Boussinesq-Burgers方程新的精确解

基于改进的投影Riccati方程的解,提出一种新的构造非线性演化方程精确解的方法.通过这种方法,我们得导到了Boussinesq-Burgers方程各种类型的精确解,包括Jacobi和Weierstrass周期函数解.这种方法与数学软件Maple结合,简单易行,有助于探索其他非线性演化方程的精确解.     

一维带限Weierstrass分形分层地面与矩形截面导体柱复合电磁散射FDTD研究

运用时域有限差分方法研究一维带限分形分层粗糙地面与矩形截面导体柱的复合电磁散射,计算复合电磁散射的双站散射系数,得到复合散射系数随散射角的变化,讨论粗糙面高度起伏均方根、分维、中间层介质、下层介质及矩形截面导体柱的参数等对复合散射系数的影响.     

Hyperelliptic surfaces are Loewner

We prove that C. Loewner's inequality for the torus is satisfied by conformal metrics on hyperelliptic surfaces as well. In genus 2, we first construct the Loewner loops on the (mildly singular) companion tori, locally isometric to away from Weierstrass points. The loops are then transplanted to , and surgered to obtain a Loewner loop on . In higher genus, we exploit M. Gromov's area estimates for -regular metrics on .

     

The Higher Derivatives of Bianalytic Functions

Bianalyticfunctionsisanewkif1doffunctionspresentedrecently-PapersL1j'[2Jdls-cussedson1ebaslcpropertiesofbianalyticfunctions-Inthispaper,wewillgetthehigherdt'rivD'-tivesandWeierstrassTheorembytheresultsofpapers[lj.[2j.5l.TheFormulaofHigherDerivativesFromF2j,wehavetherepresentatlonformulaofbianalytlcfu11ctionsProvidedthattheintegralcanbedifferentiatedunderthesignofintegrationwefi11dFronlti1edefinitionofthe(ierivativeofl)ia11alyticfu11ctionlwehaveWearegoingtc)IJrovetlIeaboveformulainfollowi…     

Moduli Spaces of Curves with Quasi-Symmetric Weierstrass GAp Seqnences

In this paper we give an explicit construction of the moduli space of the pointed complete Gorenstein curves of arithmetic genus g with a given quasi-symmetric Weierstrass semigroup, that is, a Weierstrass semigroup whose last gap is equal to 2g – 2. We identify such a curve with its image under the canonical embedding in the (g – 1)-dimensional projective space. By normalizing the coefficients of the quadratic relations and by constructing Gröbner bases of the canonical ideal, we obtain the equations of the moduli space in terms of Buchberger's criterion. Moreover, by analyzing syzygies of the canonical ideal we establish criteria that make the computations less expensive.     

Weierstrass method for quaternionic polynomial root‐finding

Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas that motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper, we propose a Weierstrass‐like method for finding simultaneously all the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.     

Regularization of optimal design problems for bars and plates,part 1

In this paper, we consider a number of optimal design problems for elastic bars and plates. The material characteristics of rigidity of an elastic nonhomogeneous medium are taken as the control variables. A linear functional of the solutions to the equilibrium boundary-value problem is minimized under additional restrictions upon the control variables.Special variations of the control within a narrow strip provide a necessary condition for a strong local minimum (Weierstrass test). This necessary condition can be used for the detailed analysis of the following problems: bar of extremal torsional rigidity; optimal distribution of isotropic material with variable shear modulus within a plate; and optimal orientation of principal axes of elasticity in an orthotropic plate. For all of these cases, the stationary solutions violate the Weierstrass test and therefore are not optimal. This is because, in the course of the approximation of the optimal solution, the curve dividing zones occupied by materials with different rigidities displays rapid oscillations sweeping over a two-dimensional region. Within this region, the material behaves as a composite medium assembled of materials of the initial class.     

New Weierstrass Semi-rational Expansion Method to Doubly Periodic Solutions of Soliton Equations

Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.     

Weierstrass Semigroups of a Pair of Points Whose First Nongaps are Three

We found all candidates for a Weierstrass semigroup at a pair of Weierstrass points whose first nongaps are three. We prove that such semigroups are actually Weierstrass semigroups by constructing examples.