We establish local (L, L) mapping properties for averages on curves. The exponents are sharp except for endpoints.

Using a new method we construct a class of orthogonal designs, o D( 4(1 + P )n; n, n, n, n, pn, pn, pn, pn) for p = 1, p a prime power == 3 (mod 4), and n = 3,5,7. This class includes new Plotkin arrays of order 24, and for the first time, of orders 40 and 56.

In a vector-like extension of the minimal standard model with mirror fermions leptoquarks can be bound states of fermion-mirror-fermion pairs held together by a new strong interaction at the TeV scale. The small couplings of leptoquarks to light fermion pairs arise due to mixing. The large Q event excess at HERA and also the high ET jet excess at Tevatron can potentially be explained.

A total perfect code in a graph is a subset of the graph’s vertices with the property that each vertex in the graph is adjacent to exactly one vertex in the subset. We prove that the tensor product of any number of simple graphs has a total perfect code if and only if each factor has a total perfect code.

We present analytic expressions for the vacuum polarization effects due to a light fermion with finite mass in the binding energy and in the wave function at the origin of QED and (weak coupling) QCD non-relativistic bound states. Applications to exotic atoms, Υ(1s) and tt̄ production near threshold are briefly discussed. Preprint submitted to Elsevier Preprint 7 February 2008

We investigate codes meeting the Griesmer bound. The main theorem of this article is the generalization of the nonexistence theorem of [7] to a larger class of codes. keywords: Griesmer bound, extending codes, nonexistence theorem, code construction

Recent results on the QCD analysis of bound states of heavy ¯ qq quarks are reviewed, paying attention to what can be derived from the theory with a reasonable degree of rigour. We report a calculation of ¯ bc bound states; a very precise evaluation of b, c quark masses from quarkonium spectrum; the NNLO evaluation of Υ → e + e − ; and a discussion of power corrections. For the b quark pole mas...

1 Chernoff Bounds 1.1 Bayesian Hypothesis Test A test using log-likelihood ratio statistic has the form, T (Y ) = logL(Y ) T τ. (1) Bound-1: The probability of error Pe is bounded as, Pe ≤ (π0 + π1e )eμT,0(s0)−s0τ , (2) where μT,0(s) = logE0[e ], and μ ′ T,0(s0) = τ . Bound-2: ∀ s ∈ [0, 1], Pe ≤ max(π0, π1e )eμT,0(s)−sτ . (3) Derivation of the above bound: Consider, Pe = π0P0(Γ1) + π1P1(Γ0), = ...