Finding the most probable nonnegative solutions of systems of linear algebraic equations by the maximum likelihood method

A probabilistic method of regularization is proposed. This method enables obtaining nonnegative solutions to systems of linear algebraic equations. A theorem of existence of the best possible solution is proved. A numerical example application of the method is given.     

利用散射波远场模第P个傅立叶系数重建声波阻尼系数

阐述了利用声波散射远场模Fourier展开的第P个傅立叶系数（声散射远场模的不完全信息）,重建声阻抗系数的一种非线性最优化方法．并给出了该方法收敛性的证明,其数值例子说明这种方法的有效性和可行性．     

Quintic B-spline for the numerical solution of the good Boussinesq equation

A numerical method is developed to solve the nonlinear Boussinesq equation using the quintic B-spline collocation method. Applying the Von Neumann stability analysis, the proposed method is shown to be unconditionally stable. An example has been considered to illustrate the efficiency of the method developed.     

The estimation of the strength of the heat source in the heat conduction problems

A general method is proposed to determine the strength of the heat source in the Fourier and non-Fourier heat conduction problems. A finite difference method, the concept of the future time and a modified Newton–Raphson method are adopted in the problem. The undetermined heat source at each time step is formulated as an unknown variable in a set of equations from the measured temperature and the calculated temperature. Then, an iterative process is used to solve the set of equations. No selected function is needed to represent the undetermined function in advance. Three examples are used to demonstrate the characteristics of the proposed method. The validity of the proposed method is confirmed by the numerical results. The results show that the proposed method is an accurate and stable method to determine the strength of the heat source in the inverse hyperbolic heat conduction problems. Furthermore, the result shows that more future times are needed in the hyperbolic equation than that of parabolic equation. Moreover, the robustness and the accuracy of the estimated results in the non-Fourier problem are not as well as those of the Fourier problem.     

Puncture alloplasty of the tendon-capsule part of the external rotators of the shoulder and subacromial bursa by fast-setting polyurethane SKU-PFL in tendonitis and chronic lacerations of the tendon of the musculus supraspinatus (clinical-biomechanical investigation)

A method is proposed for alloplastic restoration of the dynamic stability of the shoulder joint with the use of fast-setting polyurethane SKU-PFL in the most common injuries of the tendoncapsule apparatus of the shoulder joint — tendonitis and lacerations of the musculus supraspinatus. A biomechanical substantiation of the proposed method of treatment is given.     

On the accelerated iterative method for estimating the optimum overrelaxation parameter

This paper is concerned with the iterative method for estimating the optimum overrelaxation parameter. The improved power method (IP method) with the greatest rate of convergence is derived and compared with the Chebyshev polynomial iterative method (CP method) and the other iterative methods. Two algorithms (algorithms A and B) based on the IP method are presented. Some numerical results are shown.     

Exact and stable least squares solution to the linear programming problem

A linear programming problem is transformed to the finding an element of polyhedron with the minimal norm. According to A. Cline [6], the problem is equivalent to the least squares problem on positive ortant. An orthogonal method for solving the problem is used. This method was presented earlier by the author and it is based on the highly developed least squares technique. First of all, the method is meant for solving unstable and degenerate problems. A new version of the artifical basis method (M-method) is presented. Also, the solving of linear inequality systems is considered.     

On the Passage to the Limit in the Construction of Geometric Solutions of the Riemann Problem

Mathematical Notes - A method for constructing geometric solutions of the Riemann problem for an impulsively perturbed conservation law is described. A complete classification of the possible...     

On the generation of permutations and combinations

In this paper a new method of generating permutations in lexicographical order is developed. Analysis shows that the method is superior to the known method of generation by addition. A simple method of generating combinations is also described.     

An Improved Method for the Solution of the Heat Equation in Chebyshev Series

A method is given for the numerical solution of the heat equationusing Chebyshev series. A feature of the method is that thematrices which have to be inverted (apart possibly from a few22 matrices) are all triangular. The method shows a considerableimprovement in accuracy over previous Chebyshev methods, particularlyas far as the approximation to the fundamental eigenvalue isconcerned. The extension of the method to equations of the form is also described.     

