A generalized variational principle and theoretical model for magnetoelastic interaction of ferromagnetic bodies

The quantitative analysis shows that no theoretical model for 3-d magnetoelastic bodies, in literatures to date, can commonly simulate two kinds of distinct experimental phenomena on magnetoelastic interaction of ferromagnetic structures. This makes it difficult to effectively discribe the magnetoelastic mechanical behavior of structures with complex geometry, such as shells. Therefore, it is a key step for simulating magnetoelastic mechanical characteristics of structures with complex geometry to establish a 3-d model which also can commonly characterize the two distinct experimental phenomena. A theoretical model for three dimension magnetizable elastic bodies, which is commonly suitable for the two kinds of experimental phenomena on magnetoelastic interaction of ferromagnetic plates, is presented by the variational principle for the total energy functional of the coupling system of the 3-d ferromagnetic bodies. It is found that for the case of linear isotropic magnetic materials, the magnetic forces obtained by this model include not only the body magnetic force which is the same as that got from the magnetic dipole model, but also a distribution of the magnetic traction on the surface of the magnetizable body. And the value of the traction is equal to the jumping one of the Faraday electromagnetic stress on the two sides of the surface, which does not appear in any model, such as magnetic dipole model and axiomatic model.     

Calabi conjecture on hyperbolic affine hyperspheres (2)

Research supported by the Alexander von Humboldt-Stiftung, the National Natural Science Foundation of China, the Science Foundation of the Educational Committee of China     

控制调幅波耗散方程的整体吸引子的有限维

§ 1　IntroductionIn this paperwe shall study successively the equationsgiven in [1 ,2 ] .Underthe sameconditions(i.e.the initial boundary value and other conditions) as in[1 ,2 ] ,the upperbound of the dimension of their global attractor will be obtained respectively.Theexistence of the global attractors have been proved in[1 ,2 ] .This paper is organized as follows:In§ 2 ,we derive the Frechet differential of the solution operator s(t) for theperturbed system.In§ 3 ,we show the finite di…     

HAMILTONIAN CYCLES AND DECOMPOSITIONS OFCAYLEY DIGRAPHS OF FINITE ABELIAN GROUPS

In this paper, Hamiltonian cycles and decompositions of Cayley digraphs are investigat-ed. Sufficient conditions are given for these two problems respectively. Furthermore, the conditions are also necesaary for 2-regular Cayley disraphs, In addition, some known results about theCartesian products of two directed cycles are also deduced.     

A criterion for quasi-heredity and the characteristic module

The aim of this paper is to give a criterion for quasi-heredity by the existence of a faithful module, and a test for the characteristic module by using a property of faithful and partial tilting. Supported by the National Education Committee of China, the Chinese Academy of Science and the National Natural Science Foundation of China     

磁弹性耦合效应引起的铁磁直杆磁场中振动频率的改变

基于磁弹性广义变分原理和Hamilton原理,对处于外加磁场中的软铁磁体,建立了磁弹性动力学理论模型．分别通过关于铁磁杆磁标势和弹性位移的变分运算,获得了包含磁场和弹性变形的所有基本方程,并给出描述磁弹性耦合作用的磁体力和磁面力．采用摄动技术和Galerkin方法,将所建立的磁弹性理论模型用于外加磁场中铁磁直杆的振动分析．结果表明,由于磁弹性耦合效应,外加磁场将对铁磁杆的振动频率产生影响:当铁磁杆的振动位移沿着磁场方向时,其频率减小并出现磁弹性屈曲失稳;当铁磁杆的振动位移垂直于磁场方向时,其频率将会增大．理论模型能够很好地解释已有实验观测的振动频率改变现象．     

CONNECTIVITIES OF MINIMAL CAYLEY COSET DIGRAPHS

We prove that the connectivities of minimal Cayley coset digraphs are their regular degrees.     

Finite p-Groups Whose Abelian Subgroups Have a Trivial Intersection

A subgroup H of a finite group G is called a TI-subgroup if H ∩ H^x = 1 or H for all x ∈ G. In this paper, a complete classification for finite p-groups, in which all abelian subgroups are TI-subgroups, is given.     

AN EXTENSION OF CLARIAUT EQUATION AND ITS APPLICATION

The geodesic in differential geometry is eornmonly used in computer-aided filament winding (CAFW) to avoid slippage in manufacturing process. The uniqueness of the geodesic byits initial values severely restricts the choice of the fiber path and is an obstacle to the production ofoptimized structures. This paper presents a new class of more flexible non-slip trajectories on revolutional surfaces as an extension of the well-known Clariaut equation and gives its application inCAFW.     

Non-constant stationary solutions to a prey-predator model with diffusion

In this paper, a nonlinear predator reproduction and prey competition model with diffusion is discussed. Some existence and non-existence results concerning non-constant positive steady-states are presented using topological degree argument and the energy method, respectively. The first author was supported by the National Natural Science Foundation of China (No. 10771032) and the Natural Science Foundation of Jiangsu province BK2006088, and the second author was supported by National Natural Science Foundation of China (No. 10601011).