Uncertainty relation on Wigner-Yanase-Dyson skew information

We give a trace inequality related to the uncertainty relation of Wigner-Yanase-Dyson skew information. This inequality corresponds to a generalization of the uncertainty relation derived by S. Luo (2005) [8] for the quantum uncertainty quantity excluding the classical mixture.     

Borel equivalence relations between <Emphasis Type="Italic">ℓ</Emphasis><Subscript>1</Subscript> and <Emphasis Type="Italic">ℓ</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

In this paper, we show that, for each p 〉 1, there are continuum many Borel equivalence relations between Rω/l1 and Rω/p ordered by ≤B which are pairwise Borel incomparable.     

Cartesian closed categories of FƵ-domains

A subset system Z assigns to each partially ordered set P a certain collection Z（P） of subsets. In this paper, a new kind of subset systems called directable subset systems is introduced. For a directable subset system Z, the concepts of FZ-way-below relation and FZ-domain are introduced. The well-known Scott topology is naturally generalized to the Z-level and the resulting topology is called FZ-Scott topology, and the continuous functions with respect to this topology are characterized by preserving the suprema of directed Z-sets. Then, we mainly consider a generalization of the cartesian closedness of the categories DCPO of directed complete posets, BF of bifinite domains and FS of FS-domains to the Z-level. Corresponding to them, it is proved that, for a suitable subset system Z, the categories FZCPO of Z-complete posets, FSFZ of finitely separated FZ-domains and BFFZ of bifinite FZ-domains are all cartesian closed. Some examples of these categories are given.     

Conjugate Duality in Constrained Set-Valued Vector Optimization Problems

In this article, under a concept of supremum/infimum of a set, defined in terms of a closure of the set, three kinds of conjugate dual problems are proposed for a constrained set-valued vector optimization problem. Weak duality, strong duality, and stability criteria are investigated. The inclusion relations between the image sets of the dual problems are also discussed.     

Eigenvector method,consistency test and inconsistency repairing for an incomplete fuzzy preference relation

In this paper, we extend the eigenvector method (EM) to priority for an incomplete fuzzy preference relation. We give a reasonable definition of multiplicative consistency for an incomplete fuzzy preference relation. We also give an approach to judge whether an incomplete fuzzy relation is acceptable or not. We develop the acceptable consistency ratio for an incomplete multiplicative fuzzy preference relation, which is simple and similar to Saaty’s consistency ratio (CR) for the multiplicative preference relation. If the incomplete fuzzy preference relation is not of acceptable consistency, we define a criterion to find the unusual and false element (UFE) in the preference relation, and present an algorithm to repair an inconsistent fuzzy preference relation until its consistency is satisfied with the consistency ratio. As a result, our improvement method cannot only satisfy the consistency requirement, but also preserve the initial preference information as much as possible. Finally, an example is illustrated to show that our method is simple, efficiency, and can be performed on computer easily.     

On semi‐classical d‐orthogonal polynomials

In this paper a general theory of semi‐classical d‐orthogonal polynomials is developed. We define the semi‐classical linear functionals by means of a distributional equation , where Φ and Ψ are matrix polynomials. Several characterizations for these semi‐classical functionals are given in terms of the corresponding d‐orthogonal polynomials sequence. They involve a quasi‐orthogonality property for their derivatives and some finite‐type relations.     

Cluster Tilted Algebras with a Cyclically Oriented Quiver

In association with a finite dimensional algebra A of global dimension two, we consider the endomorphism algebra of A, viewed as an object in the triangulated hull of the orbit category of the bounded derived category, in the sense of Amiot. We characterize the algebras A of global dimension two such that its endomorphism algebra is isomorphic to a cluster-tilted algebra with a cyclically oriented quiver. Furthermore, in the case that the cluster tilted algebra with a cyclically oriented quiver is of Dynkin or extended Dynkin type then A is derived equivalent to a hereditary algebra of the same type.     

A Generalized Version of the Baker–Pixley Theorem

A famous theorem by Baker and Pixley states that the term functions of a finite algebra with a (d + 1)-ary near-unanimity term are precisely the functions under which all subalgebras of the algebra's dth power are closed. In this paper, we generalize the theorem to a completely abstract level. Indeed, we obtain a version of the theorem that is stated in purely category-theoretic terms, making it applicable in any concrete or abstract category. To motivate this rather abstract result, we also discuss some of its concrete applications.     

On α-Relation and Transitivity Conditions of α

The main tools in the theory of hyperstructurs are the fundamental relations. The fundamental relation on hyperring was introduced by Vougiouklis at the fourth AHA congress (1990). The fundamental relation on a hyperring is defined as the smallest equivalence relation so that the quotient would be the ring. Note that, generally, the commutativity in the ring are not assumed. In this article, we introduce a new strongly regular equivalence relation on hyperring so that the quotient is a commutative ring. Also we state the condition that is equivalent with the transitivity of this relation and finally we characterize the complete hyperring (with the fundamental relation as commutative).     

θ*-Relation on Hypermodules and Fundamental Modules Over Commutative Fundamental Rings

The main tools in the theory of hyperstructues are the fundamental relations. The fundamental relation on a hypermodule over a hyperring was already introduced by Vougiouklis. The fundamental relation on a hypermodule over a hyperring is defined as the smallest equivalence relation so that the quotient would be the module over a ring. Note that generally the commutativity with respect to both sum in the (fundemental) module and product in the (fundamental) ring are not assumed. In this article we introduce a new strongly regular equivalence relation on hypermodules so that the quotient is module (with abelin group) over a commutative ring. Also we state the conditions that is equivalent with the transitivity of this relation and finally we characterize the complete hypermodules over hyperrings.