确定热传导方程系数的反问题的又一方法

用另一种方法研究了确定热传导方程系数的反问题的存在性和唯一性     

Coefficient Matrices of a Quantum Discrete Auxiliary Linear Problem

In the present paper, we describe general properties of quantum matrices that are coefficient matrices of an auxiliary problem for quantum discrete three-dimensional integrable models. Our goal is to prove a universal functional equation for the quantum determinant in the case of a finite-dimensional representation of a local Weyl algebra. Bibliography: 4 titles.     

求解2—D波动方程系数反问题的迭代方法及收敛性

本文针对地震勘探中提出一类重要的２－Ｄ波动方程反演问题，通过定义一个新的非线性算子将２－Ｄ波动方程的反演问题归结为一个新的非线性算子方程，详细讨论了非线性算子的性质，给出了求解反问题的迭代方法，并证明了这种迭代方法的收敛性。     

一类变系数线性波动方程初值问题的求解

本文讨论了一类变系数线性波动方程初值问题的求解，获得较为理想的结果．     

Global Solutions for Leading Coefficient Problem of Polynomial-like Iterative Equations

For some technical difficulties many known results on the existence of solutions of the polynomial-like iterative equation, even though they are given globally on a closed interval between two fixed points, require the coefficient of the first order iterate term to be large. Recently, great attentions have been paid to the so-called leading coefficient problem, i.e., the existence of solutions under the most natural assumption that the coefficient of the highest order iterate term, called the leading coefficient, does not vanish but plays the main role. Some results on solutions near a fixed point were obtained. In this paper we prove the existence of continuous solutions globally on a closed interval between two fixed points, which are approximated by sequences of solutions which are locally linear near an end-point.     

奇异半线性热方程初值问题解的存在性与Blow-up问题

本文讨论如下奇异半线性热方程的初值问题其中γ＞1，σ＞O，f（x）连续有界非负但不恒为零．我们讨论了问题（1），（2）非负局部经典解的存在性和非负整体解的不存在问题，得到当0＜σ＜1且时，（1），（2）没有非负整体解．当σ＝1且时，（1），（2）没有非负整体解，当σ＞1时（1），（2）没有非负整体解．     

The Problem With Missing Shift Condition for the Gellerstedt Equation With a Singular Coefficient

For the Gellerstedt equation with singular coefficient we prove theorems of uniqueness and existence of solution to the problemwith the missing shift condition on the boundary characteristics and the Frankl type condition on the degeneration segment of the equation.     

The Steklov Problem in a Half-Plane: the Dependence of Eigenvalues on a Piecewise-Constant Coefficient

The Steklov problem considered in the paper describes free two-dimensional oscillations of an ideal, incompressible, heavy fluid in a half-plane covered by a rigid dock with two symmetric gaps. Equivalent reduction of the problem to two spectral problems for integral operators allows us to find limits for all eigenfrequencies as the distance between the gaps tends to zero or infinity. For the fundamental eigenfrequency and the corresponding eigenfunction, two terms are found in the asymptotic expansion as the distance tends to infinity. It is proved that all eigenvalues are simple for any distance. Bibliography: 15 titles.Dedicated to the centenary of V. A. Steklovs paper [1]__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 162–190.     

The Method of Fundamental Solution for a Radially Symmetric Heat Conduction Problem with Variable Coefficient

We consider an inverse heat conduction problem with variable coefficient on an annulus domain. In many practice applications, we cannot know the initial temperature during heat process, therefore we consider a non-characteristic Cauchy problem for the heat equation. The method of fundamental solutions is applied to solve this problem. Due to ill-posedness of this problem, we first discretize the problem and then regularize it in the form of discrete equation. Numerical tests are conducted for showing the effectiveness of the proposed method.     

An Iterative Algorithm for the Coefficient Inverse Problem of Differential Equations

In this paper, an iterative algorithm for solving a coefficient inverse problem is submitted. The key of the method is to project an unknown coefficient function on a finite dimensional function space. Thus, the inverse problem can be changed into a nonlinear algebraic system of equations.     

The Eigenvalue Problem for a One-Dimensional Differential Operator with a Variable Coefficient and Nonlocal Integral Conditions*

We consider conditions for the existence of the eigenvalue λ = 0 in the eigenvalue problem for a differential operator with a variable coefficient and integral conditions. We analyze how these conditions depend on such properties of the coefficient p(x) as monotonicity and symmetry and observe some other properties of the spectrum of the eigenvalue problem. Particularly, we show by a numerical experiment that the fundamental theorem on the increase of the eigenvalues in the case of increasing coefficient p(x) is not valid for the eigenvalue problem with nonlocal conditions.     

The option value of advanced R & D

Existing tools for making R&D investment decisions cannot properly capture the option value in R&D. Since many new products are identified as failures during the R&D stages, the possibility of refraining from market introduction may add a significant value to the NPV of the R&D project. This paper presents new theoretical insight by developing a stochastic jump amplitude model in a real setting. The option value of the proposed model depends on the expected number of jumps and the expected size of the jumps in a particular business. The model is verified with empirical knowledge of current research in the field of multimedia at Philips Corporate Research. This way, the gap between real option theory and the practice of decision making with respect to investments in R&D is diminished.     

波动方程系数反问题的求解方法

讨论了一维波动方程系数反演的一种求解方法,将解进行一阶渐进展开,得到相应的反问题,将其转化为第二类Volttera型积分方程组,证明了反问题解的存在唯一性.     

Local Stability for an Inverse Coefficient Problem of a Fractional Diffusion Equation

Time-fractional diffusion equations are of great interest and importance on describing the power law decay for diffusion in porous media. In this paper, to identify the diffusion rate, i.e., the heterogeneity of medium, the authors consider an inverse coefficient problem utilizing finite measurements and obtain a local Hlder type conditional stability based upon two Carleman estimates for the corresponding differential equations of integer orders.     

Hölder regularity of the SLE trace

S. Rohde and O. Schramm have recently shown that the SLE trace is Hölder continuous (2005). However, their results are not optimal for all values of and only yield a Hölder exponent near for near 0. In this paper, we give improved lower bounds on the optimal Hölder exponent for two natural parametrizations of the SLE trace. Our estimates give a Hölder exponent near 1 for near 0, as expected. The work of I. Binder and B. Duplantier (2002) suggests that our results are optimal for the two parametrizations considered.

     

Inverse Problem of Determining an Unknown Coefficient in the Beam Vibration Equation

Differential Equations - We consider the direct initial–boundary value problem for the equation of transverse vibrations of a homogeneous beam freely supported at the ends and study the...     

On One Approach to the Numerical Solution of a Coefficient Inverse Problem

Doklady Mathematics - An approach to solving the problem of determining the thermal conductivity coefficient of a substance based on the results of observing the dynamics of the temperature field...