha*>0 \mathop H\limits_a^* > 0 ; In the HaH Under the condition, Ha*<0 \mathop H\limits_a^* < 0 . proving ϕ (Ha) in Ha Is sustainable in its position. In other words, in Ha*=0 \mathop H\limits_a^* = 0 and 0 < Ha < H Under the background, there is at least an equilibrium distribution state of the skilled labour force, which proves that equilibrium is internal. The immobility of unskilled labour and the gradual change of production function f makes it impossible for all skilled labour to be concentrated in the same range. Then according to the above analysis of the content of the hypothesis, it can be obtained Ha > Hb, And because Ha + Hb = H, H is also clear, so in the subsequent studies, the control is assumed to be H/2 ≤ HaH Within this range, to study the equilibrium during operation, we can assume that the production externality function of region A is: E (Ha) = exp(ɛHa).

Corollary 4

Among them, g > 0 Represents a constant, then the production function f (Hr) needs to be analysed using c–d function: f(Hr)=Hrar=A,B f\left( {{H_r}} \right) = H_r^ar = A,B

Among them, 0 < a < 1.

Combined with the above formula analysis, the final migration equation can be obtained as follows: ϕ(Ha)H*a+(α1)logHa(α1)logHbεHa+(α1)logHa(α1)log(HHa) \matrix{ {\phi \left( {{H_a}} \right) \equiv {{\mathop H\limits^* }_a} + \left( {\alpha - 1} \right)\log {H_a} - \left( {\alpha - 1} \right)\log {H_b}} \hfill \cr { \equiv \varepsilon {H_a} + \left( {\alpha - 1} \right)\log {H_a} - \left( {\alpha - 1} \right)\log \left( {H - {H_a}} \right)} \hfill \cr }

Conjecture 5. Differential treatment of the above formula can be obtained as follows: ϕ'(Ha)=ε+(α1)[1/Ha+1/(HHa)] {\phi '}\left( {{H_a}} \right) = \varepsilon + \left( {\alpha - 1} \right)\left[ {1/{H_a} + 1/\left( {H - {H_a}} \right)} \right]

Once again, we can get: ϕn(Ha)=(1α)/Ha2(1α)/(HHa)2ϕm(Ha)=2(1α)/Ha32(1α)/(HHa)3 \matrix{ {{\phi ^n}\left( {{H_a}} \right) = \left( {1 - \alpha } \right)/H_a^2 - \left( {1 - \alpha } \right)/{{\left( {H - {H_a}} \right)}^2}} \hfill \cr {{\phi ^m}\left( {{H_a}} \right) = - 2\left( {1 - \alpha } \right)/H_a^{ - 3} - 2\left( {1 - \alpha } \right)/{{\left( {H - {H_a}} \right)}^{ - 3}}} \hfill \cr }

Combined with the above two formulas obtained by differential analysis, in H/2 ≤ HaH, ϕm (Ha) it’s strictly negative under theta. In other words, theta ϕm (Ha) in (H/2,H) The conditions are strictly decreasing. At the same time because ϕm (H/2) = 0,ϕn (H) = ∞, so ϕ′ (H/2) Belong to ϕ′ (Ha) In the interval [H/2,H] The maximum value of the range.

Manufacturer location choice model

In this paper, when studying and analysing the location choice of firms, they have price competition with each other and can obtain more benefits from location choice. The specific income distribution is shown in Table 1 below:

The payoff matrix analysis results of vendor layout

A B
A πaa πss
B πss πbb

In other words, the equilibrium payoff of both vendors can reach π A when they both exist in region A, but the equilibrium payoff of both vendors can reach π B when they both exist in region B, and the payoff of all vendors is PS when they both exist in region B.

Example 6

Within the region, the demand function of two different products produced by two manufacturers will be clarified from the perspective of consumers. The specific quadratic utility function is shown as follows: U(q1,q2)=α(q1+q2)(β/2)(q12+q22)δq1q2+z U\left( {{q_1},{q_2}} \right) = \alpha \left( {{q_1} + {q_2}} \right) - \left( {\beta /2} \right)\left( {q_{_1}^2 + q_{_2}^2} \right) - \delta {q_1}{q_2} + z

Where, qi (I = 1,2) represents the number of products of I types consumed, and z represents the number of units consumed, and is consistent α > 0 and 0 ≤ δ < β Conditions.

