射影平面上的对偶无环不可分近三角剖分地图

本文研究了球面和射影平面上对偶无环不可分近三角剖分带根地图的以根面次和内面数为参数的计数问题,得到了这类地图在球面和射影平面上的计数函数满足的方程.还得到了射影平面上2连通地图一个参数的显示表达式和渐近估计式.     

关于适约三角剖分的计数

众所周知，适约三角剖分在地图运算中有着重要作用．本文对于平面上这种三角剖分的数目进行了探讨．同时，也提供了含有两个变量的精确公式．     

柱面上有根近三角剖分的计数

柱面上的三角剖分是一类与环面上的地图紧密相关的地图．本文提供了一个计算柱面上有根近三角剖分的具有三个变量的精确公式．     

关于简单平面地图的计数

关于简单平面地图的计数,首先是以递推的方式讨论的.它依赖一般有根平面地图的计数函数(Acta Math.Appl.Sinica,English Series 2(1985),101—111).继之,得到了一个计数显式(J.Math.Res.& Expos.4∶3(1984),37—46).近来,从面剖分计数的更一般情况导出了一个函数方程(已投应用数学学报).本文提供了便于依根节点的次和边数计数有根简单平面地图的一个新的函数方程.由此出发,更直接也更简单地导出了这个计数显式.     

Klein瓶上的双奇异地图

一个地图的每条边如果不是环就是割边(即该边的两边是同一个面的边界)，则称之为双奇异地图，本文研究Klein瓶上带根双奇异地图的计数问题，得到了此类地图以边数、平面环数、手柄上本质环数和又帽上本质环数为参数的计数公式，并得到了部分计数显式。     

拟矩形剖分上的样条空间的维数

矩形剖分~(记为$\Delta_{QR}$)~是指在矩形剖分~(记为$\Delta_{R}$)的基础上进行局部修改后得到的剖分,通常包括T-剖分~(记为$\Delta_{T}$)~和L-剖分~(记为$\Delta_{L}$).本文利用光滑余因子协调方法讨论了该剖分上的二元样条空间$S^\mu_k(\Delta_{QR})$的维数.在满足一定约束条件下, 得到了仅依赖于样条空间的次数,光滑度和剖分拓扑结构的显式维数公式.     

高亏格曲面上地图的计数

本文给出了可定向曲面(亏格2,3)和不可定向曲面(亏格5)上根瓣丛以边数为参数时相应的计数显式.与此同时,考虑一类与瓣从拓扑等价的地图类: (无环,简单)近2-正则地图,通过一种组合方法,给出了多参数下平面近2一正则地图的计数显式,亦得到了任意亏格曲面上该类地图的具体个数.     

环面上近三角剖分地图的计数

本文提供了环面上带边数和根面次这两个参数的有根近三角剖分的函数方程及其参数表达式，并给出了根面次为1以边数为参数的有根近三角剖分地图的精确解．     

一个关于近-三角剖分嵌入的内插定理

一个近三角剖分嵌入是指一个图嵌入在一个曲面上,使得至多可能有一个面不是三角面。在本文中我们证明了如下结果：如果一个图G在某个可定向曲面S_h上有三角剖分嵌入,那么G在S_k上有一个近三角剖分嵌入,这里k=h,h 1,…,[β(G)/2],而β(G)是图G的Betti数。     

平面上一般地图的色和与双色和

本文研究了平面上一般带根地图的色和与双色和,得到了这类地图的色和与双色和函数方程。从这类地图的色和函数方程,导出了平面上一般无环地图、平面上二部地图和平面上欧拉地图的计数函数方程。还得到了一些计数函数的计数显式。     

Differential invariants of surfaces

The algebra of differential invariants of a suitably generic surface S⊂R³, under either the usual Euclidean or equi-affine group actions, is shown to be generated, through invariant differentiation, by a single differential invariant. For Euclidean surfaces, the generating invariant is the mean curvature, and, as a consequence, the Gauss curvature can be expressed as an explicit rational function of the invariant derivatives, with respect to the Frenet frame, of the mean curvature. For equi-affine surfaces, the generating invariant is the third order Pick invariant. The proofs are based on the new, equivariant approach to the method of moving frames.     

Cube Polynomial of Fibonacci and Lucas Cubes

The cube polynomial of a graph is the counting polynomial for the number of induced k-dimensional hypercubes (k≥0). We determine the cube polynomial of Fibonacci cubes and Lucas cubes, as well as the generating functions for the sequences of these cubes. Several explicit formulas for the coefficients of these polynomials are obtained, in particular they can be expressed with convolved Fibonacci numbers. Zeros of the studied cube polynomials are explicitly determined. Consequently, the coefficients sequences of cube polynomials of Fibonacci and Lucas cubes are unimodal.     

Decentralized method for computing Pareto solutions in multiparty negotiations

This paper presents a decentralized method for computing Pareto-optimal solutions in multiparty negotiations over continuous issues. The method is based on the well known weighting method which is decomposed by introducing an own decision variable for each decision maker and by applying the dual decomposition method to the resulting problem. The method offers a systematic way for generating some or all Pareto-optimal solutions so that decision makers do not have to know each others' value functions. Under the assumption of quasilinear value function the requirement that a decision maker knows the explicit form for his value function can be relaxed. In that case the decision maker is asked to solve a series of multiobjective programming problems where an additional artificial decision variable is introduced.     

