Recurrence relations with two indices and even trees

Recently, the author, Mansour, introduced a combinatorial problem, called Hobby's problem, to study different types of recurrence relations with two indices. Moreover, he presented several recurrence relations with two indices related to Dyck paths and Schröder paths. In this paper, we generalize Hobby's problem to study other types of recurrence relations with two indices for which a combinatorial method provides a complete solution. Combinatorially, we describe these recurrence relations as a set of lattice paths in the second octant of the plane integer lattice, and then we map bijectively these lattice paths to the set of even trees. Analytically, we use the kernel method technique to solve these recurrence relations.     

Signed words and permutations, V; a sextuple distribution

We calculate the distribution of the sextuple statistic over the hyperoctahedral group B _n that involves the flag-excedance and flag-descent numbers “fexc” and “fdes,” the flag-major index “fmaj,” the positive and negative fixed point numbers “ ” and “ ” and the negative letter number “neg.” Several specializations are considered. In particular, the joint distribution for the pair is explicitly derived.      

Duality for Anticonvex Programs

Calling anticonvex a program which is either a maximization of a convex function on a convex set or a minimization of a convex function on the set of points outside a convex subset, we introduce several dual problems related to each of these problems. We give conditions ensuring there is no duality gap. We show how solutions to the dual problems can serve to locate solutions of the primal problem.     

Kamenev-type oscillation criteria for even order neutral differential equations with deviating arguments

Sufficient conditions are established for the oscillation of even order neutral differential equations of the form

where n  2 is even integer.     

偶数维空间 Navier-Stokes 方程的扩散波

该文考虑偶数维空间一般 Navier-Stokes方程解的大时间状态.通过研究相应线性方程格林函数的逐点估计, 得到了解的渐近状态.所得结论与弱惠更斯原理相符合.     

Extending Independent Sets to Bases and the Axiom of Choice

We show that the both assertions “in every vector space B over a finite element field every subspace V ? B has a complementary subspace S” and “for every family ?? of disjoint odd sized sets there exists a subfamily ?={F_j:j ?ω} with a choice function” together imply the axiom of choice AC. We also show that AC is equivalent to the statement “in every vector space over ? every generating set includes a basis”.     

电四极矩对高次谐波产生的贡献

通过数值求解强场近似下单电子原子的含时薛定谔方程,研究了在强线偏振激光场下,氢原子电四极矩对高次谐波产生的贡献.研究结果表明,在强激光场的作用下,在偶极矩的影响下氢原子能够产生奇次谐波,当激光场强度增加到一定值时,氢原子在电四极矩的作用下产生了偶次谐波.根据谐波功率谱和时频分析图并结合半经典三步模型分析了偶次高次谐波产生机制,并对产生的物理现象做出了合理的解释.     

The existence of even factors in iterated line graphs

An even factor of a graph is a spanning subgraph of G in which all degrees are even, positive integers. In this paper, we characterize the claw-free graphs having even factors and then prove that the n-iterated line graph Lⁿ(G) of G has an even factor if and only if every end branch of G has length at most n and every odd branch-bond of G has a branch of length at most n+1.     

IMPACT OF RISK AVERSION ON THE OPTIMAL ROTATION WITH STOCHASTIC PRICE

Abstract This paper examines the effect of risk aversion on the optimal rotation when the stumpage price is stochastic. Assuming that the stumpage price is normally distributed, we show that the optimal rotation under risk aversion may be shorter than, equal to, or longer than the corresponding optimal rotation under risk neutrality. Which of these cases holds true depends on the interest rate and the real regeneration cost, and can be determined based on the marginal variance (i.e., the derivative of the variance function with respect to rotation age) evaluated at the optimal rotation under risk neutrality. Furthermore, we show that there exists a monotone continuous curve, which divides the interest rate‐regeneration cost space into two regions where risk aversion affects the optimal rotation differently. For a given interest rate, risk aversion shortens (prolongs) the optimal rotation if the regeneration cost lies below (above) the curve. Along the separating curve the optimal rotation under risk aversion coincides with the optimal rotation under risk neutrality. Two examples are presented to demonstrate the separating curve and the impacts of risk aversion on the optimal rotation.