The budget constraint conditions for consumers are as follows: y=p1q1+p2q2+z y = {p_1}{q_1} + {p_2}{q_2} + z

And Max (u–y) can be obtained by combining the above formula, and can be obtained: Pi=αβqiδqj {P_i} = \alpha - \beta {q_i} - \delta {q_j}

Where, Qi and Qj represent the quantity of two products respectively, in the case that the quantity in the price field is positive, δβ, Different product demand functions are shown as follows: q1 = abpi + d (pjpi) At this point, you get: a=α/(β+δ),b=1/(β+δ),d=δ/[(β+δ)(βδ)]. a = \alpha /\left( {\beta + \delta } \right),b = 1/\left( {\beta + \delta } \right),d = \delta /\left[ {\left( {\beta + \delta } \right)\left( {\beta - \delta } \right)} \right].

Feasibility analysis of industrial transfer under the guidance of the government
Complete information dynamic game of enterprise cooperation

It is assumed that Enterprise 1 and Enterprise 2, which produce the same products, can play a game, and they are located in the east and the west respectively. In the practical development, it is assumed that both enterprises are rational and have two alternative countermeasures of cooperation and non-cooperation. If there is a potential market for development in the west and its value is R, the potential market can only be occupied by the cooperation between Enterprise 1 and Enterprise 2, which are respectively R1 and R2 before the game, and the cooperation costs are C1 and C2. Assuming that the two enterprises cooperate in the practical development, the income efficiency of Enterprise 1 will increase by Kr-C1, while that of Enterprise 2 will increase by (1-K + S) r-C2, where K represents the distribution ratio of income R and S represents the subsidies provided by the government in the western region. If firm 1 chooses to cooperate and firm 2 does not, then firm 1 will enter the market occupied by firm 2. At this time, the return rate of firm 1 will increase k2 R2, while the return rate of firm 2 will increase −k2 R2. K2 represents the lost market share of firm 2. Under this condition, if firm 1 is unwilling to cooperate, but firm 2 is willing to cooperate, then firm 1′s income will increase −k1R1, and firm 2′s income will increase (k1 + s) R1, where k1 represents the lost market share of firm 1. But if neither co-operates, the benefits of the partnership will not change [2].

In the development of practice, it is assumed that the premise of cooperation is Kr-c > and (1-K + S) r-c >, and the game results between firm 1 and firm 2 are shown in Table 2.

Game results between firm 1 acting first and firm 2 acting later

Enterprise 2
{Cooperation, cooperation} {Cooperation, don’t cooperate} {Don’t cooperate, cooperation} {Don’t cooperate, don’t cooperate}
Cooperation 1 Cooperation 1 kRC1 kRC1 k2 R2 k2 R2
2 (1−k+s) RC2 (1−k+s) RC2 k2 R2 k2 R2
Don’t cooperate 1 k1 R1 0 k1 R1 0
2 (k1+s)R1 0 (k1+s)R1 0

Note 7. Based on the above table analysis, it can be seen that assuming that the revenue matrix of Eastern Enterprise 1 is E, then the revenue matrix of Western Enterprise 2 is W. The specific formula is as follows: E=[kRC1k2R2k1R10],W=[(1+sk)RC2k2R2(k1+s)R10] E = \left[ {\matrix{ {kR - {C_1}{k_2}{R_2}} \hfill \cr { - {k_1}{R_1}0} \hfill \cr } } \right],W = \left[ {\matrix{ {\left( {1 + s - k} \right)R - {C_2} - {k_2}{R_2}} \hfill \cr {\left( {{k_1} + s} \right){R_1}0} \hfill \cr } } \right]

