In 1979, Kazhdan and Lusztig defined a family Pu,v(q) of polynomials indexed by pairs of elements of a Coxeter group W that have proven to be fundamental objects of study in representation theory. At the same time, they can be defined combinatorially, and so have also been studied by combinatorialists. Although it is now known that Pu,v(q) depends only on the structure of the Bruhat interval [u...

A time-scale invariant burst-detection algorithm for single-unit spike train is described. This burst analysis is an auto-adaptive algorithm that uses interand intra-burst intervals for identifying the burst itself. By using a self-adaptive algorithm, a burst is de$ned by the characteristic $ring patterns within and between bursts. Bursts are detected by auto-adaptive method when the inter-burs...

here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new applications.

Most confidence intervals, whether based on asymptotic theory or the bootstrap, are implicitly based on inverting a Wald test. Since Wald test statistics are not invariant under nonlinear reparametrizations of the restrictions they test, confidence intervals based on them are not invariant either. This fact explains the well-known non invariance of bootstrap confidence intervals obtained by Hal...

In this paper, we give connection between the order of the generalized Baer-invariant of a pair of finite groups and its factor groups, when ? is considered to be the specific variety. Moreover, we give a necessary and sufficient condition in which the generalized Baer-invariant of a pair of groups can be embedded into the generalized Baer-invariant of pair of its factor groups.

The brain can hold information about multiple objects in working memory. It is not known, however, whether intervals of time can be stored in memory as distinct items. Here, we developed a novel paradigm to examine temporal memory where listeners were required to reproduce the duration of a single probed interval from a sequence of intervals. We demonstrate that memory performance significantly...

Prediction, by interval or point, of an unobserved random variable is a fundamental problem in statistics. This paper deals with constructing a prediction interval on a future observation Xr in an ordered sample of size n from an underlying distribution (under parametric uncertainty), where the first k observations X1 < X2 <  < Xk, 1k<rn, have been observed. Prediction intervals for future...

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...