模糊全半序结构

以Fodor公理为基础，给出一类重要的模糊偏好结构——模糊全半序结构的一个较为一般的定义，同时对其性质进行讨论。     

Cutting a Convex Polyhedron Out of a Sphere

Given a convex polyhedron P of n vertices inside a sphere Q, we give an O(n ³)-time algorithm that cuts P out of Q by using guillotine cuts and has cutting cost O(log² n) times the optimal.     

Infinite Faces of a Perfect Voronoi Polyhedron

Infinite faces of perfect Voronoi polyhedra are studied. The result substantially varies depending on whether the perfect Voronoi polyhedron is considered as the closed or nonclosed convex hull of the set of Voronoi points (see Theorem 1 in Sec. 5 and Theorem 2 in Sec. 7).     

Octahedral Projections of a Point onto a Polyhedron

In computational methods and mathematical modeling, it is often required to find vectors of a linear manifold or a polyhedron that are closest to a given point. The “closeness” can be understood in different ways. In particular, the distances generated by octahedral, Euclidean, and Hölder norms can be used. In these norms, weight coefficients can also be introduced and varied. This paper presents the results on the properties of a set of octahedral projections of the origin of coordinates onto a polyhedron. In particular, it is established that any Euclidean and Hölder projection can be obtained as an octahedral projection due to the choice of weights in the octahedral norm. It is proven that the set of octahedral projections of the origin of coordinates onto a polyhedron coincides with the set of Pareto-optimal solutions of the multicriterion problem of minimizing the absolute values of all components.     

一类解析多面体的奇异积分

本文利用Ｒ．Ｈａｒｖｅｙ和Ｊ．Ｐｏｒｋｉｎｇ的方法首先定义广义式的Ｃａｕｃｈｙ主值，利用同伦公式，借助积分变换技巧研究Ｗｅｉｌ型积分的边界性质，得到Ｐｌｅｍｅｌｊ公式．它有别于通常研究边界性质的方法．本文引入细复广义权和Ｃｈｏｑｕｅｔ型复广义权的概念，讨论了某些与复广义权相关的函数的拟连续性与细拟处处连续的关系．     

Generating All Vertices of a Polyhedron Is Hard

We show that generating all negative cycles of a weighted graph is a hard enumeration problem, in both the directed and undirected cases. More precisely, given a family of negative (directed) cycles, it is an NP-complete problem to decide whether this family can be extended or there are no other negative (directed) cycles in the graph, implying that (directed) negative cycles cannot be generated in polynomial output time, unless P=NP. As a corollary, we solve in the negative two well-known generating problems from linear programming: (i) Given an infeasible system of linear inequalities, generating all minimal infeasible subsystems is hard. Yet, for generating maximal feasible subsystems the complexity remains open. (ii) Given a feasible system of linear inequalities, generating all vertices of the corresponding polyhedron is hard. Yet, in the case of bounded polyhedra the complexity remains open. Equiva lently, the complexity of generating vertices and extreme rays of polyhedra remains open.     

多类型粒子模型的图表示

本文利用图表示法构造出一类具有有限程的变相速率和不同扩散速率的同类型粒子模型,刻划出了该粒子模型的演化规律。     

模糊选择函数半序合理的充分条件

在G?del t-模下,研究了模糊选择函数的半序合理性.首先给出了模糊选择函数的合理性条件FA1.然后研究了该条件与模糊选择函数半序合理性之间的关系,得到了半序合理的一个充分条件.     

Finding the Best Face on a Voronoi Polyhedron – The Strong Dodecahedral Conjecture Revisited

In this paper we prove the following theorem. The surface area density of a unit ball in any face cone of a Voronoi cell in an arbitrary packing of unit balls of Euclidean 3-space is at most [(-9p+ 30 arccos([(?3)/2]sin ([(p)/5]) ))/(5 tan([(p)/5]))]=0.77836?,{-9\pi + 30\,{\rm arccos}\left({\sqrt{3}\over 2}{\rm sin}\,\left({\pi\over 5}\right) \right)\over 5\, {\rm tan}\left({\pi\over 5}\right)}=0.77836\ldots, and so the surface area of any Voronoi cell in a packing with unit balls in Euclidean 3-space is at least [(20p· tan ( [(p)/5]))/(-9p+ 30 arccos([(?3)/2]sin ([(p)/5]) ))]=16.1445? .{20\pi\cdot\,{\rm tan}\,\left( {\pi \over 5}\right) \over -9\pi + 30\,{\rm arccos}\left({\sqrt{3}\over 2}{\rm sin}\,\left({\pi\over 5}\right) \right)}=16.1445\ldots\ . This result and the ideas of its proof support the Strong Dodecahedral Conjecture according to which the surface area of any Voronoi cell in a packing with unit balls in Euclidean 3-space is at least as large as 16.6508..., the surface area of a regular dodecahedron of inradius 1.     

