On n ‐contractive fuzzy logics

It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w. r. t. the class of all finite MTL‐chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since each finite MTL‐chain satisfies a form of this generalized contraction. Simultaneously, we also consider extensions of MTL by the generalized excluded middle laws introduced in [9] and the axiom of weak cancellation defined in [31]. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple, and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embeddability property, finite model property, decidability, and standard completeness. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Density and local order dependence of the dynamical features of water pentamers: an instantaneous normal mode investigation

We analyse liquid configurations of simulated water using the instantaneous normal mode approach along three isotherms (T=260, 300, 350 K), with densities ranging from 0.90 to 1.15 g/cm³. We focus our attention to clusters of five hydrogen-bonded molecules and project their instantaneous motion on some a priori modes related to the tetrahedral symmetry of these pentamers. We discuss the dependence of the resulting dynamical features on the density and the structural order set up by the presence of hydrogen bonding.     

Hutchison度量完备的充要条件

距离空间Ｘ上，以Ｍ（Ｘ）记定义在Ｘ的Ｂｏｒｅｌ域上的具有有界支撑的概度测度全体，Ｒ（Ｘ）记Ｍ（Ｘ）中所有Ｒａｄｏｎ测度，Ｍ（Ｘ），Ｒ（Ｘ）均赋予Ｈｕｔｃｈｉｓｏｎ度量，本文得到：Ｒ（Ｘ）完备当且仅当Ｘ完备且有界，若Ｘ可分，则：Ｍ（Ｘ）完备当且仅当Ｘ完备且有界。     

Recursively compressible sets

Classes of recursively compressible and incompressible sets as well as some other classes emerging in connection with a simple recursive-theory model of data array packing are studied. Some new completeness criteria for sets are obtained.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 9–16, July, 1998.     

A New Quantum State

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｋｎｏｗｎｔｈａｔｂｏｓｏｎｒｅａｌｉｚａｔｉｏｎａｐｐｒｏａｃｈｉｓｖｅｒｙｅｆｅｃｔｉｖｅｔｏｓｔｕｄｙｔｈｅｒｅｐｒｅｓｅｎｔａｔｉｏｎｔｈｅｏｒｙｏｆｇｒｏｕｐ，ａｎｄｔｈｅｂｏｓｏｎｒｅａｌｉｚａｔ...     

Admissibility of unbiased tests for a composite hypothesis with a restricted alternative

This paper discusses -admissiblility and d-admissiblity which are important concepts in studying the performance of statistical tests for composite hypotheses. A sufficient condition for -admissibility is presented. When =1/m, the Nomakuchi-Sakata test, which is uniformly more powerful than the likelihood ratio test for hypotheses min (₁, ₁) = 0 versus min (₁, ₁) > 0, is generalized for a class of distributions in an exponential family, and its unbiasedness and -admissibility are shown. Finally, the case of 1/m is discussed in brief.     

Properties of Tense Logics

Based on the results of [11] this paper delivers uniform algorithms for deciding whether a finitely axiomatizable tense logic

• has the finite model property,
• is complete with respect to Kripke semantics,
• is strongly complete with respect to Kripke semantics,
• is d-persistent,
• is r-persistent.

It is also proved that a tense logic is strongly complete iff the corresponding variety of bimodal algebras is complex, and that a tense logic is d-persistent iff it is complete and its Kripke frames form a first order definable class. From this we obtain many natural non-d-persistent tense logics whose corresponding varieties of bimodal algebras are complex. Mathematics Subject Classification: 03B45, 03B25.     

INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS

In this article, we give a simple proof on the energy scattering for the Hartree equations using the interaction Morawetz estimate that was originally introduced in [5].     

Optimal Redesign of Elastic Structures in the State of Initial Loading*

The problem of optimal redesign of an existing structure that is subjected to loading and initial stress is considered for the case of beam or plate structures. The addition or removal of material is associated with initial distortions and initial stresses. After formulating the problem, optimality conditions are derived and an illustrative example of frame redesign is considered.