Norms on unitizations of banach algebras revisited

Let A be an algebra without unit. If ∥ ∥ is a complete regular norm on A it is known that among the regular extensions of ∥ ∥ to the unitization of A there exists a minimal (operator extension) and maximal (ℓ₁-extension) which are known to be equivalent. We shall show that the best upper bound for the ratio of these two extensions is exactly 3. This improves the results represented by A. K. Gaur and Z. V. Kovářík and later by T. W. Palmer. The second author was partially supported by the grant No. 201/03/0041 of GAČR.     

一类二阶三点边值问题单调正解的存在性

利用范数形式的锥上不动点定理,研究了一类二阶微分方程三点边值问题单调正解的存在性．分别给出了齐次和非齐次边界条件下的三点边值问题单调正解存在的充分条件,确定了解曲线的凹凸性,并且给出了一个应用实例．     

Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.      

ON THE GENERALIZATIONS OF KALANDIA＇S LEMMA

Based on Bernstein＇s Theorem, Kalandia＇s Lemma describes the error estimate and the smoothness of the remainder under the second part of Hoelder norm when a HSlder function is approximated by its best polynomial approximation. In this paper, Kalandia＇s Lemma is generalized to the cases that the best polynomial is replaced by one of its four kinds of Chebyshev polynomial expansions, the error estimates of the remainder are given out under Hoeder norm or the weighted HSlder norms.     

代数体函数的定理

本文定义并研究了代数体函数的加法．结合杨乐的方法,将仪洪勋联系重值的亚纯函数唯一性定理推广到多值的代数体函数．     

QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS

This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.     

运输网络中最小饱和流的求解

运输网络中常常由于流量的不可控易发生堵塞现象.网络发生堵塞时的饱和流值达不到最大流值.最小饱和流是运输网络,尤其是紧急疏散网络设计中很重要的一个参数.通过建立网络的割集矩阵来确定网络的堵塞截面,基于此提出了求解最小饱和流的线性规划模型及算法.举例分析表明,利用该算法计算网络最小饱和流更加简便、更加实用.     

Functional Limit Theorems for Multiparameter Fractional Brownian Motion

We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional Lévy’s modulus of continuity and many other results are its particular cases. Applications to approximation theory are discussed.      

Long-term optimal operation of series parallel reservoirs for critical period with specified monthly generation and average monthly storage

We present in this paper an efficient approach for solving the problem of planning the long-term (multiyear) operation of a multireservoir hydroelectric power system for the critical period with a monthly variable load. This load is equal to a certain percentage of the total generation at the end of the year, subject to satisfying a number of constraints on the hydrosystem, using the minimum norm formulation.The proposed method is efficient in computing time and in calculating the total expected benefits from the system during the critical period. Numerical results are reported for a real system in operation consisting of two rivers. Each river has two series reservoirs.This work was supported by the Natural Science and Engineering Research Council of Canada, Grant No. A4146.