Assuming that the game ratio of Enterprise 1 choosing a cooperative strategy is x, then the game ratio of non-cooperative strategy is 1-x. Therefore, benefits and group average expected returns can be obtained by using these two methods respectively as follows: u1=(kRC1)x+k2R2(1x),u2=k1R1x,u¯=u1x+u2(1x) {u_1} = \left( {kR - {C_1}} \right)x + {k_2}{R_2}\left( {1 - x} \right),{u_2} = - {k_1}{R_1}x,\overline u = {u_1}x + {u_2}\left( {1 - x} \right)

Combined with the analysis of biological evolution and replication dynamic thought, the differential equation can also be obtained as follows: dxdt=x(u1u¯)=x(1x)[k2R2(kRC1+k1R1k2R2)x] {{dx} \over {dt}} = x\left( {{u_1} - \overline u } \right) = x\left( {1 - x} \right)\left[ {{k_2}{R_2} - \left( {kR - {C_1} + {k_1}{R_1} - {k_2}{R_2}} \right)x} \right]

And because 0 ≤ x ≤ 1, So in the kR − C1 > k2R2 − k1R1 Under the condition of, the above differential equation has the following three stagnation points: x1=0,x2=1,x3=k2R2/kRC1+k1R1k2R2 {x_1} = 0,{x_2} = 1,{x_3} = {k_2}{R_2}/kR - {C_1} + {k_1}{R_1} - {k_2}{R_2}

Based on the analysis of the above results, the following conclusions can be drawn: in kRC1 + k1R1 > 2k2R2 Under the condition of, x3 = k2R2/kRC1 + k1R1k2R2 It is the only policy of the system that remains undetermined.

Replication dynamics of western enterprises
Open Problem 8

Assuming that the two groups of western enterprises choose the cooperation plan, and the ratio of players is y, then the ratio of players who do not choose the cooperation strategy is 1-y, and the differential equation can be obtained as follows: dydt=y(1y){k2R2+x[(1+sk)RC2+k2R2(k1+s)R1]} {{dy} \over {dt}} = y\left( {1 - y} \right)\left\{ { - {k_2}{R_2} + x\left[ {\left( {1 + s - k} \right)R - {C_2} + {k_2}{R_2} - \left( {{k_1} + s} \right){R_1}} \right]} \right\} because 0 ≤ y ≤ 1, So in the (1 + sk)RC2 > (k1 + s)R1 Under the condition, the above equation has three stagnation points: y1=0,y1=1,y3=k2R2/[(1+sk)RC2+k2R2(k1+s)R1] {y_1} = 0,{y_{_1}} = 1,{y_3} = {k_2}{R_2}/\left[ {\left( {1 + s - k} \right)R - {C_2} + {k_2}{R_2} - \left( {{k_1} + s} \right){R_1}} \right]

The following conclusions can also be drawn from this: in (1 + sk)RC2 > (k1 + s)R1 Under the condition of, y3 = k2R2/[(1 + sk)RC2 + k2R2 − (k1 + s)R1] is the only evolutionarily stable strategy of the system.

Evolutionary stability of enterprise cooperation between the two regions

By integrating the operation stability and related strategies of the above systems, it can be seen that if the cooperative strategy ratio of Enterprise 1 is X, then the non-cooperative strategy ratio is 1-X, while the cooperative strategy ratio of western Enterprise 2 is Y, then the non-cooperative strategy ratio is 1-Y. Eastern Enterprise 1 selects two strategies for the expected revenue of the players and the average expected revenue of the group, respectively [3]: u1=(kRC1)y+k2R2(1y),u2=k1R1y,u¯=u1x+u2(1x) {u_1} = \left( {kR - {C_1}} \right)y + {k_2}{R_2}\left( {1 - y} \right),{u_2} = - {k_1}{R_1}y,\overline u = {u_1}x + {u_2}\left( {1 - x} \right)

The corresponding western Enterprise 2 is as follows: v1=[(1+sk)RC2]xk2R2(1x),v2=(k1+s)R1x,v¯=yv1+(1y)v2 {v_1} = \left[ {\left( {1 + s - k} \right)R - {C_2}} \right]x - {k_2}{R_2}\left( {1 - x} \right),{v_2} = \left( {{k_1} + s} \right){R_1}x,\overline v = y{v_1} + \left( {1 - y} \right){v_2}

