Mathematical analysis of impulsive fractional differential inclusion of pantograph type

In this article, we formulate fractional differential inclusion of pantograph type (IFDIP), incorporating impulsive behavior of the solution. The boundary conditions taken into account are nonlocal in nature. We will consider the convex problem and prove the Filippov–Wazewski-type theorem. Moreover, existence of solution, uniqueness of a solution, and the topological properties of the solution's set will be examined for the problem under consideration. In the second part, the study will be confined to the second-order impulsive fractional differential equation of pantograph type. For certain geometric characteristics of the solution's set, Aronszajn–Browder–Gupta-type results will be explored for the newly introduced differential equation. Also, it will prove the existence of solution for the first-order fractional differential equation of pantograph type having impulsive behavior of the solution.     

An example of a nonarcwise connected rim-countable locally connected continuum

An example of a rim-countable, locally connected, but nonarcwise connected continuum is constructed, which is important for the classification of locally connected continua. The point of interest in this result is that there are no metrizable locally connected continua with the above properties. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 659–666, May, 1999.     

Linear and Nonlinear Effects in Connectedness Structure: Comparison between European Stock Markets

The purpose of this research is to compare the risk transfer structure in Central and Eastern European and Western European stock markets during the 2007–2009 financial crisis and the COVID-19 pandemic. Similar to the global financial crisis (GFC), the spread of coronavirus (COVID-19) created a significant level of risk, causing investors to suffer losses in a very short period of time. We use a variety of methods, including nonstandard like mutual information and transfer entropy. The results that we obtained indicate that there are significant nonlinear correlations in the capital markets that can be practically applied for investment portfolio optimization. From an investor perspective, our findings suggest that in the wake of global crisis and pandemic outbreak, the benefits of diversification will be limited by the transfer of funds between developed and developing country markets. Our study provides an insight into the risk transfer theory in developed and emerging markets as well as a cutting-edge methodology designed for analyzing the connectedness of markets. We contribute to the studies which have examined the different stock markets’ response to different turbulences. The study confirms that specific market effects can still play a significant role because of the interconnection of different sectors of the global economy.     

无限维空间拟凸映射多目标最优化问题解集的连通性

本文在一个无限格中引入了拟凸、强拟凸和严格拟凸映射。并在约束集为紧凸条件下，证明了相应的多目标规划问题之有效解集和弱有效解集连通性结果。     

两个函数的拓扑极大极小定理

A topological minimax theorem involving two functions is derived. It generalizes Greco and Horvath＇minimax theorem given by them in 2002.     

关于子基的强连通性

在LF拓扑空间中借助于相对闭包引入了关于子基的强连通性的概念,研究了它的一些基本性质和等价刻画.结果表明,这种强连通性保持了LF拓扑空间中已有连通性的许多类似性质     

基于信息溢出网络的我国行业关联性研究

行业信息溢出网络是各行业之间风险关联的载体,其信息溢出的方向和强度与行业的风险传染特征密切相关。运用广义方差分解对申银万国行业一级指数同时构建行业收益率溢出网络和行业波动率溢出网络,分别从静态和动态角度分析我国行业信息溢出的总体情况和动态演化。研究发现:我国各行业间信息溢出水平较高,整体信息联动能力强,但各行业信息溢出随时间变化具有波动性和不确定性。长期情形下,收益率溢出网络和波动溢出网络对系统性重要行业的识别排序具有高度一致性,但短期内两者存在较大差异。长期内,银行业和非银行金融业是系统性重要(信息)接受行业,机械设备业是系统性重要(信息)传播行业;短期内,银行、非银行金融、国防军工、食品饮料及家用电器业是系统性重要行业,但它们的具体角色(信息接受或者传播)具有不确定性。研究结论对于政府产业政策制定及产业监管具有重要的现实意义。     

连通度量空间的映象

拓扑空间X称为s连通,若X不能表示为两个非空的不相交的序列开集之并.本文纠正了A.Fedeli 和A.Le Donne关于连通度量空间映象的错误论证,证明了s连通性可刻画为连通度量空间的连续的序列覆盖映象,从而导出连通的序列空间(或FrEchet空间)可刻画为连通度量空间的商映象(或伪开映象),回答了V.V.Tkachuk在Proc.Amer.Math Soc.上提出的问题.     

Topological ordered C- (resp. I-)spaces and generalized metric spaces

The following result due to Hanai, Morita, and Stone is well known: Let f be a closed continuous map of a metric space X onto a topological space Y. Then the following statements are equivalent: (i) Y satisfies the first countability axiom; (ii) for each y∈Y, f−1{y} has a compact boundary in X; (iii) Y is metrizable.In this article we obtain several related results in the setting of topological ordered spaces. In particular we investigate the upper and lower topologies of metrizable topological ordered spaces which are both C- and I-spaces in the sense of Priestley.     

Intersection Theorems with a Continuum of Intersection Points

In all existing intersection theorems, conditions are given under which a certain subset of a collection of sets has a nonempty intersection. In this paper, conditions are formulated under which the intersection is a continuum of points satisfying some interesting topological properties. In this sense, the intersection theorems considered in this paper belong to a new class. The intersection theorems are formulated on the unit cube and it is shown that both the vector of zeroes and the vector of ones lie in the same component of the intersection. An interesting application concerns the model of an economy with price rigidities. Using the intersection theorems of this paper, it is easily shown that there exists a continuum of zero points in such a model. The intersection theorems treated give a generalization of the well-known lemmas of Knaster, Kuratowski, and Mazurkiewicz (Ref. 1), Scarf (Ref. 2), Shapley (Ref. 3), and Ichiishi (Ref. 4). Moreover, the results can be used to sharpen the usual formulation of the Scarf lemma on the cube.