三角多项式类中的Birkhoff型三角插值

本文在三角多项式类中讨论了2π周期函数的一类Birkhoff型等距结点的三角插值问题,给出了此问题有解的充要条件,并构造出插值基.     

局部域上自相似函数

分形与自相似概念在 B.Mandelbrot 的著作中给出.本文给出一类自相似函数依局部域上正交系的展开.求出这种自相似函数所满足的 Lipschitz 类的精确指数并指出他们与基础 Cantor 集的 Hausdorff-Besicovitch 维数的联系,还讨论了 p 进微分学基本公式对奇异函数成立的可能性.     

一类非自治系统的稳定性

通过构造 Liapunov函数给出了一类非自治系统的稳定性的判定准则 .并给出了其有关的应用实例     

一类Turan型多项式序列的构造及其性质

应用实系数多项式的性质构造了一类满足Turan型不等式的多项式序列,证明了该多项式序列的几个性质,并给出了一些应用.     

局部域上自相似函数

分形与自相似概念在B.Mandelbrot的著作中给出。本文给出一类自相似函数依局部城上正交系的展开,求出这种自相似函数所满足的Lipsohitz类的精确指数并指出他们与基础Cantor集的Hausdorff-Besicovitoh维数的联系,还讨论了p进微分学基本公式对奇异函数成立的可能性。     

复正规多项式系统的全局通解

本文首先应用复多项式系统的强有根定理,证明了一类复多项式系统全局通解的存在性.其次,讨论了正规多项式系统全局通解的定性结构,得到了它的表示定理.最后给出了定理应用的例子.     

一类具有两个非线性项的四阶非线性系统的稳定性

利用"类比法"构造了一类四阶非线性系统的Lyapunov函数,给出了该系统零解稳定性的充分条件.     

一类多项式向量场的中心条件

本文研究一类多项式系统的高次奇点和无穷远点的中心问题,对有限奇点（原点）和无穷远点（Poincare球面上的赤道）的中心问题进行统一处理,给出了系统原点和无穷远点为中心的一个充分条件。     

具有n次多项式截面的Copula函数

本文构造一类具有n次多项式截面的Copula函数C(x,y),并给出了C(x,y)是Copula函数的两个充分必要条件,同时推导出此类Copula函数的若干性质,包括对称性和相关度量等.     

矩阵多元多项式的带余除法及其应用

给出矩阵多元多项式的带余除法,从而用微分代数的观点,得到把一类微分方程(组)化为无穷维Hamilton系统的充要条件及其具体无穷维Hamilton系统形式。再把此方法和吴方法相结合获得构造一类微分方程(组)的通解的新方法。几个例子表明这些方法都很有效的。     

基于离散网格的流形曲面构造综述

基于离散网格的流形曲面构造技术不仅能够生成具有高阶光滑性的曲面,并且该曲面可以是任意拓扑结构的.此外,在构造流形曲面时,无需进行额外的拼接操作,克服了传统曲面造型技术在进行面片之间的拼接时,计算量增大以及曲面光滑性难以保证的难题.本文介绍了流形曲面构造的流程以及构造过程中的难点,然后将目前已有的流形曲面构造技术分为三大类:传统意义上的流形构造方法;基于规范区域的流形构造方法;基于样条曲面推广的流形构造方法.并对每一类都进行详细地分类介绍.最后,对其作一个总结以及对未来的展望.     

On 6-sparse Steiner triple systems

We give the first known examples of 6-sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We then present a recursive construction which establishes the existence of 6-sparse systems for an infinite set of orders. Observations are also made concerning existing construction methods for perfect Steiner triple systems, and we give a further example of such a system. This has order 135,859 and is only the fourteenth known. Finally, we present a uniform Steiner triple system of order 180,907.     

Symmetric–Antisymmetric Orthonormal Multiwavelets and Related Scalar Wavelets

For compactly supported symmetric–antisymmetric orthonormal multiwavelet systems with multiplicity 2, we first show that any length-2Nmultiwavelet system can be constructed from a length-(2N+1) multiwavelet system and vice versa. Then we present two explicit formulations for the construction of multiwavelet functions directly from their associated multiscaling functions. This is followed by the relationship between these multiscaling functions and the scaling functions of related orthonormal scalar wavelets. Finally, we present two methods for constructing families of symmetric–antisymmetric orthonormal multiwavelet systems via the construction of the related scalar wavelets.     

