A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

Forty-nine of the 52 autosomal single nucleotide polymorphisms (SNPs) in the SNPforID 52plex were typed in 101 unrelated Iraqis living in Denmark. No significant deviation from HWE was found in all but one of the 49 SNP systems and no significant pairwise linkage disequilibrium was observed for any SNP pair. When 18 worldwide populations were compared (including populations in Iraq, Turkey, Isr...

Given an undirected n-node unweighted graph G = (V,E), a spanner with stretch function f(·) is a subgraph H ⊆ G such that, if two nodes are at distance d in G, then they are at distance at most f(d) in H. Spanners are very well studied in the literature. The typical goal is to construct the sparsest possible spanner for a given stretch function. In this paper we study pairwise spanners, where w...

We consider lower bounding the maximum achievable rate of a differential unitary spacetime transmission subject to a prescribed performance. We characterize the performance using a suitably defined distance between two unitary matrices, which was previously obtained through pairwise error probability analysis. Considering the set of all unitary or orthogonal matrices as a compact manifold with ...

We present a family of adaptive pairwise tournaments which are provably robust against large error fractions when used to determine the largest element in a set. These tournaments use nk pairwise comparisons but have only O(k + log n) depth where n is the number of players and k is a robustness parameter (for reasonable values of n and k). We show how these tournaments can be used to prove mult...

For a countable, weakly minimal theory T , we show that the SchröderBernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to each of the following: 1. For any U -rank-1 type q ∈ S(acl(∅)) and any automorphism f of the monster model C, there is some n < ω such that f(q) is not almost orthogonal to q ⊗ f(q)⊗ . . .⊗ fn−1(q); 2. T has no infinite collection of ...

The bond dissociation energies (BDEs) and radical stabilization energies (RSEs) which result from 166 reactions that lead to carbon-centered radicals of the type ˙CH(2)X, ˙CHXY and ˙CXYZ, where X, Y and Z are any of the fourteen substituents H, F, Cl, NH(2), OH, SH, CH[double bond, length as m-dash]CH(2), C[triple bond, length as m-dash]CH, BH(2), CHO, COOH, CN, CH(3), and CF(3), were calculate...

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...