Optimal expansion of competence sets with multilevel skills

The purpose of competence set expansion is to find an optimal expansion process at the minimal cost and then obtain the required competence set from the acquired competence set to solve a problem. Several models have been proposed to address the competence set expansion problem of only a single decision maker or multiple decision makers without considering multilevel skills. However, a practical competence set expansion model should involve multiple decision makers and multilevel skills. This study discusses an optimal expansion model of incorporating competence sets of group decision makers with multilevel skills. The proposed method not only obtains the optimal competence set expansion of all decision makers with the maximal total benefit but finds all optimal alternatives of the competence set expansion model. A cooperative alliance problem is solved to illustrate the usefulness of the proposed method.     

A regularization method for a Cauchy problem of Laplace's equation in an annular domain

In this paper, we propose a new regularization method based on a finite-dimensional subspace generated from fundamental solutions for solving a Cauchy problem of Laplace's equation in an annular domain. Based on a conditional stability for the Cauchy problem of Laplace's equation, we obtain a convergence estimate under the suitable choice of a regularization parameter and an a-priori bound assumption on the solution. A numerical example is provided to show the effectiveness of the proposed method from both accuracy and stability.     

Periodic and solitary wave solutions of the attractive and repulsive nonlinear Schrödinger equation

By means of symbolic computation, the first integral method is presented to obtain novel exact solutions of the nonlinear evolution equation. The obtained results include periodic and solitary wave solutions. The power of this manageable method is confirmed and the availability of symbolic computation is demonstrated.     

A collocation approach to solve the Riccati-type differential equation systems

In this paper, a collocation method is presented for the solutions of the system of the Riccati-type differential equations with variable coefficients. The proposed approach consists of reducing the problem to a nonlinear algebraic equation system by expanding the approximate solutions in terms of the Bessel polynomials with unknown coefficients. The unknown coefficients of the Bessel polynomials are found by using the matrix operations of derivatives together with the collocation method. The proposed method gives the analytic solutions when the exact solutions are polynomials. Also, an error analysis technique based on the residual function is introduced for the suggested method. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples. Comparing the methodology with some known techniques shows that the presented approach is relatively easy and highly accurate. All of the numerical calculations have been done by using a program written in Maple.     

Solution of impulsive boundary value problems on infinite intervals

In this paper, the upper and lower solution method and monotone iterative technique are employed to study the boundary value problem for a class of first-order impulsive ordinary differential equations with Carathéodory condition on infinite intervals. Several existence theorems are obtained.     

Drift conditions for estimating the first hitting times of evolutionary algorithms

For the global optimization problems with continuous variables, evolutionary algorithms (EAs) are often used to find the approximate solutions. The number of generations for an EA to find the approximate solutions, called the first hitting time, is an important index to measure the performance of the EA. However, calculating the first hitting time is still difficult in theory. This paper proposes some new drift conditions that are used to estimate the upper bound of the first hitting times of EAs for finding the approximate solutions. Two case studies are given to show how to apply these conditions to estimate the first hitting times.     

Numerical solutions of fractional advection–diffusion equations with a kind of new generalized fractional derivative

In the current paper, the numerical solutions for a class of fractional advection–diffusion equations with a kind of new generalized time-fractional derivative proposed last year are discussed in a bounded domain. The fractional derivative is defined in the Caputo type. The numerical solutions are obtained by using the finite difference method. The stability of numerical scheme is also investigated. Numerical examples are solved with different fractional orders and step sizes, which illustrate that the numerical scheme is stable, simple and effective for solving the generalized advection–diffusion equations. The order of convergence of the numerical scheme is evaluated numerically, and the first-order convergence rate has been observed.     

Polynomial solutions of certain differential equations

In this paper, the Chebyshev matrix method is applied generalisations of the Hermite, Laguerre, Legendre and Chebyshev differential equations which have polynomial solution. The method is based on taking the truncated Chebyshev series expansions of the functions in equation, and then substituting their matrix forms into the result equation. Thereby the given equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Chebyshev coefficients.     

一类差分方程组非负解的收敛性

通过考查一类差分方程组,研究其非负解的收敛性,得到了方程组的非负解收敛于方程组的平衡点的结论,该研究的主要结果改进了相关文献中的结果．     

水土保持水蚀外业调查集成化解决方案

水利信息化技术的发展推动着外业调查方式的变革,从水蚀外业调查业务需求、业务流程的现状出发,在分析规范、设备、数据等的基础上,提出了一套水土保持水蚀外业调查集成化解决方案.方案通过规范、流程、数据、硬件设备的一体化集成,改进了外业调查的整体工作流程,提高了调查效率.