Combining the above formulas, the following equations can be obtained: {dxdt=x(1x)[k2R2y(kRC1+k1R1k2R2)]dydt=y(1y){k2R2+x[(1+sk)RC2+k2R2(k1+s)R1]} \left\{ {\matrix{ {{{dx} \over {dt}} = x\left( {1 - x} \right)\left[ {{k_2}{R_2} - y\left( {kR - {C_1} + {k_1}{R_1} - {k_2}{R_2}} \right)} \right]} \hfill \cr {{{dy} \over {dt}} = y\left( {1 - y} \right)\left\{ { - {k_2}{R_2} + x\left[ {\left( {1 + s - k} \right)R - {C_2} + {k_2}{R_2} - \left( {{k_1} + s} \right){R_1}} \right]} \right\}} \hfill \cr } } \right.

This conclusion can be drawn from it. Based on the above equations meeting the following two conditions, it is proved that both eastern and western enterprises finally choose the cooperation strategy. The specific conditions are: on the one hand, kRC1 > k2R2k1R1; On the other hand, (1 + Sk)RC2 > (k1 + s)R1.

Data simulation and result analysis

It can be seen from the analysis of the above overview that, because the equations are nonlinear, it is difficult to achieve the final goal by using only a single analytical method. In this case, computer simulation software is needed for analysis, and data simulation and digital examples are combined. In the research exploration, this paper uses MA TLAB7.0 to carry out data simulation for the model, and thus obtains the relationship between the real wage difference, factor resource endowment, transportation cost and other factors in the two regions. At the same time, considering the common assumptions of NEC, the parameter μ is regarded as 0.4 and σ is regarded as 5. According to the analysis of Figure 1, the vertical axis represents the actual wage difference between the two companies, while the horizontal axis represents the cost expenditure during transportation. Comparison of results obtained in Figures 1 and 2 [4, 5].

Fig. 1

θ1 = θ2 The influence of different transportation costs on the composition of industrial transfer

Fig. 2

θ1θ2=2 {{{\theta _1}} \over {{\theta _2}}} = 2 The influence of different transportation costs on the composition of industrial transfer

To more intuitively grasp the impact of resource endowments of different factors on the composition of industrial distribution, we can make assumptions at this time and make reference therefrom. It is assumed that the factor resource endowments of the enterprises in the two regions are similar, and the actual wage levels of the two regions are the same, thus proving that the manufacturing industries of the two regions are balanced and meet the expected requirements. According to the analysis of Figure 2, it can be found that the capital advantage of the eastern region is significantly higher than that of the enterprises in the western region. In other words, the research results as shown in Figure 2 can be obtained under the condition of the first analysis at this time. The comparative analysis between the two shows that, under the condition of difference in factor resource endowment, if the manufacturing industry appears in the area with λ too large, that is, Enterprise 1, then the value will be absolutely large. According to the image analysis, this difference can be more than two times. At the same time, by analysing the vertical coordinate, it can be found that if the wage ratio of the two places keeps declining, the share of the manufacturing industry in Enterprise 1 will be lower and lower, in other words, the economy will shift to the region with low cost and rent. In addition, combined with the picture analysis, it is assumed that the actual wage level of the two places is at the same level. If the transportation cost T is too low, the share of the manufacturing industry in the eastern region will continue to decline. In other words, the manufacturing industry will move to the western region where the cost and salary are low. However, under the condition of high transportation cost T, the share of the manufacturing industry in the eastern region is very high, so the transfer process to the western region will be limited [6, 7].

In the case of large differences in resource endowments between the two places, for example, the following results can be obtained by combining the analysis in Figure 3 below: First, based on the deviation of resource endowment between the east and the west, a large number of industries will be concentrated in the eastern region. According to the analysis of different proportions, under the same wage level, the industries will move to the west, but they cannot get more advantages in labour cost. Second, based on the advantages of resources, the manufacturing industry in the eastern region will be more and more concentrated, and the corresponding quantity transferred to the western region will continue to decline., therefore, in the face of this development trend, the local governments should be based on the integration of previous development experience, according to the location of the enterprise development trend, a large number of valuable countermeasures to promote the development of the differences in different areas to control things, at the same time, the western region should also be based on its own development advantage, strengthen its infrastructure level, optimise the industrial undertaking ability, To lay the foundation for industrial transfer and development.

