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Finance is the core of the economy. For the construction of modern and innovative city, the development and function of finance can not be ignored. The research on urban planning and design based on financial support has become a hot topic. Based on this, the Grey relation analysis was used to study the modern financial support driven innovative urban planning and design. First of all, the progress of the innovative urban construction was expounded, and the progress of the research on the financial support innovative urban construction was introduced; then the content and financial planning of the innovative urban construction planning were put forward; in addition, taking the innovative urban planning and design project in Chongqing as an example, different urban areas and traffic design were introduced. The results of Grey relation analysis show that Chongqing has high comprehensive innovation value.

Owing to the importance of the efficiency of commercial banks, the aim of this paper is to find the relationship between capital regulation, monetary policy and the asymmetric effects of the commercial banks' efficiency.

First, the paper makes a static profit model of commercial banks with double constraints and then makes a proposition with numeric simulation.

In this paper, the author finds it unreasonable to calculate the commercial banks' cost and profit efficiency by SFA (DEA) directly, as there is no evidence that indicates the linearity relationship among them. Hence, more complicated solutions should be introduced.

The rate of non‐performing loans (NPL) is inversely proportional to the commercial banks' cost and profit efficiency and capital adequacy ratio (CAR) and statutory reserve ratio (SRR) show a nonlinear relationship between commercial banks' cost and profit efficiency. Hence, the paper defines the different influences of commercial banks' efficiency imposed by CAR and SRR as the asymmetric effects of commercial banks' efficiency.

The nonlinear relationship is found based on improved Kopecky and VanHoose, so excessive regulation has harmful effects on the commercial banks. The reasonable capital regulation and other prudential supervision measures should be emphasized.

First, the paper gets its proposition through the improved KV model, which displays a new perception on analyzing this problem. Second, the nonlinear relationship is discovered by this new model and the empirical results show the nonlinear relationship further.

The purpose of this study is to form a linear structure of components of the modified Korteweg–De Vries (mKdV) hierarchy. The new model includes 3rd order standard mKdV equation, 5th order and 7th order mKdV equations.

The authors investigate Painlevé integrability of the constructed linear structure.

The Painlevé analysis demonstrates that established sum of integrable models retains the integrability of each component.

The research also presents a set of rational schemes of trigonometric and hyperbolic functions to derive breather solutions.

The authors also furnish a variety of solitonic solutions and complex solutions as well.

The work formally furnishes algorithms for extending integrable equations that consist of components of a hierarchy.

The paper presents an original work for developing Painlevé integrable model via using components of a hierarchy.