We consider a Gaussian type quadrature rule for some classes of integrands involving highly oscillatory functions of the form f (x) = f 1 (x) sin ζ x + f 2 (x) cos ζ x, where f 1 (x) and f 2 (x) are smooth, ζ ∈ R. We find weights σ ν and nodes x ν , ν = 1, 2,. .. , n, in a quadrature formula of the form 1 −1 f (x) dx ≈ n ν=1 σ ν f (x ν) such that it is exact for all polynomials f 1 (x) and f 2 ...

Let q ≥ 1 be an integer, Sq be the unit sphere embedded in Rq+1, and μq be the volume element of Sq. For x0 ∈ Sq, and α ∈ (0, π), let Sα(x0) denote the cap {ξ ∈ Sq : x0 · ξ ≥ cosα}. We prove that for any integer m ≥ 1, there exists a positive constant c = c(q,m), independent of α, with the following property. Given an arbitrary set C of points in Sα(x0), satisftying the mesh norm condition max ...

In this paper we wish to present a new class of tight frames on the sphere. These frames have excellent pointwise localization and approximation properties. These properties are based on pointwise localization of kernels arising in the spectral calculus for certain self-adjoint operators, and on a positive-weight quadrature formula for the sphere that the authors have recently developed. Improv...

Recent theories posit that adult neurogenesis supports dentate gyrus pattern separation and hence is necessary for some types of discrimination learning. Using an inducible transgenic mouse model, we investigated the contribution of adult-born neurons to spatial and nonspatial touch-screen discriminations of varying levels of difficulty. Arresting neurogenesis caused a modest but statistically ...

Lord (1980) proposed formulas that provide direct relationships between IRT discrimination and difficulty parameters and conventional item statistics. The purposes of the present study were to determine (1) the veracity of the two formulas within the context that Lord proposed, and (2) the robustness of the formulas beyond the initial and restrictive conditions identified by Lord. Simulation an...

We investigate two forms of dependence between variables and/or formulas within a propositional knowledge base: controllability (a set of variables X controls a formula if there is a way to fix the truth value of the variables in X in order to achieve to have a prescribed truth value) and definability (X defines a variable y if every truth assignment of the variables inX enables us finding out ...

This chapter focuses on the usage of image orthogonal moments as discrimination features in pattern recognition applications and discusses their main properties. Initially, the ability of the moments to carry information of an image with minimum redundancy is studied, while their capability to enclose distinctive information that uniquely describes the image’s content is also examined. Along th...

Concerning quartics, two particular quantifier elimination (QE) problems of historical interests and practical values are studied. We solve the problems by the theory of complete discrimination systems and negative root discriminant sequences for polynomials that provide a method for real (positive/negative) and complex root classification for polynomials. The equivalent quantifier-free formula...