Characterizing the measures on the unit circle with exact quadrature formulas in the space of polynomials

In the present paper we characterize the measures on the unit circle for which there exists a quadrature formula with a fixed number of nodes and weights and such that it exactly integrates all the polynomials with complex coefficients. As an application we obtain quadrature rules for polynomial modifications of the Bernstein measures on [−1,1], having a fixed number of nodes and quadrature coefficients and such that they exactly integrate all the polynomials with real coefficients.     

The representations and computations of generalized inverses $$A^{(1)}_{T,S}$$, $$A^{(1,2)}_{T,S}$$AT,S(1,2) and the group inverse

In this paper, we derive novel representations of generalized inverses \(A^{(1)}_{T,S}\) and \(A^{(1,2)}_{T,S}\), which are much simpler than those introduced in Ben-Israel and Greville (Generalized inverses: theory and applications. Springer, New York, 2003). When \(A^{(1,2)}_{T,S}\) is applied to matrices of index one, a simple representation for the group inverse \(A_{g}\) is derived. Based on these representations, we derive various algorithms for computing \(A^{(1)}_{T,S}\), \(A^{(1,2)}_{T,S}\) and \(A_{g}\), respectively. Moreover, our methods can be achieved through Gauss–Jordan elimination and complexity analysis indicates that our method for computing the group inverse \(A_{g}\) is more efficient than the other existing methods in the literature for a large class of problems in the computational complexity sense. Finally, numerical experiments show that our method for the group inverse \(A_{g}\) has highest accuracy among all the existing methods in the literature and also has the lowest cost of CPU time when applied to symmetric matrices or matrices with high rank or small size matrices with low rank in practice.     

基于W_2~1再生核支持向量机的模式分类研究

支持向量机是基于统计学习理论的模式分类器。它通过结构风险最小化准则和核函数方法,较好地解决了模式分类器复杂性和推广性之间的矛盾,引起了大家对模式识别领域的极大关注。近年来,支持向量机在手写体识别、人脸识别、文本分类等领域取得了很大的成功。文章将一种新的核函数用于虹膜识别,并与传统的多项式核函数、高斯核函数进行了比较。初步结果显示了该核函数的应用潜力。     

On the system of word equations x i 1 x i 2…x i m=y i 1 y i 2…y i n (i=1, 2, …) in a free monoid

 It is proved that the system of word equations x ⁱ ₁=y ⁱ ₁ y ⁱ ₂…y ⁱ _n , i=1, 2,…, ⌈n/2⌉ +1, has only cyclic solutions. Some sharpenings concerning the cases n=5, 7 and n≥9 are derived as well as results concerning the general system of equations x ⁱ ₁ x ⁱ ₂…x ⁱ _m =y ⁱ ₁ y ⁱ ₂…y ⁱ _n , i=1, 2,… . Applications to test sets of certain bounded languages are considered. Received: 18 May 1995/2 January 1996     

改进灰色GM(1,m)模型在变压器故障预测中的应用

针对灰色模型在预测变压器故障时对波动数据序列的预测误差较大的问题,提出了一种灰色GM(1,m)预测模型改进方案:对原始数据序列进行处理,使其具有更好的指数规律,以满足预测模型对光滑性的要求;对处理过的原始数据序列进行灰关联度分析,以得到各变量之间的关系;优化预测模型的背景值并用其建模;采用等维新息模型预测数据。采用改进的灰色GM(1,m)模型预测某变压器油中7种特征气体的体积分数,所得预测数据的平均残差和后验相对误差均小于GM(1,1)模型和传统GM(1,m)的预测结果,表明其具有更好的预测精确度。     

Optimal algorithms for the minimization of functions grom the classes C 1,L,N' n C 1,L,N,ε n C 1,L,N,δ ≈n

Cybernetics and Systems Analysis -     

Optimal integration of rapidly oscillating functions in the class W 2,L,N with the use of different information operators

The problem of computing integrals of rapidly oscillating differentiable functions using various information operators is considered. Quadrature formulas of optimal accuracy are derived and optimal estimates are obtained.     

Classification of 2D grayscale objects in a space of the multiresolution representations

A new approach is developed for fast voting-based classification of 2D patterns given by the grayscale images and represented by the trees of elliptic primitives. Due to a multiresolution property of the representations, the fast search algorithm is suggested to make voting-based decisions about the classes of the submitted objects and it is shown that this algorithm requires much smaller computations as compared with a full search algorithm for the decision. A computational complexity of the fast algorithm is O(KlogK) when a number of the classes K is large. An efficiency of the proposed approach is shown by experimental results on signature and hand gesture recognition in terms of the error rate as the function of the resolution level.     

