偏序集的零调性与可缩性

本文将给出偏序集零调与可缩的几个充分条件，它们包含和深化了文［１］和［２］中的一些结果，把［２］中的一些结果推广到无限偏序集的情形．     

Openness properties for parametric set-valued mappings and implicit multifunctions

The aim of this paper is to obtain some openness results in terms of normal coderivative for parametric set-valued mappings acting between infinite dimensional spaces. Then, implicit multifunction results are obtained by simply specializing the openness results. Moreover, we study a kind of metric regularity of the implicit multifunction. The results of the paper generalize several recent results in literature.     

New type of fixed point result of F-contraction with applications

The purpose of this paper is to prove theorem which generalize the corresponding results of Rhoades [B. E. Rhoades, Two New Fixed Point Theorems, Gen. Math. Notes, 2015, 27(2), 123--132]. This paper is to introduce the notion of dynamic process for generalized $F-$contraction mappings and to obtain coincidence and common fixed point results for such process. It is worth mentioning that our results do not rely on the commonly used range inclusion condition. We provide some examples to support our results. As an application of our results, we obtain the existence and uniqueness of solutions of dynamic programming and integral equations. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.     

Positive curvature,symmetry, and topology

We depict recent developments in the field of positive sectional curvature, mainly, but not exclusively, under the assumption of isometric torus actions. After an elaborate introduction to the field, we shall discuss various classification results, before we provide results on the computation of Euler characteristics. This will be the starting point for an examination of more involved invariants and further techniques. In particular, we shall discuss the Hopf conjectures, related decomposition results like the Wilhelm conjecture, results in differential topology and index theory as well as in rational homotopy theory, geometrically formal metrics in positive curvature and much more. The results we present will be discussed for arbitrary dimensions, but also specified to small dimensions. This survey article features mainly depictions of our own work interest in this area and cites results obtained in different collaborations; full statements and proofs can be found in the respective original research articles.     

Comparisons in the mean residual life order of coherent systems with identically distributed components

The comparisons of the performance of coherent systems (under different stochastic criteria) is an important task in the reliability theory. Several results have been obtained in the literature for the stochastic, hazard rate and likelihood ratio orders. In this paper, we obtain comparison results for the mean residual life order of coherent systems with identically distributed (ID) component lifetimes. These results can be applied not only to the usual case of systems with independent and identically distributed components but also to the case of systems with exchangeable components and to the more general case of just ID components. The results obtained are based on the representation of the system distribution as a distorted distribution of the common components' distribution. Some specific comparison results are given to illustrate the theoretical results. The comparison results for distorted distributions given here can also be applied to other statistical concepts such as order statistics, generalized order statistics or record values. Copyright © 2015 John Wiley & Sons, Ltd.     

On the Controllability of Linear and Semilinear Impulsive Systems

In this paper, we establish some su?cient conditions for the complete controllability of linear and semilinear impulsive systems. For the semilinear systems, we assume that nonlinearities are Lipschitzian type. We invoke the tools of nonlinear functional analysis and fixed point theorems to establish the results. The results are also compared with the existing results in the literature in order to show the effectiveness of the results obtained. Few illustrative examples are provided to substantiate the results.     

Quintic and septic Eisenstein series

Using results that were well-known to Ramanujan, we give proofs of some results for Eisenstein series in the lost notebook. Our proofs have the additional advantage that it is not necessary to know the results in advance; that is, the proofs are derivations as opposed to verifications.      

Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras

We extend conjugacy results from Lie algebras to their Leibniz algebra generalizations. The proofs in the Lie case depend on anti-commutativity. Thus it is necessary to find other paths in the Leibniz case. Some of these results involve Cartan subalgebras. Our results can be used to extend other results on Cartan subalgebras. We show an example here and others will be shown in future work.     

Coupled common fixed point theorems for w-compatible mappings in ordered cone metric spaces

We establish coupled coincidence point results for mixed g-monotone mappings under general contractive conditions in partially ordered cone metric spaces over solid cones. We also present results on existence and uniqueness of coupled common fixed points. Our results generalize, extend and unify several well known comparable results in the literature. To illustrate our results and to distinguish them from the earlier ones, we equip the paper with examples.     

