Iterative process for G-multi degree reduction of Bézier curves

In this paper, the issue of multi-degree reduction of Bézier curves with C¹ and G²-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method.     

Symmetry property of the throughput in closed tandem queueing networks with finite buffers

In this paper we consider closed tandem queueing networks with finite buffers and blocking before service. With this type of blocking, a server is allowed to start processing a job only if there is an empty space in the next buffer. It was recently conjectured that the throughput of such networks is symmetrical with respect to the population of the network. That is, the throughput of the network with population N is the same as that with population C − N, where C is the total number of buffer spaces in the network. The main purpose of this paper is to prove this result in the case where the service time distributions are of phase type (PH-distribution). The proof is based on the comparison of the sample paths of the network with populations N and C − N. Finally, we also show that this symmetry property is related to a reversibility property of this class of networks.     

The dual of C ps (X)

This is a study of the dual space of continuous linear functionals on the function space C_ps(X) with a natural norm inherited from a larger Banach space. Here ps denotes the pseudocompact-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X. The lattice structure and completeness of this dual space have been studied. Since this dual space is inherently related to a space of measures, the measure-theoretic characterization of this dual space has been studied extensively. Due to this characterization, a special kind of topological space, called pz-space, has been studied. Finally the separability of this dual space has been studied.      

Une étude mathématique d'un modèle de Rotenberg

In this paper, a cell proliferation model of Rotenberg is mathematically studied. Each cell of this population is distinguished by its degree of maturity μ and its maturation velocity v. We equipped this mathematical model by boundary conditions wich generalize all biological rules imposed by Rotenberg. We show that this model is governed by a strongly continuous semigroup. We also develop some properties of this semigroup and we study its asymptotic behaviour in the uniform topology.     

Interior-Point Algorithms for Semidefinite Programming Based on a Nonlinear Formulation

Recently in Burer et al. (Mathematical Programming A, submitted), the authors of this paper introduced a nonlinear transformation to convert the positive definiteness constraint on an n × n matrix-valued function of a certain form into the positivity constraint on n scalar variables while keeping the number of variables unchanged. Based on this transformation, they proposed a first-order interior-point algorithm for solving a special class of linear semidefinite programs. In this paper, we extend this approach and apply the transformation to general linear semidefinite programs, producing nonlinear programs that have not only the n positivity constraints, but also n additional nonlinear inequality constraints. Despite this complication, the transformed problems still retain most of the desirable properties. We propose first-order and second-order interior-point algorithms for this type of nonlinear program and establish their global convergence. Computational results demonstrating the effectiveness of the first-order method are also presented.     

On the Laplacian energy of a graph

In this paper we consider the energy of a simple graph with respect to its Laplacian eigenvalues, and prove some basic properties of this energy. In particular, we find the minimal value of this energy in the class of all connected graphs on n vertices (n = 1, 2, ...). Besides, we consider the class of all connected graphs whose Laplacian energy is uniformly bounded by a constant α ⩾ 4, and completely describe this class in the case α = 40.     

Boundedness, one-point extensions and B-extensions

The general concept of boundedness in a topological space generalizes both metric boundedness and relative compactness. A one-point extension o(ℱ _X) of the space X is naturally associated to each boundedness ℱ _X and every Hausdorff one-point extensions of a space X can be obtained in this way. Imitating this construction, it is possible to define a much more general class of Hausdorff extensions of a locally bounded space with respect to a given boundedness, the so-called B-extensions. In this paper we study separation properties and metrizability of this kind of extension.      

A filtering problem with a small nonlinear term

In this paper, we consider a filtering problem where the signal X _t satisfies a slightly nonlinear stochastic differential equation and we want to obtain estimates of X _t. To this end, we decompose the nonlinearity with two techniques—a deterministic one and a stochastic one—and this leads us to two sequences of estimates which can be computed by solving finite dimensional equations. We want to compare their performances: we solve this problem in most cases if we restrict ourselves to sufficiently small times t and we give conditions which permit to conclude also for larger times     

The finiteness obstruction for loop spaces

For finitely dominated spaces, Wall constructed a finiteness obstruction, which decides whether a space is equivalent to a finite CW-complex or not. It was conjectured that this finiteness obstruction always vanishes for quasi finite H-spaces, that are H-spaces whose homology looks like the homology of a finite CW-complex. In this paper we prove this conjecture for loop spaces. In particular, this shows that every quasi finite loop space is actually homotopy equivalent to a finite CW-complex. Received: March 25, 1999.     

模糊环境下带交易费用的权证定价模型——纪念李国平院士吴新谋教授诞辰100周年

该文综合考虑我国证券市场中广泛存在的隐性交易费用, 建立了模糊环境下带交易费用的权证定价模型. 在假设交易费用率为三角型模糊数的前提下导出了新的权证价格区间, 并通过引入模糊期望的概念, 将区间数转化为与投资者主观判断无关的准确数. 基于此模型, 对模型中三角型模糊数的关键参数 进行了灵敏度分析和投资策略分析.     

Induced residuated maps

The purpose of this paper is to introduce a class of mappings from a lattice L, whose elements are residuated maps, into itself. The main results of this paper identify certain injective residuated mappings of L and order automorphisms of a sublattice of L with mappings from this class.     