Fig. 3

θ1θ2=5 {{{\theta _1}} \over {{\theta _2}}} = 5 The influence of different transportation costs on the composition of industrial transfer

Fig. 4

θ1θ2=1 {{{\theta _1}} \over {{\theta _2}}} = 1 The influence of high, medium and low transportation cost on industrial transfer under the condition

When transportation cost impact on the industrial transfer form, to facilitate the observation analysis, need to clear this condition, and then will transport costs T as 1.2, 2.5, 2.8 and 8, according to the result of image analysis shows that under the condition of high transport costs, if manufacturing in the western region, then the eastern part of the labour costs will be lower than that of the western region, At this time the industry continues to move to the west, it is difficult to show their own advantages. However, under the condition of low-cost expenditure, if the proportion of wage level meets the requirements of local factor resource endowment, then the transfer of the manufacturing industry will be affected by the distance between labour cost and spatial separation. From a practical point of view, under the condition of continuous reduction of transportation costs in China, the opening level of inter-regional industries is getting higher and higher, which is in line with the integration process proposed by Krugman and Venables. In other words, as long as transportation costs continue to decline, there is still the left side of the “inverted U curve”. Therefore, the reduced transportation cost can enhance the construction model of this paper.

Conclusion

In conclusion, according to the analysis of the model constructed in this study and the analysis of the lag of China’s inter-regional industrial transformation and various influencing factors in the numerical simulation, it can be found that, firstly, the manufacturing industry in the eastern region of China does not reach the critical value of the industrial transfer, and the control of the actual transportation cost does not meet the requirements at all. Secondly, based on optimising the regional factor resource endowment, it is necessary to strengthen the industry carrying level and supporting capacity of local enterprises, which is also an important task of industrial transformation and development nowadays. Finally, the local district government should initiate to provide more powerful resources, such as transportation, finance and access to information, communication and cooperation, actively promote the regional industry and provide more supporting facilities for the transfer of industry and the environment, such that it not only supports the industrial chain of the market but also promotes industrial transfer at the same time, which will improve local economic development. Therefore, in the future construction and development, it is necessary to start from China’s inter-regional industrial transformation, combined with the accumulated experience and values of previous development to conduct a comprehensive exploration.

Fig. 1

θ1 = θ2 The influence of different transportation costs on the composition of industrial transfer
θ1 = θ2 The influence of different transportation costs on the composition of industrial transfer

Fig. 2

θ1θ2=2
{{{\theta _1}} \over {{\theta _2}}} = 2


 The influence of different transportation costs on the composition of industrial transfer
θ1θ2=2 {{{\theta _1}} \over {{\theta _2}}} = 2 The influence of different transportation costs on the composition of industrial transfer

Fig. 3

θ1θ2=5
{{{\theta _1}} \over {{\theta _2}}} = 5


 The influence of different transportation costs on the composition of industrial transfer
θ1θ2=5 {{{\theta _1}} \over {{\theta _2}}} = 5 The influence of different transportation costs on the composition of industrial transfer

Fig. 4

θ1θ2=1
{{{\theta _1}} \over {{\theta _2}}} = 1


 The influence of high, medium and low transportation cost on industrial transfer under the condition
θ1θ2=1 {{{\theta _1}} \over {{\theta _2}}} = 1 The influence of high, medium and low transportation cost on industrial transfer under the condition

Game results between firm 1 acting first and firm 2 acting later

Enterprise 2
{Cooperation, cooperation} {Cooperation, don’t cooperate} {Don’t cooperate, cooperation} {Don’t cooperate, don’t cooperate}
Cooperation 1 Cooperation 1 kRC1 kRC1 k2 R2 k2 R2
2 (1−k+s) RC2 (1−k+s) RC2 k2 R2 k2 R2
Don’t cooperate 1 k1 R1 0 k1 R1 0
2 (k1+s)R1 0 (k1+s)R1 0

The payoff matrix analysis results of vendor layout

A B
A πaa πss
B πss πbb

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