An inner approximation method incorporating a branch and bound procedure for optimization over the weakly efficient set

In this paper, we consider an optimization problem which aims to minimize a convex function over the weakly efficient set of a multiobjective programming problem. From a computational viewpoint, we may compromise our aim by getting an approximate solution of such a problem. To find an approximate solution, we propose an inner approximation method for such a problem. Furthermore, in order to enhance the efficiency of the solution method, we propose an inner approximation algorithm incorporating a branch and bound procedure.     

An approach for solving of a moving boundary problem

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.     

L—Fuzzy偏序集

借助L-fuzzy关系在L-fuzzy中集中引入L-fuzzy偏序,自然地有了L-fuzzy偏序集,进一步借助水平截集刻画了L-fuzzy偏序集。     

Discontinuous local semiflows for Kurzweil equations leading to LaSalle's invariance principle for differential systems with impulses at variable times

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle's invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle's invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times.     

随机环境中的马氏链的不变测度与遍历性

本文考虑了一类特殊的随机环境的马氏链。假设随机“Doeblin”条件成立，我们证明了随机环境的马氏链的不变测度存在，且任何初始分布以指数收敛速度到些不变测度。进一步的，存在关于绕积算子遍历的不变测度。最后，我们得到了随机马氏链的强大数定律。     

An exact penalty method for weak linear bilevel programming problem

In this paper, we present an exact penalty method, which is different from the existing penalty method, for solving weak linear bilevel programming problem. Then, we establish an existence result of solutions for such a problem. Finally, we propose an algorithm and give two examples to illustrate its feasibility.     

Optimal control of nonlinear evolution inclusions

In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.This research was supported by NSF Grant No. DMS-88-02688.     

On essential sets and essential components of efficient solutions for vector optimization problems

In this paper, we first introduce the notions of an essential set and an essential component of the set of efficient solutions for continuous vector optimizations on a nonempty compact subset of a metric space. Then we show that for each of these vector optimizations, each set of all efficient solutions corresponding to the same optimal values is essential. Basing on this result, we give full characterizations of an essential point, an essential set and an essential component, respectively. As an application, we prove that for continuous quasiconvex vector optimization problems on a nonempty compact subset of a metric vector space, each component of the set of efficient solutions is essential even though the efficient solution set is not connected.     

半监督度量学习内蕴最速下降算法的收敛性分析

主要研究对称正定矩阵群上的内蕴最速下降算法的收敛性问题.首先针对一个可转化为对称正定矩阵群上无约束优化问题的半监督度量学习模型,提出对称正定矩阵群上一种自适应变步长的内蕴最速下降算法.然后利用李群上的光滑函数在任意一点处带积分余项的泰勒展开式,证明所提算法在对称正定矩阵群上是线性收敛的.最后通过在分类问题中的数值实验说明算法的有效性.     

Existence of Nonoscillatory Solutions for a Rational Difference Equation of Higher Order

In this paper, we investigate a rational difference equation of higher order for the existence of nonoscillatory solutions. To prove our main results, we use an inclusion theorem stated and proved in \cite{L1}. In this way, we give an answer of an open problem formulated in \cite{FPB}.     

On a constructive approximation of the efficient outcomes in bicriterion vector optimization

For bicriterion quasiconvex optimization problems, we present a constructive procedure for an approximation of the efficient outcomes. Performing this procedure we can estimate the accuracy of the approximation. Conversely, if we prescribe an accuracy for the approximation, we can calculate the number of points which have to be computed by a certain scalarization method to remain under the given accuracy. Finally, we give a numerical example.     

Approximation of conformal mappings of annular regions

Summary. In this paper we examine the convergence rates in an adaptive version of an orthonormalization method for approximating the conformal mapping of an annular region onto a circular annulus. In particular, we consider the case where has an analytic extension in compl() and, for this case, we determine optimal ray sequences of approximants that give the best possible geometric rate of uniform convergence. We also estimate the rate of uniform convergence in the case where the annular region has piecewise analytic boundary without cusps. In both cases we also give the corresponding rates for the approximations to the conformal module of . Received February 2, 1996     

Representations of torsion-free arithmetic matroids

We study the representability problem for torsion-free arithmetic matroids. After introducing a “strong gcd property” and a new operation called “reduction”, we describe and implement an algorithm to compute all essential representations, up to equivalence. As a consequence, we obtain an upper bound to the number of equivalence classes of representations. In order to rule out equivalent representations, we describe an efficient way to compute a normal form of integer matrices, up to left-multiplication by invertible matrices and change of sign of the columns (we call it the “signed Hermite normal form”). Finally, as an application of our algorithms, we disprove two conjectures about the poset of layers and the independence poset of a toric arrangement.     

关于Bell多项式及其它的一些恒等式

本文引入了一个新的多项式,即Bell多项式.利用初等数论及组合方法,证明了包含该多项式的一些恒等式.作为这些恒等式的应用,给出了关于Bell数的同余式.     

A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

In the present paper, we consider a five-dimensional Riemannian manifold with an irreducible SO(3)-structure as an example of an abstract statistical manifold. We prove that if a five-dimensional Riemannian manifold with an irreducible SO(3)-structure is a statistical manifold of constant curvature, then the metric of the Riemannian manifold is an Einstein metric. In addition, we show that a five-dimensional Euclidean sphere with an irreducible SO(3)-structure cannot be a conjugate symmetric statistical manifold. Finally, we show some results for a five-dimensional Riemannian manifold with a nearly integrable SO(3)-structure. For example, we prove that the structure tensor of a nearly integrable SO(3)-structure on a five-dimensional Riemannian manifold is a harmonic symmetric tensor and it defines the first integral of third order of the equations of geodesics. Moreover, we consider some topological properties of five-dimensional compact and conformally flat Riemannian manifolds with irreducible SO(3)-structure.     

Optimal estimates for an average of Hurwitz class numbers

The Ramanujan Journal - In this paper, we give an optimal estimate of an average of Hurwitz class numbers. As an application, we give an equidistribution result of the family $$\Big...     

Isosceles-orthogonality preserving property and its stability

For real normed spaces, we consider the class of linear operators, preserving approximately the relation of isosceles-orthogonality. We show some general properties of such mappings. Next, we examine whether an approximately orthogonality preserving mapping admits an approximation by an orthogonality preserving one. In regard to this, we generalize some results obtained earlier for inner product spaces with standard orthogonality relation.     

Invariant properties of representations under cleft extensions

The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable.     

弱完全并既约元及其应用

首先,引入弱完全并既约元的概念,讨论它的一些基本性质,并给出完全并既约元另一等价定义。其次,借助于下邻给出了并既约元为弱完全并既约元的一个内部刻画。最后,研究了各种既约元,素元,弱完全并既约元以及紧元之间的关系。