给定匹配数和独立数时图零度的上界

设G是一个有n个点的简单图,分别记η(G),m(G)和α(G)为图G的零度、匹配数和独立数.设θ(G)是一个非负整数,定义为使图G成为二部图至少需要从G的边集中删去的边数.本文运用二部划分运算,证明了对于有n个点并且不含有圈长为2的倍数的圈为子图的简单图G,有η(G)≤n-2m(G)+20(G)和η(G)≤2α(G)+2θ(G)-n.     

Conditionally evenly convex sets and evenly quasi-convex maps

Evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces. We introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar theorem. This notion is then applied to obtain the dual representation of conditionally evenly quasi-convex maps, which turns out to be a fundamental ingredient in the study of quasi-convex dynamic risk measures.     

Average Distance,Independence Number,and Spanning Trees

Let G be a connected graph of order n and independence number α. We prove that G has a spanning tree with average distance at most , if , and at most , if . As a corollary, we obtain, for n sufficiently large, an asymptotically sharp upper bound on the average distance of G in terms of its independence number. This bound, apart from confirming and improving on a conjecture of Graffiti [8], is a strengthening of a theorem of Chung [1], and that of Fajtlowicz and Waller [8], on average distance and independence number of a graph.     

Risk aggregation and stochastic claims reserving in disability insurance

We consider a large, homogeneous portfolio of life or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic–demographic environment. Using a conditional law of large numbers, we establish the connection between claims reserving and risk aggregation for large portfolios. Further, we derive a partial differential equation for moments of present values. Moreover, we show how statistical multi-factor intensity models can be approximated by one-factor models, which allows for solving the PDEs very efficiently. Finally, we give a numerical example where moments of present values of disability annuities are computed using finite-difference methods and Monte Carlo simulations.     

Time dependent random fields on spherical non-homogeneous surfaces

We introduce a class of isotropic time dependent random fields on the non-homogeneous sphere which is represented by a time-changed spherical Brownian motion of order ν∈(0,1]$\nu \in (0,1]$. We can capture some anisotropies in Cosmology with this model. This process is a time-changed rotational diffusion (TRD) or the stochastic solution to the equation involving the spherical Laplace operator and a time-fractional derivative of order ν$\nu$. TRD is a diffusion on the non-homogeneous sphere and therefore, the spherical coordinates given by TRD represent the coordinates of a non-homogeneous sphere by means of which an isotropic random field is indexed. The time dependent random fields we present in this work are therefore realized through composition and can be viewed as isotropic random field on randomly varying sphere.     

球面稳定同伦群中的$\xi_n$-相关元素的非平凡性

利用Adams谱序列与May谱序列, 发掘了球面稳定同伦群中一族$\xi_n$的相关元素. 这里$\xi_n\in\pi_* M$在Adams 谱序列中由$h_0h_n\in \ext_A^{2,p^n q+q}(H^* M,\zz_p)$所表示, 其中$p\geqslant 7,\ n>3,\ q=2(p-1).$     

Regulating the Deposition of Insoluble Sulfur Species for Room Temperature Sodium-Sulfur Batteries

Room temperature sodium-sulfur(RT-Na-S) batteries are regarded as promising candidates for next-generation high-energy-density batteries. However, in addition to the severe shuttle effect, the inhomogeneous deposition of the insoluble sulfur species generated during the discharge/charge processes also contributes to the rapid capacity fade of RT-Na-S batteries. In this work, the deposition behavior of the insoluble sulfur species in the traditional slurry-coated sulfur cathodes is investigated using microporous carbon spheres as model sulfur host materials. To achieve uniform deposition of insoluble sulfur species, a self-supporting sulfur cathode fabricated by assembling microporous carbon spheres is designed. With homogeneous sulfur distribution and favorable electron transport pathway, the self-supporting cathode delivers remarkably enhanced rate capability(509 mA·h/g at 2.5 C, 1 C=1675 mA/g), cycling stability(718 mA·h/g after 480 cycles at 0.5 C) and areal capacity(4.98 mA·h/cm² at 0.1 C), highlighting the great potential of manipulating insoluble sulfur species to fabricate high-performance RT-Na-S batteries.     

A criterion for the half-plane property

We establish a convenient necessary and sufficient condition for a multiaffine real polynomial to be stable, and use it to verify that the half-plane property holds for seven small matroids that resisted the efforts of Choe, Oxley, Sokal, and Wagner [Y.-B. Choe, J.G. Oxley, A.D. Sokal, D.G. Wagner, Homogeneous polynomials with the half-plane property, Adv. Appl. Math. 32 (2004) 88-187].     

A note on semiextensions of stable circuits

A semiextension of a circuit C in a graph G provides a possible means of finding a cycle double cover of G with C as a prescribed circuit. Recently we conjectured [E.E. García Moreno, T.R. Jensen, On semiextensions and circuit double covers, J. Combin. Theory Ser. B 97 (2007) 474-482] that if G is cubic and 2-edge-connected, then a semiextension of C in G exists. If true, this would imply several long-standing conjectures.If there is a circuit C^′ in G with C^′≠C and V(C)⊆V(C^′), then C^′ is called an extension of C, a special case of a semiextension. If there is no such circuit, then C is said to be stable in G. Hence the existence question for semiextensions is easy except for stable circuits. Not many examples of graphs with stable circuits have been published. In this note we show that the members of a particular class of stable circuits described by M. Kochol have semiextensions.