有限水深中的极限非线性波

本文用参数优化方法.计算出有限水深中的极限Stokes波.计算的精度高,效率也高.从而进一步证明了用优化手段求stokes波动解里的待定系数是一个合理的、行之有效的方法.     

Asymptotics of a Solution of a Three-Dimensional Nonlinear Wave Equation near a Butterfly Catastrophe Point

We consider an optimal distributed control problem in a planar convex domain with smooth boundary and a small parameter at the highest derivatives of an elliptic operator. The zero Dirichlet condition is given on the boundary of the domain, and the control is included additively in the inhomogeneity. The set of admissible controls is the unit ball in the corresponding space of square integrable functions. Solutions of the obtained boundary value problems are considered in the generalized sense as elements of a Hilbert space. The optimality criterion is the sum of the squared norm of the deviation of the state from a given state and the squared norm of the control with a coefficient. This structure of the optimality criterion makes it possible to strengthen, if necessary, the role of either the first or the second term of the criterion. In the first case, it is more important to achieve the desired state, while, in the second case, it is preferable to minimize the resource consumption. We study in detail the asymptotics of the problem generated by the sum of the Laplace operator with a small coefficient and a first-order differential operator. A feature of the problem is the presence of the characteristics of the limit operator which touch the boundary of the domain. We obtain a complete asymptotic expansion of the solution of the problem in powers of the small parameter in the case where the optimal control is an interior point of the set of admissible controls.     

Limiting Distributions for the Maximum of a Symmetric Function on a Random Point Set

Let U ₁, U ₂, ... be a sequence of independent random points taking values in a measurable space (S, Σ) according to a common probability P and let R be a symmetric, Borel/ -measurable function. Let H _n = max{h(U _i ,U _j ): 1≤ i < j≤ n} denote the maximum h-value over pairs of distinct points from U ₁,U ₂,...,U _n . Assumptions on the distribution of h(U ₁,·) are provided under which a continuous function of H _n converges in law to an extreme-value distribution upon suitable rescaling. The work is complementary to that appearing in Appel et al. (1999) J. Theor. Probab. 12, 27–47. on the almost-sure limiting behavior of H _n . In the first of two examples, the main result applied to the case of i.i.d. points distributed uniformly on the surface of a unit hypersphere in R ^d provides the limiting distribution of the maximum pairwise distance (chord length) among the first n of the points. The second example exhibits the limiting distribution of the minimum pair-wise distance among the first n of i.i.d. uniform points in a compact subset of R ^d .      

外界场作用下的波前曲率关系和波形变化

研究外界场作用下,激发介质的波前曲率关系和波形变化·　理论分析波前曲率关系,得到外界场作用下,波前的法向速度与波前平均曲率、平面波速和外界场之间的线性关系·　数值分析外界场作用下,激发介质的Bar_Eiswirth模型,得到外界场作用下激发介质的波形图案·　这里的理论分析、数值结果与BZ反应的实验结果完全一致,从而解释了外界场作用下的BZ现象,且由数值结果可知激发介质包含丰富的波形图案·     

Mathematical Modeling of the Telluric Field near Extended Conductors

A procedure is proposed for simulating the telluric field near nonhomogeneous hollow cylindrical extended conductors of arbitrary finite length. The procedure allows for the nonhomogeneous conductivity of the conductor with a thin insulating coating. The surrounding medium is layered with three-dimensional nonhomogeneities, which may intersect the conductor. The external telluric field is specified based on actual distributional information.     

Asymptotics of Eigenvalues for a Class of Jacobi Matrices with Limiting Point Spectrum

In this paper, we study a class of Jacobi matrices with very rapidly decreasing weights. It is shown that the Weyl function (the matrix element of the resolvent of the operator) for the class under study can be expressed as the ratio of two entire transcendental functions of order zero. It is shown that the coefficients in the expansion of these functions in Taylor series are proportional to the generating functions of the number of integral solutions defined by certain Diophantine equations. An asymptotic estimate for the eigenvalues is obtained.     

