The limiting semigroup of the Bernstein iterates: degree of convergence

Summary We study the degree of approximation of the iterated Bernstein operators to the members (T(t)) _{t ≧0}, of their limiting semigroup. This yields a full quantitative version of an earlier convergence result by Karlin and Ziegler.     

Singular problem for a third-order nonlinear ordinary differential equation arising in fluid dynamics

Results concerning singular Cauchy problems, smooth manifolds, and Lyapunov series are used to correctly state and analyze a singular “initial-boundary” problem for a third-order nonlinear ordinary differential equation defined on the entire real axis. This problem arises in viscous incompressible fluid dynamics and describes self-similar solutions to the boundary layer equation for the stream function with a zero pressure gradient (plane-parallel flow in a mixing layer). The analysis of the problem suggests a simple numerical method for its solution. Numerical results are presented.     

Loop代数上一种Toda力学系统的求解问题

研究Loop代数上的一种Toda系统L=[L,M], 其Lax Pair中的M是反对称矩阵,而L=L⁺+M, L⁺是准上三角矩阵(包含对角部分), 证明这种系统的Lax方程的求解问题与相关的正则Riemann-Hilbert问题等价. 按此方法, 发现在某些特定的初值条件下系统是可积的. 并给出实例求解这一问题, 得到了精确解.     

Approximate Homomorphisms of Ternary Semigroups

A mapping f : (G ₁,[ ]₁)→ (G ₂,[ ]₂) between ternary semigroups will be called a ternary homomorphism if f([xyz]₁)=[f(x)f(y)f(z)]₂. In this paper, we prove the generalized Hyers–Ulam–Rassias stability of mappings of commutative semigroups into Banach spaces. In addition, we establish the superstability of ternary homomorphisms into Banach algebras endowed with multiplicative normsMathematics Subject Classifications (2000). Primary 39B52, Secondary 39B82, 46B99, 17A40     

On the equivalence of a theorem of Kisynski and the Hille-Yosida generation theorem

We show that a theorem of Kisynski on the generation of Banach-algebra homomorphisms of certain convolution algebras is equivalent to the Hille-Yosida theorem on the generation of operator-valued one-parameter semigroups.

     

On the lindblad equation with unbounded time-dependent coefficients

We prove newa priori estimates for the resolvent of a minimal quantum dynamical semigroup. These estimates simplify well-known conditions sufficient for conservativity and impose continuity conditions on the time-dependent operator coefficients ensuring the existence of conservative solutions of the Markov evolution equations. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 125–140, January, 1997. Translated by A. M. Chebotarev     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

ON THE DIFFERENTIABILITY OF THE PARITY PROGRESSIVE POPULATION SEMIGROUP

ＯＮＴＨＥＤＩＦＦＥＲＥＮＴＩＡＢＩＬＩＴＹＯＦＴＨＥＰＡＲＩＴＹＰＲＯＧＲＥＳＳＩＶＥＰＯＰＵＬＡＴＩＯＮＳＥＭＩＧＲＯＵＰ￥ＳＨＩＤＥＭＩＮＧＡＮＤＹＡＮＧＬＵＳＨＡＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅ...     

Invariant subspaces for positive operators on locally convex solid Riesz spaces

We prove that an x₀-quasinilpotent semigroup S of continuous positive linear operators on a locally convex solid Riesz space X has a common invariant subspace. Using this, a result which implies the main theorem of Abramovich, Aliprantis and Burkinshaw [J. Funct. Anal. 115 (1993) 418424] is also given.     

具有正则*-断面的正则半群的结构

设S是一个正则半群,如果存在一个S的子半群S~*及上的一元运算*满足条件：(1)(?)x∈S,x~*∈S~*∩V(x)；(2)(?)x∈S~*,(x~*)~*=x；(3)(?)x,y∈S,(x~*y)~*=y~*x~(**),(xy~*)~*=y~(xx)x~*则称S~*是S的一个正则*_-断面．本文刻画了具有正则*_-断面的正则半群的结构。