Two results on the equivariant Ginzburg-Landau vortex in arbitrary dimension

We characterize the O(N)-equivariant vortex solution for Ginzburg-Landau type equations in the N-dimensional Euclidean space and we prove its local energy minimality for the corresponding energy functional.     

A Brézis-Browder principle on partially ordered spaces and related ordering theorems

Through a simple extension of Brézis-Browder principle to partially ordered spaces, a very general strong minimal point existence theorem on quasi ordered spaces, is proved. This theorem together with a generic quasi order and a new notion of strong approximate solution allow us to obtain two strong solution existence theorems, and three general Ekeland variational principles in optimization problems where the objective space is quasi ordered. Then, they are applied to prove strong minimal point existence results, generalizations of Bishop-Phelps lemma in linear spaces, and Ekeland variational principles in set-valued optimization problems through a set solution criterion.     

Cones with a mapping cone symmetry in the finite-dimensional case

In the finite-dimensional case, we present a new approach to the theory of cones with a mapping cone symmetry, first introduced by Størmer. Our method is based on a definition of an inner product in the space of linear maps between two algebras of operators and the fact that the Jamio?kowski-Choi isomorphism is an isometry. We consider a slightly modified class of cones, although not substantially different from the original mapping cones by Størmer. Using the new approach, several known results are proved faster and often in more generality than before. For example, the dual of a mapping cone turns out to be a mapping cone as well, without any additional assumptions. The main result of the paper is a characterization of cones with a mapping cone symmetry, saying that a given map is an element of such cone if and only if the composition of the map with the conjugate of an arbitrary element in the dual cone is completely positive. A similar result was known in the case where the map goes from an algebra of operators into itself and the cone is a symmetric mapping cone. Our result is proved without the additional assumptions of symmetry and equality between the domain and the target space. We show how it gives a number of older results as a corollary, including an exemplary application.     

Counting colored planar maps: Algebraicity results

We address the enumeration of properly q-colored planar maps, or more precisely, the enumeration of rooted planar maps M weighted by their chromatic polynomial χM(q) and counted by the number of vertices and faces. We prove that the associated generating function is algebraic when q≠0,4 is of the form 2+2cos(jπ/m), for integers j and m. This includes the two integer values q=2 and q=3. We extend this to planar maps weighted by their Potts polynomial PM(q,ν), which counts all q-colorings (proper or not) by the number of monochromatic edges. We then prove similar results for planar triangulations, thus generalizing some results of Tutte which dealt with their proper q-colorings. In statistical physics terms, the problem we study consists in solving the Potts model on random planar lattices. From a technical viewpoint, this means solving non-linear equations with two “catalytic” variables. To our knowledge, this is the first time such equations are being solved since Tutte?s remarkable solution of properly q-colored triangulations.     

Common fixed point results for two new classes of hybrid pairs in symmetric spaces

Some common fixed point theorems due to Abbas and Khan [M. Abbas, A.R. Khan, Common fixed points of generalized contractive hybrid pairs in symmetric spaces, Fixed Point Theor. Appl. 2009 (2009) 11, Article ID 869407, doi:10.1155/2009/869407], and Abbas and Rhoades [M. Abbas, B.E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings defined on symmetric spaces, Pan. Amer. Math. J. 18 (1) (2008) 55-62] are proved for two new classes of hybrid pair of mappings which contain occasionally weakly compatible hybrid pairs as a proper subclass. Consequently, some results proved by Hussain et al. [N. Hussain, M.A. Khamsi, A. Latif, Common fixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal. 74 (2011) 2133-2140], Bhatt et al. [A. Bhatt, et al., Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal. 73 (2010) 176-182] and many others are extended to hybrid pair of mappings. Examples are also presented to support the concepts defined in the paper.     

Homoclinic Flip Bifurcations Accompanied by Transcritical Bifurcation

The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the existence of homoclinic orbit and the periodic orbit is studied for the system accompanied with transcritical bifurcation.     

标准算子代数上满足某些等式的广义导子的刻画(英文)

令H为复数域C上的Hilbert空间,A为H上的标准算子代数.设δ:A→B(H)是线性映射.本文证明了,如果对任意A∈A成立δ(AA~*A)=δ(A)A~*A-Aδ(A~*)A+AA~*δ(A),则存在λ∈C及算子S,T∈B(H)满足S+T=λI,使得对所有的A∈A都有δ(A)=SA-AT.     

集值Subpramart的另一类Riesz逼近

假定(X,‖.‖)为可分的Banach空间,X*为其对偶空间,X*可分。设(Ω,Φ,P)为完备的概率空间,{Φn,n≥1}为Φ的上升子σ-域族,且Φ=∨Φn本文首先讨论了集值Subpramart若干性质,在此基础上,给出了集值Subpramart的一类Riesz鞅逼近。     

集值模糊测度的伪自连续性

在实赋范空间X的所有非空有界闭子集构成的集类上,利用Hausdorff距离定义了集值模糊测度,其次,给出了伪零可加、伪零可减、伪自连续性、一致伪自连续性等的定义,进而研究了它们之间的蕴涵关系.