We show that if P (x) is a polynomial with nondecreasing, nonnegative coefficients, then the coefficient sequence of P (x+ 1) is unimodal. Applications are given.

The paper solves the enumeration of set partitions in which nondecreasing sequence parts , is contained a degree-2 polynomial . This generalization number into arithmetic progressions. We also study problem dividing whose differences between consecutive are integers. In particular, we focus on sum triangular numbers.

Two finite real sequences (aI , . . . . ak) and (b, , . . . . bk) are cross-monotone if each is nondecreasing and ai + 1 -ci > bi + 1 bt for all i < k. A sequence ((x, , . . . , on) of nondecreasing reals is in class CM(k) if it has disjoint k-term subsequences that are cross-monotone. The paper shows that f(k), the smallest n such that every nondecreasing (o, , . . . , on) is in CM(k), is boun...

This article is concerned with symmetry properties of the solutions of the reaction-diiusion equation u + f (u) = 0 in a bounded connected domain in R N (N = 2; 3; : : :). Of especial interest are nonlinear source terms f of the type f (u) = u p ? u q with 0 q < p 1. Two results are presented. The rst result concerns the solution of a free boundary problem, where the domain is unknown and u and...

This paper is concerned with the asymptotic propagations for a nonlocal dispersal population model shifting habitats. In particular, we verify that invading speed of species determined by c habitat edge and behaviours near infinity species’ growth rate which nondecreasing along positive spatial direction. case where declines negative , conclude extinction occurs if &gt; *(∞), while &lt; spreadi...

This paper studies finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject into account such total dominates nondecreasing floor process at each intermediate time. The problem formulated to minimize cost of accumulated injection. We first transform original with constraints an unconstrained cont...