高阶线性微分方程的解及其解的导数的不动点

研究了复域齐次和非齐次线性微分方程的解及其解的导数的不动点与超级问题,得到了整函数系数的齐次和非齐次线性微分方程的解及其解的导数的不动点的两个结果,所得结果推广了一些相关结果.     

某些差分多项式的亏量

Halburd和Korhonen指出研究复域差分的值分布问题对进一步研究复域差分与差分方程具有十分重要的意义.本文得到了关于有限级亚纯函数的差分多项式的亏量为一些结果,其中部分结果可视为微分多项式相应结果的差分模拟.同时,我们在一定条件下给出了经典的Valiron-Mohon'ko定理的一个差分模拟结果,并且作为本文中的一个重要工具出现.这些结果推广了前人已有结果.     

一类具有时滞和反馈控制的非线性离散模型的持久性

研究了一类具有时滞和反馈控制的非线性单种群离散模型的持久性,获得了该系统持久的充分条件,并通过例子表明结果的可行性,所得结果推广了已有文献的相关结果.     

一类奇异非线性两点边值问题的 Galerkin 解的误差估计

本文对一类奇异两点边值问题采用了对称的Galerkin方法.通过利用Green函数,对线性问题得到了拟最优的最大范数误差估计并将这一结果推广到了非线性问题.本文最后列举了一些数值试验结果,这些结果很好地验证了理论结果.     

关于平面调和映射的Bloch常数的估计

考虑了拟正则调和映射和开的平面调和映射的Bloch常数, 得到了较好的结果,
所得结果推广了陈怀惠等及Grigoryan的结果.     

具有连续变量的差分方程的振动性

本文建立了具有连续交量差分方程的振动性判据，其结果改进了文献中的某些已知结果．     

模糊群决策结果的可信性评估

模糊数是群决策中常用的决策结果表达形式.研究了模糊群决策结果的可信性评估问题.认为群决策结果的可信性与模糊群决策结果的模糊度和一致度存在强相关,因此,模糊群决策结果可信性评估主要就是对群决策结果的模糊度和一致度的计算,创新提出了基于群隶属函数的模糊度和一致度的计算方法,并给出了基于模糊度和一致度的专家模糊数决策结果综合评价值的计算方法,最后,在此基础上求得专家模糊评估结果的可信度和群决策结果的可信度.     

行为NA的随机变量阵列的完全收敛性

本文研究了行为NA的随机变量阵列的完全收敛性.利用陈平炎等[4]研究的结果,得到了行为NA的随机变量阵列完全收敛的系列充分条件,这些结果推广和改进了Kuczmaszewska[3]相应的结果.     

关于“预拓扑与网族的预收敛类”的注

本文研究了预拓扑空间中的收敛问题.利用完备格同构的方法,获得了预拓扑与预收敛类可以相互确定的结果,推广了拓扑与收敛类可以相互确定的结果,同时推广了文献[1]的结果.     

具无限时滞的非自治捕食者-食饵系统的持久性

本文采用新的方法研究了具无限时滞的非自治、非卷积的捕食者－食饵系统的持久性问题，得到了新的、有趣的结果。本文的结果包含已知的结果作为特例．     

Quasi-planar graphs have a linear number of edges

A graph is calledquasi-planar if it can be drawn in the plane so that no three of its edges are pairwise crossing. It is shown that the maximum number of edges of a quasi-planar graph withn vertices isO(n).Work on this paper by Pankaj K. Agarwal, Boris Aronov and Micha Sharir has been supported by a grant from the U.S.-Israeli Binational Science Foundation. Work on this paper by Pankaj K. Agarwal has also been supported by NSF Grant CCR-93-01259, by an Army Research Office MURI grant DAAH04-96-1-0013, by an NYI award, and by matching funds from Xerox Corporation. Work on this paper by Boris Aronov has also been supported by NSF Grant CCR-92-11541 and by a Sloan Research Fellowship. Work on this paper by János Pach, Richard Pollack, and Micha Sharir has been supported by NSF Grants CCR-91-22103 and CCR-94-24398. Work by János Pach was also supported by Grant OTKA-4269 and by a CUNY Research Award. Work by Richard Pollack was also supported by NSF Grants CCR-94-02640 and DMS-94-00293. Work by Micha Sharir was also supported by NSF Grant CCR-93-11127, by a Max-Planck Research Award, and by grants from the Israel Science Fund administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development. Part of the work on this paper was done during the participation of the first four authors in the Special Semester on Computational and Combinatorial Geometry organized by the Mathematical Research Institute of Tel Aviv University, Spring 1995.     

带干扰的Erlang(2)过程

本篇论文主要讨论带干扰的E rlang(2)过程,首先通过指数分布的可加性来推得生存概率所满足的积分微分方程,进而得到破产概率(由干扰引起和由索赔引起)所满足的积分微分方程,最后得到破产概率的拉氏变换所满足的方程.     

A five facets frame for the design of heuristics

The author suggested to distinguish between the ‘engineering approach’ and the ‘mathematical approach’ in connection with the design of heuristics. Stainton and Papoulias extended the scope by suggesting the ‘relational approach’. Based upon this extension, a five facets frame is presented here which is suggested to precede and accompany the ‘technical’ design of the heuristic. The facets are: coverage by participation, experience by doing, abstraction by structuring, extension by comparison, exploration by creativity.     

