随机环境中马氏链的最小闭集

主要研究了随机环境中马氏链的最小闭集的一些性质,并就保守集C在何种情况下存在最小闭子集的开问题结合Foguel的L1-理论进行了讨论,得到了一些结果.     

Hausdorff graph topology, proximal graph topology and the uniform topology for densely continuous forms and minimal USCO maps

For metric spaces (X, d _x) and (Y, d _y) we consider the Hausdorff metric topology on the set (CL(X × Y), ρ) of closed subsets of the product metrized by the product (box) metric ρ and consider the proximal topology defined on CL(X × Y). These topologies are inherited by the set G(X, Y) of closed-graph multifunctions from X to Y, if we identify each multifunction with its graph. Finally, we consider the topology of uniform convergence τ _uc on the set F(X, 2^Y) of all closed-valued multifunctions, i.e. functions from X to the set (CL(Y),) of closed subsets of Y metrized by the Hausdorff metric . We show the relationship between these topologies on the space G(X, Y) and also on the subspaces of minimal USCO maps and locally bounded densely continuous forms. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-006904. The authors would like to thank.ubica Holá for suggestions and comments.     

Approximations of parabolic integro-differential equations using wavelet-Galerkin compression techniques

Error estimates for Galerkin discretizations of parabolic integro-differential equations are presented under minimal regularity assumptions. The analysis is applicable in case that the full Galerkin matrix A associated to the integral operator is replaced by a compressed “sparse” matrix using wavelet basis techniques. In particular, a semi-discrete (in space) scheme and a fully-discrete scheme which is discontinuous in time but conforming in space are analyzed. AMS subject classification (2000)  65R20, 65M60     

Exponential stabilization of a flexible structure with a local interior control and under the presence of a boundary infinite memory

In this paper, we deal with the interior stabilization problem of a flexible structure governed by a hyperbolic partial differential equation coupled to two ordinary differential equations. Contrary to the previous works on the system, the boundary control is subject to the presence of an infinite memory term. In order to deal with such a nonlocal term, the minimal state approach is invoked. Specifically, a localized interior control is proposed in order to compensate the infinite memory effect. Thereafter, reasonable assumptions on the memory kernel are evoked so that the closed-loop system is shown to be well-posed thanks to semigroups theory of linear operators. Furthermore, the resolvent method is used to establish the exponential stability of the system.     

Uncontrollable expansion of PbZn1/3Nb2/3O3-PbTiO3 perovskite⇒pyrochlore transition during spark plasma sintering: Mechanism proposal using infinite periodic minimal surfaces

The PbZn_1/3Nb_2/3O₃-PbTiO₃ phase (PZN-PT) prepared by mechanosynthesis exhibits interesting relaxor properties when transformed into nanostructured ceramic by spark plasma sintering. When trying to obtain denser ceramic to enhance physical properties, the PZN-PT phase transformation from perovskite to pyrochlore structure induces the graphite die explosion. An explanation of this phenomenon is based on the reorganization of the lone pairs corresponding to Pb²⁺ cations into the large cavities of pyrochlore network, inducing an important cell volume increase, together with the speed of transformation depicted in the light of infinite periodic minimal surfaces describing the perovskite (P-surface) and the pyrochlore (F-surface) networks, respectively.     

Hochschild (co)homology of exterior algebras using algebraic Morse theory

In [1 Han, Y., Xu, Y. (2007). Hochschild (co)homology of exterior algebras. Comm. Algebra 35(1):115–131.[Web of Science ®] , [Google Scholar]], the authors computed the additive and multiplicative structure of HH*(A;A), where A is the n-th exterior algebra over a field. In this paper, we derive all their results using a different method (AMT) as well as calculate the additive structure of HH_k(A;A) and HH^k(A;A) over ?. We provide concise presentations of algebras HH_?(A;A) and HH*(A;A) as well as determine their generators in the Hochschild complex. Finally, we compute an explicit free resolution (spanned by multisets) of the A^e-module A and describe the homotopy equivalence to its bar resolution.     

Minimal graded free resolutions for monomial curves in 𝔸4 defined by almost arithmetic sequences

Let m = (m₀, m₁, m₂, n) be an almost arithmetic sequence, i.e., a sequence of positive integers with gcd(m₀, m₁, m₂, n) = 1, such that m₀ < m₁ < m₂ form an arithmetic progression, n is arbitrary and they minimally generate the numerical semigroup Γ =m₀? +m₁? +m₂? +n?. Let k be a field. The homogeneous coordinate ring k[Γ] of the affine monomial curve parametrically defined by X₀ = t^m₀, X₁ = t^m₁, X₂ = t^m₂, Y = tⁿ is a graded R-module, where R is the polynomial ring k[X₀, X₁, X₂, Y] with the grading degX_i: = m_i, degY: = n. In this paper, we construct a minimal graded free resolution for k[Γ].     

Proper minimal points of nonconvex sets in Banach spaces in terms of the limiting normal cone

In this paper, proper minimal elements of a given nonconvex set in a real ordered Banach space are defined utilizing the limiting (Mordukhovich) normal cone. The newly defined points are called limiting proper minimal (LPM) points. It is proved that each LPM is a proper minimal in the sense of Borwein under some assumptions. The converse holds in Asplund spaces. The relation of LPM points with Benson, Henig, super and proximal proper minimal points are established. Under appropriate assumptions, it is proved that the set of robust elements is a subset of the set of LPM points, and the set of LPM points is dense in that of minimal points. Another part of the paper is devoted to scalarization-based and distance function-based characterizations of the LPM points. The paper is closed by some results about LPM solutions of a set-valued optimization problem via variational analysis tools. Clarifying examples are given in addition to the theoretical results.     

On vector optimization problems and vector variational inequalities using convexificators

In this paper, we establish some results which exhibit an application of convexificators in vector optimization problems (VOPs) and vector variational inequaities involving locally Lipschitz functions. We formulate vector variational inequalities of Stampacchia and Minty type in terms of convexificators and use these vector variational inequalities as a tool to find out necessary and sufficient conditions for a point to be a vector minimal point of the VOP. We also consider the corresponding weak versions of the vector variational inequalities and establish several results to find out weak vector minimal points.