基于xL（a）n－1（x）之零点的（0，1，…，m－2，m）插值

本文给出了基于xL^（a）_n－1（x）之零点的（０，１，…，ｍ－２，ｍ）插值的正则性的充要条件，其中xL^（a）_n－1（x）为（ｎ－１）次Ｌａｇｕｅｒｒｅ多项式。同时基函数（若存在的话）的明显表达式也在文中给出。再者，还证明了，若该插值问题有无穷多个解，则其解的一般形式为ｆ₀（ｘ）＋Ｃｆ₁（ｘ）这里Ｃ为任意常数。     

半值环的两个交换结果

定理１设Ｒ是半值环，ｎ为固定的正整数，如果Ｒ满足条件：存在依赖于(?)_ｘ，ｙ的两个字ｋ（Ｘ，Ｙ），ｔ（Ｘ，Ｙ），其中｜ｋ｜_X＞１，｜ｔ｜_X＝１，｜ｋ｜_Y≥｜ｔ｜_Y，｜ｔ｜_Y≤ｎ，使ｋ（ｘ，ｙ）－ｔ（ｘ，ｙ）∈Ｉ（Ｒ），则Ｒ是交换环。定理２设Ｒ是半值环，如果Ｒ满足条件：存在正整数ｍ＝ｍ（ｘ，ｙ）＞１，ｎ＝ｎ（ｙ），使得（ｘ^ｎｙ）^m－ｘ     

关于Bernstein的一个插值多项式

本文证得(?)｜Ｐ_ｎ（ｆ，ｘ）｜＝＋∞，因此Ｐ_ｎ（ｆ，ｘ）不能对一切ｆ（ｘ）Ｃ_{［－１，１］}在［－１，１］上一致收敛于ｆ（ｘ）     

关于一类修正的三角插值多项式

本文构造出一个以｛θ_ｋ＝ｋ/(ｎ＋１)π｝^ｎ_ｋ＝１为插值节点的ｆ（θ）∈Ｃ_２π且为奇函数的修正的三角插值多项式Ｗ_n（ｆ;ｒ,θ）（ｒ为自然数）．Ｗ_n（ｆ;ｒ,θ）对每个以２π为周期的奇连续函数都能在全实轴上一致地收敛到ｆ（θ）;若ｆ（θ）∈Ｃ^ｊ_２π（０≤ｊ≤ｒ－１）且是奇的,Ｗ_n（ｆ;ｒ,θ）对其收敛阶均达到最     

φ－满射环上GLｎ（R）中元素的三角分解

本文结果是：设Ａ是φ－满射环Ｒ上的非拟纯量可逆ｎ×ｎ矩阵，β_j，γ_j（1≤ｊ≤ｎ）是Ｒ中任意元素，它们满足Π_j=1^{nβ_jγ_j＝ｄｅｔＡ，则存在ｎ阶阵Ｂ和Ｃ满足ＰＡＰ－１＝ＢＣ，其中Ｂ是下三角阵，Ｃ是上三角阵，Ｐ∈ＧＬ_ｎ（Ｒ）．进一步，可以取Ｂ使β_j（１≤ｊ≤ｎ）位于Ｂ的主对角线上，同时可以取Ｃ使γ_j（１≤ｊ≤ｎ）位于Ｃ的主对角线上．}     

单纯形上Bernstein多项式的一些性质

设Ｂ_m（ｆ，·）为函数ｆ在ｄ维单纯形σ上的ｎ阶Ｂｅｒｎｓｔｅｉｎ多项式，本文对ｆ∈Ｃ^ｒ（σ）及ｆ∈Ｃ^r+2（σ）给出了ｆ的各阶编导数用Ｂ_n（ｆ，·）相应偏导数逼近的误差估计．同时也考虑了整系数Ｂｅｒｎｓｔｅｉｎ多项式的Ｌ_p模估计     

Dirac定理的局部化与Hamilton图

设Ｇ为一个ｎ阶２－连通图，ｎ≥３．若｜Ｄ_ｎ／２（Ｋ_１，３）｜≥２且满足下述条件之一：ｉ）｜Ｄ_ｎ／２（Ｋ_１，３＋ｅ）｜≥２，ii）若Ｋ_１，３＋ｅ→Ｇ，ｘｙ(?)Ｅ（Ｋ_１，３＋ｅ），则ｍａｘ｛ｄＧ（ｘ），ｄＧ（ｙ）｝≥ｎ／２，则Ｇ是一个Ｈａｍｉｌｔｏｎｉａｎ图或其闭包为ｓＰ|⊕Ｈ，这里ｓＰ⊕Ｈ是一类极小２－边连通图．     

