一个新的GLKKM定理及其对抽象经济的应用(英文)

In this paper,a new GLKKM theorem in L-convex spaces is established.As applications,a new fixed point theorem and a maximal element theorem are obtained in Lconvex spaces.Finally,equilibrium existence theorems for economies and qualitative games in L-convex spaces are yielded.     

Convex optimization approaches to maximally predictable portfolio selection

In this article we propose a simple heuristic algorithm for approaching the maximally predictable portfolio, which is constructed so that return model of the resulting portfolio would attain the largest goodness-of-fit. It is obtained by solving a fractional program in which a ratio of two convex quadratic functions is maximized, and the number of variables associated with its nonconcavity has been a bottleneck in spite of continuing endeavour for its global optimization. The proposed algorithm can be implemented by simply solving a series of convex quadratic programs, and computational results show that it yields within a few seconds a (near) Karush–Kuhn–Tucker solution to each of the instances which were solved via a global optimization method in [H. Konno, Y. Takaya and R. Yamamoto, A maximal predictability portfolio using dynamic factor selection strategy, Int. J. Theor. Appl. Fin. 13 (2010) pp. 355–366]. In order to confirm the solution accuracy, we also pose a semidefinite programming relaxation approach, which succeeds in ensuring a near global optimality of the proposed approach. Our findings through computational experiments encourage us not to employ the global optimization approach, but to employ the local search algorithm for solving the fractional program of much larger size.     

On the Wielandt Subgroup in a p-Group of Maximal Class

The Wielandt subgroup of a group G,denoted by w(G),is the intersection of the normalizers of all subnormal subgroups of G.In this paper,the authors show that for a p-group of maximal class G,either wi(G) = ζi(G) for all integer i or wi(G) = ζi+1(G) for every integer i,and w(G/K) = ζ(G/K) for every normal subgroup K in G with K = 1.Meanwhile,a necessary and suflcient condition for a regular p-group of maximal class satisfying w(G) = ζ2(G) is given.Finally,the authors prove that the power automorphism group PAut(G) is an elementary abelian p-group if G is a non-abelian pgroup with elementary ζ(G) ∩ 1(G).     

The influence of cation additives on the NIR luminescence intensity of Er3+-doped borate glasses

Er3+-doped 25BaO-(25-x)SiO2-xAl2O3-25B2O3 transparent glasses are prepared with x = 0,12.5 and 25 by a solid-state reaction.The Er-related NIR luminescence intensity,which corresponds to the transition of 4I15/2-4I13/2,is obviously altered with different silicon/aluminum ratios.The Judd-Ofelt parameters of the Er3+ ions are adopted to explain the intensity change in the NIR fluorescence,and the Raman scattering intensity versus the amount of Al and/or Si components are discussed.The spectra of the three samples are quite similar in the peak positions,but different in intensity.The maximal phonon density of state for the samples is calculated from the Raman spectra and is correlated to the NIR luminescence efficiency.     

Stochastic flows of SDEs with irregular coefficients and stochastic transport equations

In this article we study (possibly degenerate) stochastic differential equations (SDEs) with irregular (or discontinuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere stochastic (invertible) flow associated with the SDE in the sense of Lebesgue measure. In the case of constant diffusions and BV drifts, we obtain such a result by studying the related stochastic transport equation. In the case of non-constant diffusions and Sobolev drifts, we use a direct method. In particular, we extend the recent results on ODEs with non-smooth vector fields to SDEs.     

Semilinear evolution equations on discrete time and maximal regularity

This paper deals with the existence and stability of solutions for semilinear equations on Banach spaces by using recent characterizations of discrete maximal regularity. As application we examine the asymptotic behavior of discrete control systems.     

某些算子和交换子在非齐型空间上的Morrey-Herz空间中的有界性

引入了非齐型空间上的齐次Morrey-Herz 空间和弱齐次Morrey-Herz空间并建立了Hardy-Littlewood极大算子,Calder\'on-Zygmund算子和分数次积分算子在齐次Morrey-Herz空间中的有界性以及在弱齐次Morrey-Herz空间中的弱型估计. 此外,还证明了$\rb$函数与Calder\'on-Zygmund算子或分数次积分算子生成的多线性交换子以及与Hardy-Littlewood极大算子相关的极大交换子在齐次Morrey-Herz空间中的有界性.     

On the Andrews-Stanley refinement of Ramanujan's partition congruence modulo and generalizations

In a recent study of sign-balanced, labelled posets, Stanley introduced a new integral partition statistic

where denotes the number of odd parts of the partition and is the conjugate of . In a forthcoming paper, Andrews proved the following refinement of Ramanujan's partition congruence mod :

where () denotes the number of partitions of with and is the number of unrestricted partitions of . Andrews asked for a partition statistic that would divide the partitions enumerated by () into five equinumerous classes.

In this paper we discuss three such statistics: the ST-crank, the -quotient-rank and the -core-crank. The first one, while new, is intimately related to the Andrews-Garvan (1988) crank. The second one is in terms of the -quotient of a partition. The third one was introduced by Garvan, Kim and Stanton in 1990. We use it in our combinatorial proof of the Andrews refinement. Remarkably, the Andrews result is a simple consequence of a stronger refinement of Ramanujan's congruence mod . This more general refinement uses a new partition statistic which we term the BG-rank. We employ the BG-rank to prove new partition congruences modulo . Finally, we discuss some new formulas for partitions that are -cores and discuss an intriguing relation between -cores and the Andrews-Garvan crank.

     

On the work of Basil Gordon

A review is given of several aspects of the work of Basil Gordon. These include: Rogers-Ramanujan identities, plane partitions, the method of weighted words, modular forms and partition congruences, and the asymptotics of partitions and related q-series.