Riemann boundary-value problem with index minus infinity on a rectifiable curve

The author investigates the piecewise-continuous Riemann boundary-value problem with index minus infinity on a closed rectifiable Jordan curve; the index of the problem is a measure of the integral effect exerted on the solvability of the problem by the argument and modulus of the coefficient, and also by the properties of the junction curve. Discontinuities of the second kind are admitted in the logarithm of the coefficient and in the free term. The solution of the problem is constructed explicitly in the class of functions having a weak power singularity.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 10, pp. 1350–1356, October, 1990.     

一类相关性指标优化IOWHA区间预测模型的比较研究——以民航客运量为例

单点值预测有其局限性,因为客观世界许多影响因素都呈现出动态的范围区间.运用变权系数区间组合思想,引入相关性指标,将相关性指标与IOWHA结合,研究相关性指标优化IOWHA区间组合算法的可行性,建立基于区间中点和区间半径的相关性指标优化IOWHA区间组合预测模型,基于偏好系数把多目标最优化问题转化为单目标最优化问题.实例演算得出基于相关系数、向量夹角余弦和灰色关联度优化的IOWHA区间模型能有效地提高预测精度,证实了相关性指标优化IOWHA区间组合模型的有效性与合理性.     

Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. I

We study the Riemann boundary problem with infinite index of logarithmic order on an open rectifiable Jordan spiral-form contour, here the influence of the contour on the solvability of the problem is comparable with the influence of the argument of its coefficient. An explicit solution of the problem is constructured in the class of functions admitting weak-power singularities at the ends of a line of conjugacy.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1509–1517, November, 1990.     

Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. II

We study the inhomogeneous Riemann boundary problem with infinite index of logarithmic order on an open rectifiable spiral-form Jordan contour where the influence of the contour on the solvability of the problem is comparable with the influence of the argument of its coefficient. A solution of the problem is constructed explicitly in the class of functions admitting weak power singularities at the ends of a line of conjugacy.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1672–1681, December, 1990.     

Ad Hoc网络区域划分和资源分配问题研究

主要利用图论、概率统计及优化理论对Ad-Hoc网络进行了数学建模.研究了等圆(不等圆)区域覆盖、带障碍区域的覆盖、确定性点覆盖、信道分配、抗毁度、节能性和通信质量等问题.定义了覆盖效率、抗毁性概率指标、覆盖系数、期望覆盖系数、网络寿命等一系列评价系数和衡量标准,提出了基于单位距离覆盖系数和期望覆盖系数的启发式寻优算法,并编程加以实现,得到较满意的近似解.     

A homogeneous Hilbert problem with discontinuous coefficients and two-side curling at infinity point of order 1/2 ≤ ρ < 1

We study a homogeneous Riemann??Hilbert boundary-value problem in the upper half of the complex plane with a countable set of coefficient discontinuities and two-side curling at infinity. We obtain a general solution in the case when the problem index has a power singularity of order ??, 1/2 ?? ?? < 1, and study the solvability conditions.     

On some constructive methods for the matrix Riemann–Hilbert boundary-value problem

In this paper we consider the relations between the Riemann–Hilbert monodromy problem and the matrix Riemann–Hilbert boundary-value problem with piecewise continuous coefficient and construct the so-called canonical matrix for the boundary-value problem for a piecewise continuous matrix-function. The formula for the calculation of the index is also obtained.     

Solving a nonlinear inverse Robin problem through a linear Cauchy problem

ABSTRACT

Considered in this paper is an inverse Robin problem governed by a steady-state diffusion equation. By the Robin inverse problem, one wants to recover the unknown Robin coefficient on an inaccessible boundary from Cauchy data measured on the accessible boundary. In this paper, instead of reconstructing the Robin coefficient directly, we compute first the Cauchy data on the inaccessible boundary which is a linear inverse problem, and then compute the Robin coefficient through Newton's law. For the Cauchy problem, a parameter-dependent coupled complex boundary method (CCBM) is applied. The CCBM has its own merits, and this is particularly true when it is applied to the Cauchy problem. With the introduction of a positive parameter, we can prove the regularized solution is uniformly bounded with respect to the regularization parameter which is a very good property because the solution can now be reconstructed for a rather small value of the regularization parameter. For the problem of computing the Robin coefficient from the recovered Cauchy data, a least square output Tikhonov regularization method is applied to Newton's law to obtain a stable approximate Robin coefficient. Numerical results are given to show the feasibility and effectiveness of the proposed method.     

