Synthesizing Switching Controllers for Hybrid Systems by Continuous Invariant Generation

We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating continuous invariants with a qualitative approach for predefining templates. Our synthesis method is relatively complete with regard to a given family of predefined templates. Using qualitative analysis, we discuss heuristics to reduce the numbers of parameters appearing in the templates. To avoid too much human interaction in choosing templates as well as the high computational complexity caused by QE, we further investigate applications of the SOS (sum-of-squares) relaxation approach and the template polyhedra approach in continuous invariant generation, which are both well supported by efficient numerical solvers

Abstraction of Elementary Hybrid Systems by Variable Transformation

Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in safety-critical domains. Due to the non-polynomial expressions which lead to undecidable arithmetic, verification of EHSs is very hard. Existing approaches based on partition of state space or over-approximation of reachable sets suffer from state explosion or inflation of numerical errors. In this paper, we propose a symbolic abstraction approach that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all non-polynomial terms with newly introduced variables. Thus the verification of EHSs is reduced to the one of PHSs, enabling us to apply all the well-established verification techniques and tools for PHSs to EHSs. In this way, it is possible to avoid the limitations of many existing methods. We illustrate the abstraction approach and its application in safety verification of EHSs by several real world examples

Global Existence and Asymptotic Behavior of Solutions to the Generalized Damped Boussinesq Equation

We investigate the Cauchy problem for the generalized damped Boussinesq equation. Under small condition on the initial value, we prove the global existence and optimal decay estimate of solutions for all space dimensions n≥1. Moreover, when n≥2, we show that the solution can be approximated by the linear solution as time tends to infinity

Logarithmically Improved Blow up Criterion for Smooths Solution to the 3D Micropolar Fluid Equations

Blow-up criteria of smooth solutions for the 3D micropolar fluid equations are investigated. Logarithmically improved blow-up criteria are established in the Morrey-Campanto space

The dual environmental and economic effects of the emission trading scheme under local fiscal pressure: “efficient markets” and “promising governments”

Compared with developed economies, China implements the Emission Trading Scheme (ETS) within a fundamentally distinct political-economic-institutional context. This study aims to investigate the internal mechanisms and external constraints of emission trading scheme in achieving the dual benefits of environmental preservation and economic advancement within the institutional context of fiscal decentralization. We demonstrate that the transmission from emission reduction to economic returns inherently facilitates the realization of dual benefits, and further propose a restrictive effect of local fiscal pressure on the effectiveness of the emission trading scheme. Using panel data of 284 prefectural-level cities from 2003 to 2017, we conduct a quasi-experiment based on China’s emission trading scheme pilot policy in 2007. The results indicate three primary conclusions: First, the implementation of emission trading scheme in China generally yields dual environmental-economic benefits, with emission reduction serving as a transmission channel for realizing economic gains. Second, high fiscal pressure on local governments not only directly undermines policy effects but also indirectly affects the transmission channel. Finally, the dual benefits have been realized in eastern China, but not yet in the central and western regions. This study contributes to the research on market-oriented environmental governance under fiscal decentralization. The theoretical logic of this study can be applied to a wide range of market-based mechanisms for green factors trading, providing valuable insights for countries facing similar challenges

The performance of commercial banks in China during 2012-2019: Analyzing the cost efficiency and profitability determinants.

The paper analyzes empirically what the cost efficiency level of Chinese commercial banks and how bank-variables and macroeconomic variables determine the bank profitability. The paper finds that Chinese banking sector holds a quite high level of cost efficiency for the period 2012-2019. The change of price of labour will affect bank cost remarkably, which implies the problem of heavy staff in Chinese banking system. Besides, the banking system is considered to be under economies of scale, since banks could gain more profit by rising inputs. it is found that big banks are more efficient than small banks overall. In terms of bank profitability, the paper finds that the impaired loans to gross loans ratio, equity to total assets ratio, cost to income ratio, cost efficiency, GDP growth rate and inflation rate are negatively correlated to bank profitability，and lagged return on assets, bank size, loans to deposits, z-score, diversification and concentration ratio have positive influence on bank performance. The study discovers increasing capital adequacy will reduce bank profitability. In addition, banks can generate more profit by expanding the scales. Additionally, the paper finds that Chinese banks could rise loans to deposit ratio to improve bank performance, although they may face high liquidity risk. The paper obtains an unexpected result of the relationship between cost efficiency and bank profitability, in which increasing cost efficiency cannot enhance Chinese commercial bank profitability. At the end of the paper, some limitations in regression results are put forward, at the same time, the paper gives two improved methods. Key words: Chinese commercial banks, cost efficiency, bank profitabilit