On 3-Steiner simplicial orderings

Let G be a connected graph and S a nonempty set of vertices of G. A Steiner tree for S is a connected subgraph of G containing S that has a minimum number of edges. The Steiner interval for S is the collection of all vertices in G that belong to some Steiner tree for S. Let k≥2 be an integer. A set X of vertices of G is k-Steiner convex if it contains the Steiner interval of every set of k vertices in X. A vertex x∈X is an extreme vertex of X if X?{x} is also k-Steiner convex. We call such vertices k-Steiner simplicial vertices. We characterize vertices that are 3-Steiner simplicial and give characterizations of two classes of graphs, namely the class of graphs for which every ordering produced by Lexicographic Breadth First Search is a 3-Steiner simplicial ordering and the class for which every ordering of every induced subgraph produced by Maximum Cardinality Search is a 3-Steiner simplicial ordering.     

InOOH压致氢键对称化及其弹性性质

利用第一性原理研究了InOOH在高压下的氢键对称化行为及其对InOOH弹性等性质的影响.结果表明约在18 GPa时InOOH中的氢键发生了对称化转变,导致轴比率b/c对压力的斜率由负值变为正值;压缩弹性常数、非对角弹性常数、体积模量和纵波波速出现异常增加,如体积模量增加了20%—40%.高压下InOOH弹性性质呈现出更加明显的各向异性.常压下InOOH呈现韧性,且伴随着氢键对称化韧性异常增加.对畸变金红石型MOOH(M=Al,In,Ga,Fe,Cr)化合物在高压下的弹性性质转变与氢键性质转变的耦合规律进行了初探.     

Simple Signed Steiner Triple Systems

Let X be a v‐set, be a set of 3‐subsets (triples) of X, and be a partition of with . The pair is called a simple signed Steiner triple system, denoted by ST, if the number of occurrences of every 2‐subset of X in triples is one more than the number of occurrences in triples . In this paper, we prove that exists if and only if , , and , where and for , . © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 332–343, 2012     

4‐*GDD(6n)s and Related Optimal Quaternary Constant‐Weight Codes

Constant‐weight codes (CWCs) have played an important role in coding theory. To construct CWCs, a K‐GDD (where GDD is group divisible design) with the “star” property, denoted by K‐*GDD, was introduced, in which any two intersecting blocks intersect in at most two common groups. In this paper, we consider the existence of 4‐*GDDs. Previously, the necessary conditions for existence were shown to be sufficient for , and also sufficient for with prime powers and . We continue to investigate the existence of 4‐*GDD(6ⁿ)s and show that the necessary condition for the existence of a 4‐*GDD(6ⁿ), namely, , is also sufficient. The known results on the existence of optimal quaternary (n, 5, 4) CWCs are also extended.     

Polynomial Time Approximation Scheme for Symmetric Rectilinear Steiner Arborescence Problem

The Symmetric Rectilinear Steiner Arborescence (SRStA) problem is defined as follows: given a set of terminals in the positive quadrant of the plane, connect them using horizontal and vertical lines such that each terminal can be reached from the origin via a y-monotone path and the total length of all the line segments is the minimum possible. Finding an SRStA has applications in VLSI design, in data structures used in some optimization algorithms and in dynamic server problems. In this paper, we provide a polynomial time approximation scheme for the SRStA problem, improving the previous best approximation ratio of 3 for this problem.     

Generalized Steiner systems GS4 (2, 4, v,g) for g = 2, 3, 6

Generalized Steiner systems GS_d(t, k, v, g) were first introduced by Etzion and used to construct optimal constant‐weight codes over an alphabet of size g + 1 with minimum Hamming distance d, in which each codeword has length v and weight k. Much work has been done for the existence of generalized Steiner triple systems GS(2, 3, v, g). However, for block size four there is not much known on GS_d(2, 4, v, g). In this paper, the necessary conditions for the existence of a GS_d(t, k, v, g) are given, which answers an open problem of Etzion. Some singular indirect product constructions for GS_d(2, k, v, g) are also presented. By using both recursive and direct constructions, it is proved that the necessary conditions for the existence of a GS₄(2, 4, v, g) are also sufficient for g = 2, 3, 6. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 401–423, 2001     

The Euclidean Steiner tree problem in Rn: A mathematical programming formulation

A nonconvex mixed-integer programming formulation for the Euclidean Steiner Tree Problem (ESTP) in Rⁿ is presented. After obtaining separability between integer and continuous variables in the objective function, a Lagrange dual program is proposed. To solve this dual problem (and obtaining a lower bound for ESTP) we use subgradient techniques. In order to evaluate a subgradient at each iteration we have to solve three optimization problems, two in polynomial time, and one is a special convex nondifferentiable programming problem. This revised version was published online in June 2006 with corrections to the Cover Date.     

Invariant Measures and Symmetry Property of Lévy Type Operators

Second order elliptic integro-differential operators (Lévy type operators) are investigated. The notion of regular (infinitesimal) invariant probability measures for such operators is posed. Sufficient conditions for the existence of such regular infinitesimal invariant probability measures are obtained and the symmetrization problem is discussed.     

关于Steiner比猜想

本文所讨论的是Ｓｔｅｉｎｅｒ比猜想。全文共分两部分：第一部分包括历史回顾和对ｎ＝３,４,５三种情况对该猜想的正确性给出了简单的证明;第二部分则对于一般的ｎ给出了一个证明。     

Simplified Scheme for Testing Symmetrization Postulate for Photons

We propose a scheme for testing the small violations of the symmetrization postulate （SP） for photons in cavity QED. In the scheme, a degenerate A-type three-level atom is sent through a cavity field initially in a q-deformed coherent state. After an appropriate interaction time, the atom is measured by a state-selective detector. The probability that the atom makes a transition from one of the lower states to the other characterizes the violation of the SP. In the scheme, only one atom is required and classical fields are unnecessary, which is prior to the previous schemes.