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.

Two results are obtained that give upper bounds on partial spreads and partial ovoids respectively. The first result is that the size of a partial spread of the Hermitian polar space H(3, q) is at most ( 2p+p 3 )t +1, where q = p, p is a prime. For fixed p this bound is in o(q), which is asymptotically better than the previous best known bound of (q + q + 2)/2. Similar bounds for partial spread...

Let ρC be the regularity of the Hilbert function of a projective space curve C over an algebraically closed field, αI be the initial degree of the defining ideal I of C and βI the least degree t such that the depth of the ideal generated by I≤t is depth(I). Then the Castelnuovo-Mumford regularity reg(C) of C is upper bounded by max{ρC +1, αI +βI −1}. We study in deep and refine the above bound ...

Recently, it was proved that the index of an economy with incomplete real asset markets is typically +1 when the degree of incompleteness, which is defined as the difference between the number of states and the number of securities, is an even number. This paper considers the case where the degree of incompleteness is an odd number and proves that any odd number can be realized as the index of ...

S.M. Lee proposed the conjecture: for any n > 1 and any permutation f in S(n), the permutation graph P (Pn, f) is graceful. For any integer n > 1 and permutation f in S(n), we discuss the gracefulness of the permutation graph P (Pn, f) if f = ∏l−1 k=0(m + 2k, m + 2k + 1), and ∏l−1 k=0(m+4k, m+4k +2)(m+4k +1, m+4k +3) for any positive integers m and l.