采用广义Curry线搜索的重新开始共轭梯度算法及其全局收敛性

本文对无约束最优化问题：ｍｉｎｆ（ｘ），ｘ∈Ｒ^ｎ，提出一种新的重新开始共轭梯度算法．该算法采用一类广义Ｃｕｒｒｙ线搜索原则，参数β_ｋ可在一个有限闭区间内选择，且允许β_ｋ取负值．在较弱的条件下证明了该算法的全局收敛性．     

关于多项式系数微分方程复振荡理论的两个结果

本文证明了：如果ａ_ｋ－ｊ（ｊ＝１，…，ｋ）为多项式，ｄｅｇａ_ｋ－ｊ＝ｎ_ｋ－ｊ，存在某个ａ_ｋ－s（１≤ｓ≤ｋ）满足：当１≤ｊ＜ｓ时，ｎ_ｋ－ｊ／ｊ≤ｎ_ｋ－s／ｓ；当ｓ＜ｊ≤ｋ时，ｎ_ｋ－ｊ＜ｎ_ｋ－s－（ｊ－ｓ）．如果Ｆ≠０是整函数且满足σ（Ｆ）＝β＜（ｎ_ｋ－s＋ｓ）／ｓ，那么微分方程ｆ^（ｋ）＋ａ     

关于G-Matlis自反模的换环定理

设Ｒ和Ｔ是Ｎｏｅｔｈｅｒ完备半局部环，Ｒ→Ｔ是环同态．本文证明了，若Ｔ是有限生成或ＡｒｔｉｎＲ－模，Ｍ为Ｇ－Ｍａｔｌｉｓ自反Ｒ－模，则对所有ｎ≥０，Ｅｘｔ^Ｒ_ｎ（Ｔ，Ｍ），Ｅｘｔ^Ｒ_ｎ（Ｍ，Ｔ），Ｔｏｒ^Ｒ_ｎ（Ｔ，Ｍ）以及Ｔｏｒ^Ｒ_ｎ（Ｍ，Ｔ）均是Ｇ－Ｍａｔｌｉｓ自反Ｔ－模．所得结果推广了Ｒ．Ｂｅｌｓｈｏｆ的结果．     

Analysis of the M X /G/1 Queue Under D-Policy

Abstract

We study the queue length of the M ^X /G/1 queue under D-policy. We derive the queue length PGF at an arbitrary point of time. Then, we derive the mean queue length. As special cases, M/G/1, M ^X /M/1, and M/M/1 queue under D-policy are investigated. Finally, the effects of employing D-policy are discussed.     

The smallness problem for -algebras

Akemann showed that any von Neumann algebra with a weak^* separable dual space has a faithful normal representation on a separable Hilbert space. He posed the question: If a C^*-algebra has a weak^* separable state space, must it have a faithful representation on a separable Hilbert space? Wright solved this question negatively and showed that a unital C^*-algebra has the weak^* separable state space if and only if it has a unital completely positive map, into a type I factor on a separable Hilbert space, whose restriction to the self-adjoint part induces an order isomorphism. He called such a C^*-algebra almost separably representable. We say that a unital C^*-algebra is small if it has a unital complete isometry into a type I factor on a separable Hilbert space. In this paper we show that a unital C^*-algebra is small if and only if the state spaces of all n by n matrix algebras over the C^*-algebra are weak^*-separable. It is natural to ask whether almost separably representable algebras are small or not. We settle this question positively for simple C^*-algebras but the general question remains open.     

F*-Rings Are O*

O ^*-rings were introduced by Fuchs and recently characterized by Steinberg. A ring R is called O ^* if every partial order on R extends to a total order. We weaken the condition on the ordering of the ring by requiring that every partial order on R extends to an f-order. We call those rings F ^*-rings. We show that the two classes of rings coincide.     

