Eight-node conforming straight-side quadrilateral element with high-order completeness (QH8-C1)

A new eight-node conforming quadrilateral element with high-order completeness, denoted as QH8-C1, is proposed in this article. First, expressions for the interpolation displacement function satisfying the requirements for high-order completeness in the global coordinate system are constructed. Second, the displacement function expression in global coordinates is transformed into isoparametric coordinates, and the relationships between the two series of coefficients for the two kinds of displacement function expressions are found. Third, the displacement function expression is modified to satisfy the requirements of nodal freedom and interelement boundary continuity. The key to the new element construction is the derivation of the linear relationship expressions among 12 coefficients of element displacement interpolation polynomials in the global and isoparametric coordinate systems. As a result, the relationship between quadratic completeness and interelement continuity is explicitly given, and a proof of the completeness and the continuity was conducted to theoretically guarantee the validity of the derivation results. Furthermore, in order to verify the correctness of the theoretical work, nine numerical examples were performed. The computation results from these examples demonstrate that QH8-C1 exhibited excellent performance, including high simulation accuracy, fast convergence, insensitivity to mesh distortion, and monotonic convergence.     

LPNN-based approach for LASSO problem via a sequence of regularized minimizations

In compressive sampling theory, the least absolute shrinkage and selection operator (LASSO) is a representative problem. Nevertheless, the non-differentiable constraint impedes the use of Lagrange programming neural networks (LPNNs). We present in this article the -LPNN model, a novel algorithm that tackles the LASSO minimization together with the underlying theory support. First, we design a sequence of smooth constrained optimization problems, by introducing a convenient differentiable approximation to the non-differentiable -norm constraint. Next, we prove that the optimal solutions of the regularized intermediate problems converge to the optimal sparse signal for the LASSO. Then, for every regularized problem from the sequence, the -LPNN dynamic model is derived, and the asymptotic stability of its equilibrium state is established as well. Finally, numerical simulations are carried out to compare the performance of the proposed -LPNN algorithm with both the LASSO-LPNN model and a standard digital method.     

Eu@C86 isomers: Calculated relative populations

Abstract

Relative populations of four energy-lowest IPR (isolated-pentagon-rule) isomers of Eu@C₈₆ are computed using the Gibbs energy based on characteristics from density functional theory calculations (M06-2X/3-21G?～?SDD entropy term, M06-2X/6-31G*～SDD or B2PLYP(D)/6-31G*～SDD energetics). The calculations confirm that the recently isolated Eu@C₁(7)-C₈₆ species is a major isomer in a relevant temperature region. Relationship to the empty C₈₆ cages is discussed, too.     

On solving systems of ordinary differential equations on MIMD-computers

The error of solution of Cauchy problems for systems of ordinary differential equations is estimated in the case where the input data are approximate. It is shown how to prepare a program for computing the right-hand sides of the system automatically and simultaneously. Diagrams are presented to illustrate the efficiency of parallelization. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 175–182, March–April 2007.     

A Modified Variational-Gradient Method for Quasilinear Equations

A modified variational-gradient method is proposed and substantiated for quasilinear operator equations in a Hilbert space.     

时滞系统控制问题块脉冲算子解的收敛性

本文给出了一种基于块脉冲算子的离散逼近格式.应用这种逼近格式,可以获得时滞非 线性最优控制问题的块脉冲级数解.本文证明了这种块脉冲级数解将收敛于这类问题的精 确解,并具有一阶收敛速度.     

Hammerstein系统参数的集员辨识

本文运用多输入多输出系统参数的集员辨识的结果讨论了Ｈａｍｍｅｒｓｔｅｉｎ系统参数的集员辨识．在系统动态噪声有界的假定下导出了Ｈａｍｍｅｒｓｔｅｉｎ系统参数的成员集是个椭球，并证明了在一定条件下椭球趋向于一点，文中还给出了仿真例子．