集值测度的延拓定理

讨论了集值测度的若干基本性质，在此基础上，研究了集值测度凸性，紧性及其靠拢定理，特别是到紧凸值集值测度的延拓定理。     

基于模糊值Choquet积分定义集函数的S性与PGP性

针对模糊测度空间上已建立的模糊值Choquet积分,将这种积分整体看成可测空间上取值于模糊数的集函数,当模糊测度满足一般S性和PGP性时,研究了这种模糊值集函数所保持的遗传性质.     

多目标决策非凸锥Λ－有效点的存在性与控制性质

本文提出了多目标决策偏好及最优解的一般概念和集诱导偏好的概念．给出了判断ρ－完备集的一系列条件，从而指出了ρ－完备集是十分广泛的集类．得到了集合的Λ－有效点的存在性定理和ρ－下闭集与截面的Λ－有效点的性质．通过引入函数Λ－下半连续的概念，得到了多目标决策一般集诱导偏好最优解的存在性定理．在这些结果的基础上，最后得到了集合Ｙ关于Λ和多目标决策问题的控制性质．     

L-fuzzy子域与L-fuzzy线性空间的新刻画

本文研究了L-fuzzy子域与L-fuzzy线性空间的性质.借助于Fuzzy集A的水平截集A(a),得到了若干新的等价刻画.且直接和方便于应用.     

样本深度的基本性质

本文讨论由L2深度修正得到的(L)2深度相应的样本深度的性质,得到了样本深度的相合性和渐近正态性,并证明了它在任意紧集上的一致相合性.最后,基于上述性质简要讨论了样本深度等高的一些性质.     

(L)2样本深度的基本性质

本文讨论由L^2深度修正得到的L^2深度相应的样本深度的性质，得到了样本深度的相合性和渐近正态性，并证明了它在任意紧集上的一致相合性．最后，基于上述性质简要讨论了样本深度等高的一些性质．     

~2样本深度的基本性质

本文讨论由L2深度修正得到的L2深度相应的样本深度的性质,得到了样本深度的相合性和渐近正态性,并证明了它在任意紧集上的一致相合性．最后,基于上述性质简要讨论了样本深度等高的一些性质．     

一类具有非线性阻尼和源项的Petrovsky方程整体解的存在性与渐近性

研究了一类具有非线性阻尼和源项的Petrovsky方程u_(tt) △~2u au_t|u_t|~(m-2)= bu|u|~(p-2)的初边值问题.在对m,p的大小关系不加任何限制的情况下,利用稳定集证明了整体解的存在性,并且得到了整体解的渐近性质.     

带有强吸收项的半线性热方程解的相关性质

研究了一类带有强吸收项的半线性热方程的Cauchy问题,得出了解的存在性和惟一性,并利用比较原理给出了解的支集的瞬间收缩性质和解的有限时间淹没性质及指标p的最优性.     

不分明化拓扑中近似紧性和几乎紧性

在不分明化拓扑空间中,从正则开集出发引入了近似紧性和几乎紧性的概念,并且给出了它们的一些性质.这些概念的结合有助于我们对不分明化拓扑的研究。     

On characterizing properties of the value sets and the equilibrium point sets of non-cooperative two-person games

In this paper, for certain subfamilies of the family of bounded measurable two-person games in normal form, the value sets are characterized by three properties, called the maximum property, the minimum property and the adjunction property. Furthermore, one of the papers of Vilkas is critically discussed. Finally, for bimatrix games, two systems of characterizing properties for the equilibrium point sets are given.     

On the class of disjoint limited completely continuous operators

We introduce and study new class of sets (almost L-limited sets). Also, we introduce new concept of property in Banach lattice (almost Gelfand–Phillips property) and we characterize this property using almost L-limited sets. On the other hand, we introduce the class of disjoint limited completely continuous operators which is a largest class than that of limited completely continuous operators, we characterize this class of operators and we study some of its properties.     