甲苯与异戊二烯合成2,6-二甲基萘的热力学计算

2,6-二甲基萘是合成聚2,6-萘二甲酸乙二酯的重要起始原料。本文讨论了以大宗化工原料甲苯与异戊二烯为起始原料合成2,6-二甲基萘的可能性,并对各种可能化学反应的热力学过程进行了分析,通过分析发现以甲苯与异戊二烯为起始原料经过烷基化、环化及异构化反应可以合成2,6-二甲基萘。同时指出了只有控制异戊二烯合适位置上的碳原子参与烷基化反应才能最终得到目标产物。     

The Use of Legendre Polynomial Expansions in Solving Optimal Control Problems in the Space l 2

A method for solving a class of general deterministic optimal control problems is presented here. The method consists of relating the functions involved in the problem to sequences and then converting the problem to one which deals with these sequences alone. The function-sequence correspondence is defined by representing each function by its Legendre polynomial expansion and then relating the function to the sequence of coefficients in this expansion. After this is done, the problem is converted to one in l ²; by determining the equivalents in l ²; of differentiation, inner multiplication, and multiplication.

The resulting problem in l ²; is a non-linear programming problem which consists of an infinite array of equations, inequalities, and expressions, each of which involves infinite polynomial expressions. To solve a problem of this type it must be approximated by a finite non-linear programming problem. After this is done various methods can bo used for solving the final problem.     

Optimal design of 2D conducting graded materials by minimizing quadratic functionals in the field

We explore a typical optimal design problem in 2D conductivity: given fixed amounts of two isotropic dielectric materials, decide how we are to mix them in a 2D domain so as to minimize a certain cost functional depending on the underlying electric field. We rely on a reformulation of the optimal design problem as a vector variational problem and examine its relaxation, taking advantage of the explicit formulae for the relaxed integrands recently computed in Pedregal (2003). We provide numerical evidence, based on our relaxation, that Tartar’s result Tartar (1994) is verified when the target field is zero (also for divergence-free fields) and optimal solutions are given by first-order laminates. This same evidence also holds for a general quadratic functional in the field.     

Optimal loading conditions in the design and identification of structures. Part 1: discrete formulation

The paper is concerned with a class of structural optimization problems for which loading distribution and orientation are unspecified. The optimal loading conditions correspond to the extremal structural response, which can be used in assessment of structural safety or in generating the maximum structure stiffness or compliance. In identification problems the optimal load distribution is selected in order to minimize the distance norm between model prediction and experimental data. The sensitivity derivatives and optimality conditions are derived in the paper using discretized formulations. The generalized coaxiality conditions of loading and displacement or adjoint displacement vectors generate eigenvalue problems specifying stationary solutions. The paper is illustrated by examples of optimal loading distribution in structure design and identification.     

On the L(2, 1)-labelling of block graphs

The distance-two labelling problem of graphs was proposed by Griggs and Roberts in 1988, and it is a variation of the frequency assignment problem introduced by Hale in 1980. An L(2, 1)-labelling of a graph G is an assignment of non-negative integers to the vertices of G such that vertices at distance two receive different numbers and adjacent vertices receive different and non-consecutive integers. The L(2, 1)-labelling number of G, denoted by λ(G), is the smallest integer k such that G has a L(2, 1)-labelling in which no label is greater than k.

In this work, we study the L(2, 1)-labelling problem on block graphs. We find upper bounds for λ(G) in the general case and reduce those bounds for some particular cases of block graphs with maximum clique size equal to 3.     

Control of the System of Optimal Parallel Data Processing in Local Computer Networks: Models, Algorithms, Interface

The models, algorithms, and interface to control the system of optimal parallel data processing in local computer networks developed by the North Caucasian State Technological University were described with the aim of analyzing the efficiency of cluster resource utilization according to the targets and specific features of the tasks at hand. The majority of the described algorithms were illustrated by examples. Search of the optimal strategy is supported by a friendly interface which is intuitively understandable.     

2D—SROP—1测量仪的相移装置设计与实现

介绍采用参考压电振动干涉法研制开发的高精表面粗糙度光学轮廓仪（２Ｄ－ＳＲＯＰ—１）。本文在阐述其工作原理之后。叙述了压电振动相移器ＰＺＴ及其驱动器的设计与实现。     

1 1/2片联合树算法在动态贝叶斯网精确推理中的应用

基于动态贝叶斯网络处理动态不确定性问题的过程中推理是非常重要的,而推理算法的优劣决定着推理的执行效率。该文提出一种较简单的112片联合树算法,在不需要限制消去顺序且只作一次扩展的条件下构造联合树,所以算法简单且具有较小的复杂度。