In the present paper we study the weak lower semicontinuity of the functional

We consider the capability of p-groups of class two and odd prime exponent. We use linear algebra and counting arguments to establish a number of new results. In particular, we settle the 4-generator case, and prove a sufficient condition based on the ranks of G/Z(G) and [G, G].

The discrete-time fractional Gaussian noise (DFGN) has been proven to be a regular process. Therefore, an autoregressive (AR) model of an infinite order can describe DFGN based on Wold and Kolmogorov theorems. A fast estimation algorithm on the Hurst exponent of DFGN or discrete-time fractional Brownian motion (DFBM) has been proposed, but the algorithm did not consider the order selection of A...

This paper investigates two conjectures for calculating the density dependence of the density-scaling exponent γ of a single-component, pair-potential liquid with strong virial potential-energy correlations. The first conjecture gives an analytical expression for γ directly in terms of the pair potential. The second conjecture is a refined version of this involving the most likely nearest-neigh...

A major issue in statistical physics literature is the study of the long range dependence phenomenon usually presented in natural, social and financial processes. In particular, a big part of this literature relies on the determination of a parameter known as the Hurst exponent. Although many methods have been proposed to deal with this task, none of them are suitable for any time series and so...

We show how to use a noisy feedback link to yield high-reliability streaming data communications. We demonstrate a strategy that can maintain the best known reliability function (error exponent) in delay, even when the feedback link is noisy. Only the capacity of the feedback channel need be sufficiently large for this result to hold. More detailed characterization of the feedback link, e.g., i...

An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold α > 0 such that |∆(E)| & q whenever |E| & q, where E ⊂ Fq , the d-dimensional vector space over a finite field with q elements (not necessarily prime). Here ∆(E) = {(x1 − y1) 2 + · · ·+ (xd − yd) 2 : x, y ∈ E}. The second listed author and Misha Rudnev ([4]) established the threshold d+1 2 , an...

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthé, Holton, and Zamboni and the Diophan...