On parabolic equations with a small parameter

A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed.     

An initial boundary value problem for a pseudoparabolic equation with a nonlinear boundary condition

An initial boundary value problem for a quasilinear equation of pseudoparabolic type with a nonlinear boundary condition of the Neumann–Dirichlet type is investigated in this work. From a physical point of view, the initial boundary value problem considered here is a mathematical model of quasistationary processes in semiconductors and magnets, which takes into account a wide variety of physical factors. Many approximate methods are suitable for finding eigenvalues and eigenfunctions in problems where the boundary conditions are linear with respect to the desired function and its derivatives. Among these methods, the Galerkin method leads to the simplest calculations. On the basis of a priori estimates, we prove a local existence theorem and uniqueness for a weak generalized solution of the initial boundary value problem for the quasilinear pseudoparabolic equation. A special place in the theory of nonlinear equations is occupied by the study of unbounded solutions, or, as they are called in another way, blow-up regimes. Nonlinear evolutionary problems admitting unbounded solutions are globally unsolvable. In the article, sufficient conditions for the blow-up of a solution in a finite time in a limited area with a nonlinear Neumann–Dirichlet boundary condition are obtained.     

Banach空间中依中间意义渐近非扩张映象具误差的三步平均值迭代序列收敛问题

研究了Banach空间中依中间意义渐近非扩张映象具误差的三步平均值迭代序列收敛问题,所得结果改进和发展了相关文献中的结果.     

Solving linear systems of differential and difference equations with respect to a part of the unknowns

The existence of solutions y to a linear differential or difference system whose components $y_{i_1 } ,...,y_{i_m } $ belong to a given class of functions and the problem of constructing such components are considered.     

Fixed points for operators in a space of continuous functions and applications

This paper investigates the fixed points for self-maps of a closed set in a space of abstract continuous functions. Our main results essentially extend the Banach contracting mapping principle. An application to integro-differential equations is given.

     

Computation of the scattering amplitude for a scattering wave produced by a disc — Approach by a fundamental solution method

Our fundamental solution method gives an analytic representation of the approximate solution for the reduced wave problem in the exterior region of a disc. The asymptotic behavior of this representation yields an approximate formula for the scattering amplitude. An error estimate for this formula is given. We add two numerical tests: the numerical estimate of errors; and profiles of scattering cross sections and the far-field coefficient. Both tests include cases of high wave numbers.     

The Weierstrass semigroup of a pair of GaloisWeierstrass points with prime degree on a curve

We describe the Weierstrass semigroup of a Galois Weierstrass point with prime degree and the Weierstrass semigroup of a pair of Galois Weierstrass points with prime degree, where a Galois Weierstrass point with degree n means a total ramification point of a cyclic covering of the projective line of degree n.*Supported by Korea Research Foundation Grant (KRF-2003-041-C20010).**Partially supported by Grant-in-Aid for Scientific Research (15540051), JSPS.     

战争设计工程中定性定量相结合方法研究

定性定量相结合方法是战争设计工程的技术基础,如何有效地运用定性定量相结合去解决战争复杂系统的设计问题,是战争设计工程的关键.在战争设计工程的基础上,分析了战争设计工程中定性定量相结合的特点,论述了战争设计工程中定性定量在任务逻辑上、专家上和人与计算机上的分工机制及战争设计工程中定性定量的结合模式,给出战争设计工程解决问题的技术路线.     

Asymptotics of a second-order differential equation with a small parameter in the case when the reduced equation has two solutions

The boundary value problem for a second-order nonlinear ordinary differential equation with a small parameter multiplying the highest derivative is examined. It is assumed that the reduced equation has two solutions with intersecting graphs. Near the intersection point, the asymptotic behavior of the solution to the original problem is fairly complex. A uniform asymptotic approximation to the solution that is accurate up to any prescribed power of the small parameter is constructed and justified.     