The Automorphism Group and the Convex Subgraphs of the Quadratic Forms Graph in Characteristic 2

We determine the automorphism group and the convex subgraphs of the quadratic forms graph Quad(n,q),q even.A. Munemasa: A part of this research was completed during this author's visit at the Institute for System Analysis, Moscow, as a Heizaemon Honda fellow of the Japan Association for Mathematical SciencesD.V. Pasechnik: A part of this research was completed when this author held a position at the Institute for System Analysis, MoscowS.V. Shpectorov: A part of this research was completed during this author's visit at the University of Technology, Eindhoven     

Randomized k-server algorithms for growth-rate bounded graphs

The k-server problem is a fundamental online problem where k mobile servers should be scheduled to answer a sequence of requests for points in a metric space as to minimize the total movement cost. While the deterministic competitive ratio is at least k, randomized k-server algorithms have the potential of reaching o(k)-competitive ratios. Prior to this work only few specific cases of this problem were solved. For arbitrary metric spaces, this goal may be approached by using probabilistic metric approximation techniques. This paper gives the first results in this direction, obtaining o(k)-competitive ratio for a natural class of metric spaces, including d-dimensional grids, and wide range of k.     

Geometrical and physical interpretation of evolution governed by general complex algebra

In this paper we explore a geometrical and physical matter of the evolution governed by the generator of General Complex Algebra, GC₂. The generator of this algebra obeys a quadratic polynomial equation. It is shown that the geometrical image of the GC₂-number is given by a straight line fixed by two given points on Euclidean plane. In this representation the straight line possesses the norm and the argument. The motion of the straight line conserving the norm of the line is described by evolution equation governed by the generator of the GC₂-algebra. This evolution is depicted on the Euclidean plane as rotational motion of the straight line around the semicircle to which this line is tangent. Physical interpretation is found within the framework of the relativistic dynamics where the quadratic polynomial is formed by mass-shell equation. In this way we come to a new representation for the momenta of the relativistic particle.     

An algorithm and self-reproducing systems

Let G be a group and let N be a normal subgroup of G. We set cd(G|N) to be the degrees of the irreducible characters of G whose kernels do not contain N. We associate a graph with this set. The vertices of this graph are the primes dividing degrees in cd(G|N), and there is an edge between p and q if pq divides some degree in cd(G|N). In this paper, we study this graph when it is disconnected, and we study its diameter when it is connected.     

An analytical formula for pricing m-th to default swaps

The computational effort of pricing an m-th to default swap depends highly on the size n of the underlying basket. Usually, n different default times are modeled, but in fact the valuation only depends on the m-th smallest default time of this tuple. In this paper we attain an analytical formula for the distribution of this m-th default time. With the help of this distribution we simplify the valuation problem from an n-dimensional quadrature to a one-dimensional quadrature and break the curse of dimensionality. Applications of this modification are efficient pricing of m-th to default swaps, estimation of sensitivities and pricing of European max/min options.     

Weak convergence of empirical and quantile processes in sup-norm metrics via kmt-constructions

There has been much interest recently in the specially constructed empirical processes of Komlós, Major and Tusnády [2]; as one would guess, much of the application has come from the Hungarian school.In this note we contribute to the unifying effect this profound work has had by showing how the major theorem of O'Reilly [4] follows in rather elementary fashion from this powerful construction. We also take this opportunity to restate O'Reilly's criterion in an elementary form that is far more intelligible.     

Un semi-groupe régularisé pour un modèle de Lebowitz–RubinowA regularized semigroup for a Lebowitz–Rubinow's model

In this Note, we complete [1] and we study the Lebowitz–Rubinow's model with the biological law of perfect memory. In this model, each cell is characterized by its cell cycle length l (0?l₁<l<l₂<∞) and its age a (0<a<l). If l₁>0, a complete study of this model can be found in [1]. Here we show that if l₁=0 then this model becomes ill-posed. We use the theory of generalized semigroups to remedy to this model. To cite this article: M. Boulanouar, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 865–868.     

一类一维的辐射流体力学方程组激波的存在性

该文主要讨论一维空间中一类辐射流体力学方程组的激波. 由Rankine-Hugoniot条件及熵条件得此问题可表述为关于辐射流体力学方程组带自由边界的初边值问题. 首先通过变量代换, 将其自由边界转换为固定边界, 然后研究关于此非线性方程组的一个初边值问题解的存在唯一性. 为此先构造了此问题的一个近似解, 然后分别通过Picard迭代与Newton迭代对此非线性问题构造近似解序列. 通过一系列估计与紧性理论得到此近似解序列的收敛性, 其极限即为原辐射热力学方程组的一个激波.     

Symmetric designs with parameters (69, 17, 4) and F39 as a group of automorphisms

According to Mathon and Rosa [The CRC handbook of combinatorial designs, CRC Press, 1996] there is only one known symmetric design with parameters (69, 17, 4). This known design is given in Beth, Jungnickel, and Lenz [Design theory, B. I. Mannheim, 1985]; the Frobenius group F₃₉ of order 39 acts on this design, where Z₁₃ has exactly 4 fixed points and Z₃ has exactly 9 fixed points. The purpose of this article is to investigate the converse of this fact with the hope of obtaining in this way at least one more design with these parameters. In fact we obtain exactly one new such design. In this article we have classified all such designs invariant under F₃₉. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 231–233, 1998