Weak choice principles

We consider several weak forms of the Axiom of Choice obtained debilitating some well known choice principles. Implication relations among them and independence results are established using, in some cases, permutation models or symmetric models. The relationship between Ramsey's Theorem and these choice principles is also explored, showing that, in this context, the known results are the best possible.

     

Vector variational inequalities and vector optimization problems on Hadamard manifolds

In this paper, we introduce a Minty type vector variational inequality, a Stampacchia type vector variational inequality, and the weak forms of them, which are all defined by means of subdifferentials on Hadamard manifolds. We also study the equivalent relations between the vector variational inequalities and nonsmooth convex vector optimization problems. By using the equivalent relations and an analogous to KKM lemma, we give some existence theorems for weakly efficient solutions of convex vector optimization problems under relaxed compact assumptions.     

Pairwise weakly and pairwise strongly irresolute functions

In this paper we consider a new weak and strong forms of irresolute functions in bitopological spaces, namely, ij-quasi-irresolute functions and strongly irresolute functions. Several characterizations and basic properties of these functions are given. We investigate the relationships among some weak forms of continuity and other generalizations of continuous mappings in bitopological spaces.     

对一些弱连续性的讨论

引入了弱半连续及弱准连续性的概念,讨论了他们的一些性质,并对某些弱连续性之间的关系进行了探讨.     

Maass–Jacobi Poincaré series and Mathieu Moonshine

Mathieu moonshine attaches a weak Jacobi form of weight zero and index one to each conjugacy class of the largest sporadic simple group of Mathieu. We introduce a modification of this assignment, whereby weak Jacobi forms are replaced by semi-holomorphic Maass–Jacobi forms of weight one and index two. We prove the convergence of some Maass–Jacobi Poincaré series of weight one, and then use these to characterize the semi-holomorphic Maass–Jacobi forms arising from the largest Mathieu group.     

The weak isotropy of quadratic forms over field extensions

The weak isotropy index (or equivalently, sublevel) of arbitrary quadratic forms is studied. Its relationship to the level of a form is investigated. The problem of determining the set of values of the weak isotropy index of a form as it ranges over field extensions is addressed, with both admissible and inadmissible numbers being determined. An analogous investigation with respect to the level of a form is also undertaken. A treatment of forms for which the above invariants coincide concludes this article, with some recently-raised questions being resolved.     

偏序集中的弱理想和弱滤子

在偏序集上利用上集算子和下集算子引入了弱理想,弱滤子,弱素理想,弱素滤子,弱极大理想和弱极大滤子等概念,研究了它们的若干性质,同时给出了偏序集上的(DPI),(BPI),(DMI),(BUF)公理并建立了它们与Zorn引理之问的相互关系.     

Tame algebras and Tits quadratic forms

We solve a long standing problem concerning the connection between the tameness of simply connected algebras and the weak nonnegativity of the associated Tits integral quadratic forms, and derive some consequences.     

Constructing an ample monoid from a weak Loganathan pair

This paper is based on a categorical approach to the study of inverse monoids. The main idea is to extend this to the class called ample monoids (type A monoids). We generalise the notion of a Loganathan category pair to obtain what we call a weak Loganathan category pair and take two categories associated with an ample monoid and examine their properties. We prove that each of these categories together with its subcategory of idempotents forms a weak Loganathan category pair. Then we construct an ample monoid from them.     

A Modified Weak Galerkin Finite Element Method for Sobolev Equation

For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete $H^1$ and $L^2$ norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.     

齐型空间上的双线性Calderon-Zygmund奇异积分算子

文在齐型空间上引入双线性Calderon-Zygmund奇异积分算子的基本概念, 研究了其基本性质以及在L^1× L¹上的弱有界性.     

On self-distributive weak Heyting algebras

We use the left self-distributive axiom to introduce and study a special class of weak Heyting algebras, called self-distributive weak Heyting algebras (SDWH-algebras). We present some useful properties of SDWH-algebras and obtain some equivalent conditions of them. A characteristic of SDWH-algebras of orders 3 and 4 is given. Finally, we study the relation between the variety of SDWH-algebras and some of the known subvarieties of weak Heyting algebras such as the variety of Heyting algebras, the variety of basic algebras, the variety of subresiduated lattices, the variety of reflexive WH-algebras (RWH-algebras), and the variety of transitive WH-algebras (TWH-algebras).     

A maximum principle for hypersurfaces with constant scalar curvature and applications

In this article, we establish a weak maximum principle for complete hypersurfaces with constant scalar curvature into Riemannian space forms, and give some applications to estimate the norm of the traceless part of its second fundamental form.     

α-FUZZY PAIRWISE RETRACT OF L-VALUED PAIRWISE STRATIFICATION SPACES

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0, 1] was introduced by Martin (1980). Lin and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.     

α-FUZZY PAIRWISE RETRACT OF L-VALUED PAIRWISE STRATIFICATION SPACES

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0,1] was introduced by Martin (1980). Liu and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.     

Ideal-like properties of generalized microscopic sets

We show that not every family of generalized microscopic sets forms an ideal. Moreover, we prove that some of these families have some weaker additivity properties and some of them do not have even that.     

Poincar and Weak Poincar Inequalities for the Mixed Poisson Measure

By using the Mecke identity, we study a class of birth-death type Dirichlet forms associated with the mixed Poisson measure. Both Poincar and weak Poincar inequalities are established, while another Poincar type inequality is disproved under some reasonable assumptions.     

ON NON-UNIFORM CONDITIONS GIVING WEAK NORMAL STRUCTURE

Abstract

Several non-uniform conditions sufficient for weak normal structure have recently been introduced. We show that some of these are in fact equivalent and also utilize them in applications towards a 3-space property for weak normal structure, thereby improving on earlier results.     

Polynomials,Symmetric Multilinear Forms and Weak Compactness

In this paper we obtain some versions of weak compactness James theorem, replacing bounded linear functionals by polynomials and symmetric multilinear forms.     

Weak embedding of planar graphs

A weak embedding of a graphG is an embedding ofG with all the faces being tours. In this paper, for some planar graphs the weak maximum genus of them are given. And for the planar graphG, a characterization of whetherG can be weakly embedded on the nonspherical surfaces is obtained.