The critical group of <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> × <Emphasis Type="Italic">C</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

In this paper, the structure of the critical group of the graph K _m × C _n is determined, where m, n ≥ 3.     

Some sufficient conditions for tunnel numbers of connected sum of two knots not to go down

In this paper, we show the following result: Let K _i be a knot in a closed orientable 3-manifold M _i such that (M _i ,K _i ) is not homeomorphic to (S ₂ ×S ₁, x ₀ ×S ₁), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(K _i ) is less than the difference of one and twice of the tunnel number of K _i . Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive.     

Six-flows on almost balanced signed graphs

In 1983, Bouchet conjectured that every flow-admissible signed graph admits a nowhere-zero 6-flow. By Seymour's 6-flow theorem, Bouchet's conjecture holds for signed graphs with all edges positive. Recently, Rollová et al proved that every flow-admissible signed cubic graph with two negative edges admits a nowhere-zero 7-flow, and admits a nowhere-zero 6-flow if its underlying graph either contains a bridge, or is 3-edge-colorable, or is critical. In this paper, we improve and extend these results, and confirm Bouchet's conjecture for signed graphs with frustration number at most two, where the frustration number of a signed graph is the smallest number of vertices whose deletion leaves a balanced signed graph.     

Maximum‐norm a posteriori error bounds for a collocation method applied to a singularly perturbed reaction–diffusion problem in three dimensions

Collocation with triquadratic C¹‐splines for a singularly perturbed reaction–diffusion problem in three dimension is studied. A posteriori error bound in the maximum norm is derived for the collocation method on arbitrary tensor‐product meshes which is robust in the perturbation parameter. Numerical results are presented that support our theoretical estimate.     

Stochastic sensitivity of attractors for a piecewise smooth neuron model

ABSTRACT

We consider a one-dimensional model of neural activity, given by a piecewise smooth discontinuous map. Fold bifurcations as well as border collision bifurcations are described in detail. Using the method of stochastic sensitivity functions, noise-induced phenomena, such as transitions within attractor and between attractors, and spike generation, are described. Statistical characteristics of interspike intervals depending on noise intensity are studied.     

面板数据公共变点的非参数最大似然估计

Gao Pengli;Xia Zhiming(School of Mathematics,Northwest University,Xi'an 710127,China)     

关于Tsallis型非对称熵的若干研究

基于Tsallis熵和非对称熵,本文提出了Tsallis型非对称熵,该熵推广了Tsallis熵和非对称熵,证明了最大的Tsallis型非对称熵原理,并且从该原理中可以获得比Tsallis熵及非对称熵原理更多的分布,从而说明该原理的有用性.     

Topological properties of strongly monotone planar vector fields

We consider strongly monotone continuous planar vector fields with a finite number of fixed points. The fixed points fall into three classes, attractors, repellers and saddles. Naturally, the relative positions of the fixed points must obey a set of restrictions imposed by monotonicity. The study of these restrictions is the main goal of the paper. With any given vector field, we associate a matrix describing the arrangement of the fixed points on the plane. We then use these matrices to formulate simple necessary and sufficient conditions which allow one to determine whether a finite set of attractors, repellers and saddles at given positions on the plane can be realized as the fixed point set of a strongly monotone vector field.     

Piston Problems of Two-Dimensional Chaplygin Gas

In this paper, the authors study the piston problem for the unsteady two-dimensional Euler system for a Chaplygin gas. The angle of the piston is allowed to vary in a wide range. The piston can be pushed forward into the static gas, or pulled back from the gas. The global existence of solution to the piston problem with any initial speed is established, and the structures of the global solutions are clearly described. The authors find that for the proceeding piston problem the front shock can be detached, attached or even adhere to the surface of the piston depending on the parameters of the flow and the piston; while for the receding problem the front rarefaction wave is always detached and the concentration will never occur.     

The maximum surplus in a finite‐time interval for a discrete‐time risk model with exchangeable,dependent claim occurrences

This paper investigates a discrete‐time risk model that involves exchangeable dependent loss generating claim occurrences and compound binomially distributed aggregate loss amounts. First, a general framework is presented to derive the distribution of a surplus sequence using the model. This framework is then applied to obtain the distribution of any function of a surplus sequence in a finite‐time interval. Specifically, the distribution of the maximum surplus is obtained under nonruin conditions. Based on this distribution, the computation of the minimum surplus distribution is given. Asset and risk management–oriented implications are discussed for the obtained distributions based on numerical evaluations. In addition, comparisons are made involving the corresponding results of the classical discrete‐time compound binomial risk model, for which claim occurrences are independent and identically distributed.