Classification of block-toeplitz h-normal operators

In our previous paper [2] a special class of normal operators acting in spaces with indefinite scalar product was introduced. The operators from this class are characterized by the property that in appropriate sip orthogonal bases their matrices have diagonal block-Toeplitz forms. In the present paper we find a complete system of invariants and canonical form for operators belonging to this class.     

Classification of block-toeplitz h-normal operators

In our previous paper [2] a special class of normal operators acting in spaces with indefinite scalar product was introduced. The operators from this class are characterized by the property that in appropriate sip orthogonal bases their matrices have diagonal block-Toeplitz forms. In the present paper we find a complete system of invariants and canonical form for operators belonging to this class.     

调和单叶函数族的一些结果

借用著名的Ruscheweyh导数,引入了一类单叶保向调和函数族. 通过建立极值理论,得到了关联该族的最优系数边界、最优增长定理和最优偏差定理. 同时,给出了该族与先前已有调和函数族之间的转换半径. 最后,讨论了基于该族的修正哈达玛乘积结果.     

Generalizations of the area theorem for meromorphic univalent functions with nonzero pole

In this article, we consider meromorphic univalent functions f in the unit disc of the complex plane having a simple pole at z = α ∈ (0, 1) with nonzero residue b at z = α. In 1969, P.N. Chichra proved an area theorem for such functions. In this note, we generalize this theorem and prove an interesting consequence of this result.     

On Green’s functions for positive,elliptic differential operators on closed,Riemannian manifolds and some consequences for semi-linear PDE

In this article, we establish the non-negativity of Green’s functions for a class of elliptic differential operators on closed, Riemannian manifolds. The method used is the calculus of variations with a unilateral constraint. Consequences of this result are then explored, with a maximum principle-type result established for a broad class of semi-linear elliptic PDE as a result. Finally, a result regarding the positivity of the principal eigenfunction of an operator in this class is proven as well.     

The Skolemization of prenex formulas in intermediate logics

The skolem class of a logic consists of the formulas for which the derivability of the formula is equivalent to the derivability of its Skolemization. In contrast to classical logic, the skolem classes of many intermediate logics do not contain all formulas. In this paper it is proven for certain classes of propositional formulas that any instance of them by (independent) predicate sentences in prenex normal form belongs to the skolem class of any intermediate logic complete with respect to a class of well-founded trees. In particular, all prenex sentences belong to the skolem class of these logics, and this result extends to the constant domain versions of these logics.     

On Vector Variational Inequalities in Reflexive Banach Spaces

In this paper, we study the solvability for a class of vector variational inequalities in reflexive Banach spaces. By using Brouwer fixed point theorem, we prove the solvability for this class of vector variational inequalities without monotonicity assumption. The solvability results for this class of vector variational inequalities with monotone mappings are also presented by using the KKM-Fan lemma This paper is dedicated to Professor Franco Giannessi for his 68th birthday     

Weakly absolute retracts for bicompacts

The notion of a weakly absolute extensor for the class of bicompacts is introduced in [5]. In this paper, the notion of a weakly absolute retract for bicompacts is introduced. It is shown that the class of weakly absolute retracts for bicompacts coincides with the class of weakly absolute extensors for bicompacts.     

Supervised learning algorithms for multi-class classification problems with partial class memberships

In several application domains such as biology, computer vision, social network analysis and information retrieval, multi-class classification problems arise in which data instances not simply belong to one particular class, but exhibit a partial membership to several classes. Existing machine learning or fuzzy set approaches for representing this type of fuzzy information mainly focus on unsupervised methods. In contrast, we present in this article supervised learning algorithms for classification problems with partial class memberships, where class memberships instead of crisp class labels serve as input for fitting a model to the data. Using kernel logistic regression (KLR) as a baseline method, first a basic one-versus-all approach is proposed, by replacing the binary-coded label vectors with [0,1]-valued class memberships in the likelihood. Subsequently, we use this KLR extension as base classifier to construct one-versus-one decompositions, in which partial class memberships are transformed and estimated in a pairwise manner. Empirical results on synthetic data and a real-world application in bioinformatics confirm that our approach delivers promising results. The one-versus-all method yields the best computational efficiency, while the one-versus-one methods are preferred in terms of predictive performance, especially when the observed class memberships are heavily unbalanced.     

Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions

In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this class of SOC merit functions. This fact will lay a building block when the merit function approach as well as the Newton-type method are employed for solving the second-order cone complementarity problem with this class of merit functions.     

On the spectral theory of trees with finite cone type

We study basic spectral features of graph Laplacians associated with a class of rooted trees which contains all regular trees. Trees in this class can be generated by substitution processes. Their spectra are shown to be purely absolutely continuous and to consist of finitely many bands. The main result gives stability of the absolutely continuous spectrum under sufficiently small radially label symmetric perturbations for non-regular trees in this class. In sharp contrast, the absolutely continuous spectrum can be completely destroyed by arbitrary small radially label symmetric perturbations for regular trees in this class.     

