Search results for "combinatoric"
showing 10 items of 1776 documents
A note on correlation and local dimensions
2015
Abstract Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.
Characteristic Sturmian words are extremal for the Critical Factorization Theorem
2012
We prove that characteristic Sturmian words are extremal for the Critical Factorization Theorem (CFT) in the following sense. If p x ( n ) denotes the local period of an infinite word x at point n , we prove that x is a characteristic Sturmian word if and only if p x ( n ) is smaller than or equal to n + 1 for all n ≥ 1 and it is equal to n + 1 for infinitely many integers n . This result is extremal with respect to the \{CFT\} since a consequence of the \{CFT\} is that, for any infinite recurrent word x, either the function p x is bounded, and in such a case x is periodic, or p x ( n ) ≥ n + 1 for infinitely many integers n . As a byproduct of the techniques used in the paper we extend a r…
Cross-diffusion effects on stationary pattern formation in the FitzHugh-Nagumo model
2022
<p style='text-indent:20px;'>We investigate the formation of stationary patterns in the FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on the effects of cross-diffusion on the Turing mechanism. Linear stability analysis indicates that positive values of the inhibitor cross-diffusion enlarge the region in the parameter space where a Turing instability is excited. A sufficiently large cross-diffusion coefficient of the inhibitor removes the requirement imposed by the classical Turing mechanism that the inhibitor must diffuse faster than the activator. In an extended region of the parameter space a new phenomenon occurs, namely the exis…
The minimal free resolution of fat almost complete intersections in ℙ1 x ℙ1
2017
AbstractA current research theme is to compare symbolic powers of an ideal I with the regular powers of I. In this paper, we focus on the case where I = IX is an ideal deûning an almost complete intersection (ACI) set of points X in ℙ1 × ℙ1. In particular, we describe a minimal free bigraded resolution of a non-arithmetically Cohen-Macaulay (also non-homogeneous) set 𝒵 of fat points whose support is an ACI, generalizing an earlier result of Cooper et al. for homogeneous sets of triple points. We call 𝒵 a fat ACI.We also show that its symbolic and ordinary powers are equal, i.e, .
Statistical Properties of Generalized Strain Criterion for Multiaxial Random Fatigue
1989
ABSTRACT Statistical properties of generalized criterion of the maximum shear and normal strains on the fracture plane have been presented, Functions of probability distribution and spectral density of the equivalent strain have been analysed on the assumption that a random tensor of strain state is a six-dimensional stationary and ergodic Gaussian process. The expected value and variance of the equivalent strain have been determined as well. From spectral analysis a new limitation has been derived for extension of some multiaxial cyclic fatigue criteria to random loadings. It is connected with the fact that in some cases the frequency band of the equivalent strain is greater than that for …
A Dido problem for domains in ?2 with a given inradius
1990
We find which are the simply connected domains in ℝ2 satisfying the Dido condition for a straight shoreline, with a given area A and a fixed inradius ϱ, which minimize the length of the free boundary. There are three different cases according to the values of A and ϱ.
New results for finding common neighborhoods in massive graphs in the data stream model
2008
AbstractWe consider the problem of finding pairs of vertices that share large common neighborhoods in massive graphs. We give lower bounds for randomized, two-sided error algorithms that solve this problem in the data-stream model of computation. Our results correct and improve those of Buchsbaum, Giancarlo, and Westbrook [On finding common neighborhoods in massive graphs, Theoretical Computer Science, 299 (1–3) 707–718 (2004)]
Quasi-Newton approach to nonnegative image restorations
2000
Abstract Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform (FFT) based schemes result in efficient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an image consists of positive light intensities, and thus a nonnegativity constraint should be enforced. This constraint and other ways of incorporating a priori information have been suggested in various applications, and can lead to substantial improvements in the reconstructions. Neverth…
Bounds for the relative n-th nilpotency degree in compact groups
2009
The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for this kind of probability, providing information on the group structure. We have recently obtained some generalizations of his results for finite groups. Here we improve them in the context of the compact groups.
Integral-geometrical consideration of density matrices
1995
The ensemble N-representability problem for the k-th order reduced density matrix (k-RDM) as well as the problem of reconstruction of the N-particle system density matrices (N-DM) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators {Theta}{sub {lambda}} are represented using particular values (at specially chosen {Xi} = {Xi}{sub o}) of the Radon transform D{sub N{lambda}} D{sub N{lambda}}({Xi}) of the N-DM spatial parts (or their sums) D{sub N{lambda}}({chi}{prime}{vert_bar}{chi}{double_prime}) (here, {Xi} is a d-plane in the n-space {Re}{double_prime} of {chi} = ({chi}{prime}, {chi}{double_prime}), with n = 6N, d = 3(N - k), {chi}{p…