Abstract Adhesion between an elastic body and a smooth, rigid substrate can lead to large tensile stresses them. However, most macroscopic objects are microscopically rough, which strongly suppresses adhesion. A fierce debate has unfolded recently as whether local or global parameters determine the crossover small Here, we report simulations revealing that dependence of pull-off force F n on su...

We propose a method based on a penalised likelihood criterion, for estimating the number on non-zero components of the mean of a Gaussian vector. Following the work of Birgé and Massart in Gaussian model selection, we choose the penalty function such that the resulting estimator minimises the Kullback risk. Mathematics Subject Classification. 62G05, 62G09. Received January 13, 2004. Revised Sep...

Based on the problem of determining the hidden dimensionality (or the number of latent factors) of Factor Analysis (FA) model, this paper provides a theoretic comparison on several classical model selection criteria, including Akaike’s Information Criterion (AIC), Bozdogan’s Consistent Akaike’s Information Criterion (CAIC), Hannan–Quinn information criterion (HQC), Schwarz’s Bayesian Informatio...

Saturday, Sep 23 On some results and problems involving Hardy’s function Z(t) Aleksandar Ivić Serbian Academy of Arts and Sciences, Belgrade Hardy’s classical function Z(t) is defined, for real t, as Z(t) := ζ( 1 2 + it)χ( 1 2 + it)−1/2, ζ(s) = χ(s)ζ(1− s), This talk will cover some problems involving Hardy’s function, including moments at points where |Z(t)| is maximal, large values of Hardy’s...

and Applied Analysis 3 where θn 1 − αn Ln − 1 diamC 2 → 0 as n → ∞ and prove that {xn} defined by 1.5 converges strongly to P∩n 1F Tn x. In this paper, we establish strong convergence theorems for finding common fixed points of a countable family of Lipschitzian mappings in a real Hilbert space. Moreover, we also apply our results for asymptotically nonexpansive mappings. 2. Preliminaries Let H...

Let A be a transition probability kernel on finite state space Δo={1,…,d} such that A(x,y)>0 for all x,y∈Δo. Consider reinforced chain given as sequence {Xn,n∈N0} of Δo-valued random variables, defined recursively according to, Ln=1n∑i=0n−1δXi,P(Xn∈⋅∣X0,…,Xn−1)=LnA(⋅). We establish large deviation principle {Ln,n∈N}. The rate function takes strikingly different form than the Donsker–Varadhan as...

The purpose of this paper is to inquire the connection between maximal inner interval estimates of the solution sets to interval linear system and solutions of the dualization equation in Kaucher interval arithmetic. The results of our work are as follows: 1) a criterion of inner interval estimate of the solution set, 2) a criterion for a solution of dualization equation to be a maximal inner i...

We propose a criterion for identifying the orientation of the X-line when two regions of plasma with arbitrary densities, temperatures, and magnetic fields undergo reconnection. The X-line points in the direction that maximizes the (suitably-defined) Alfvén speed characterizing the reconnection outflow. For many situations a good approximation is that the X-line bisects the angle formed by the ...