Projective S-acts and Exact Functors

Let S be a semigroup. In this paper, projective S-acts and exact sequences in S-Act are studied. It is shown that, for a unitary S-act P, the functor Hom(P, –) is exact if and only if P Se for some idempotent e S.The research was supported by the National Natural Science Foundation of China.1991 Mathematics Subject Classification: 20M50     

Diverse acoustic wave propagation to confirmable time–space fractional KP equation arising in dusty plasma

In this study, the (3+1)-dimensional fractional time–space Kadomtsev–Petviashivili (FTSKP) equation is considered and analyzed analytically, which propagates the acoustic waves in an unmagnetized dusty plasma. The fractional derivatives are studied in a confirmable sense. The new modified extended direct algebraic (MEDA) approach is adopted to investigate the diverse nonlinear wave structures. A variety of new families of hyperbolic and trigonometric solutions are obtained in single and different combinations. The obtained results are also constructed graphically with the different parametric choices.     

集中载荷作用下弹性地基圆薄板大挠度问题的精确解

本文处理了winkler型弹性地基上圆板受集中载荷作用的大挠度问题,第一次获得了这类问题的精确解的解析式,并用此精确解进行了具体求解,其结果可供工程直接使用,这较之已有文献中的近似处理方法具有更好的可靠性,同时也为研究大挠度理论提供了可靠的依据。     

A finite element approach to the chaotic motion of geometrically exact rods undergoing in-plane deformations

The paper is concerned with a hybrid finite element formulation for the geometrically exact dynamics of rods with applications to chaotic motion. The rod theory is developed for in-plane motions using the direct approach where the rod is treated as a one-dimensional Cosserat line. Shear deformation is included in the formulation. Within the elements, a linear distribution of the kinematical fields is combined with a constant distribution of the normal and shear forces. For time integration, the mid-point rule is employed. Various numerical examples of chaotic motion of straight and initially curved rods are presented proving the powerfulness and applicability of the finite element formulation.     

Kinematically Excited Stokes Flow in a Right-Angle Wedge (Plane Problem)

An exact solution is obtained for a Stokes flow in a right-angle wedge. The flow is kinematically excited at the bottom edge and discontinues at the corner point __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 60–69, September 2005.     

A note on solutions to pomeron functional equations

We construct exact solutions to the pomeron functional equation and ageneralization of it. These results clarify and extend previous workon this problem.     

非平面应变状态下的叠层厚壁筒

抛弃任何有关位移或应力模式的人为假设，在轴对称情况下，导出正交异性厚壁筒的状态方程。在沿筒轴方向任意分布的轴对称荷载下，给出叠层厚壁筒静力问题的精确解。此解满足所有弹性力学基本方程，包含了全部弹性常数，可满足任意精度要求。数值结果和ＳＡＰ５有限元解进行了对比。     

Exact Solutions of the Problem of Unsteady Flow of a Viscoplastic Medium in a Circular Pipe

Two one-parameter series of real solutions describing the process of deceleration and acceleration of a viscoplastic medium under the action of a time-varying pressure gradient are obtained. The problem of axisymmetric unsteady viscoplastic flow is reduced to the solution of the Stefan boundary-value problem for the heat conduction equation with a nonlinear condition on the boundary of the quasi-rigid core. By a self-similar change of variables the problem can be reduced to a second-order ordinary differential equation. The solutions of this equation are represented in terms of Bessel and elementary functions. As a result, two one-parameter series of solutions, the first of which describes the acceleration and the second the deceleration of a viscoplastic medium in a pipe under the action of a time-varying pressure gradient are obtained.     

New exact solution of the problem of rotationally symmetric Couette-Poiseuille flow

An exact solution is obtained for the problem of steady-state viscous incompressible flow under a pressure difference in the gap between coaxial cylinders for the case where the inner cylinder rotates at a constant angular velocity. The solution differs from the classical Couette-Poiseuille result by the presence of radial mass transfer, which provides for interaction between the poloidal and azimuthal circulations. The flow rate is found to depend linearly on the angular velocity of rotation of the inner cylinder. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 71–77, September–October, 2007.     

纯平荫罩振动固有频率的研究

在高清晰度电视(HDTV)用的纯平彩色显像管中，由于荫罩的振动从而导致图像色纯度的降低．首先讨论了纯平荫罩振动的固有频率各种分析方法，然后应用弹性力学的基本理论，在建立薄膜横向振动基本方程的基础上，分析了纯平荫罩在四边简支条件下振动的固有频率和振型问题，得出了纯平荫罩振动频率的精确解，实例应用表明，在四边简支条件下的计算结果与实验结果基本一致，说明该方法确定纯平荫罩的振动固有频率是可行的、有效的，所得结果为减小荫罩振动进而对其结构参数进行优化设计提供了依据。