We discuss the evaluation of power corrections to hard scattering and decay processes for which an operator product expansion is applicable. The Wilson coefficient of the leading-twist operator is the difference of two perturbative series, each of which has a renormalon ambiguity of the same order as the power corrections themselves, but which cancel in the difference. We stress the necessity o...

We propose a novel approach for designing a low power datapath in wireless communication systems. Especially, we focus on the digital FIR filter. Our proposed approach can reduce the power consumption and the circuit area of the digital FIR filter by optimizing the bitwidth of the each filter coefficient with keeping the filter calculation accuracy. At first, we formulate the constraints about ...

We analyse power corrections to longitudinal and transverse fragmentation processes in ee annihilation, based on the assumption of ultraviolet dominance of power corrections. Under this assumption, we determine the dependence of power corrections on the scaling variable x from the infrared renormalon asymptotics of leading power coefficient functions. Our results suggest that the longitudinal a...

We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski (2001). For sparse graphs with positive clustering coefficient, we examine statistical dependence between the (local) clustering coefficient and the degree. Our results are mathematically rigorous. They are consistent...

The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time interv...

Given an integer m ≥ 1, let ‖·‖ be a norm in R and let S+ denote the set of points d = (d0, . . . , dm) in R with nonnegative coordinates and such that ‖d‖ = 1. Consider for each 1 ≤ j ≤ m a function fj(z) that is analytic in an open neighborhood of the point z = 0 in the complex plane and with possibly negative Taylor coefficients. Given n = (n0, . . . , nm) in Z with nonnegative coordinates, ...

We derive an asymptotic expansion as n → ∞ for a large range of coefficients of (f (z))n, where f(z) is a power series satisfying |f(z)| < f(|z|) for z ∈ C, z ∉R+. When f is a polynomial and the two smallest and the two largest exponents appearing in f are consecutive integers, we use the expansion to generalize results of Odlyzko and Richmond (1985) on log concavity of polynomials, and we prov...

To each reduced root system Φ of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r variables, whose group of functional equations is isomorphic to the Weyl group of Φ. The coefficients in these Dirichlet series exhibit a multiplicativity that reduces the specification of the coefficients to those that are powers of a single prime p. For each p, ...

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...