Riemann boundary problem with index plus-infinity on a rectifiable curve

A piecewise-continuous Riemann boundary problem with index plus-infinity on a closed rectifiable Jordan curve is studied; here the index of the problem takes into account the integral influence on its solvability of the argument and modulus of the coefficient of the problem and also the properties of the line of conjugation. One permits discontinuities of the second kind in the logarithm of the coefficient and the free term of the problem. The solution of the problem is constructed explicitly in the class of functions admitting a weak-power singularity.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 9, pp. 1204–1213, September, 1990.     

Integral equations related to the study of an inverse coefficient problem for a system of partial differential equations

We consider an inverse coefficient problem for a linear system of partial differential equations. The values of one solution component on a given curve are used as additional information for determining the unknown coefficient. The proof of the uniqueness of the solution of the inverse problem is based on the analysis of the unique solvability of a homogeneous integral equation of the first kind. The existence of a solution of the inverse problem is proved by reduction to a system of nonlinear integral equations.     

Iterative method for solving an inverse coefficient problem for a hyperbolic equation

For a hyperbolic equation, we consider an inverse coefficient problem in which the unknown coefficient occurs in both the equation and the initial condition. The solution values on a given curve serve as additional information for determining the unknown coefficient. We suggest an iterative method for solving the inverse problem based on reduction to a nonlinear operator equation for the unknown coefficient and prove the uniform convergence of the iterations to a function that is a solution of the inverse problem.     

非线性回归方法的应用与比较

比较了非线性回归3种方法的数学原理:曲线直线化方法、非线性最小二乘方法、近似非线性法.说明了用方差分析确定回归模型的统计学意义、用决定系数R2描述曲线的拟合效果的理论依据.通过对同一问题用3种方法分析得出结论:非线性回归与近似非线性拟合方法决定系数相近(0.9966与0.9965),而曲线直线化决定系数为0.9738.因为近似非线性拟合方法无需选初值.建议应用近似非线性拟合方法.     

Reconstruction of the Linear Ordinary Differential System Based on Discrete Points

In this paper, we discuss an inverse problem, i.e., the reconstruction of a linear differential dynamic system from the given discrete data of the solution. We propose a model and a corresponding algorithm to recover the coefficient matrix of the differential system based on the normal vectors from the given discrete points, in order to avoid the problem of parameterization in curve fitting and approximation. We also give some theoretical analysis on our algorithm. When the data points are taken from the solution curve and the set composed of these data points is not degenerate, the coefficient matrix $A$ reconstructed by our algorithm is unique from the given discrete and noisefree data. We discuss the error bounds for the approximate coefficient matrix and the solution which are reconstructed by our algorithm. Numerical examples demonstrate the effectiveness of the algorithm.     

Inverse problems for a quasilinear hyperbolic equation in the case of moving observation point

We consider two inverse coefficient problems for a quasilinear hyperbolic equation, where the additional information used for finding the coefficients is the values of the solution on some curve. (This corresponds to measurements performed at a moving observation point.) The unknown coefficient depends on the space variable in the first inverse problem and on the solution of the equation in the second inverse problem. We prove theorems of uniqueness of solution to the inverse problems.     

Index form for nonholonomic distributions

The purpose of this paper is to derive an invariant Jacobi equation for horizontal geodesics on a nonholonomic distribution. The classical Bliss??s theory is known to be not geometrically invariant; it also produces ??extra?? conjugate points. ??Extra?? conjugate points also appear in the accessory problem in the optimal control theory. Hence the restriction of the functional of the index form of a curve to the distribution is considered. It is assumed that the distribution satisfies the cyclicity condition. A sufficient condition for the positive definiteness of the index form and the optimality of a curve is obtained.     

An Oscillation Theorem for Self-Adjoint Differential Equations

We consider a class of degenerate classical pseudodifferential operators on a closed curve and compute their index in Sobolev spaces. The index is expressed as a winding number by means of the principal and the subprincipal symbol. Furthermore, applications to the smoothness of solutions and the degenerate oblique derivative problem in the plane are given.     

Strongly polynomial algorithm for a class of combinatorial LCPs

We show that an LCP with positive definite coefficient matrix can be solved in time polynomially bounded by the size of the numbers in the coefficient matrix. As a special case, we have a strongly polynomial algorithm for the problem of fitting the best convex curve to a given set of points in R².     

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.     

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.     

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.     

农村卫生资源配置公平性研究——基于2003-2005年黑龙江省13个地区的数据分析

运用多种评价指标研究黑龙江省农村卫生资源配置公平性,发现黑龙江省十三个地区各类卫生资源的三种公平性指数高度一致;卫生资源主要是按人口分布配置的,且公平性在逐渐降低;哈尔滨市、绥化市等地区资源配置公平性较高.同时显示政府的认识和重视程度影响资源配置的公平性.     

Rethinking an ROC partial area index for evaluating the classification performance at a high specificity range

The area under a receiver operating characteristic (ROC) curve is valuable for evaluating the classification performance described by the entire ROC curve in many fields including decision making and medical diagnosis. However, this can be misleading when clinical tasks demand a restricted specificity range. The partial area under a portion of the ROC curve (\({ pAUC}\)) has more practical relevance in such situations, but it is usually transformed to overcome some drawbacks and improve its interpretation. The standardized \({ pAUC}\) (\({ SpAUC}\)) index is considered as a meaningful relative measure of predictive accuracy. Nevertheless, this \({ SpAUC}\) index might still show some limitations due to ROC curves crossing the diagonal line, and to the problem when comparing two tests with crossing ROC curves in the same restricted specificity range. This paper provides an alternative \({ pAUC}\) index which overcomes these limitations. Tighter bounds for the \({ pAUC}\) of an ROC curve are derived, and then a modified \({ pAUC}\) index for any restricted specificity range is established. In addition, the proposed tighter partial area index (\({ TpAUC}\)) is also shown for classifier when high specificity must be clinically maintained. The variance of the \({ TpAUC}\) is also studied analytically and by simulation studies in a theoretical framework based on the most typical assumption of a binormal model, and estimated by using nonparametric bootstrap resampling in the empirical examples. Simulated and real datasets illustrate the practical utility of the \({ TpAUC}\).     

Shape recovery for sparse‐data tomography

A two‐dimensional sparse‐data tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A nonuniform rational basis splines (NURBS) curve is used as a computational representation of the boundary. This approach conveniently provides the result in a format readily compatible with computer‐aided design software. However, the linear tomography task becomes a nonlinear inverse problem because of the NURBS‐based parameterization. Therefore, Bayesian inversion with Markov chain Monte Carlo sampling is used for calculating an estimate of the NURBS control points. The reconstruction method is tested with both simulated data and measured X‐ray projection data. The proposed method recovers the shape and the attenuation coefficient significantly better than the baseline algorithm (optimally thresholded total variation regularization), but at the cost of heavier computation.     

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.     

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.