关于亚纯函数的ρ(r)相对亏量

该文定义并研究ρ(0<ρ<+∞)级亚纯函数的ρ(r)相对亏量,得到了四个结果,其中定理2包含了Sarangi和Patil的结果,定理4表明具有极值ρ(r)亏量和的亚纯函数不再有非零有穷ρ(r) 相对亏值.     

具有根性质的一个充要条件

本文给出(D)类算子的一个扰动结果,并指出这个扰动结果只能对X上的(D)类算子成立;同时指出文[3]A.G.Ramm的结果仅能对H中的(D)类算子成立;在(D)类算子的条件下,我们推广了A.G.Ramm的结果。     

一般赋范空间上连续函数的Korovkin型定理

本文引入一种连续模的新的控制泛函，利用直接方法（避免使用Ｋ－泛函）得到了一般赋范空间上连续函数的Ｋｏｒｏｖｋｉｎ型定理，得到的结果与Ｈ．Ｇｏｎｓｋａ用Ｋ－泛函得到的结果相比各有优点。     

FKKM-型定理的推广及应用

本文得到ＦＫＫＭ－型定理的几个新的推广定理,并将所得结果应用于研究重合点问题．文中的结果统一和包含了一些作者的最新成果．     

（Ω,Aab）场论中测地线的进动

本文的目的在于推算余桑提出的（Ω，Ａ＿（ａｂ））场论￣［１］中测地线的进动。并将所得结果与Ｓｃｈｗａｒ－ｚｓｅｈｉｌｄ轨道作了比较。     

在右半平面收敛的Laplace-Stieltjes变换的增长性

本文研究了在右平面收敛的Ｌａｐｌａｃｅ－Ｓｔｉｅｌｔｊｅｓ变换的增长性,得到了与指数级数类似的结果     

故障树计算的一种新方法

本文提出的顶事件发生概率的算法不借助割集，直接采用自顶向下的技术对故障树进行分割求解。该算法的时间和内存耗用与故障树的节点数目没有必然联系，而仅仅取决于故障树中不同的重复事件的个数。     

二分(mg,mf)-图中的(g,f)-因子

设G是一个二分图具有顶点集V（G）和边集E（G）。设g和f是定义在V（G）上的两个正整值函数使对任意的x∈V（G）有g(x)≤f(x)，G的一个（g,f）－因子H是G的一个生成子图满足g(x)≤dH(x)≤f(x）。若图G本身是一个（g,f）－因子，则称G是一个（g,f）－图。本文得到一个（mg,mf）－图具有特殊性质的（g,f）－因子的充分条件，从而推广了文献[6]中的一个结果。     

不具有性质(wa)的拓扑空间

设（X，T）是拓扑空间，如果对于任意的开覆盖u和任意的稠密子集D存在X的离散子集F∪→D使得St(F,u)=∪{U∈u:U∩F≠φ}=X，则称（X，T）具有性质（wa)，每一正规空间都具有性质（wa)。M.V.Matveev举例说明了T1空间可以不具有性质(wa)，本文证明了存在很多Hausdorff空间不具有性质（wa)，且进一步举例说明了Tychonoff空间可以不具有性质（wa)，这些结果回答了Matveev的问题。     

广义Laplace-Stieltjes变换的准确零(R)级

本文对广义Ｌａｐｌａｃｅ－Ｓｔｉｅｌｔｊｅｓ变换确定的解析函数引进了准确零（Ｒ）级的概念，得到了这样的函数有准确零（Ｒ）级的两个充要条件．其结果类似于指数级数     

Efficiency of purchasing and selling agents in markets with quality uncertainty: The case of illicit drug transactions

Since Akerlof’s theory of lemons, economists have viewed quality uncertainty as an informational advantage for sellers. Drawing on frontier techniques, we propose in this paper a simple method for measuring inefficiency of both sellers and buyers in markets for goods with different levels of quality. We apply a non-parametric robust double-frontier framework to the case of illicit substance markets, which suffer from imperfect information about drug quality for purchasers and to a lesser extent for sellers. We use unique data on cannabis and cocaine transactions collected in France that include information about price, quantity exchanged and purity. We find that transactional inefficiency does not really benefit either dealers or purchasers. Furthermore, information influences the performance of agents during market transactions.     

广义Calderón-Zygmund算子交换子的有界性

讨论了广义Calderón-Zyginund算子与Lipschitz函数生成的交换子在Lebe-sgue空间及Hardy空间上的有界性,同时得到了其端点估计.     

