The Kemperman Structure Theorem (KST) yields a recursive description of the structure of a pair of finite subsets A and B of an abelian group satisfying |A + B| ≤ |A| + |B| − 1. In this paper, we introduce a notion of quasi-periodic decompositions and develop their basic properties in relation to KST. This yields a fuller understanding of KST, and gives a way to more effectively use KST in prac...

A procedure for designing exact reconstruction lter banks for tree-structured sub-band coders. where p(n) = jx(n)j 2 =kxk 2. Note that d = exp H(x) where H(x), deened in Equation 55 above, is the entropy of the sequence x. Beylkin in 1] observed earlier that computing the periodic discrete wavelet transform of all N circulant shifts of an N-point periodic signal requires computing only N log 2 ...

A recurrent theme in the description of phase portraits of dynamical systems is that of elliptic islands in a chaotic sea. Usually this picture is invoked in the context of smooth twist maps of the annulus or the torus, like the standard map. In this setting ‘elliptic islands’ refers to the topological disks bounded by periodic smooth curves surrounding elliptic periodic points. Establishing th...

‎in this paper‎, ‎we investigate a damped korteweg-de‎ ‎vries equation with forcing on a periodic domain‎ ‎$mathbb{t}=mathbb{r}/(2pimathbb{z})$‎. ‎we can obtain that if the‎ ‎forcing is periodic with small amplitude‎, ‎then the solution becomes‎ ‎eventually time-periodic.

A subset C of an abelian group G is said to be a minimal additive complement W⊆G if C+W=G and C′+W≠G for any proper C′⊂C. In this paper, we study certain subsets the integers that arise or do not as complements. Following suggestion Kwon, show bounded-below sets with arbitrarily large gaps Moreover, our construction shows such set belongs co-minimal pair, strengthening result Biswas Saha lacuna...

1 1. Introduction This paper is devoted to the study of asymptotic almost periodicity of bounded solutions for the following time almost periodic one dimensional scalar parabolic equation:    u t = u xx + f (t, x, u, u x), t > 0, 0 < x < 1, u(t, 0) = u(t, 1) = 0, t > 0, (1.1) where f : IR 1 × [0, 1] × IR 1 × IR 1 → IR 1 is a C 2 function, and f (t, x, u, p) with all its partial derivatives (...

Let $S$ be a dense subsemigroup of $(0,+infty)$. In this paper, we state   definition of thick near zero, and also  we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman  and Leader in [6].  We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions un...