具广义Calderón-Zygmund核的多线性振荡奇异积分极大算子的有界性

本文研究了具有广义Calderon-Zygmund核的多线性奇异积分极大算子和多线性振荡奇异积分极 大算子,证明了这类极大算子的Lp-有界性．     

A class of operator equilibrium problems

In this paper, we consider a class of operator equilibrium problems (OEP for short) with operator solutions and derive a Minty type lemma for this class of problems. Further, using this lemma and KKM theorem, we establish some existence theorems for OEP. The theorems presented in this paper generalize, improve and unify many known results.     

求解变延迟微分方程的一类线性多步方法的收缩性

This paper presents a sufficient condition on the contractivity of theoretical solution for a class of nonlinear systems of delay differential equations with many variable delays(MDDEs), which is weak,compared with the sufficient condition of previous articles.In addition,it discusses the numerical stability properties of a class of special linear nmltistep methods for this class nonlinear problems.And it is pointed out that not only the backwm‘d Euler method but also this class of linear multistep methods are GRNm-stable if linear interpolation is used.     

The -digraph optimization problem and the greedy algorithm

In this paper we present a new optimization problem and a general class of objective functions for this problem. We show that optimal solutions to this problem with these objective functions are found with a simple greedy algorithm. Special cases include matroids, Huffman's data compression problem, a special class of greedoids, a special class of min cost max flow problems (related to Monge sequences), a special class of weighted f-factor problems, and some new problems.     

Compact representation of the full Broyden class of quasi‐Newton updates

In this paper, we present the compact representation for matrices belonging to the Broyden class of quasi‐Newton updates, where each update may be either rank one or rank two. This work extends previous results solely for the restricted Broyden class of rank‐two updates. In this article, it is not assumed that the same Broyden update is used in each iteration; rather, different members of the Broyden class may be used in each iteration. Numerical experiments suggest that a practical implementation of the compact representation is able to accurately represent matrices belonging to the Broyden class of updates. Furthermore, we demonstrate how to compute the compact representation for the inverse of these matrices and a practical algorithm for solving linear systems with members of the Broyden class of updates. We demonstrate through numerical experiments that the proposed linear solver is able to efficiently solve linear systems with members of the Broyden class of matrices with high accuracy. As an immediate consequence of this work, it is now possible to efficiently compute the eigenvalues of any limited‐memory member of the Broyden class of matrices, allowing for the computation of condition numbers and the ability to perform sensitivity analysis.     

Application of fractional calculus operators for a new class of univalent functions with negative coefficients defined by Hohlov operator

In this paper, we introduce a new class W(a, b, c, γ, β) which consists of analytic and univalent functions with negative coefficients in the unit disc defined by Hohlov operator, we obtain distortion theorem using fractional calculus techniques for this class. Also coefficient inequalities and some results for this class are obtained.     

Stochastic Epidemic SEIRS Models with a Constant Latency Period

In this paper, we consider the stability of a class of deterministic and stochastic SEIRS epidemic models with delay. Indeed, we assume that the transmission rate could be stochastic and the presence of a latency period of r consecutive days, where r is a fixed positive integer, in the “exposed” individuals class E. Studying the eigenvalues of the linearized system, we obtain conditions for the stability of the free disease equilibrium, in both the cases of the deterministic model with and without delay. In this latter case, we also get conditions for the stability of the coexistence equilibrium. In the stochastic case, we are able to derive a concentration result for the random fluctuations and then, using the Lyapunov method, to check that under suitable assumptions the free disease equilibrium is still stable.     

一类多值多导数方法的收敛性与稳定性

1 引言 对于多值多导数方法,由于其多值多导的结构特点有利于提高解的精度,以及其包容性大,它包含了当今常用的多种常微数值方法,诸如:线性多步法,单支方法,多步多导方法,多(单)步Runge—Kutta方法,多导Runge-Kutta方法以及混合方法等.因此收敛性与稳定性的研究具有重要的实践意义和广泛的理论指导意义,也正因如此,这方面的研究工作引起了众多数值工作者们的兴趣,近年来,多值多导法求解刚性问题的B—收敛及其非线性稳定性的研究工作巳获得较大进展,其相应成果可参见文献[1—3],在文献[4,5]中笔者则针对Banach空间中一类非刚性问题-K~((p))类问题,分别探讨了多步多导法及单支方法的收敛性     

Mutually-adjoint boundary-value problems with deviation from the characteristic for a multidimensional Gellerstedt equation

In this paper, we study mutually-adjoint boundary-value problems with a deviation from the characteristic for multidimensional Gellerstedt equation. In [3, 4], for the equation of the vibration of a string, the boundary-value problem with a deviation from the characteristic was studied, where the main attention was paid to the study of such problems for hyperbolic equations. For hyperbolic equations on the plane, this problem was studied in [5, 9].