Some existence and construction results of polygonal designs

This paper revisits the existence and construction problems for polygonal designs (a special class of partially balanced incomplete block designs associated with regular polygons). We present new polygonal designs with various parameter sets by explicit construction. In doing so we employ several construction methods — some conventional and some new. We also establish a link between a class of polygonal designs of block size 3 and the cyclically generated ‘λ-fold triple systems’. Finally, we show that the existence question for a certain class of polygonal designs is equivalent to the existence question for ‘perfect grouping systems’ which we introduce.     

On a class of hybrid methods for smooth constrained optimization

With reference to smooth nonlinearly constrained optimization problems, we consider combinations of locally superlinearly convergent methods with globally convergent ones. The aim of this paper is threefold: to give a survey on well-known as well as possible unknown hybrid optimization methods, based on a special construction principle; to present a general convergence result for the class of hybrid algorithms; and to derive further methods for this class with new convergence properties.The authors thank the anonymous referees for their useful suggestions.     

An explication of secret sharing schemes

This paper is an explication of secret sharing schemes, emphasizing combinatorial construction methods. The main problem we consider is the construction of perfect secret sharing schemes, for specified access structures, with the maximum possible information rate.In this paper, we present numerous direct constructions for secret sharing schemes, such as the Shamir threshold scheme, the Boolean circuit construction of Benaloh and Leichter (for general access structures), the vector space construction of Brickell, and the Simmons geometric construction. We discuss the connections between ideal schemes (i.e., those with information rate equal to one) and matroids. We also mention the entropy bounds of Capocelli et al. Then we give a very general construciton, called the decomposition construction, and numerous applications of it. In particular, we study schemes for access structures based on graphs and the many interesting bounds that can be proved; and we determine the exact value of the optimal information rate for all access structures on at most four participants.Research supported by NSERC (Canada) grant A9287.     

Conjunctors and their Residual Implicators: Characterizations and Construction Methods

In many practical applications of fuzzy logic it seems clear that one needs more flexibility in the choice of the conjunction: in particular, the associativity and the commutativity of a conjunction may be removed. Motivated by these considerations, we present several classes of conjunctors, i.e. binary operations on [0, 1] that are used to extend the boolean conjunction from {0, 1} to [0, 1], and characterize their respective residual implicators. We establish hence a one-to-one correspondence between construction methods for conjunctors and construction methods for residual implicators. Moreover, we introduce some construction methods directly in the class of residual implicators, and, by using a deresiduation procedure, we obtain new conjunctors. The third author was supported by the grant VEGA 1/3006/06 and MSM 619 8898 701. The fourth author gratefully acknowledges the support of the project “Metodi Stocastici in Finanza Matematica” of the Italian M.I.U.R.     

A tour construction heuristic for the travelling salesman problem

The tour construction heuristic that generates initial tours for the tour improvement heuristics plays an important role in solving the travelling salesman problem (TSP). With the help of an effective tour construction heuristic, the performance of a heuristic can be improved. In this study we present a new tour construction algorithm, the construction priority (CP). We incorporate the performance of the CP into metaheuristics such as tabu search, genetic algorithm, space smoothing, and noising methods. The performance of the CP is empirically compared with the nearest neighbour (NN) approach. Extensive computational comparison shows that the CP is considerably more effective compared to NN.     

A New Construction of Group Divisible Designs with Nonuniform Group Type

The construction of group divisible designs (GDDs) is a basic problem in design theory. While there have been some methods concerning the constructions of uniform GDDs, the construction of nonuniform GDDs remains a challenging problem. In this paper, we present a new approach to the construction of nonuniform GDDs with group type and block size k. We make a progress by proposing a new construction, in which generalized difference sets, a truncating technique, and a difference method are combined to construct nonuniform GDDs. Moreover, we present a variation of this new construction by employing Rees' product constructions. We obtain several infinite families of nonuniform GDDs, as well as many examples whose block sizes are relatively large.     

Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization

In this paper, we present several methods for the construction of elliptic curves with large torsion group and positive rank over number fields of small degree. We also discuss potential applications of such curves in the elliptic curve factorization method (ECM).