行列式的几何意义及多面体体积的计算

通过引入体积坐标证明了行列式和多面体体积的关系,使得每一个行列式都有了它的几何解释,有助于形象地理解行列式的概念,并利用行列式的几何意义计算空间多面体的体积.     

Irreducible System of Constraints for a General Polyhedron of Arrangements

We construct a system of constraints for a general polyhedron of arrangements that does not contain superfluous inequalities. The derivation of an irreducible system enables one to substantially reduce the number of operations necessary for finding exact solutions of optimization problems on arrangements.     

The Combinatorics of a Class of Representation Functions

In the study of the irreducible representations of the unitary groupU(n), one encounters a class of polynomials defined onn²indeterminatesz_ij, 1i, jn, which may be arranged into ann×nmatrix arrayZ=(z_ij). These polynomials are indexed by double Gelfand patterns, or equivalently, by pairs of column strict Young tableaux of the same shape. Using the double labeling property, one may define a square matrixD(Z), whose elements are the double-indexed polynomials. These matrices possess the remarkable “group multiplication property”D(XY)=D(X) D(Y) for arbitrary matricesXandY, even though these matrices may be singular. ForZ=UU(n), these matrices give irreducible unitary representations ofU(n). These results are known, but not always fully proved from the extensive physics literature on representation of the unitary groups, where they are often formulated in terms of the boson calculus, and the multiplication property is unrecognized. The generality of the multiplication property is the key to understanding group representation theory from the purview of combinatorics. The combinatorial structure of the general polynomials is expected to be intricate, and in this paper, we take the first step to explore the combinatorial aspects of a special class which can be defined in terms of the set of integral matrices with given row and column sums. These special polynomials are denoted byL_{α, β}(Z), whereαandβare integral vectors representing the row sums and column sums of a class of integral matrices. We present a combinatorial interpretation of the multiplicative properties of these polynomials. We also point out the connections with MacMahon's Master Theorem and Schwinger's inner product formula, which is essentially equivalent to MacMahon's Master Theorem. Finally, we give a formula for the double Pfaffian, which is crucial in the studies of the generating function of the 3n−jcoefficients in angular momentum theory. We also review the background of the general polynomials and give some of their properties.     

任意凸多面体上布点均匀性的度量

均匀性度量是构作均匀设计的基础,本文从距离概念出发,通过对称的方法,得到一种新的距离函数-势函数,并将势函数作为衡量任意凸多面体上布点均匀性好坏的准则.数值例子和多变量Kendall 协和系数检验表明,当试验区域限制在单位立方体上时,势函数与目前常用的两种偏差-中心化L_2-偏差和可卷L_2.偏差在度量布点均匀性方面结论一致.     

The Representation of Some Integers as a Subset Sum

Let A N. The cardinality (the sum of the elements) of A willbe denoted by |A| ((A)). Let m N and p be a prime. Let A {1, 2,...,p}. We prove thefollowing results. If |A| [(p+m–2)/m]+m, then for every integer x such that0 x p – 1, there is B A such that |B| = m and (B) x mod p. Moreover, the bound is attained. If |A| [(p+m–2)/m]+m!, then there is B A such that |B| 0 mod m and (B) = (m – 1)!p. If |A| [(p + 1)/3]+29, then for every even integer x such that4p s x p(p + 170)/48, there is S A such that x = (S). In particular,for every even integer a 2 such that p 192a – 170, thereare an integer j 0 and S A such that (S) = a^j+1.     

A Tight Bound for the Delaunay Triangulation of Points on a Polyhedron

We show that the Delaunay triangulation of a set of n points distributed nearly uniformly on a p-dimensional polyhedron (not necessarily convex) in d-dimensional Euclidean space is $O(n^{\frac{d-k+1}{p}})$ , where $k = \lceil\frac{d+1}{p+1} \rceil$ . This bound is tight in the worst case and improves on the prior upper bound for most values of?p.     

Polyhedron Theorems for Non-Smooth Cell Complexes

Results like EULER'S polyhedron theorem or relations for the EULER characteristic are extended to signed curvature measures of p-dimensional topological polyhedra in R^d. The cells are assumed to be finite unions of compact manifolds with boundary and positive reach. By means of generalized unit normal bundles and generalized principal curvatures provided with a certain set additive index function the global problems can be reduced to local variants.     

一类效应代数的态表示定理

1994年, Foulis和Bennett在表示不可精确测量的量子逻辑结构时引入了效应代数. 该文用直接构造的方法, 给出一类效应代数上的态表示定理. 即, 若Ω是紧的 Hausdorff 拓扑空间, 令E(Ω)={f: f∈C(Ω), 0≤f≤1}, 则φ 是(E(Ω),Ο, 0, 1) 上的态当且仅当Ω 上存在唯一的正则Borel 概率测度μ使得对每个f (E(Ω),Ο, 0, 1),φ (f)=∫_Ω f dμ.