AN ITERATIVE ALGORITHM FOR DETERMINING TIME－DEPENDENT COEFFICIENT OF TWO DIMENSIONAL LINEAR WAVE EQUATION

ＡＮＩＴＥＲＡＴＩＶＥＡＬＧＯＲＩＴＨＭＦＯＲＤＥＴＥＲＭＩＮＩＮＧＴＩＭＥ－ＤＥＰＥＮＤＥＮＴＣＯＥＦＦＩＣＩＥＮＴＯＦＴＷＯＤＩＭＥＮＳＩＯＮＡＬＬＩＮＥＡＲＷＡＶＥＥＱＵＡＴＩＯＮ（苏超伟）西北工业大学，邮编：７１００７２ＳｕＣｈａｏｗｅｉ（Ｎ...     

On the Robust Stability of 2D Schur Polynomials

In this note, the problem of the robust stability for a two-dimensional (two-variable) Schur polynomial which is the characteristic polynomial of a discrete-time linear time-invariant system is investigated. A new approach based on the Rouché theorem is adopted. The extension to the robust stability for multidimensional (multivariable) polynomials is also provided. Interesting sufficient conditions for such robust stability are derived. A two-dimensional example is included to support the theoretical result.     

Exchanged toric tilings,Rauzy substitution,and bounded remainder sets

This paper is devoted to the two-dimensional problem of the distribution of the fractional parts of a linear function. A new class of tilings of the two-dimensional torus into bounded remainder sets with an effective estimate of the remainder is introduced. It is shown that examples of the tilings under consideration can be obtained by using the geometric version of the Rauzy substitution.     

A scheme for the RCP pattern of the nano-structure

IntroductionThe balls-ffeng is a haous and dimcult problem. The meaning is the material ba1lswhich contains in it fill spare. This is an older problem. the Random-Continuous-Pile (RCP)problem. that can be trared bark to the l8th centur};'.. There are man}' unknown mysteriesin the RCP structure. With the materiaJ science de\-elopment. this old RCP problem has bee11paid attention to. Especially. in the nan(pmetre mdterial. bubble fluids. amorphous solid5.tlle RCP problem shows its titali…     

Convergence analysis of a space-time approximation to a two-dimensional system of shallow water equations

A characteristic-Galerkin approximation of a new two-dimensional Shallow Water viscous parabolic model is presented and a semi-implicit-Lagrangian finite element scheme is used. A convergence result is proved and numerical experiments on academic tests are shown.     

Approaches to the space-time modelling of infectious disease behaviour

A new approach to the space-time modelling of infectious diseasesis considered. A modulated heterogeneous Poisson process withintensity defined as a function of a two-dimensional susceptibilityfield is proposed. The model is fitted to a measles epidemicusing a proportional hazards approximation.     

New Integrable Two-Dimensional Systems Generated by Deformed Susy Algebras

New solutions of intertwining relations for two-dimensional scalar quantum Hamiltonians by second-order supercharges with Lorentz and degenerate metrics are obtained. The symmetry operators for components of superhamiltonian that lead to integrability of corresponding systems are found. Expressions for the Hamiltonians and the symmetry operators in the classical limit are constructed. A new class of integrable two-dimensional classical systems with integrals of motion of fourth order in momenta is obtained. Bibliography: 23 titles.     

一种新的二维区域上嵌入式数值积分公式构造方法

The purpose of this paper is to study a new strategy to construct embedded cubature formulae over two-dimensional regions.A new kind of embedded cubature formulae with some nodes along the selected algebraic curve is constructed.Some examples on the unit disk are presented to illustrate the validity of this strategy.     

Generalized Polak-Ribière algorithm

A new generalized Polak-Ribière conjugate gradient algorithm is proposed for unconstrained optimization, and its numerical and theoretical properties are discussed. The new method is, in fact, a particular type of two-dimensional Newton method and is based on a finite-difference approximation to the product of a Hessian and a vector.     

