The Equation of Motion of a Vortex Layer of Small Thickness

The equation governing the evolution of a vortex layer whose thickness is small compared to its radius of curvature and in which the vorticity is everywhere the same is obtained, viscous and compressibility effects being neglected. The method of matched asymptotic expansions is applied and results in an extension, which is unexpectedly simple, of Birkhoff's integro-differential equation for vortex sheets. The equation is applied to long waves on a straight vortex layer of uniform thickness.     

Kolmogorov-Spieqel-Siveshinky方程大时间问题的Fourier拟谱逼近

该文讨论了Kolmogorov-Spieqel-Siveshinky方程的周期初值问题, 研究了半离散Fourier拟谱解的长时间行为, 证明了半离散系统的收敛性和整体吸引子的存在性. 构造了全离散的三层显式Fourier拟谱格式, 并证明了该格式的收敛性, 最后通过数值计算验证了格式的可信性. 数值结果表明: 该格式是长时间稳定并可取时间大步长. 作者模拟了方程的解在相空间的轨线, 得到了一些有意义的结论.     

固定-固定型无阻尼弹簧质点系统的质量约束问题

本文讨论了系统总质量约束下的固定一固定型无阻尼弹簧质点系统的构造问题，得到了该问题的可解性条件，给出了解的表达式和数值算法，算例说明算法是有效的．     

Homology of products and joins of reflexive relations

The homology of products and joins of reflexive relations is computed. Rota's homology of the products of two lattices is computed. The homology of finite polyspherical posets is determined by Euler characteristic and length. The category of polyspherical posets is closed under joins and special products but not products. A special product of nonvoid reflexive relations is simply connected.     

Numerical evaluation of the temperature field of steady-state rolling tires

Rubber is the main component of pneumatic tires. The tire heating is caused by the hysteresis effects due to the deformation of the rubber during operation. Tire temperatures can depend on many factors, including tire geometry, inflation pressure, vehicle load and speed, road type and temperature and environmental conditions. The focus of this study is to develop a finite element approach to computationally evaluate the temperature field of a steady-state rolling tire. For simplicity, the tire is assumed to be composed of rubber and body-ply. The nonlinear mechanical behavior of the rubber is characterized by a Mooney–Rivlin model while the body-ply is assumed to be linear elastic material. The coupled effects of the inflation pressure and vehicle loading are investigated. The influences of body-ply stiffness are studied as well. The simulation results show that loading is the main factor to determine the temperature field. The stiffer body-ply causes less deformation of rubber and consequently decreases the temperature.     

Estimation of the sum of values of the divisor function

The problem of estimation of the sum of values of a divisor function is considered in the paper. The previously known estimate is improved and the result is generalized to the case of divisor function values raised into a given power.     

Method of elastic solutions of problems of thermoviscoelasticity

The quasi-static mixed boundary value problem is considered for a viscoelastic body with time-dependent properties and a singular nondegenerate relaxation kernel. The existence of a time-temperature (or similar) analogy is not assumed. A method of reducing the viscoelastic problem to the solution of a series of uniform elastic problems is proposed and its convergence proved. The method is illustrated with reference to examples of solutions of specific viscoelastic problems.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 4, pp. 603–614, July–August, 1970.     

快速分析松脂澄清脂液中松节油含量的新方法

本文用统计方法研究思茅松松脂澄清脂液中松节油含量与酸值的相关关系，建立了不同于通常所用蒸馏法的新分析方法──酸值法。新方法快速、简捷、准确、经济、缩短分析时间５０分钟（７１％）；重复试验的极差的均值为０．１％，降低分析成本７０％；已用于云南省地方标准。     

Absolute Continuity of Measures in the Class of Markov and Semi-Markov Processes of Diffusion Type

The property of absolute continuity of measures in the class of one-dimensional semi-Markov processes of diffusion type is investigated. The measure of such a process can be composed of two measures. The first one is a distribution of a random track, and the second one is a conditional distribution of a time run along the track. The desired density is represented in the form of product of two corresponding densities.     

Impact of the cost of the time resource on efficiency of economic processes

The objective of the paper is to simulate behavior of economic agents with a special emphasis on the use of the time resource in economic processes. The case studied is from the fishing industry. With simulations, the study analyzes the behavior of economic agents as they lead their processes through time. The paper estimates the value of time in a fishery operation, and shows that the time cost is essential in clarifying some phenomena in the economic behavior of agents. Among the conclusions is that the difference in economic efficiency between strong and weak ownership is due to difference in time costs. The secondary goal of the paper is to develop a simulation tool for analyzing a range of problems in the fishing industry, ranging from decision situations onboard fishing vessels to serving as a tool for fishery managers and legislators.     

