We analyze the finite-size corrections to the energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a torus. We extend the analysis of Ferdinand and Fisher to compute the correction of order L−3 to the energy and the corrections of order L−2 and L−3 to the specific heat. We also obtain general results on the form of the finite-size corrections to these quantities: onl...

Motivated by the vacuum selection problem of string/M theory, we study a new geometric invariant of a positive Hermitian line bundle (L, h) → M over a compact Kähler manifold: the expected distribution Kcrit h (z) of critical points d log |s(z)|h = 0 of a Gaussian random holomorphic section s ∈ H(M,L) with respect to h. It is a measure on M whose total mass is the average number N crit h of cri...

The collective dynamics of ensembles of chemically powered sphere dimer motors is investigated. Sphere dimers are self-propelled nanomotors built from linked catalytic and noncatalytic spheres. They consume fuel in the environment and utilize the resulting self-generated concentration gradients to produce directed motion along their internuclear axes. In collections of such motors, the individu...

In this paper we study the function χ(x1, x2, g) that determines the dressing phase that appears in the all-loop Bethe Ansatz equations for the SL(2) sector of N = 4 super Yang-Mills theory. First, we consider the coefficients cr,s(g) of the expansion of χ(x1, x2, g) in inverse powers of x1,2. We obtain an expression in terms of a single integral valid for all values of the coupling g. The expr...

Using word duration as a representative of pronunciation variation, the objective of this research was to delineate a set of variables known to affect word duration and determine the total amount of variation in duration accounted for by them in a multiple linear regression model. More importantly, computing the amount of variation each variable contributes (independently of the others) is cruc...

Let R be a commutative ring, q a unit of R and P a multiplicatively antisymmetric matrix with coefficients which are integer powers of q. Denote by SE(q,P) the multiparameter quantum matrix bialgebra associated to q and P. Slightly generalizing [H-H], we define a multiparameter deformation Lλ/μVP of the classical skew Schur module. In case R is a field and q is not a root of 1, arguments like t...

We give an overview of the use of asymptotic expansions of gamma and related functions — ratio of gamma functions, powers, digamma and polygamma functions. The aim is to introduce a general theory which can unify various particular formulas for factorial functions and binomial coefficients. The connection with inequalities for gamma function is established. Also, a systematic approach to asympt...

This paper shows that the usual multiplicative synthesis of alternative priorities for benefits, opportunities, costs and risks, obtained from separate Analytic Hierarchy or Network models, can be ambiguous. The ratio of benefit and opportunity priorities to cost and risk priorities can be misleading when assessing the profitability of a project. The same holds for their additive synthesis, alt...

In this note, we solve the Loewner equation in the upper halfplane with forcing function ξ(t), for the cases in which ξ(t) has a power-law dependence on time with powers 0, 1/2 and 1. In the first case the trace of singularities is a line perpendicular to the real axis. In the second case the trace of singularities can do three things. If ξ(t) = 2 √ κt, the trace is a straight line set at an an...

For periodic Toda chains with a large number N of particles we consider states which are N−2−close to the equilibrium and constructed by discretizing any given C2−functions with mesh size N−1. For such states we derive asymptotic expansions of the Toda frequencies (ωN n )0<n<N and the actions (I N n )0<n<N , both listed in the standard way, in powers of N−1 as N → ∞. At the two edges n ∼ 1 and ...