A Sine-Collocation Method for the Computation of the Eigenvalues of the Radial Schr?dinger Equation

A collocation scheme using sine function basis elements is developedand used to approximate the eigenvalues of the radial Schr?dingerequation. The method is shown to apply to problems with singulareigensolutions and error bounds for the approximate eigenvaluesare given. The method is applied to a few test examples to indicateboth the accuracy and the implementation of the method.     

Application of the Newton Method for Calculating the Axisymmetric Thermoelastoplastic State of Flexible Laminar Branched Shells Using the Shear Model

A method for calculating the thermoelastoplastic geometrically nonlinear state of branched laminar shells is elaborated. The method is based on the shear kinematic model for the whole package of layers and on the theory of simple loading processes. The linearization of geometrically nonlinear equations is realized using the Newton method.     

On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods

A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms built up from Ostrowski’s method for solving systems of nonlinear equations are written and analyzed. A direct computation of the local order of convergence for these variants of Ostrowski’s method is given. In order to preserve the local order of convergence, any divided difference operator is not valid. Two counterexamples of computation of a classical divided difference operator without preserving the order are presented. A rigorous study to know a priori if the new method will preserve the order of the original modified method is presented. The conclusion is that this fact does not depend on the method but on the systems of equations and if the associated divided difference verifies a particular condition. A new divided difference operator solving this problem is proposed. Furthermore, a computation that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced. This study can be applied directly to other Newton’s type methods where derivatives are approximated by divided differences.     

Speedup estimates for some variants of the parallel implementations of the branch-and-bound method

The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered. A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of the computation process is constructed and used to obtain estimates of the maximum possible speedup. Examples of problems in which none of these two parallel implementations can speed up the computations are considered.     

关于TOPSIS法应用中的逆序问题及消除的方法

在多指标决策问题中,TOPSIS法是一种常用的方法,然而传统的TOPSIS法在实际应用中容易产生逆序的现象.本文分析了逆序产生的主要原因,并提出了一种改进的方法-RTOPSIS法.应用本文的方法不仅能消除逆序的现象,而且还能正确反映指标权重对决策结果的影响.     

A method for the automatic selection and tuning of the parameters of a sparse SLE solver

A technique for the automatic selection of the method for solution of a sparse system of linear algebraic equations (SLE) and selection of the method parameters from the analysis of the SLE matrix of coefficients is presented. The parameters are selected so as to maximize the performance metric. A formal model of the performance of a SLE solver is presented and is used to formulate an algorithm for construction, precedent learning, and application of the proposed method. The method is approved for iterative SLE solvers from the PETSc parallel library of the MVS-100K supercomputer platform at the Interdepartmental Supercomputer Center of the Russian Academy of Sciences.     

On solutions to the Goldshtik problem

The Goldshtik model for separated flows in an incompressible fluid is considered. A solution to this two-dimensional problem of mathematical physics for a finite domain is found with a finite element method. Estimates of the differential operator are obtained. A result on the number of solutions to the Goldshtik problem is obtained using a variational method.     

模糊决策综合评价法在职称评聘工作中的应用

在高等院校和科研院所 ,职称评聘工作是一项比较难的工作 .由于评聘中 ,许多指标具有模糊性 ,提出用模糊决策综合评价法进行职称评聘工作 ,将其定量化 ,使职称评聘工作更容易 ,并且尽量减少人为因素的干扰 ,是一种科学有效的方法 .     

On the convergence of the UOBYQA method

We analyze the convergence properties of Powell's UOBYQA method. A distinguished feature of the method is its use of two trust region radii. We first study the convergence of the method when the objective function is quadratic. We then prove that it is globally convergent for general objective functions when the second trust region radius ρ converges to zero. This gives a justification for the use of ρ as a stopping criterion. Finally, we show that a variant of this method is superlinearly convergent when the objective function is strictly convex at the solution.     

Solution of the Incompressible Boundary Layer Equations via the Galerkin Kantorovich Technique

A multi-moment method for the approximate solution of the incompressiblelaminar boundary layer equations is presented. The method isformulated in a general manner and is then applied to solvefour well-known boundary layer problems.