We consider the estimation of covariance a stationary Gaussian process on multi-dimensional grid from observations taken general acquisition domain. derive spectral-norm risk rates for multi-taper estimators. When applied to one-dimensional intervals, these show that Thomson's classical has optimal rates, as they match known benchmarks. also extend existing lower bounds grids and conclude estim...

We propose a fast variant of the Gaussian algorithm for the reduction of two– dimensional lattices for the l1−, l2− and l∞−norm. The algorithm runs in at most O(nM(B) log B) bit operations for the l∞−norm and in O(n log n M(B) log B) bit operations for the l1− and l2−norm on input vectors a, b ∈ ZZ with norm at most 2 where M(B) is a time bound for B-bit integer multiplication. This generalizes...

So far, computational complextity of the general formula for the extended t-norm does not allow to construct fuzzy logic systems of type-2 other than interval type. In this paper, we derive new formulae for extended t-norms for arguments with Gaussian and piecewise-Gaussian membership functions basing on our original theorems.

\. INTRODUCTION Let {X(t); 0 < t < 1} be a real-valued mean-zero Gaussian process, and let "||.||" be a semi-norm on the space of real functions on [0, 1]. The so called "small ball estimates" or "small deviation estimates" refer to the asymptotic behavior of This type of problem is quite delicate, and the asymptotic decay rate in (1.1), up to a constant, depends heavily on the process X(t) and...

Researchers have identified and defined β- approach normed space if some conditions are satisfied. In this work, we show that every is a space.However, the converse not necessarily true by giving an example. addition, define β – Banach space, examples given. We also solve problems. discuss finite β-dimensional app-normed β-complete consequent app- space. explain metric but give propositions. If...

The aim of this study was to determine to what extent the theory of planned behaviour (TPB) extended with moral norm and descriptive norm is able to predict intentions not to drink and drive. We also wanted to examine whether different processes guide intentions among young drivers (35 years and below) versus drivers aged above 35 years, and women's versus men's intentions. Questionnaires were ...