Real <Emphasis Type="Italic">AW</Emphasis><Superscript>*</Superscript>-Algebras of type I

Let R be a real AW ^*-algebra, and suppose that its complexification M = R + iR is also a (complex) AW ^*-algebra. We prove that R is of type I if and only if so is M.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 79–81, 2004Original Russian Text Copyright © by Sh. A. Ayupov     

Largeness of the set of finite products in a semigroup

We investigate when the set of finite products of distinct terms of a sequence 〈x _n 〉 _n=1^∞ in a semigroup (S,⋅) is large in any of several standard notions of largeness. These include piecewise syndetic, central, syndetic, central*, and IP*. In the case of a “nice” sequence in (S,⋅)=(ℕ,+) one has that FS(〈x _n 〉 _n=1^∞) has any or all of the first three properties if and only if {x _n+1−∑ _t=1 ⁿ x _t :n∈ℕ} is bounded from above. N. Hindman acknowledges support received from the National Science Foundation via Grant DMS-0554803.     

Extended Best Polynomial Approximation Operator in Orlicz Spaces

In this article we consider the best polynomial approximation operator, defined in an Orlicz space L ^Φ(B), and its extension to L ^?(B) where ? is the derivative function of Φ. A characterization of these operators and several properties are obtained.     

C*-Isomorphisms Associated with Two Projections on a Hilbert C*-Module*

Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies C^*-isomorphisms associated with two projections by introducing the matched triple and the semi-harmonious pair of projections. A triple (P, Q, H) is said to be matched if H is a Hilbert C^*-module, P and Q are projections on H such that their infimum P ∧ Q exists as an element of L(H), where L(H) denotes the set of all adjointable operators on H. The C^*-subalgebras of L(H) generated by elements in {P - P ∧ Q, Q - P ∧ Q, I} and {P, Q, P ∧ Q, I} are denoted by i(P, Q, H) and o(P, Q, H), respectively. It is proved that each faithful representation (π, X) of o(P, Q, H) can induce a faithful representation (π, X e) of i(P, Q, H) such that e π(P - P ∧ Q) = π(P) - π(P) ∧ π(Q),eπ(Q - P ∧ Q) = π(Q) - π(P) ∧ π(Q).When (P, Q) is semi-harmonious, that is, R(P + Q) and R(2I - P - Q) are both orthogonally complemented in H, it is shown that i(P, Q, H) and i(I - Q, I - P, H) are unitarily equivalent via a unitary operator in L(H). A counterexample is constructed, which shows that the same may be not true when (P, Q) fails to be semi-harmonious. Likewise, a counterexample is constructed such that (P, Q) is semi-harmonious, whereas (P, I - Q) is not semi-harmonious. Some additional examples indicating new phenomena of adjointable operators acting on Hilbert C^*-modules are also provided.     

Global Existence for the n-Dimensional Semilinear Tricomi-Type Equations

In this article we investigate the issue of global existence of the solutions of the Cauchy problem for semilinear Tricomi-type equations in ? ⁿ⁺¹, n > 1. We give some sufficient conditions for existence of the global weak solutions. These conditions tie together nonlinearity with the speed of propagation and with the dimension n. We also prove necessity of these (or close) conditions. In fact, we extend these necessity results to the nonlocal semilinear equations.     

Positive functionals on BP*-algebras

A new class of locally convex algebras, called BP^*-algebras, is introduced. It is shown that this class properly includes MQ^*-algebras which were introduced and studied by the first author andR. Rigelhof [10]. Among other results, it is proved that each positive functional on a BP^*-algebraA is admissible but not necessarily continuous as shown by an example. However, ifA, in addition, is either (i) a Q-algebra, or (ii) has an identity and is barrelled, or (iii)A is endowed with the inductive limit topology, then each positive functional onA is continuous.This work was supported by an N.R.C. Grant.     

Classification of extensions of classifiable -algebras

For a certain class of extensions of C^*-algebras in which B and A belong to classifiable classes of C^*-algebras, we show that the functor which sends to its associated six term exact sequence in K-theory and the positive cones of K₀(B) and K₀(A) is a classification functor. We give two independent applications addressing the classification of a class of C^*-algebras arising from substitutional shift spaces on one hand and of graph algebras on the other. The former application leads to the answer of a question of Carlsen and the first named author concerning the completeness of stabilized Matsumoto algebras as an invariant of flow equivalence. The latter leads to the first classification result for nonsimple graph C^*-algebras.