Rational solution axioms and efficient sets

In situations where there is no clear criterion for determining optimal solutions, one seeks for solution sets which have specific properties. One particular, and central, solution set, is the efficient set. This paper considers a range of solution sets, and properties, and determines the properties satisfied by each solution set. One of these properties is that the solution set should be contained in the efficient set. This particular property is important in view of the modern interests in finding special subsets of efficient sets using L_p metrics, lexicographic ideas, and so on, and not all solution satisfy this property.     

Exclusive and essential sets of implicates of Boolean functions

In this paper we study relationships between CNF representations of a given Boolean function f and certain sets of implicates of f. We introduce two definitions of sets of implicates which are both based on the properties of resolution. The first type of sets, called exclusive sets of implicates, is shown to have a functional property useful for decompositions. The second type of sets, called essential sets of implicates, is proved to possess an orthogonality property, which implies that every CNF representation and every essential set must intersect. The latter property then leads to an interesting question, to which we give an affirmative answer for some special subclasses of Horn Boolean functions.     

On almost rc-Lindelöf sets

In [4], Dlaska introduced the class of almost rc-Lindelöf sets and studied some basic properties of such sets. In this paper, we obtain further results concerning almost rc-Lindelöf sets. We also introduce new concepts to obtain several mapping properties concerning almost rc-Lindelöf sets and almost rc-Lindelöf spaces. The property of being an almost rc-Lindelöf set is invariant under functions which are slightly continuous and weakly θ-irresolute. It is also shown that the property of being an almost rc-Lindelöf space is inverse invariant under functions which are weakly almost open, ω-regular open, and whose fibers are S-sets.     

Orders of Indescribable Sets

We extract some properties of Mahlo’s operation and show that some other very natural operations share these properties. The weakly compact sets form a similar hierarchy as the stationary sets. The height of this hierarchy is a large cardinal property connected to saturation properties of the weakly compact ideal.     

Self-similar sets satisfying the common point property

A self-similar set is a fixed point of iterated function system (IFS) whose maps are similarities. We say that a self-similar set satisfies the common point property if the intersection of images of the attractor under the maps of the IFS is a singleton and this point has a common pre-image, under the maps of the IFS, and the pre-image is in the attractor.Self-similar sets satisfying the common point property were introduced in Sirvent (2008) in the context of space-filling curves. In the present article we study some basic topological and dynamical properties of self-similar sets satisfying the common point property. We show examples of this family of sets.We consider attractors of a sub-IFS, an IFS formed from the original IFS by removing some maps. We put conditions on this attractors for having the common point property, when the original IFS have this property.     

Hyperplane sections and the subtlety of the Lefschetz properties

The weak and strong Lefschetz properties are two basic properties that Artinian algebras may have. Both Lefschetz properties may vary under small perturbations or changes of the characteristic. We study these subtleties by proposing a systematic way of deforming a monomial ideal failing the weak Lefschetz property to an ideal with the same Hilbert function and the weak Lefschetz property. In particular, we lift a family of Artinian monomial ideals to finite level sets of points in projective space with the property that a general hyperplane section has the weak Lefschetz property in almost all characteristics, whereas a special hyperplane section does not have this property in any characteristic.     

Strong CHIP, normality, and linear regularity of convex sets

We extend the property (N) introduced by Jameson for closed convex cones to the normal property for a finite collection of convex sets in a Hilbert space. Variations of the normal property, such as the weak normal property and the uniform normal property, are also introduced. A dual form of the normal property is derived. When applied to closed convex cones, the dual normal property is the property (G) introduced by Jameson. Normality of convex sets provides a new perspective on the relationship between the strong conical hull intersection property (strong CHIP) and various regularity properties. In particular, we prove that the weak normal property is a dual characterization of the strong CHIP, and the uniform normal property is a characterization of the linear regularity. Moreover, the linear regularity is equivalent to the fact that the normality constant for feasible direction cones of the convex sets at is bounded away from 0 uniformly over all points in the intersection of these convex sets.