A general method is developed by using nonstandard analysis for formulating and proving a theorem about upper Banach density parallel to each theorem about Shnirel'man density or lower asymptotic density. There are many interesting results about Shnirel'man density or lower asymptotic density (see [4, Chapter 1] for example) in additive number theory. There are also a few interesting results ab...

In the classical theory of probability we start by a pair (Ω, ), with Ω set of elementary events and σ-algebra of subsets of Ω, called events. A probability on is defined as a countable additive and positive function p such that p(Ω)=1. If A and B are two events, the conditional probability p(A/B) is defined if and only if p(B) is not null, by considering the quotient p(AB)/p(B). In the theory ...

The aim of this study was to compare pseudo-ECGs produced by different configurations of re-entry in a computational model. We initiated single, double and multiple re-entrant waves in a cuboid with Fitz-Hugh Nagumo excitability. We estimated one component of the pseudo-ECG, and applied linear time-frequency and nonlinear dimensional analysis. The pseudo-ECG produced by a single re-entrant wave...

We develop a test for the linear no cointegration null hypothesis in a threshold vector error correction model. We adopt a sup-Wald type test and derive its null asymptotic distribution. A residual-based bootstrap is proposed, and the first-order consistency of the bootstrap is established. A set of Monte Carlo simulations shows that the bootstrap corrects size distortion of asymptotic distribu...

We consider goodness–of–fit testing for multivariate stable distributions. The proposed test statistics exploit a characterizing property of the characteristic function of these distributions and are consistent under some conditions. The asymptotic distribution is derived under the null hypothesis as well as under local alternatives. Conditions for an asymptotic null distribution free of parame...

Testing a low-dimensional null hypothesis against a high-dimensional alternative in a generalized linear model may lead to a test statistic that is a quadratic form in the residuals under the null model. Using asymptotic arguments, we show that the distribution of such a test statistic can be approximated by a ratio of quadratic forms in normal variables, for which algorithms are readily availa...

We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it in two prominent families of point sets, namely the so-called double circle and double chain. The latter has asymptotically 12n pointed pseudo-triangulations, which lies significantly above the maximum number of triangulations in a planar point set known so far.

We present an analytic method for calculating the late-time tails of a linear scalar field outside a Kerr black hole. We give the asymptotic behavior at timelike infinity (for fixed r), at future null infinity, and along the event horizon (EH). In all three asymptotic regions we find a power-law decay. We show that the power indices describing the decay of the various modes at fixed r differ fr...

In this paper, a new pseudo affine projection (AP) algorithm based on Gauss-Seidel (GS) iterations is proposed for acoustic echo cancellation (AEC). It is shown that the algorithm is robust against near-end signal variations (including double-talk). Keywords—pseudo affine projection algorithm, acoustic echo cancellation, double-talk.