Criterions for detecting the existence of the exponential dichotomies in the asymptotic behavior of the solutions of variational equations

We prove that the admissibility of any pair of vector-valued Schäffer function spaces (satisfying a very general technical condition) implies the existence of a “no past” exponential dichotomy for an exponentially bounded, strongly continuous cocycle (over a semiflow). Roughly speaking the class of Schäffer function spaces consists in all function spaces which are invariant under the right-shift and therefore our approach addresses most of the possible pairs of admissible spaces. Complete characterizations for the exponential dichotomy of cocycles are also obtained. Moreover, we involve a concept of a “no past” exponential dichotomy for cocycles weaker than the classical concept defined by Sacker and Sell (1994) in [23]. Our definition of exponential dichotomy follows partially the definition given by Chow and Leiva (1996) in [4] in the sense that we allow the unstable subspace to have infinite dimension. The main difference is that we do not assume a priori that the cocycle is invertible on the unstable space (actually we do not even assume that the unstable space is invariant under the cocycle). Thus we generalize some known results due to O. Perron (1930) [14], J. Daleckij and M. Krein (1974) [7], J.L. Massera and J.J. Schäffer (1966) [11], N. van Minh, F. Räbiger and R. Schnaubelt (1998) [26].     

A fractional version of the peano-sard theorem

Sard's classical generalization of the Peano kernel theorem provides an extremely useful method for expressing and calculating sharp bounds for approximation errors. The error is expressed in terms of a derivative of the underlying function. However, we can apply the theorem only if the approximation is exact on a certain set of polynomials.

In this paper, we extend the Peano-Sard theorem to the case that the approximation is exact for a class of generalized polynomials (with non-integer exponents). As a result, we obtain an expression for the remainder in terms of a fractional derivative of the function under consideration. This expression permits us to give sharp error bounds as in the classical situation. An application of our results to the classical functional (vanishing on polynomials) gives error bounds of a new type involving weighted Sobolev-type spaces. In this way, we may state estimates for functions with weaker smoothness properties than usual.

The standard version of the Peano-Sard theory is contained in our results as a special case.     

Concerning a Kind of Integrals of Cinmplex-Valued Functions of Large Numbers

ＣｏｎｃｅｒｎｉｎｇａＫｉｎｄｏｆｉｎｔｅｇｒａｌｓｏｆＣｏｍｐｌｅｘ－ＶａｌｎｅｄＦｕｎｃｔｉｏｎｓｏｆＬａｒｇｅＮｎｍｂｅｒｓＬ．Ｃ．Ｈｓｕ（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｓｃｉ．，ＤａｌｉａｎＵｎｉｖ．ｏｆＴｅｃｈ，Ｄａｌｉａｎ１１００２３）Ｃｏｎｃ...     

A stochastic multiscale model for electricity generation capacity expansion

Long-term planning for electric power systems, or capacity expansion, has traditionally been modeled using simplified models or heuristics to approximate the short-term dynamics. However, current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics. We present an efficient method for coupling multiple temporal scales using the framework of singular perturbation theory for the control of Markov processes in continuous time. We show that the uncertainties that exist in many energy planning problems, in particular load demand uncertainty and uncertainties in generation availability, can be captured with a multiscale model. We then use a dimensionality reduction technique, which is valid if the scale separation present in the model is large enough, to derive a computationally tractable model. We show that both wind data and electricity demand data do exhibit sufficient scale separation. A numerical example using real data and a finite difference approximation of the Hamilton–Jacobi–Bellman equation is used to illustrate the proposed method. We compare the results of our approximate model with those of the exact model. We also show that the proposed approximation outperforms a commonly used heuristic used in capacity expansion models.     

A RIEMANN-TYPE DEFINITION OF N-TH CESARO-PERRON INTEGRALS

In this paper, We give a varlational-type definition of (CnP) integrals. It is equivalent to the original definition of Perron-type and to the definition of Riemann-type, in this way the problem on definition of(CnP)′s Riemann-type has been solved completely.     

Inversion of a block Löwner matrix

In this paper, we give a fast algorithm to compute the parameters of an inversion formula for any nonsingular block Löwner matrix. The connection with matrix rational interpolation is given.     

收敛函数列一致(R)可积的一个必要条件

给出了收敛的一致(R)可积函数列的一致有界性定理,并指出一致有界是收敛的(R)可积函数列一致(R)可积的必要条件,但不是充分条件.     

Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories

Abstract

We study the transfer via functors between abelian categories of the (dual) relative splitness of objects with respect to a fully invariant short exact sequence. We mainly consider fully faithful functors and adjoint pairs of functors. We deduce applications to Grothendieck categories, (graded) module categories and comodule categories.