基于灰类敏感度系数的评价指标客观权重极大熵配置模型

评价指标权重的确定是多属性决策问题中至关重要的环节。然而,既有研究利用评价指标值之间的差异性进行指标的客观赋权,往往忽略了评价指标对被评价对象全体及所在系统的重要性。本文基于事物自然本质属性差异,运用灰色关联聚类将评价对象划分到预设的类别;借鉴有无对比分析法的思想,定义了反映指标对全体被评价对象类别影响程度的灰类敏感度系数;根据极大熵准则,建立了基于灰类敏感度系数的客观权重极大熵配置模型,以确定多属性决策指标的权重。并通过与文献[21,26]中实际案例的对比分析,说明了本模型的有效性与更贴近现实性,为解决多属性决策指标客观赋权问题提出了一个新思路。     

Analytical solutions of the boundary layer flow of power-law fluid over a power-law stretching surface

This article discusses analytical solutions for a nonlinear problem arising in the boundary layer flow of power-law fluid over a power-law stretching surface. Using perturbation method analytical solution is presented for linear stretching surface. This solution covers large range of shear thinning and shear thickening fluids and matches excellently with the numerical solution. Furthermore, some new exact solutions are found for particular combination of m (power-law stretching index) and n (power-law fluid index). This leads to generalize the case of linear stretching to nonlinear stretching surface. The effects of fluid index n on the boundary layer thickness and the skin friction for nonlinear stretching surface is analyzed and discussed. It is observed that the boundary layer thickness and the skin friction coefficient increase as non-linear parameter n decreases. This study gives a new dimension to obtain analytical solutions asymptotically for highly nonlinear problems which to the best of our knowledge has not been examined so far.     

基于改进模糊综合评判的分销商评价研究

随着制造业逐渐向买方市场转变,供应链分销管理成为企业发展的驱动力之一。分销商在该环节发挥着关键作用,选择和管理分销商的前提是对其进行科学的评价。在回顾分销商评价方法的基础上,提出了基于模糊综合评判的分销商评价模型。针对传统模糊综合评判在指标赋权方面的不足,采用组合赋权法加以改进,首先对多种指标权数计算结果进行事前检验,根据检验结果确定最佳组合方式,然后通过事后检验保证组合权数的合理性。指标权数确定后,再经过因素集与评判集的确定、单因素评判、综合评判等阶段对分销商进行评价。最后将改进方法与传统方法进行了比较分析,并以某大型家电企业为例,验证了该方法能更为合理地解决分销商评价问题。     

Optical Tomography for Variable Refractive Index with Angularly Averaged Measurements

In optical tomography one seeks to use near-infrared light to determine the optical absorption and scattering properties of a medium X ? ? ⁿ . If the refractive index is constant throughout the medium, the steady-state case is modeled by the stationary linear transport equation in terms of the Euclidean metric. In this work we consider the case of variable refractive index where the dynamics are modeled by writing the transport equation in terms of a Riemannian metric; in the absence of interaction, photons follow the geodesics of this metric. In particular we study the problem where our measurements allow the application of an in-going flux depending on both position and direction, but we allow only a weighted average measurement of the out-going flux. We show that making measurements on all of ? X determines the extinction coefficient and that once this is known, under additional assumptions, measurements at a single point on ? X determine the scattering kernel.     

