Supersymmetric Dirichlet operators

A canonical supersymmetric extension of classical Dirichlet forms and operators given by measures on linear spaces is considered. In the case of log-concave measures, the supersymmetric Dirichlet operator generates a hypercontractive semigroup. This setting is appropriate for infinite-dimensional geometry and quantum field theory.Dedicated to Yu. M. Berezanskii on the occasion of his seventieth birthdayPublished in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 583–592, May, 1995.The present work was supported by the DFG.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NONLINEAR THIRD-ORDER ROBIN BOUNDARY VALUE PROBLEM WITH A TURNING POINT

The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above.     

The fracture energy of materials under pulse microsecond-scale loading

Based on the results of fracture in polymethyl methacrylate and a spheroplastic using a magnetic-pulse setup, the specific work of the formation of a new surface is estimated, which is similar to Griffith’s surface energy for quasi-static tests. The value obtained is greater than the corresponding value determined from the quasi-static tests by an order of magnitude and tends to increase as the loading time decreases.     

New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit RCL oscillator with delay in a feedback loop.     

Characteristics and structures of weak efficient surfaces of production possibility sets

This paper studies the characteristics and structure of the weak surface of the production possibility set. We apply techniques and methods of transferring a polyhedral cone from its intersection form to its sum form, identify an intersection representation of the production possibility set. We give the structure theorem of weak surface of the production possibility set, which includes three complementary slackness conditions. We define the input weak efficiency and output weak efficiency for different DEA models according to the representation of the intersection form. It investigates the characteristics of the weak surfaces, and proves the structure theorems of input weak DEA efficiency and output weak DEA efficiency. The structure theorems establish weighted combination of inputs and outputs that are weak DEA efficient. Numerical examples are provided for illustration.     

Embedding and wavelet decomposition of spaces of minimal splines

On a sequence of embedded nonuniform grids, chains of embedded spaces of minimal splines (not necessarily polynomial) are constructed. The wavelet decomposition is given. The basis wavelets are compactly supported and admit simple analytic representation. The corresponding decomposition and reconstruction formulas are derived. The variety of spaces under consideration is identified with the variety of complete sequences of points of the direct product of an interval and a projective plane. Bibliography: 20 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 35, 2007, pp. 15–31     

Inhomogeneous configurations of magnetization of ferromagnetic films with biaxial anisotropy

The system of the Landau-Lifshitz equations and magnetostatic equations for a ferromagnetic film with biaxial anisotropy and a Q-factor smaller than unity is reduced to a single scalar equation for the magnetostatic potential. Such a procedure is possible if the magnetization modulation scale in the sample considerably exceeds the characteristic magnetic length. The solutions to this equation describing inhomogeneous periodic magnetic configurations are obtained. The energy analysis of these configurations is carried out.     

湖南省各市州经济发展水平评价

本文利用主成分分析法分析了湖南各市州的经济发展水平和经济综合实力,对湖南省14个市州的经济发展情况做出综合评价,得出了各市州在湖南省的经济地位.最后用系统聚类分析法进行了验证,结果表明用多元统计分析法来评价地区经济发展水平是可行的.     

链形线性元件电路的解题技巧

对一线性电路,若输入端的电压或电流变化,则组成电路中线性元件的电压、电流也将成比例地变化.所以,可假设输出端的电压或电流为一容易计算的值,逐步向前推导.推出假设的输入电压或电流,最后与实际电压或电流立一正比例式,即可求解.