This paper presents an explicit construction for an ((n = 2qt, k = 2q(t−1), d = n−(q+1)), (α = q(2q)t−1, β = α q )) regenerating code over a field FQ operating at the Minimum Storage Regeneration (MSR) point. The MSR code can be constructed to have rate k/n as close to 1 as desired, sub-packetization level α ≤ r nr for r = (n− k), field size Q no larger than n and where all code symbols can be ...

A function f is called an odd-even graceful labeling of a graph G if f: V(G) → {0,1,2,...,q} is injective and the induced function f : E(G) → { { 0,2,4,...,2q+2i/i= 1 to n} such that when each edge uv is assigned the label |f(u) – f(v)| the resulting edge labels are {2,4,6,...,2q}. A graph which admits an odd-even graceful labeling is called an odd-even graceful graph. In this paper, the odd-ev...

conclusions in conclusion, chit1 24 bp duplication might not be a candidate gene for susceptibility to ptb. larger studies are necessary to confirm these findings in various populations. results homozygous wild type, heterozygous and homozygous mutant frequencies of chit1 24 bp duplication polymorphism were 43.9%, 43.9% and 12.2% in controls and 42.8%, 45.1% and 12.1% in ptb patients. we found ...

objective(s): umbilical cord blood is a good source of the mesenchymal stem cells that can be banked, expanded and used in regenerative medicine.  the objective of this study was to test whether amniotic membrane extract, as a rich source of growth factors such as basic-fibroblast growth factor, can promote the proliferation potential of the umbilical cord mesenchymal stem cells. materials and ...

The Ramsey number r(H,G) is defined as the minimum N such that for any coloring of the edges of the N -vertex complete graph KN in red and blue, it must contain either a red H or a blue G. In this paper we show that for any graph G without isolated vertices, r(K3, G) ≤ 2q + 1 where G has q edges. In other words, any graph on 2q + 1 vertices with independence number at most 2 contains every (iso...

For a given finite field Fq, we study sufficient conditions to guarantee that the set {θ 1 + θ y 2 : 1 ≤ x ≤ M1, 1 ≤ y ≤ M2} represents all the nonzero elements of Fq. We investigate the same problem for θ 1 − θ y 2 and as a consequence we prove that any element in the finite field of q elements has a representation of the form θ − θ, 1 ≤ x, y ≤ √ 2q whenever θ has multiplicative order at least...

Objective(s): Umbilical cord blood is a good source of the mesenchymal stem cells that can be banked, expanded and used in regenerative medicine.  The objective of this study was to test whether amniotic membrane extract, as a rich source of growth factors such as basic-fibroblast growth factor, can promote the proliferation potential of the umbilical cord mesenchymal stem cells. Materials and ...

A graph with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f:V(G){0, 2, 4, ... 2q-2,2q} such that the induced map f*: E(G) {1, 3, 5, ... 2q-1} defined by f*(uv)=     f u f v 2  is a bijection. A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. In this paper we pay our attention to p...