EXACT－VOLUME DIFFERENTIAL FORM DE RHAM COHOMOLOGY AND HAMILTON VARIATIONAL PRINCIPLE

ＥＸＡＣＴ－ＶＯＬＵＭＥＤＩＦＦＥＲＥＮＴＩＡＬＦＯＲＭＤＥＲＨＡＭＣＯＨＯＭＯＬＯＧＹＡＮＤＨＡＭＩＬＴＯＮＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＷａｎｇＪｉｃｈｕｎ（王继春）（Ｄｅｐｔ．Ｍａｔｈ．Ｐｈｙｓ．ｏｆＷｕｈａｎＵｎｌｙ．ｏｆＴｅｃｈｎ...     

Soliton solutions and a Bäcklund transformation for a generalized nonlinear Schrödinger equation with variable coefficients from optical fiber communications

Under investigation in this paper is a generalized nonlinear Schrödinger model with variable dispersion, nonlinearity and gain/loss, which could describe the propagation of optical pulse in inhomogeneous fiber systems. By employing the Hirota method, one- and two-soliton solutions are obtained with the aid of symbolic computation. Furthermore, a general formula which denotes multi-soliton solutions is given. Some main properties of the solutions are discussed simultaneously. As one important property of nonlinear evolution equation, the Bäcklund transformation in bilinear form is also constructed, which is helpful on future research and as far as we know is firstly proposed in this paper.     

On Browkin''''s conjecture about the elements of order five in K_2(Q)

Based on the work of Lenstra, a succinct proof of Browkin's conjecture about the elements of order five in K2(Q) is given.     

Delay induced oscillation in predator–prey system with Beddington–DeAngelis functional response

The Beddington–DeAngelis predator–prey system with distributed delay is studied in this paper. At first, the positive equilibrium and its local stability are investigated. Then, with the mean delay as a bifurcation parameter, the system is found to undergo a Hopf bifurcation. The bifurcating periodic solutions are analyzed by means of the normal form and center manifold theorems. Finally, numerical simulations are also given to illustrate the results.     

On the theory of periodic layers in incompressible fluid

A conceptual error in the formally closed but physically incomplete Kim-Moin-Moser form of equations for viscous incompressible fluid in a horizontal periodic layer is corrected. This form, which has lately become popular, assumes that the vertical projections of the rotor and the second rotor of the field of accelerations vanish. This assumption considerably simplifies the calculations; however, it is insufficient for the equations of motion. In this paper, the fulfillment of these assumptions is ensured by the additional condition that the vector of the horizontal projection averaged over the period of the acceleration vorticity vanishes, which opens new possibilities. The resulting complete form of the equations with the rotors of three orders admits a reduction to two scalar equations (of the fourth and the sixth orders), which, however, are not less complicated than the equivalent Navier-Stokes equations.     

General Sobolev type inequalities for symmetric forms

A general Sobolev type inequality is introduced and studied for general symmetric forms by defining a new type of Cheeger's isoperimetric constant. Finally, concentration of measure for the Lp type logarithmic Sobolev inequality is presented.     

Poincaré type theorems for non-autonomous systems

In this paper we establish analytic equivalence theorems of Poincaré and Poincaré-Dulac type for analytic non-autonomous differential systems based on the dichotomy spectrum of their linear part. As applications of the theorem, normal forms linearize for two illustrative examples.     

单位球面上具有非负M bius截面曲率的超曲面

Let x:M→S~(n 1)be a hypersurface in the (n 1)-dimensional unit sphere S~(n 1)without umbilic point. The M(?)bius invariants of x under the M(?)bius transformation group of S~(n 1) are M(?)bius metric,M(?)bius form,M(?)bius second fundamental form and Blaschke tensor.In this paper,we prove the following theorem: Let x:M→S~(n 1)(n＞2)be an umbilic free hypersurface in S~(n 1) with nonnegative M(?)bius sectional curvature and with vanishing M(?)bius form.Then x is locally M(?)bius equivalent to one of the following hypersurfaces:(i)the torus S~k(a)×S~(n-k)((1-a~2)~(1/2))with 1≤k≤n-1;(ii)the pre-image of the stereographic projection of the standard cylinder S~k×R~(n-k)(?)R~(n 1) with 1≤k≤n-1;(iii)the pre-image of the stereographic projection of the cone in R~(n 1):(?)(u,v,t)=(tu,tv), where(u,v,t)∈S~k(a)×S~(n-k-1)((1-a~2)~(1/2))×R~ .     

Duality Maps of Finite Abelian Groups and Their Applications to Spin Models

Duality maps of finite abelian groups are classified. As a corollary, spin models on finite abelian groups which arise from the solutions of the modular invariance equations are determined as tensor products of indecomposable spin models. We also classify finite abelian groups whose Bose-Mesner algebra can be generated by a spin model.