Efficient solutions in generalized linear vector optimization

This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized linear vector optimization problems is obtained. We also prove that the efficient solution set of a generalized linear vector optimization problem in a locally convex Hausdorff topological vector space is the union of finitely many generalized polyhedral convex sets and it is connected by line segments.     

On fuzzy cliques in fuzzy networks

A definition of fuzzy clique in social networks is suggested which overcomes five limitations of current definitions. This definition is based on the networks in which the 0–1 strengths, the weighted strengths, and fuzzy strengths are all allowed. The fuzzy distance in such a network is defined. The node‐clique and clique‐clique coefficients are suggested. The core and the periphery of fuzzy cliques are discussed formally. A “cone like” property of the cores is discovered. The network structures are discussed using the new definition. A “no circle” property of networks is found. Basic fuzzy tools and the related algorithms are also discussed. Some examples are analyzed to demonstrate the theory.     

Generalized Derivations with Engel Conditions on Polynomials

Let R be a noncommutative prime ring with extended centroid C, and let D: R → R be a nonzero generalized derivation, f(X ₁,…, X _t ) a nonzero polynomial in noncommutative indeterminates X ₁,…, X _t over C with zero constant term, and k ≥ 1 a fixed integer. In this article, D and f(X ₁,…, X _t ) are characterized if the Engel identity is satisfied: [D(f(x ₁,…, x _t )), f(x ₁,…, x _t )] _k  = 0 for all x ₁,…, x _t  ∈ R.     

Some Simple Derivations of k[x,y]

It is shown that the derivation y ^r ? _x  + (xy ^s  + g)? _y , where 0 ≤ r < s are integers, is a simple derivation of k[x, y], the polynomial ring in two variables over a field k of characteristic zero.     

On Noncommutative Integral Standard Generalized Table Algebras of Dimension 6

We will investigate the structure of noncommutative imprimitive association schemes of rank 6 and the representation of their adjacency algebras. From this investigation, we will construct new integral standard generalized table algebras with three parameters. These algebras are noncommutative, imprimitive, and 6-dimensional.     

病态线性方程组新的Jacobi迭代解法

给出了解病态线性方程组的一种新的Jacobi迭代算法,并证明了算法的收敛性;通过具体算例说明了算法的实用性和有效性.     

Finite-dimensional simple modular Lie superalgebra ℳ

A new family of finite-dimensional simple modular Lie superalgebra ? is constructed based on results of Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321: 3601–3619]. The simplicity and generators of ? are discussed and the derivation superalgebra of ? is characterized. Furthermore, the invariance of the nonnatural filtration of ? is determined by the method of minimal dimension of image spaces.     

Optimal consumption and portfolio under inflation and Markovian switching

In this paper, a financial market with Markovian switching and inflation is described, and the problem of maximizing expected utility of consumption discounted by inflation is given. Then, by a generalized Itô formula for Markov-modulated processes, the verification theorems of optimal policies are derived. Finally, the optimal consumption and portfolio policies for the constant relative risk aversion utility are given explicitly, and an economic analysis is made by numerical examples.     

CALCULATING AN ELEMENT OF B-DIFFERENTIAL FOR A VECTOR-VALUED MAXIMUM FUNCTION*

In this paper, we propose a method of calculating an element of B-differential, also an element of Clarke generalized Jacobian, for a vector-valued maximum function. This calculation is required in many existing numerical methods for the solution of nonsmooth equations and for the nonsmooth optimization. The generalization of our method to a vector-valued smooth composition of maximum functions is also discussed. Particularly, we propose a method of obtaining the set of B-differential for a vector-valued maximum of affine functions.