An asymptotically optimal lower bound on the OBDD size of the middle bit of multiplication for the pairwise ascending variable order

We prove that each OBDD (ordered binary decision diagram) for the middle bit of n-bit integer multiplication for one of the variable orders which so far achieve the smallest OBDD sizes with respect to asymptotic order of growth, namely the pairwise ascending order x₀,y₀,…,x_n−1,y_n−1, requires a size of Ω(2^(6/5)n). This is asymptotically optimal due to a bound of the same order by Amano and Maruoka (2007) [1].     

Multiplication operator on the weighted Bergman space of the unit ball北大核心CSCD

Multiplication operator is an important class of operators in function space. We mainly research the properties of the multiplication operator on the weighted Bergman space of the unit ball. ©, 2015, Chinese Academy of Sciences. All right reserved.     

Multiplication Modules in Which Every Prime Submodule is Contained in a Unique Maximal Submodule

Abstract

Let R be a commutative ring. An R-module M is called a multiplication module if for each submodule N of M, N?=?IM for some ideal I of R. An R-module M is called a pm-module, i.e., M is pm, if every prime submodule of M is contained in a unique maximal submodule of M. In this paper the following results are obtained. (1) If R is pm, then any multiplication R-module M is pm. (2) If M is finitely generated, then M is a multiplication module if and only if Spec(M) is a spectral space if and only if Spec(M)?=?{PM?|?P?∈?Spec(R) and P???M ^⊥}. (3) If M is a finitely generated multiplication R-module, then: (i) M is pm if and only if Max(M) is a retract of Spec(M) if and only if Spec(M) is normal if and only if M is a weakly Gelfand module; (ii) M is a Gelfand module if and only if Mod(M) is normal. (4) If M is a multiplication R-module, then Spec(M) is normal if and only if Mod(M) is weakly normal.     

Generalized Weighted Composition Operators on Weighted Bergman Spaces

The boundedness and compactness of the generalized weighted composition operator on weighted Bergman spaces are discussed.     

A chaos secure communication scheme based on multiplication modulation

A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.     

L-模糊自然数的乘法运算和幂运算

在L是完全分配格时,定义了L-模糊自然数的乘法运算和幂运算,研究了乘法运算、幂运算的交换律、结合律以及乘法对加法的分配律等性质。     

乘法运算和虚数单位的几何定义

对于自然数,乘法是加法一种简明的表达式;但由自然数系扩展为整数系时,乘法却需要补充的几何定义,以加深对运算律的理解。为此,任何有向线段a与(-1)的乘积定义为有向线段a绕其起点逆时针旋转π角所生成的有向线段;任何有向线段a与j的乘积定义为有向线段a绕其起点逆时针旋转π/2角所生成的有向线段,由此可推导出j即是虚数单位,j=i=(-1)～(1/2)。eiθ既是单位向量,又是平面向量的乘法旋转算子。文中还阐明了复数的指数形式为平面向量的最佳表达式,以及平面向量三种乘法的对应关系。     

Sobolev Spaces with Respect to Measures in Curves and Zeros of Sobolev Orthogonal Polynomials

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the uniform bound of the zeros of the corresponding Sobolev orthogonal polynomials, and this fact allows to obtain the asymptotic behavior of Sobolev orthogonal polynomials. We also obtain some non-trivial results about these Sobolev spaces with respect to measures; in particular, we prove a main result in the theory: they are Banach spaces. J.M. Rodriguez supported in part by three grants from M.E.C. (MTM 2006-13000-C03-02, MTM 2006-11976 and MTM 2007-30904-E), Spain, and by a grant from U.C.III M./C.A.M. (CCG07-UC3M/ESP-3339), Spain. J.M. Sigarreta supported in part by a grant from M.E.C. (MTM 2006-13000-C03-02), Spain, and by a grant from U.C.III M./C.A.M. (CCG07-UC3M/ESP-3339), Spain.     

新颖的S波段宽带八倍频链

本文介绍使用双平衡混频器设计制作Ｓ波段宽带八倍频链带宽大于１３％，谐波抑制大于４５ｄＢ、输出波动小于１ｄＢ的良好性能。