Let h be an arbitrary n-cycle in S n . Assume h ' is another n-cycle in S n . Then if σ = (h) 1 − h ' , σ is an element of A n , the alternating group of S n . From elementary group theory, every element of S n can be written as a product of (not necessarily disjoint) 3-cycles. Thus, h ' = hσ 1σ 2 ...σ r where each σ i (i = 1,2,...,r) is a 3-cycle. Defining h i = hσ 1σ 2 ...σ i , we now stipula...

It is now unders tood [2, 31 t h a t the t u r b o decoding algorithm is a n instance of a probabil i ty propagation a lgor i thm (PPA) o n a g raph wi th many cycles. I n this paper we investigate t h e behavior of a n P P A in graphs wi th a single cycle such as the g raph of a tail-biting code. First , we show t h a t for strictly positive local kernels, t h e i terations of the P P A conver...

Let D be a directed graph of order n. An anti-directed Hamilton cycle H in D is a Hamilton cycle in the graph underlying D such that no pair of consecutive arcs in H form a directed path in D. We prove that if D is a directed graph with even order n and if the indegree and the outdegree of each vertex of D is at least 23n then D contains an anti-directed Hamilton cycle. This improves a bound of...

Sources of plasma glucose and glucose turnover were investigated in 8-week-old (pre-diabetic) and 13-week-old (diabetic) Zucker (fa/fa) rats after a 24-h fast. Intraperitoneal (2)H(2)O was administered and [3,4-(13)C(2)]glucose and [U-(13)C(3)]propionate were infused into conscious active rats. (13)C nuclear magnetic resonance analysis of monoacetone glucose derived from blood glucose indicated...

A cycle C in a graph G is dominating if every edge of G is incident with at least one vertex of C. For a set H of connected graphs, a graph G is said to be H-free if G does not contain any member of H as an induced subgraph. When |H| = 2, H is called a forbidden pair. In this paper, we investigate the characterization of the class of the forbidden pairs guaranteeing the existence of a dominatin...

As an extension of the Brooks theorem, Catlin in 1979 showed that if H is neither odd cycle nor a complete graph with maximum degree Δ(H), then has vertex Δ(H)-coloring such one color classes independent set. Let G be connected order at least 2. A G-free k-coloring partition set into V1,…,Vk H[Vi], subgraph induced on Vi, does not contain any isomorphic to G. generalization Catlin's Theorem we ...

Let F and H be k-uniform hypergraphs. We say is F-saturated if does not contain a subgraph isomorphic to F, but H+e for any hyperedge e∉E(H). The saturation number of denoted satk(n,F), the minimum edges in an hypergraph on n vertices. C3(3) denote 3-uniform loose cycle 3 edges. In this work, we prove that(43+o(1))n≤sat3(n,C3(3))≤32n+O(1). This first non-trivial result fixed short cycle.

In mammals the light-dark (LD) cycle is known to be the major cue to synchronize the circadian clock. In arid and desert areas, the camel (Camelus dromedarius) is exposed to extreme environmental conditions. Since wide oscillations of ambient temperature (Ta) are a major factor in this environment, we wondered whether cyclic Ta fluctuations might contribute to synchronization of circadian rhyth...