Invariant Lagrangians and a new method of integration of nonlinear equations

A method for solving the inverse variational problem for differential equations admitting a Lie group is presented. The method is used for determining invariant Lagrangians and integration of second-order nonlinear differential equations admitting two-dimensional noncommutative Lie algebras. The method of integration suggested here is quite different from Lie's classical method of integration of second-order ordinary differential equations based on canonical forms of two-dimensional Lie algebras. The new method reveals existence and significance of one-parameter families of singular solutions to nonlinear equations of second order.     

Steady Nonsymmetrical Gravity Waves with Shear in Water

A new type of steady two-dimensional inviscid gravity wave with shear is computed numerically. These waves appear at relatively low amplitudes and lack symmetry with respect to any crest or trough. A boundary integral formulation is used to obtain a one-parameter family of nonsymmetrical solutions through a symmetry-breaking bifurcation.     

The eigenvalue problem for elliptic partial differential equation with multi-point nonlocal conditions

We study the spectral problem for the system of difference equations of a two-dimensional elliptic partial differential equation with nonlocal conditions. A new form of two-point nonlocal conditions that involve interior points is proposed. The matrix of the difference system is nonsymmetric thus different types of eigenvalues occur. The conditions for the existence of the eigenvalues and their corresponding eigenvectors are presented for the one dimensional problem. Then, these relations are generalized to the two-dimensional problem by the separation of variables technique.     

New Approach to Solving a Two-Dimensional Problem for an Orthotropic Plate

A new approach to solving a two-dimensional problem for an orthotropic multiply connected plate is proposed in place of the standard approach which reduces the problem to integrating a fourth-order differential equation. The new method reduces the problem to integrating second-order differential equations that can be solved successively using a perturbation technique.     

Numerical algorithm for solving diffusion equations on the basis of multigrid methods

A new effective algorithm based on multigrid methods is proposed for solving parabolic equations. The algorithm preserves implicit-scheme advantages (such as stability, accuracy, and conservativeness) while it involves a considerably reduced amount of arithmetic operations at every time level. The absolute stability, conservativeness, and convergence of the algorithm is proved theoretically using one- and two-dimensional initial-boundary value model problems for the heat equation. The error of the solution is estimated. The good accuracy of the method is demonstrated using two-dimensional model problems, including ones with discontinuous coefficients.     

A finite volume element method for simulating secondary settling tanks

This contribution summarizes a new finite volume element (FVE) method as a unified scheme for coupled sedimentation-flow problems in secondary settling tanks in wastewater treatment. The model is two-dimensional in an axisymmetric setting. A new numerical example is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Jordan-Wachspress parameters in three dimensions

This paper describes a new technique which uses the Jordan-Wachspress parameters of the two-dimensional elliptic problem in the three-dimensional one. Thus A.D.I.-like schemes are obtained which, as is shown, converge faster than even the fastest ones known so far.     

Congruent Harmonic and Space Charge Electrostatic Fields

All the two-dimensional space charge equipotential surfaceswhich are congruent to the equipotential surfaces of equivalentharmonic problems are determined. The known list of solutionsof the high-pressure space charge equation is thereby increased.A voltage-current characteristic derived from the new solutionsis compared with experimental data for unipolar DC transmissionlines.     

A Generalized Nonclassical Model of Stress-Strain State in the Problems of Statics,Dynamics, and Contact Interaction of Layered Plates and Shells

A new generalized two-dimensional nonclassical model for the dynamic stress-strain state of layered anisotropic plates and shallow shells is constructed. A feature of the model is the complete account of the factors which represent the spatial character of their deformation; in particular, the transverse shear and transverse compression strains as well as the geometrical nonlinearity and dynamic action of the load are accounted for.     

A new superconvergence property of Wilson nonconforming finite element

Summary. In this paper the Wilson nonconforming finite element method is considered to solve a class of two-dimensional second-order elliptic boundary value problems. A new superconvergence property at the vertices and the midpoints of four edges of rectangular meshes is obtained. Received May 5, 1995 / Revised version received November 11, 1996