Applications of Duality to the Pure-injective Envelope

Given an R-T-bimodule _R K _T and R-S-bimodule _R M _S , we study how properties of _R K _T affect the K-double dual M** = Hom _T [Hom _R (M, K), K] considered as a right S-module. If _R K is a cogenerator, then for every R-S-bimodule, the natural morphism Φ _M : M → M** is a pure-monomorphism of right S-modules. If _R K is the minimal (injective) cogenerator and K _T is quasi-injective, then M ^** is a pure-injective right S-module. If _R K is the minimal (injective) cogenerator, and T = End _R K it is shown that K _T is quasi-injective if and only if the K-topology on R is linearly compact. If the _R K-topology on R is of finite type, then the natural morphism Φ _R : R → R** is the pure-injective envelope of R _R as a right module over itself. The author is partially supported by NSF Grant DMS-02-00698.     

模糊决策器的硬件实现

本文提出了一种硬件实现模糊决策的方法，从理论上论证了这种方法的正确性，并通过实验证明其可行。它可以应用于模糊硬件系统，以实现对连续或离散模糊信号的去模糊。     

计算网络最小割的问题的注记

对网络最小割的计算进行了研究,给出了简化求最小割的理论依据.     

Temporal logic of linearly ordered <Emphasis Type="Italic">α</Emphasis>-spaces

Using the language of temporal logic, we construct a decidable calculus L* α and prove that the calculus is complete w.r.t. the class of all strictly linearly ordered α-frames. Supported by RFBR (project No. 06-01-00358) and by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-335.2008.1). __________ Translated from Algebra i Logika, Vol. 47, No. 6, pp. 723–749, November–December, 2008.     

On the completeness of a new intuitionistic connective

A. V. Bessonov suggested an example of an intuitionistic calculus that defines a new connective in the sense of P. S. Novikov. Using the Bessonov logic as an example, this definition is compared with a similar definition suggested by D. M. Gabbay to show that the Bessonov logic does not comply with Gabbay's definition. An example of a calculus that satisfies Novikov's definition but has no disjunctive property is constructed. Translated fromMatematickeskie Zametki, Vol. 60, No. 3, pp. 423–433, September, 1996.     

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     

S~6中具有常数Kahler角的极小曲面

球面Ｓ６具有典型的近复结构，因而对于其中的曲面可引入Ｋａｈｌｅｒ角的概念．本文研究Ｓ６内具有常数Ｋａｈｌｅｒ角的极小曲面，得到了刚性定理．结合已有结果，易知Ｓｉｍｏｎ猜想对于这类曲面成立．     

格的内蕴拓扑与完全分配律

本文以Ｓｃｏｔｔ拓扑，Ｚａｒｉｓｋｉ拓扑，区间拓朴等刻划了完全分配律；获得了格的特殊元的存在性与区间拓扑连通性等之间的众多制约关系，给出了若干应用实例和重要反例．     

Non-standard aspects of Minkowski causal logic

The Minkowski causal logic, which is already known to be a complete orthomodular lattice, is found to be also an atomistic and irreducible logic, but to have no other essential properties to be represented in terms of all the subspace of some Hilbert space. Alternative representation of the logic in terms of subspaces of a real vector space or of the states in terms of probability measures are suggested.