拓扑空间中新的广义L-KKM型定理及其应用

In this paper, some new generalized L-KKM type theorems with finitely open values and with finitely closed values are established without any convexity structure in topological spaces. As applications, some new matching theorem, fixed point theorem and existence the orem of equilibrium problem with lower and upper bounds are also given under some suitable conditions. These theorems presented in this paper unify and generalize some corresponding known results in recent literatures.     

Coherent sequences of polynomial ideals on Banach spaces

This article deals with the relationship between an operator ideal and its natural polynomial extensions. We define the concept of coherent sequence of polynomial ideals and also the notion of compatibility between polynomial and operator ideals. We study the stability of these properties for maximal and minimal hulls, adjoint and composition ideals. We also relate these concepts with conditions on the underlying tensor norms (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Closed graph and open mapping theorems for topological $ \tilde \lc $‐modules and applications

We present closed graph and open mapping theorems for ‐linear maps acting between suitable classes of topological and locally convex topological ‐modules. This is done by adaptation of De Wilde's theory of webbed spaces and Adasch–Ernst–Keim's theory of barrelled spaces to the context of locally convex and topological ‐modules, respectively. We give applications of the previous theorems to Colombeau theory as well to the theory of Banach ‐modules. In particular we obtain a necessary condition for ??^∞‐hypoellipticity on the symbol of a partial differential operator with generalized constant coefficients (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

HYPERBOLIC MEAN CURVATURE FLOW：EVOLUTION OF PLANE CURVES

In this paper we investigate the one-dimensional hyperbolic mean curvatureflow for closed plane curves. More precisely, we consider a family of closed curves F ： S1 × [0, T ） → R^2 which satisfies the following evolution equation δ^2F /δt^2 （u, t） = k（u, t）N（u, t）-▽ρ（u, t）, ∨（u, t） ∈ S^1 × [0, T ） with the initial data F （u, 0） = F0（u） and δF/δt （u, 0） = f（u）N0, where k is the mean curvature and N is the unit inner normal vector of the plane curve F （u, t）, f（u） and N0 are the initial velocity and the unit inner normal vector of the initial convex closed curve F0, respectively, and ▽ρ is given by
▽ρ Δ=（δ^2F /δsδt ,δF/δt） T , in which T stands for the unit tangent vector. The above problem is an initial value problem for a system of partial differential equations for F , it can be completely reduced to an initial value problem for a single partial differential equation for its support function. The latter equation is a hyperbolic Monge-Ampere equation. Based on this, we show that there exists a class of initial velocities such that the solution of the above initial value problem exists only at a finite time interval [0, Tmax） and when t goes to Tmax, either the solution convergesto a point or shocks and other propagating discontinuities are generated. Furthermore, we also consider the hyperbolic mean curvature flow with the dissipative terms and obtain the similar equations about the support functions and the curvature of the curve. In the end, we discuss the close relationship between the hyperbolic mean curvature flow and the equations for the evolving relativistic string in the Minkowski space-time R^1,1.     

GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES

In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.     

Gas‐phase fragmentation of protonated C60‐pyrimidine derivatives

Electrospray ionization mass spectrometry/mass spectrometry (ESI/MS/MS) and multiple stage mass spectrometry (MSⁿ, n > 2) were used in the positive ion mode, with two different types of mass spectrometers, a quadrupole time‐of‐flight and an ion trap, to characterize two sets of different types of C₆₀‐aminopyrimidine exohedral derivatives. In one set, the pyrimidine moiety bears an amino acid methyl ester residue, and in the other the pyrimidine ring is part of a nucleoside‐type moiety, the latter existing as two separated diastereoisomers. We have found that retro‐cycloaddition processes occur for the closed shell protonated species formed by electrospraying C₆₀ derivatives synthesized by Diels–Alder reactions, whereas for the C₆₀ derivatives synthesized via 1,3‐dipolar cycloadditions, these processes did not occur. Formation of diagnostic ions allowed the differentiation between the two groups of fullerene derivatives, and between the diastereoisomers of C₆₀ derivatives with a nucleoside‐type moiety. In general, the fragmentation processes are strongly dependent on the protonation sites and on the structure of the exohedral moieties. Copyright © 2009 John Wiley & Sons, Ltd.     

On Whitney numbers of the order ideals of generalized fences and crowns

We solve some recurrences given by E. Munarini and N. Zagaglia Salvi proving explicit formulas for Whitney numbers of the distributive lattices of order ideals of the fence poset and crown poset. Moreover, we get a method to obtain explicit formulas for Whitney numbers of lattices of order ideals of fences with higher asymmetric peaks.     

Coherence theory and coherence phenomena in a closed spin‐1/2 system

A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence Ξ, and discuss in some detail a general coherence theory and its elementary results. As expected, decoherence is understood as a statistical process that is caused by the dynamics of the system, similar to the growth of entropy. It appears that coherence is an important measure that helps to understand quantum properties of a system, e.g., the decoherence time can be derived from the coherence function Ξ(t), but not from the entropy dynamics. Moreover, the concept of decoherence time is applicable in closed and finite systems. However, in most cases, the decay of off‐diagonal elements differs from the usual exp(‐t/τ_d) behaviour. For concreteness, we report the form of decoherence time τ_d in a finite Heisenberg model with respect to the number of particles N, density n_ρ, spatial dimension D and ? in a η/r^?‐type of potential.     

Martin–Löf random generalized Poisson processes

Martin–Löf randomness was originally defined and studied in the context of the Cantor space $2^{\omega }$. In [2] probability theoretic random closed sets (RACS) are used as the foundation for the study of Martin–Löf randomness in spaces of closed sets. We use that framework to explore Martin–Löf randomness for the space of closed subsets of $\mathbb{R}$ and a particular family of measures on this space, the generalized Poisson processes. This gives a novel class of Martin–Löf random closed subsets of $\mathbb{R}$. We describe some of the properties of these Martin–Löf random closed sets; one result establishes that a real number is Martin–Löf random if and only if it is contained in some Martin–Löf random closed set.