The vibration and stability of non-homogeneous orthotropic conical shells with clamped edges subjected to uniform external pressures

In this paper an analytical procedure is given to study the free vibration and stability characteristics of homogeneous and non-homogeneous orthotropic truncated and complete conical shells with clamped edges under uniform external pressures. The non-homogeneous orthotropic material properties of conical shells vary continuously in the thickness direction. The governing equations according to the Donnell’s theory are solved by Galerkin’s method and critical hydrostatic and lateral pressures and fundamental natural frequencies have been found analytically. The appropriate formulas for homogeneous orthotropic and isotropic conical shells and for cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Several examples are presented to show the accuracy and efficiency of the formulation. The closed-form solutions are verified by accurate different solutions. Finally, the influences of the non-homogeneity, orthotropy and the variations of conical shells characteristics on the critical lateral and hydrostatic pressures and natural frequencies are investigated, when Young’s moduli and density vary together and separately. The results obtained for homogeneous cases are compared with their counterparts in the literature.     

秩函数在研究独立空间拥有一对互斥基的特征上之作用

利用秩函数,本文给出如何判定一个独立空间拥有一对互斥基的一些充要条件.其目的是回答这样一个公开问题:在什么条件下,一个独立空间可以拥有一对互斥基.该问题是Welsh于1976年提出的.     

Latin squares with disjoint subsquares of two orders

Let and . The integer partition of n is said to be realized if there is a latin square of order n with pairwise disjoint subsquares of order for each . In this paper, we construct latin squares realizing partitions of the form ; that is, partitions with s parts of size a and t parts of size b, where . Heinrich (1982) showed that (1) if and , then there is a latin square realizing , (2) is realized if and only if , and (3) is realized if and only if . In this paper, we resolve the open cases. We show that is realized if and only if and is realized if and only if .     

A symmetrical linear maxmin approach to disjoint bilinear programming

Received June 24, 1996 / Revised version received May 22, 1997 Published online February 25, 1999     

Small degree out‐branchings

Using a suitable orientation, we give a short proof of a strengthening of a result of Czumaj and Strothmann 4 : Every 2‐edge‐connected graph G contains a spanning tree T with the property that for every vertex v. As an analogue of this result in the directed case, we prove that every 2‐arc‐strong digraph D has an out‐branching B such that . A corollary of this is that every k‐arc‐strong digraph D has an out‐branching B such that , where . We conjecture that in this case would be the right (and best possible) answer. If true, this would again imply a strengthening of a result from 4 concerning spanning trees with small degrees in k‐connected graphs when k ≥ 2. We prove that for acyclic digraphs the existence of an out‐branching satisfying prescribed bounds on the out‐degrees of each vertex can be checked in polynomial time. A corollary of this is that the existence of arc‐disjoint branchings , , where the first is an out‐branching rooted at s and the second an in‐branching rooted at t, can be checked in polynomial time for the class of acyclic digraphs © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 297–307, 2003     

Heegaaed分解有不交曲线性质的一个充分条件

In the paper,we give two conditions that the Heegaard splitting admits the disjoint cnrve property.The main result is that for a genus g(g≥2)strongly irreducible Heegaard splitting(C1,C2;F),let Di be an essential disk in Ci,i=1,2,satisfying(1)at least one of (の)D4 and (の)D2 is separating in F and |(の)D1 (∩)(の)D2|≤ 2g-1;or(2)both (の)D1 and (の)D2 are non-separating in F and |(の)D1 (∩)(の)D2|≤ 2g-2,then(C1,C2;F)has the disjoint curve property.     

The Existence of (v,4,1) Disjoint Difference Families with a Prime Power

A(υ,κ,λ,)difference family((υ,κ,λ,)-DF in short)over an abelian group G of order v,is a collection F = {B_i|i∈I}ofκ-subsets of G,called base blocks,such that any nonzero element of G can be represented in preciselyλways as a difference of two elements lying in some base blocks in F.A(υ,κ,λ,)-DDF is a difference family with disjoint blocks.In this paper,by using Weil's theorem on character sum estimates,it is proved that there exists a(p~n,4,1)-DDF,where p≡1(rood 12)is a prime number and n≥1.     

Bosonization theory for tunneling spectra in smooth edges of quantum Hall systems

We calculate the spectral function of a smooth edge of a quantum Hall system in the lowest Landau level by means of a bosonization technique. We obtain a general relationship between the one electron spectral function and the dynamical structure factor. The resulting – characteristics exhibit, at low voltage and temperature, power law scaling, generally different from the one predicted by the chiral Luttinger liquid theory, and in good agreement with recent experimental results.     

Concavity cuts for disjoint bilinear programming

We pursue the study of concavity cuts for the disjoint bilinear programming problem. This optimization problem has two equivalent symmetric linear maxmin reformulations, leading to two sets of concavity cuts. We first examine the depth of these cuts by considering the assumptions on the boundedness of the feasible regions of both maxmin and bilinear formulations. We next propose a branch and bound algorithm which make use of concavity cuts. We also present a procedure that eliminates degenerate solutions. Extensive computational experiences are reported. Sparse problems with up to 500 variables in each disjoint sets and 100 constraints, and dense problems with up to 60 variables again in each sets and 60 constraints are solved in reasonable computing times. Received: October 1999 / Accepted: January 2001?Published online March 22, 2001     

Hopping conductivity and activated transport in InxGa1-xAs quantum wells

We present measurements of the diagonal R_xx and off-diagonal R_xy magnetoresistance under quantum Hall conditions on several high electron mobility transistors (HEMT) based on In_xGa_1-xAs quantum wells. From the magnetoresistance tensor we obtain the longitudinal conductivity σ _xx . We study the transport mechanisms near the σ _xx minima at temperatures ranging between 2 K and 35 K; activated transport is the dominant mechanism for temperatures above 7 K while variable range hopping conductivity is significant for lower temperatures. We show that electron-electron correlations should be taken into account to explain the conductivity vs temperature behaviour below 5 K. Finally, we study the behaviour of the localization length as a function of Landau level filling and obtain a critical exponent γ = 3.45±0.15. Received 6 June 2001 and Received in final form 16 October 2001