The stability of non-conservative systems and an estimate of the domain of attraction

The stability of mechanical systems, on which dissipative, gyroscopic, potential and positional non-conservative forces act, is investigated. The condition for asymptotic stability is obtained using the Lyapunov function and an estimate of the domain of attraction is also found in terms of the system being considered. A precessional system is also examined. It is shown that the condition for the asymptotic stability of a system is the condition of acceptability in the sense of the stability of a precessional system. The results obtained are applied to the problem of the stabilization, using external moments, of the steady motion of a balanced gyroscope in gimbals.     

Well-posedness of a kind of nonlinear coupled system of fractional differential equations

We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder, the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle.     

提示信息特征对秘书问题决策影响的仿真实验研究

针对具有提示信息的秘书问题,首先分析了提示信息特征变化对决策结果的可能影响.然后在此基础上,提出了在最大值标杆策略下研究提示信息的变化特征对决策结果的影响,接着阐述了仿真试验的理论假设和设计,通过仿真试验考察了提示信息的不同变化对仿真结果的影响;最后给出了对仿真结果的分析和探讨,仿真结果验证了理论假设的判断.     

Computation of flow-induced motion of floating bodies

A computational procedure for the prediction of motion of rigid bodies floating in viscous fluids and subjected to currents and waves is presented. The procedure is based on a coupled iterative solution of equations of motion of a rigid body with up to six degrees of freedom and the Reynolds-averaged Navier–Stokes equations describing the two- or three-dimensional fluid flow. The fluid flow is predicted using a commercial CFD package which can use moving grids made of arbitrary polyhedral cells and allows sliding interfaces between fixed and moving grid blocks. The computation of body motion is coupled to the CFD code via user-coding interfaces. The method is used to compute the 2D motion of floating bodies subjected to large waves and the results are compared to available experimental data, showing favorable agreement.     

Asymptotic analysis of the growth of cake layers in filters

The problem of fluid flow in a two-dimensional pleated filteris considered. Of particular interest is the change in the flowdue to cake build-up on the surface of the filter material.The flow is taken to be Darcy flow in the cake and the filtermaterial, with Stokes' flow outside the cake. The particlesin the flow are taken to be transported with the flow and tostick to the cake without slippage or resuspension, and thecake is taken to be incompressible. The flow is considered invarious geometries, particularly long thin filters and corners.The main parameter in the problem is the ratio of the filter-materialresistance to the cake resistance, and limiting cases are considered.Travelling waves of cake build-up are found for arbitrary time-dependentvariations in the inflow conditions. The time taken for thefilter to become clogged by the cake is also considered.     

Domain dependence of eigenvalues of elliptic type operators

The dependence on the domain for the Dirichlet eigenvalues of elliptic operators considered in bounded domains is studied. The proximity of domains is measured by a norm of the difference of two orthogonal projectors corresponding to the reference domain and the perturbed one; this allows to compare eigenvalues corresponding to domains that have non-smooth boundaries and different topology. The main result is an asymptotic formula in which the remainder is evaluated in terms of this quantity. Applications of this result are given. The results are new for the Laplace operator.     

Cluster dynamics of a uniform chain of dissipatively coupled rotators

The existence and stability of stationary cluster structures in uniform chains of dissipatively coupled rotators is investigated. Cluster synchronization is interpreted as the classical synchronization of cluster rotators, which are elementary structure-forming objects. The complete set of types of cluster rotators and simple cells is defined. This definition is equivalent to the definition of the complete set of types of cluster structures. The completeness of this set is proved. The problem of the stability of cluster structures is solved. Physical examples of chains of rotators and a physical interpretation of the results of this research are given.     

Stationary problem of complex heat transfer in a system of semitransparent bodies with boundary conditions of diffuse reflection and refraction of radiation

A boundary value problem describing complex (radiation-conductive) heat transfer in a system of semitransparent bodies is considered. Complex heat transfer is described by a system consisting of a stationary heat equation and an equation of radiative transfer with the boundary conditions of diffuse reflection and diffuse refraction of radiation. The dependence of the radiation intensity and optical properties of bodies on the frequency of radiation is taken into account. The unique existence of the weak solution to this problem is established. The comparison theorem is proven. Estimates of the weak solution are derived, and its regularity is established.     

Optimization of open cross sections of thin-walled beams with plate-shell-flanges

The paper is devoted to a monosymetrical cold-formed thin-walled beam with open cross section. Its flange consists of plates and circular shells. The beam is under pure bending. The cross section is characterized by dimensionless parameters. The authors are searching for an optimal cross section shape of considered beam. This optimal shape is determined by means of parametric optimization. The dimensionless objective function is so defined as to comprise both cross section area and a maximal allowable bending moment. The constraints follow from the local buckling conditions and geometric restrictions. Moreover, there are optimized cross sections of beams, for which the shear center is located either in the web or in the centroid of the cross section. Results are compared and analyzed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)