Explicit formulations versus recursive formulations - studies based on the Fibonacci sequence and the factorial function

Although Fibonacci sequences have often been observed in nature, the original rabbit problem was posed as an exercise in classroom additions and not as a model of biological population prediction. As far as the author could ascertain, an explicit fomulation for the Fibonacci sequence has not been developed. On the other hand, the factorial function itself is both explicit and recursive. If explicit and recursive formulations are available for the same problem, much insight can be gained from mappings between the two forms. Recently the author succeeded in developing a generalized and explicit Fibonacci generating function. This gives the opportunity to carry out mappings between the two forms. By varying the reproductive sequences of parent and child pairs in the Fibonacci sequence, the author was able to find unique mappings between explicit and recursive forms. In the case of Fibonacci sequences, mappings from the explicit to the recursive forms are possible but not in the reversed direction. Computationally, the factorial function can be used either explicitly or recursively which suggests that there is no advantage in the sequence algebraic form. On the other hand, the explicit Fibonacci formula is found to be more accurate than its recursive counterpart.     

Bergmansche Polynom-Erzeugende Erster Art

This paper is concerned with special Bergman operators for linear partial differential equations. E. Kreyszig introduced a class of equations which possess polynomials as generating functions for Bergman operators. These generating functions permit an integral-free representation of the solutions which can also be obtained by K. W. Bauer's and E. Peschl's differential operators, as was shown by M. Kracht and E. Kreyszig. For an extension of Kreyszig's class by W. Watzlawek we state conditions that are necessary and sufficient for the existence of a polynomial generating function of the first kind. We give an explicit characterization of the corresponding subclass and a representation of those generating functions, which are important for developing a function theory of the equations considered.     

A solution to the distribution problems arising in the studies of a two-sex population process

Given a population of two sexes, the birth rate of one sex of which depends upon the population size of the other, it is very difficult to find an explicit expression for the probability distribution of the former. In this paper we have explicitly found the probability generating function of the joint distribution from which individual probability distributions and, in particular, moments of all orders in each case can be obtained in principle. As an example, using this probability generating function we have worked out explicitly the first and second order moments of the male and female populations and the explicit expression for the distribution of the male population in a particular case. This method can be successfully applied for the same purpose in the studies of chemical and biological processes where the synthesis or production of one species depends upon the concentration of another species.     

On a discrete risk model with two-sided jumps

In this paper, we consider a discrete renewal risk model with phase-type interarrival times and two-sided jumps. In this model, downward jumps represent claim loss, while upward jumps are also allowed to represent random gains. Assume that the downward jumps have an arbitrary probability function and the upward jumps have a rational probability generating function. We study the (Gerber-Shiu) discounted penalty function. The generating function, the recursive formula as well as an explicit expression for the discounted penalty function are obtained.     

Approximation Error for Quasi-Interpolators and (Multi-)Wavelet Expansions

We investigate the approximation properties of general polynomial preserving operators that approximate a function into some scaled subspace of L²via an appropriate sequence of inner products. In particular, we consider integer shift-invariant approximations such as those provided by splines and wavelets, as well as finite elements and multi-wavelets which use multiple generators. We estimate the approximation error as a function of the scale parameterTwhen the function to approximate is sufficiently regular. We then present a generalized sampling theorem, a result that is rich enough to provide tight bounds as well as asymptotic expansions of the approximation error as a function of the sampling stepT. Another more theoretical consequence is the proof of a conjecture by Strang and Fix, which states the equivalence between the order of a multi-wavelet space and the order of a particular subspace generated by a single function. Finally, we consider refinable generating functions and use the two-scale relation to obtain explicit formulae for the coefficients of the asymptotic development of the error. The leading constants are easily computable and can be the basis for the comparison of the approximation power of wavelet and multi-wavelet expansions of a given orderL.     

An abundance of invariant polynomials satisfying the Riemann hypothesis

In 1999, Iwan Duursma defined the zeta function for a linear code as a generating function of its Hamming weight enumerator. It can also be defined for other homogeneous polynomials not corresponding to existing codes. If the homogeneous polynomial is invariant under the MacWilliams transform, then its zeta function satisfies a functional equation and we can formulate an analogue of the Riemann hypothesis. As far as existing codes are concerned, the Riemann hypothesis is believed to be closely related to the extremal property.In this article, we show there are abundant polynomials invariant by the MacWilliams transform which satisfy the Riemann hypothesis. The proof is carried out by explicit construction of such polynomials. To prove the Riemann hypothesis for a certain class of invariant polynomials, we establish an analogue of the Eneström-Kakeya theorem.     

Comparison of single and double channel I/O-configurations

This paper is concerned with the performance evaluation of I/O-configurations composed of channels and I/0 devices (magnetic disk, drum ...). The question to be answered is: what performance improvement can be expected when the number of channels is increased or when the I/0-devices are multiple-ported instead of single-ported? To that end Markov chain models are developed for three different I/0-configurations. These models are analyzed under the assumption that a stochastic equilibrium is reached, and the probability generating function of the system occupancy is derived. From this function important performance measures, such as throughput and mean system occupancy are obtained as explicit functions of the system parameters. A quantitative comparison between the three alternatives is made.