in this paper we consider a petrovsky viscoelastic inverse source problem with memory term in the boundary condition. we obtain sufficient conditions on relaxation function and initial data for which the solutions of problem are asymptotically stable when the integral overdetermination tends to zero as time goes to infinity.

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

This correspondence analyzes the momentum LMS algorithm and other momentum algorithms using asymptotic techniques that provide information regarding the almost sure behavior of the parameter estimates and their asymptotic distribution. The analysis does not make any assumptions on the autocorrelation function of the input process.

This paper discusses asymptotic properties, especially asymptotic stability of neutral stochastic diierential delay equations. New techniques are developed to cope with the neutral delay case, and the results of this paper are more general than the author's earlier work within the delay equations.

in this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by jones [12] for length-biased data.the approach is based on the invariance principle for the empirical processes proved by horváth [10]. all simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

the purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of sturm-liouville problem with equation of the form w??=(?2f(x)?r(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in c2(a,b which has a single zero (so called turning point) at point 0x=x and r(x) is a continuously differentiable function. ...

In this paper we consider the Laplace-Dirichlet equation in a polygonal domain perturbed at the small scale ε near a vertex. We assume that this perturbation is self-similar, that is, derives from the same pattern for all relevant values of ε. We construct and validate asymptotic expansions of the solution in powers of ε via two different techniques, namely the method of multiscale expansions a...

Although many nonlinear models of cognition have been proposed in the past 50 years, there has been little consideration of corresponding statistical techniques for their analysis. In analyses with nonlinear models, unmodeled variability from the selection of items or participants may lead to asymptotically biased estimation. This asymptotic bias, in turn, renders inference problematic. We show...

Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of univariate generating functions with algebraic singularities. These results have been extended to classes of multivariate generating functions by Gao and Richmond (1992) and Hwang (1996, 1998), in both cases by reducing the multivariate case to the univariate case. Pemantle and Wilson (2013) outlined new mult...