Symmetry Reductions of the Combined KdV—mKdV Equation

ＳｙｍｍｅｔｒｙＲｅｄｕｃｔｉｏｎｓｏｆｔｈｅＣｏｍｂｉｎｅｄＫｄＶ－ｍＫｄＶＥｑｕａｔｉｏｎＺｈａｎｇＪｉｅｆａｎｇ（张解放）；ＸｕＸｕｅｊｕｎ（许学军）；ＣｈｅｎｇＤｅｓｈｅｎｇ（程德声）（ＤｅｐａｒｔｍｅｎｔｏｆＰｈｙｓｉｃｓ，Ｚｈｅｊｉａｎｇ...     

A New Characterization of the Mathieu Groups and Alternating Groups with Degrees Primes

In the past thirty years, several kinds of quantitative characterizations of finite groups especially finite simple groups have been investigated by many mathematicians. Such as quantitative characterizations by group order and element orders, by element orders alone, by the set of sizes of conjugacy classes, by dimensions of irreducible characters, by the set of orders of maximal abelian subgroups and so on. Here the authors continue this topic in a new area tending to characterize finite simple groups with given orders by some special conjugacy class sizes, such as largest conjugacy class sizes, smallest conjugacy class sizes greater than 1 and so on.     

“运价”为负的运输模型计算机求解问题的处理

为解决一些计算机软件求解"运价"既有正值又有负值运输模型时"不可求解"的问题,本文采用"运价同额增减法"决策模型转换的方法,将原模型的"运价"全部转换为正值后再用计算机软件求解,并分别编写了EXCEL求解模板和求解程序对该方法的计算加以印证。结果表明,采用该方法求解得出的最优解(最优决策方案)与原模型求得的最优解完全一样,而最优值(最优决策效果)减去虚增(或加上虚减)的部分就是原模型的最优值。采用这种方法能成功地解决一些计算机软件"不可求解"的问题。     

Approximate Gradient Projection Method with Runge-Kutta Schemes for Optimal Control Problems

We consider an optimal control problem for systems governed by ordinary differential equations with control constraints. The state equation is discretized by the explicit fourth order Runge-Kutta scheme and the controls are approximated by discontinuous piecewise affine ones. We then propose an approximate gradient projection method that generates sequences of discrete controls and progressively refines the discretization during the iterations. Instead of using the exact discrete directional derivative, which is difficult to calculate, we use an approximate derivative of the cost functional defined by discretizing the continuous adjoint equation by the same Runge-Kutta scheme and the integral involved by Simpson's integration rule, both involving intermediate approximations. The main result is that accumulation points, if they exist, of sequences constructed by this method satisfy the weak necessary conditions for optimality for the continuous problem. Finally, numerical examples are given.     

Interpolation on lattices generated by cubic pencils

Principal lattices are distributions of points in the plane obtained from a triangle by drawing equidistant parallel lines to the sides and taking the intersection points as nodes. Interpolation on principal lattices leads to particularly simple formulae. These sets were generalized by Lee and Phillips considering three-pencil lattices, generated by three linear pencils. Inspired by the addition of points on cubic curves and using duality, we introduce an addition of lines as a way of constructing lattices generated by cubic pencils. They include three-pencil lattices and then principal lattices. Interpolation on lattices generated by cubic pencils has the same good properties and simple formulae as on principal lattices. Dedicated to C.A. Micchelli for his mathematical contributions and friendship on occasion of his sixtieth birthday Mathematics subject classifications (2000) 41A05, 41A63, 65D05. J.M. Carnicer: Partially supported by the Spanish Research Grant BFM2003-03510, by Gobierno de Aragón and Fondo Social Europeo.     

Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs

We characterize intrinsic regular submanifolds in the Heisenberg group as intrinsic differentiable graphs. G. Arena is supported by MIUR (Italy), by INDAM and by University of Trento. R. Serapioni is supported by MIUR (Italy), by GALA project of the Sixth Framework Programme of European Community and by University of Trento.     

Adaptive robot under fuzzy control

This paper deals with the problem of ranking n fuzzy subsets of the unit interval. A number of methods suggested in the literature is reviewed and tested on a group of selected examples, where the fuzzy sets can be nonnormal and/or nonconvex.The ranking is obtained from: (i) the index of strict preference defined by Watson, (ii) three indexes proposed by Yager, (iii) the algorithm used by Chang, (iv) three versions of the a-preference index suggested by Adamo, (v) the index defined by Baas and Kwakernaak, (vi) three modified versions used by Baldwin and Guild, (vii) the method proposed by Kerre, (viii) three forms of the index suggested by Jain, (ix) the four grades of dominance studied by Dubois and Prade.In simple cases the results are good for all the methods, with some exceptions. In questionable cases, where the decision must be probably modelled in accordance with the context in which it is imbedded, the best indexes seem to be the dominances suggested by Dubois and Prade. These indexes do not force any particular choice, but clearly describe the situation, hence allowing the decision-maker himself to make his ‘best’ choice.