Smoothing minimally supported frequency wavelets: Part II

The main purpose of this paper is to give a procedure to “mollify” the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA. Hence, we are able to approximate (in the L ² -norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Although the MSF wavelets we consider are bandlimited, this may not be true for their smooth approximations. This phenomena is related to the invariant cycles under the transformation x ↦2x (mod2π). We also give a characterization of all low-pass filters for MSF wavelets. Throughout the paper new and interesting examples of wavelets are described.     

Order splitting in single sourcing with scheduled-release orders

Traditional inventory models assume that a buyer places one order with a supplier in each order cycle. A large number of researchers have studied the benefits of dual sourcing such that an order quantity is split and placed simultaneously with two suppliers. We show that many of the benefits of dual sourcing are due to order splitting rather than using two suppliers. We investigate order splitting with one supplier such that the first part of the order is sent out immediately but the second part of the order is released later (scheduled-release). Through extensive computational results, we show that in many situations where dual sourcing or the use of a cheaper supplier would be cost effective, single sourcing with order splitting using scheduled-release orders is better. The paper provides a quantitative rationale to continue with one supplier. We also summarize the qualitative reasons to prefer single sourcing or multiple sourcing.     

Flat rank of automorphism groups of buildings

The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural distance on the space of compact open subgroups of G. For a topological Kac-Moody group G with Weyl group W, we derive the inequalities alg-rk(W) ≤ flat-rk(G) ≤ rk(|W|₀). Here, alg-rk(W) is the maximal Z-rank of abelian subgroups of W, and rk(|W|₀) is the maximal dimension of isometrically embedded flats in the CAT0-realization |W|₀. We can prove these inequalities under weaker assumptions. We also show that for any integer n ≥ 1 there is a simple, compactly generated, locally compact, totally disconnected group G, with flat-rk(G) = n and which is not linear.     

Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach

The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique. This work was supported by the National Natural Science Fund of China (No. 10371096) for ZM Gao and YC Ma.     

Study on a Cross Diffusion Parabolic System

This paper considers a kind of strongly coupled cross diffusion parabolic system,which can be usedas the multi-dimensional Lyumkis energy transport model in semiconductor science.The global existence andlarge time behavior are obtained for smooth solution to the initial boundary value problem.When the initialdata are a small perturbation of an isothermal stationary solution,the smooth solution of the problem under theinsulating boundary condition,converges to that stationary solution exponentially fast as time goes to infinity.     

光致变色多阶游程光存储研究

多阶游程存储是一种不改变光学系统而显著提高光存储容量和数据传输率的新方法.介绍了光致变色多阶游程存储原理和实验系统.提出了基于光致变色原理的多阶游程存储数学模型，该模型反映了记录符反射率与曝光功率、曝光时间之间的非线性关系，并在此基础上确定了光致变色多阶游程存储的写策略.基于650nm光致变色材料进行了4阶游程存储的动态实验.结果表明，实验中采用的650nm光致变色材料可用于多阶游程存储，采用的写策略能够有效地使记录信道线性化，利于采用适合线性系统的信号处理方法. 关键词： 多阶游程 光致变色 光存储 写策略     

Some Properties of an Operator on L^∞（△） and Its Applications

In this paper, we introduce an operator Hμ（z） on L^∞（△） and obtain some of its properties. Some applications of this operator to the extremal problem of quasiconformal mappings are given. In particular, a sufficient condition for a point r in the universal Teichmfiller space T（△） to be a Strebel point is obtained.     

The characteristic of noncompact convexity and random fixed point theorem for set-valued operators

Let (Ω, Σ) be a measurable space, X a Banach space whose characteristic of noncompact convexity is less than 1, C a bounded closed convex subset of X, KC(C) the family of all compact convex subsets of C. We prove that a set-valued nonexpansive mapping T: C → KC(C) has a fixed point. Furthermore, if X is separable then we also prove that a set-valued nonexpansive operator T: Ω × C → KC(C) has a random fixed point.     

EXISTENCE OF GLOBAL SMOOTH SOLUTION FOR SCALAR CONSERVATION LAWS WITH DEGENERATE VISCOSITY IN 2-DIMENSIONAL SPACE

This article concerns the existence of global smooth solution for scalar conservation laws with degenerate viscosity in 2-dimensional space. The analysis is based on successive approximation and maximum principle.     

On the equitability of multiply-connected monolayered cyclofusene

Multiply-connected monolayered cyclofusene (MMC) is a fused hexacyclic system with an exterior region and at least two interior empty regions called holes, as in figure 1. Each hexacyle has either: (a) two edges belonging to an exterior boundary and at least one hole, or (b) two edges belonging to boundaries of at least two holes. Let G be the graph of a given MMC. We show that G is equitable if and only if the set of vertices belonging to three hexacycles is equitable.