Some results on multi-valued weakly jungck mappings in <Emphasis Type="Italic">b</Emphasis>-metric space

In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Picard iteration in a complete metric space is extended to the case of multi-valued weak contraction for the Jungck iteration in a complete b-metric space. While our main results generalize the recent results of Berinde and Berinde [8], they also extend, improve and unify several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Our results also improve the recent results of Daffer and Kaneko [16].      

锥度量空间中c-距离下的不动点定理

在锥度量空间中,用压缩性函数代替具体实数,获得了c-距离下的映射的新的不动点定理.所得结果在条件上不要求映射的非减性,且第一个定理去掉了锥的正规性,第二个定理去掉了映射的连续性,改进了原有的许多重要结论,并给出了相应的例子.     

On the negative value of information in informationally inefficient markets: Calculations for large number of traders

In informationally inefficient markets, classical decision theory assumes the value of information to be positive. Recent developments, however, contradict this paradigm. Schredelseker [Schredelseker, K., 2001. Is the usefulness approach useful? Some reflections on the utility of public information. In: McLeay, S., Riccaboni, A. (Eds.), Contemporary Issues in Accounting Regulation, Kluwer Academic Publishers, Boston, pp. 135–153] proposed a simulation model wherein a single security is traded among non-cooperating and asymetrically informed traders. One of the main results was the fact that badly informed traders could expect higher returns than traders with more information. But Schredelseker was able to give exact results for a small number of traders only. The aim of this paper is to give reliable results for a sufficiently large number of traders for both the expected gain and the probability of gain larger than zero. We are using combinatorial methods in order to get exact results for badly informed traders and simulation techniques for results of traders with higher level of information. The exact results are used (error between exact results and simulation results for the first traders) to determine the number of samples which have to be drawn with the simulation algorithm.     

类拟b-距离空间中几类循环压缩映射不动点定理

在类拟b-距离空间中建立了几种类型的循环映射的不动点定理,所得结果改进并统一了前人文献中的主要结果.而且,给出了几个非平凡的例子突出了其主要结果的优越性.     

初值问题

In this paper we shall study the solvability of discontinuous functional equations, and apply the so-obtained results to discontinuous implicit initial value problems in ordered Banach spaces. The proofs are based on fixed point results in ordered spaces proved recently by the author. A concrete example is solved to demonstrate the obtained results.     

Stationary queuing systems with dependencies

The fundamental results relating to queuing systems with dependencies are presented in condensed form in the present survey. Particular attention is paid to the extension of the results obtained earlier for classical systems to systems with dependencies, and certain early classical results in queuing theory are discussed.     

IMGS方法对于,H -矩阵的若干令人满意的改进

该文给出线性方程组改进的Gauss-Seidel迭代法（被称之为IMGS方法）对于H -矩阵的收敛性定理,并且对其参数a_i与SOR迭代法的参数ω的取值范围进行了比较. 所用方法及所得结论优于近年来相关结论,并且表明这种IMGS方法对,H -矩阵是有效的.     

On scalar equilibrium problem in generalized convex spaces

In this paper we prove the existence of a solution to the scalar equilibrium problem in generalized convex space. As applications, we derive results on the best approximations and simultaneous approximations. The results of this paper generalize some known results in the literature.     

On solving large instances of the capacitated facility location problem

We present two sets of results pertaining to the solution of capacitated facility location problems that are large, especially with regard to the number of customers. One set of results relates to customer aggregation, while another set of results concerns the judicious selection of variable-upper-bounding (VUB) constraints to include in the initial integer-programming formulation.     

On several results about convex set functions

In 1979, in an interesting paper, R.J. Morris introduced the notion of convex set function defined on an atomless finite measure space. After a short period this notion, as well as generalizations of it, began to be studied in several papers. The aim was to obtain results similar to those known for usual convex (or generalized convex) functions. Unfortunately several notions are ambiguous and the arguments used in the proofs of several results are not clear or not correct. In this way there were stated even false results. The aim of this paper is to point out that using some simple ideas it is possible, on one hand, to deduce the correct results by means of convex analysis and, on the other hand, to emphasize the reasons for which there are problems with other results.     

Properties of functions in an auxiliary spline space

Summary This note examines functions in an auxiliary spline space related to geometrically continuous splines. Previous work [3, 4] required results about the existence and number of zeros of certain functions in this space, as well as results on how to combine these functions. This note provides improved versions of these results.