Introduction (organization) The introduction is inviting, states the main topic, and previews the structure of the paper. The introduction clearly states the main topic and previews the structure of the paper, but it is not particularly inviting to the reader. The introduction states the main topic, but does not adequately preview the structure of the paper nor is it particularly inviting to th...

J.P. Roudnee as well as R. Aharoni and R. Ziv conjectured that every-critical linear hyper-graph has at most ? +1 2 edges. In this note we prove this conjecture for 5, and obtain a nontrivial upper bound for general .

We survey some known facts and open questions concerning the global properties of 3+1 dimensional space–times containing a compact Cauchy surface. We consider space–times with an l–dimensional Lie algebra of space–like Killing fields. For each l ≤ 3, we give some basic results and conjectures on global existence and cosmic censorship. For the case of the 3+1 dimensional Einstein equations witho...

We study the the Casimir effect of a massless conformally coupled scalar field in the background of a conformally flat brane-world geometries, where the scalar field satisfying Robin boundary conditions on two parallel plates. In the general case of Robin boundary conditions formula are derived for the vacuum expectation values of the energy-momentum tensor. Further the surface energy per unit ...

This study investigates the influence of Facebook applications and activities on consumers purchase intention and provide insights into whether consumers take notice of their peer’s activity on Facebook and whether that activity influences consumer purchase intention. Regression analyses conducted on the results from a survey of 215 Facebook users suggests that the use of Facebook’s like button...

The 3-metric gij and extrinsic curvature (second fundamental form) Kij are the fundamental variables describing the geometry in any space+time decomposition of the Einstein equations. (g,K) describe the local geometry of a single space-like hypersurface M , and it is then natural to describe the evolution of the space-time geometry by a 1-parameter family (g(t), K(t)), describing the local geom...

The motion of a test Dq-brane in a Dp-brane background is studied. The induced metric on the test brane is then interpreted as the cosmology of the test brane universe. One is then able to resolve the resulting cosmological singularities. In particular, for a D3-brane in a D5-brane background, one finds a 3+1 dimensional FRW universe with equation of state p = ε. It has been argued that this ma...

We examine the location of the eigenvalues of the generator G of a semi-group V (t) = etG, t ≥ 0, related to the wave equation in an unbounded domain Ω ⊂ Rd with dissipative boundary condition ∂νu − γ(x)∂tu = 0 on Γ = ∂Ω. We study two cases: (A) : 0 < γ(x) < 1, ∀x ∈ Γ and (B) : 1 < γ(x), ∀x ∈ Γ. We prove that for every 0 < 1, the eigenvalues of G in the case (A) lie in the region Λ = {z ∈ C : |...

We prove that for any r.v. X such thatE{X} = 0, E{X} = 1, andE{X} = μ, and for any ε ≥ 0 P (X ≥ ε) ≥ K0 μ − K1 √ μ ε+ K2 μ √ μ ε, where absolute constants K0 = 2 √ 3 − 3 ≈ 0.464, K1 = 1.397, and K2 = 0.0231. The constant K0 is sharp for μ ≥ 3 3+1 ≈ 1.09. Some other bounds and examples are given.

We prove a version of the Loebl-Komlós-Sós Conjecture for dense graphs. For any q > 0 there exists a number n0 ∈ N such that for any n > n0 and k > qn the following holds: if G be a graph of order n with at least n/2 vertices of degree at least k, then any tree of order k +1 is a subgraph of G.