Recently, Došlić, and Liu and Wang developed techniques for dealing with the log-convexity of sequences. In this paper, we present a criterion for the log-convexity of some combinatorial sequences. In order to prove the log-convexity of a sequence satisfying a three-term recurrence, by our method, it suffices to compute a constant number of terms at the beginning of the sequence. For example, i...

We have studied the initial stages of the oxidation of the Cu(1 0 0) surface using ab initio calculations. Both atomic and molecular oxygen are addressed. We show that subsurface oxygen is not energetically favourable, but gets stabilized by on-surface O. We discuss the adsorption of molecular oxygen using elbow plots, which can be used in order to qualitatively understand the measured sticking...

In this paper we study recurrences concerning the combinatorial sum k≡r (mod m) n k and the alternate sum k≡r (mod m) (−1) (k−r)/m n k , where m > 0, n 0 and r are integers. For example, we show that if n m − 1 then

Biological control of Canada thistle using Puccinia punctiformis has been largely unsuccessful in part due to a low incidence of systemically infected shoots and heterogeneous distribution of teliospores in the soil. The present study investigated the feasibility of strategic mowing to improve incidence of systemically infected shoots, and enhance intraand/or inter-season disease development in...

General solution methods for linear vector recurrences are considered; an algorithm based on partial fraction expansion is shown to be the most efficient way of solving this problem.

We solve some recurrences given by E. Munarini and N. Zagaglia Salvi proving explicit closed formulas for Whitney numbers of the distributive lattices of order ideals of the fence poset and crown poset. Moreover, we get explicit closed formulas for Whitney numbers of lattices of order ideals of fences with higher asymmetric peaks.

Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on Z for the initial configuration of all rotors aligned. If n particles in turn perform rotor walks starting from the origin, we show that the number that escape (i.e., never return to the origin) is of order n in dimensions d ≥ 3, and of order n/ log n in dimension 2.

A Mathematica package for finding recurrences for q-hypergeometric multiple sums is introduced. Together with a detailed description of the theoretical background, we present several examples to illustrate its usage and range of applicability. In particular, various computer proofs of recently discovered identities are exhibited.

Elementary geometric properties of toral automorphisms give sufficient control over the distribution of residues modulo m of certain linear recurrences to give a new, noncomputational proof, that Q( √ 2 + √ 2) is a norm-Euclidean number field.

Musical patterns that recur in approximate, rather than identical, form within the body of a musical work are considered to be of considerable importance in music analysis. Here we consider the “evolutionary chain problem”: this is the problem of computing a chain of all “motif” recurrences, each of which is a transformation of (“similar” to) the original motif, but each of which may be progres...