Matrix displacement mappings in the numerical solution of functional and nonlinear differential equations with the tau method

The use of matrix displacement mappings reduces most matrix operations required in the construction of an approximate solution of a functional or differential equation by means of Ortiz' formulation of the Tau method to index shifts. The coefficient vector of the approximate solution is defined implicitly by a very sparse system of linear algebraic equations. The contributions of the differential or functional operator, and of the supplementary conditions of the problem (initial, boundary, or multipoint conditions) are treated with a single and versatile procedure of remarkable simplicity, which can be easily implemented in a computer. We give two nontrivial examples on the application of this approach: the first is a nonlinear boundary value problem with a continuous locus of singular points and multiple solutions, where stiffness is present, the second is a functional differential equation arising in analytic number theory. In both cases we obtain results of nigh accuracy.     

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 problem of recovering the permittivity coefficient from the modulus of the scattered electromagnetic field

Under consideration is the stationary system of equations of electrodynamics relating to a nonmagnetic nonconducting medium. We study the problem of recovering the permittivity coefficient ε from given vectors of electric or magnetic intensities of the electromagnetic field. It is assumed that the field is generated by a point impulsive dipole located at some point y. It is also assumed that the permittivity differs from a given constant ε₀ only inside some compact domain Ω ? R³ with smooth boundary S. To recover ε inside Ω, we use the information on a solution to the corresponding direct problem for the system of equations of electrodynamics on the whole boundary of Ω for all frequencies from some fixed frequency ω ₀ on and for all y ∈ S. The asymptotics of a solution to the direct problem for large frequencies is studied and it is demonstrated that this information allows us to reduce the initial problem to the well-known inverse kinematic problem of recovering the refraction index inside Ω with given travel times of electromagnetic waves between two arbitrary points on the boundary of Ω. This allows us to state uniqueness theorem for solutions to the problem in question and opens up a way of its constructive solution.     

On noninferior performance index vectors

The noninferior vector index problem of optimal control theory is investigated in an effort to establish some basic properties of the noninferior index surface in the generalN-dimensional index problem. The vector performance index problem is first converted to a family of scalar index problems by forming an auxiliary scalar index as a function of the vector index and a vector of weighting parameters. The functional relationship between noninferior vectors and the weighting vectors of the auxiliary index problem is investigated for the particular case in which the auxiliary index is a weighted sum of the vector index elements. Special attention is devoted to the noninferior index problem for whichN = 2.     

Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation

New weighted modifications of direct statistical simulation methods designed for the approximate solution of the nonlinear Smoluchowski equation are developed on the basis of stratification of the interaction distribution in a multiparticle system according to the index of a pair of interacting particles. The weighted algorithms are validated for a model problem with a known solution. It is shown that they effectively estimate variations in the functionals with varying parameters, in particular, with the initial number N ₀ of particles in the simulating ensemble. The computations performed for the problem with a known solution confirm the semiheuristic hypothesis that the model error is O(N ₀ ^?1 ). Estimates are derived for the derivatives of the approximate solution with respect to the coagulation coefficient.     

On the nonresonance property of linear differential-algebraic systems

We consider a system of linear ordinary differential equations in which the coefficient matrix multiplying the derivative of the unknown vector function is identically singular. For systems with constant and variable coefficients, we obtain nonresonance criteria (criteria for bounded-input bounded-output stability). For single-input control systems, we consider the problem of synthesizing a nonresonant system in the stationary and nonstationary cases. An arbitrarily high unsolvability index is admitted. The analysis is carried out under assumptions providing the existence of a so-called “equivalent form” with separated “algebraic” and “differential” components.     

Two inverse problems of finding a coefficient in a parabolic equation

For a parabolic equation, we consider inverse problems of reconstructing a coefficient that depends on the space variables alone. The first problem is to find a lower-order coefficient c(x) multiplying u(x, t), and the second problem is to find the coefficient a(x) multiplying Δu. As additional information, the integral of the solution with respect to time with some weight function is given. The coefficients of the equation depend both on time and on the space variables. We obtain sufficient conditions for the existence of generalized solutions of our problems; moreover, for the first problem, we also prove uniqueness and construct an iterative sequence that converges to the desired coefficient almost everywhere in the domain. We present examples of input data of these problems for which the assumptions of our theorems are necessarily true.