The heavy-quark expansion for inclusive semi-leptonic B decays introduces Λ̄ and λ1, which are matrix elements in heavy-quark effective field theory. We review how they can be obtained from an analysis of the heavy quark mass dependence of heavy-light meson masses in lattice QCD. We present preliminary results for the bottom quark mass, mb, using Λ̄ and λ1 for the Bs meson from a 2+1 sea-flavor u...

We prove fourteen equivalent conditions for a set of time-frequency shifts on a lattice Λ, {e2g(t − λ1) : (λ1, λ2) ∈ Λ} ⊆ L (R), to be a frame for L(R). Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the invertibility of the frame operator on L(R), it suffices to verify that it is one-to-one on a certain subspace of tempered d...

We present arguments that the structure of the spectrum of the supersymmetric matrix model with 16 real supercharges in the large N limit is rather nontrivial, involving besides the natural energy scale ∼ λ1/3 = (g2N)1/3 also a lower scale ∼ λ1/3N−5/9. This allows one to understand a nontrivial behaviour of the mean internal energy of the system E ∝ T 14/5 predicted by AdS duality arguments.

secreted cytokines of th1 (t-helper)/th2 cells play an important role in the pathogenesis of many diseases. th1 cells secrete predominantly ifn-γ and il-2 which regulate cell-mediated immunity against intracellular pathogens and tumors. in this study, expression of ifn-γ was studied using semiquantitative rt-pcr. in brief, lymphocytes of a healthy donor were stimulated with pha (1μg/106 cell/ml...

A basic eigenvalue bound due to Alon and Boppana holds only for regular graphs. In this paper we give a generalized Alon-Boppana bound for eigenvalues of graphs that are not required to be regular. We show that a graph G with diameter k and vertex set V , the smallest nontrivial eigenvalue λ1 of the normalized Laplacian L satisfies λ1 6 1− σ ( 1− c k ) for some constant c where σ = 2 ∑ v dv √ d...

We study the boundary value problem −div((|∇u|1 + |∇u|2)∇u) = λ|u|u in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in R with smooth boundary, λ is a positive real number, and the continuous functions p1, p2, and q satisfy 1 < p2(x) < q(x) < p1(x) < N and maxy∈Ω q(y) < Np2(x) N−p2(x) for any x ∈ Ω. The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ...

In this paper we analyze some properties of the principal eigenvalue λ1(Ω) of the nonlocal Dirichlet problem (J∗u)(x)−u(x) = −λu(x) in Ω with u(x) = 0 in R \Ω. Here Ω is a smooth bounded domain of R and the kernel J is assumed to be a C compactly supported, even, nonnegative function with unit integral. Among other properties, we show that λ1(Ω) is continuous (or even differentiable) with respe...

The set of integral flows on a finite graph Γ is naturally an integral lattice Λ1(Γ) in the Euclidean space Ker(∆1) of harmonic real-valued functions on the edge set of Γ. Various properties of Γ (bipartite character, girth, complexity, separability) are shown to correspond to properties of Λ1(Γ) (parity, minimal norm, determinant, decomposability). The dual lattice of Λ1(Γ) is identified to th...

We analyze the largest eigenvalue and eigenvector for the adjacency matrices of sparse random graph. Let λ1 be the largest eigenvalue of an n-vertex graph, and v1 be its corresponding normalized eigenvector. For graphs of average degree d log n, where d is a large enough constant, we show λ1 = d log n + 1 ± o(1) and 〈1, v1〉 = √ n ( 1−Θ ( 1 logn )) . It shows a limitation of the existing method ...