A graph G with n vertices and maximum degree 1G cannot be given weak sense of direction using less than 1G colours. It is known that n colours are always sufficient, and it was conjectured that just 1G + 1 are really needed, that is, one more colour is sufficient. Nonetheless, it has just been shown [2] that for sufficiently large n there are graphs requiring ω(n/ log n) more colours than 1G . ...

Lastly, Erdös [2] proved that for p sufficiently large (1 .5) g(p) p' 2(log p) . This last result, of course, is not directly comparable with the others, giving better results for some primes and worse results for others . In any event, all of the results are very weak (as is evidenced by a glance at tables of primitive roots [1]) in relationship to the conjecture that the true order of g(p) is...

Radio networks (RN) are distributed systems (ad hoc networks) consisting in n ≥ 2 radio stations. Assuming the number n unknown, two distinct models of RN without collision detection (no-CD) are addressed: the model with weak no-CD RN and the one with strong no-CD RN. We design and analyze two distributed leader election protocols, each one running in each of the above two (no-CD RN) models, re...

During 2009-10, real time RT-PCR and conventional RT-PCR techniques Used for detecting BTVs RNA in 310 blood samples. For real time and gel based RT-PCR segment-1 and segment-10 selected as conserve genes to search any BTV strains. Using these methods, 58 (%18.7) and 14 (%4.5) positive samples were detected among the clinically suspected sheep. Sensitivity of both molecular techniques evalua...

In a recent paper, Lee and Moharrami [13] construct a family of metrics (Xn, dn) with |Xn| = N , such that (Xn, √ dn) embeds into L2 with constant distortion, but embedding (Xn, dn) into a metric of negative type requires distortion Ω̃(log 1N). In this paper, we build on their analysis, and improve their result by showing an Ω̃(log 1N) lower bound for embedding (Xn, dn) into a metric of negative ...

during 2009-10, real time rt-pcr and conventional rt-pcr techniques used for detecting btvs rna in 310 blood samples. for real time and gel based rt-pcr segment-1 and segment-10 selected as conserve genes to search any btv strains. using these methods, 58 (%18.7) and 14 (%4.5) positive samples were detected among the clinically suspected sheep. sensitivity of both molecular techniques evalua...

Let X be a log Q-Fano variety, i.e, there exists an effective Q-divisor D such that (X,D) is Kawamata log terminal (klt) and −(KX + D) is nef and big. By a result of Miyaoka-Mori [15], X is uniruled. The conjecture ([10], [16]) predicts that X is rationally connected. In this paper, apply the theory of weak (semi) positivity of (log) relative dualizing sheaves f∗(KX/Y + ∆) (which has been devel...

Let { Xij } be a double sequence of pairwise independent random variables. If P {|Xmn| ≥ t}≤ P{|X| ≥ t} for all nonnegative real numbers t and E|X|p( log+ |X|)3 <∞, for 1 <p < 2, then we prove that ∑m i=1 ∑n j=1 ( Xij−EXij ) (mn)1/p → 0 a.s. as m∨n →∞. (0.1) Under the weak condition of E|X|p log+ |X| <∞, it converges to 0 in L1. And the results can be generalized to an r -dimensional array of r...

In this article we present a Ladyženskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak L norms in the space variables and log improvement in the time variable. Mathematics Subject Classification (2010). Primary 76D03; Secondary 76D05, 35Q30.

Abstract We show that certain singular structures (Hölderian cusps and mild divergences) are transported by the flow of homeomorphisms generated an Osgood velocity field. The structure these singularities is related to modulus continuity results shown be sharp in sense slightly more cannot generally propagated. For 2D Euler equation, we prove preserved motion, e.g. a system $$\log \log _+(1/|x|...