一类巨灾风险—地震灾害债券的设计

巨灾保险风险证券化是国际上分散巨灾风险的一项金融保险创新.对我国而言,发展巨灾保险风险证券化最适宜的证券品种是巨灾债券.收集1969~2004年我国地震直接经济损失在9900万元以上的损失数据,利用非寿险精算技术分析我国地震损失分布和次数,并在此基础上利用CAPM和债券定价原理计算地震灾害债券的收益率和价格,从而对地震灾害债券作了初步设计.     

Small periodic solutions of nonlinear systems of differential equations with constant deviation

We consider a nonlinear system of differential equations in a general case with a singular matrix at the derivatives, with a vector deviation which depends on a parameter. We seek for a periodic solution to the system in the set of trigonometric series such that the sequences of their coefficients belong to the space l ₁.We use the method, representing a space as a direct sum of subspaces, and the method of a fixed point of a nonlinear operator as the main investigation techniques.We reduce the question on the existence of a periodic solution to that of the solvability of an operator equation, whose principal part is defined in a finite-dimensional space.     

Deza graphs with parameters (v,k,k−2,a)

A Deza graph with parameters $\left(v,k,b,a\right)$ is a $k$‐regular graph on $v$ vertices in which the number of common neighbors of two distinct vertices takes one of the following values: $b$ or $a$, where $b\ge a$. In the previous papers Deza graphs with $b=k?1$ were characterized. In this paper, we characterize Deza graphs with $b=k?2$.     

幂律速度运动表面上磁流体在驻点附近的滑移流动

从理论上研究了具有非线性延伸表面的磁流体在滑移流区的动量传输问题.通过Lie群变换把控制方程组转化为常微分方程组,利用同伦分析方法求得了问题的近似解析解.获得的级数解与文献中的数值解吻合得较好.另外,利用级数解分析滑移参数、磁场强度、速度比率参数、吸入喷注参数和幂律指数对流动的影响.结果显示这些参数对壁剪切力和边界层内流场有较大的影响.     

Permanental sequences related to a Markov chain example of Kolmogorov

Permanental sequences with non-symmetric kernels that are generalization of the potentials of a Markov chain with state space $\{0,1∕2,\dots ,1∕n,\dots \}$ and a single instantaneous state that was introduced by Kolmogorov, are studied. Depending on a parameter in the kernels we obtain an exact rate of divergence of the sequence at 0, an exact local modulus of continuity of the sequence at 0, or a precise bounded discontinuity for the sequence at 0.     

时标上拥有积分边界条件的一阶脉冲动力方程解的存在性

考虑时标上一阶拥有积分边界条件的脉冲动力方程,通过上下解方法结合单调迭代技术得到解存在的充分条件,所得结果包括了周期边值问题、初值问题并且改进和丰富了已有文献的结论,并举例说明其应用.     

Inverse coefficient problem for a wave equation in a bounded domain

The nonlinear inverse problem for a wave equation is investigated in a three-dimensional bounded domain subject to the Dirichlet boundary condition. Given a family of solutions to the equation defined on a closed surface within the original domain, it is required to reconstruct the coefficient determining the velocity of sound in the medium. The solutions used for this purpose correspond to the acoustic medium perturbations localized in the neighborhood of a certain closed surface. The inverse problem is reduced to a linear integral equation of the first kind, and the uniqueness of the solution to this equation is established. Numerical results are presented.     

On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers

The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 10³. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ～ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ～ 5 × 10³.     

Stability analysis of a stochastic logistic model with nonlinear diffusion term

This paper presents an asymptotic analysis of a stochastic logistic population model with nonlinear diffusion term. The classical probability method is applied to obtain the criteria of asymptotic behavior for the considered model. The numerical simulations validate the efficiency of the theory analysis.     

一类反应扩散方程非负平衡解的存在性

本文利用锥映象不动点指数计算方法,结合极值原理、上下解方法以及算子的谱分析,得出了一类反应扩散方程非负平衡解的存在性。     

一类具阻尼非线性波动方程的Cauchy问题

本文研究一类具阻尼非线性波动方程Cauchy问题整体广义解和整体古典解的存在唯一性,并用凸性方法给出解爆破的充分条件.