The Sylow p-Subgroups of a Limiting (Stable) Linear Group over an Algebraically Closed Field

In Math. Zh. 36(3) (1963), 240–246, we considered the classification of Sylow p-subgroups of a countable (finitary) symmetric group. Later, we extended this classification to Sylow p-subgroups of a limiting (stable) linear group over a finite field GF(q) with char(GF(q)) p. In this paper, the classification of the Sylow p-subgroups of the limiting (stable) linear group GL() is given for an algebraically closed field of characteristic p. Every Sylow p-subgroup is characterized by a p-adic integer together with a finite or countable cardinal.     

不可压缩橡胶类材料裂纹尖端应力应变场*

本文对平面应变情况下不可压缩橡胶类材料裂纹尖端弹性场进行了有限变形分析.裂纹尖端场被分为收缩区和扩张区.借助于新的应变能函数和变形模式,推出了尖端场各区的渐近方程,得到了尖端场的完整描述.本文对奇异性作了讨论,得到了不可压缩橡胶类材料裂纹尖端应力及应变分布曲线,揭示了裂纹尖端应力应变场的特性.     

The Limiting Absorption Principle for Elastic Wave Propagation Problems in Perturbed Stratified Media ℝ3

We consider the self-adjoint operator governing the propagation of elastic waves in perturbed stratified media ℝ³ with free boundary–interface conditions. In this paper we establish the limiting absorption principle for this self-adjoint operator in appropriate Hilbert space. The proof of the limiting absorption principle is based on the division theorem which is proved by means of eigenfunction expansions for the self-adjoint operator governing the propagation of elastic waves in unperturbed stratified media ℝ³.     

The Broken Ray Transform on the Square

We study a particular broken ray transform on the Euclidean unit square and establish injectivity and stability for \(C_{0}^{2}\) perturbations of a vanishing absorption parameter \(\sigma \equiv 0\) . Given an open subset \(E\) of the boundary, we measure the attenuation of all broken rays starting and ending at \(E\) with the standard optical reflection rule applied to \(\partial \Omega {\setminus } E\) . Using the analytic microlocal approach of Frigyik et al. for the X-ray transform on generic families of curves, we show injectivity via a path unfolding argument under suitable conditions on the available broken rays. Then we show that with a suitable decomposition of the measurement operator via smooth cutoff functions, the associated normal operator is a classical pseudo differential operator of order \(-1\) , which leads to the desired result.     

The Behavior of Solutions to a Special Abel Equation of the Second Kind near a Nodal Singular Point

Computational Mathematics and Mathematical Physics - The propagation of a diffusion–reaction plane traveling wave (for example, a flame front), the charge distribution inside a heavy atom in...     

The Gravitational Field of an Electrically Charged Mass Point and the Causality Principle in the RTG

We find the effective Riemannian space–time corresponding to the gravitational field generated by a charged mass point in the framework of the relativistic theory of gravity. The causality principle plays an important role in solving this problem. The analytic form and the domain of definition, i.e., the gravitational radius, of the obtained solution differ from the corresponding results in Einstein's general relativity theory.     

Solitary Wave Solutions of Delayed Coupled Higgs Field Equation

This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|²-2uv-τu(|u|²)x=0 vtt+vxx-β(|u|^x)xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.     

Field theory and anisotropy of a cubic ferromagnet near the Curie point

It is known that critical fluctuations can change the effective anisotropy of a cubic ferromagnet near the Curie point. If the crystal undergoes a phase transition into the orthorhombic phase and the initial anisotropy is not too strong, then the effective anisotropy acquires the universal value A* = v*/u* at T _c, where u* and v* are the coordinates of the cubic fixed point of the renormalization group equations in the scaling equation of state and expressions for nonlinear susceptibilities. Using the pseudo-?-expansion method, we find the numerical value of the anisotropy parameter A at the critical point. Padé resummation of the six-loop pseudo-?-expansions for u*, v*, and A* leads to the estimate A* = 0.13 ± 0.01, giving evidence that observation of anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is entirely possible.     

Bound States of a Particle in the Field of Receding Point Potentials

We study bound states in a nonstationary system of receding δ-centers. We consider the states characterized by different depths of point spectrum levels in one-dimensional and three-dimensional problems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 385–392, December, 2005.