Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

Electronic Properties of Red P-Type Tl2S5 Single Crystals

Single crystals of red Tl2S5 were prepared by a special modified vertical Bridgman and Stockbarger technique.This growth was performed in our laboratory. The influences of temperature on the electrical conductivity, Hall mobility, carrier concentration, and thermoelectric power (TEP) were carried out in the temperature range 277-413K. Throughout these measurements, various physical parameters such as effective mass of charge carriers,carrier mobility, diffusion coefficient, and the relaxation time for both majority and minority carriers were found.     

活动标形及其在点啮合齿轮传动误差分析中的应用

活动标形法的论述首推苏步青译，佐佐木重夫著《微分几何学》，还有的著作从外微分形式引入活动标形,本文论证取曲面的正交曲率网为参数网时，曲面论的基本公式就是活动标形的微分形式，并用其分析了点啮合齿轮传动误差．     

Optical and Acoustical Frequencies in a Nonlinear Helicoidal Model of DNA Molecules

We compare optical and acoustical frequencies in the Peyrard-Bishop-Dauxois model, i.e. an extended Peyrard-Bishop model, of DNA molecules. We discuss how ratio of those frequencies depends on a value of the harmonic constant of the helicoidal spring K. Also, we suggest that the most favourable mode could be a resonance mode.     

GENERALIZED CIRCLES AND THEIR CONFORMAL MAPPING IN A SUBSPACE OF A WEYL SPACE

The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions under which a generalized concircular transformation of one Weyl space onto another induces a generalized transformation oil its subspaces. Finally, it is shown that any totally geodesic or totally umbilical hypersurface of a generalized concircularly flat Weyl space is also generalized concircularly flat.     

Pre—Separation Axioms in Fuzzifying Topology

1　 IntroductionYing[5,6 ] introduced and elementally developed so called fuzzifying topology with the semanticmethod of continuous valued L ogic.Shen[7] introduced and studied T0 -,T1-,T2 (Hausdorff) -,T3(regularity) -,T4 (normality) -separation axioms in fuzzifying topology.In [3 ]the concepts of thefamily of fuzzifying pre-open sets,fuzzifying pre-neighbourhood structure of a point and fuzzifyingpre-closure are introduced and studied.It is worth to mention that pre-separation axioms are …     

Second Order Nonlinear Evolution Inclusions Ⅰ： Existence and Relaxation Results

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.     

基于平面声源实施结构声辐射有源控制的理论研究

研究了利用分布式平面声源对结构声辐射进行有源控制的问题。首先建立了系统的数学模型,然后推导了有源控制条件下次级声源的强度和声功率降低的计算公式。在实际应用中,次级声源参数(面积大小、安放位置、个数等)对控制效果有重要影响,本文基于有源控制的物理机理和数值仿真研究这些问题。结果表明:一般情况下,次级声源板的振动模态分布与初级结构振动模态分布不相同,因此,在低频范围内,需要至少4个分布式次级声源,方能有效地控制初级结构声辐射。     

Calculation of the Specific Heats for the Ⅱ—Ⅲ and Ⅱ—Ⅳ Phase transitions in NH4I

This study gives our calculation for the specific heats CVI due to an Ising model using the observed Cp data for the Ⅱ-Ⅲ and Ⅱ-VI phase transitions in NH4I.By fitting to the CP data we determine the values of the critical exponent for the pressure of 0.14GPa(Ⅱ-Ⅲ phase transition)and for the pressures of 0.75,1.35and 1.97 GPa (II-IV phase transition)in NH4I.Our exponent values values are close to the predicted values of the specific heat in a three-dimensional Ising model.Our calculated CVI are in good agreement with the experimental CP for NH4I in most cases.