We construct a constrained trivariate extension of the univariate normalized B-basis of the vector space of trigonometric polynomials of arbitrary (finite) order n ∈ N defined on any compact interval [0, α], where α ∈ (0, π). Our triangular extension is a normalized linearly independent constrained trivariate trigonometric function system of dimension δn = 3n (n+ 1) + 1 that spans the same vect...

The rotation curves of a sample of 46 low- and high-surface brightness galaxies are considered in the context of Milgrom's modi_ed dynamics (MOND) to test a new interpolating function proposed by Zhao et al. (2010) [1] and compare with the results of simple interpolating function. The predicted rotation curves are calculated from the total baryonic matter based on the B-band surface photometry,...

The Theory of Approximation. By Dunham Jackson. New York (American Mathematical Society Colloquium Publications, Volume 11), published by this Society, 1930. v+178 pp. In 1885 Weierstrass announced his now famous theorem: Any continuous function j•(#)> defined over a finite interval (a, b), can be approximated in (a, b) uniformly and indefinitely by a sequence of polynomials Pn(x), whose degree...

A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of r...

The paper deals with the spectral condition numbers (Tn(b)) of sequences of Toeplitz matrices Tn(b) = (bj k) n j;k=1 as n goes to in nity. The function b(ei ) = P k bke ik is referred to as the symbol of the sequence fTn(b)g. It is well known that (Tn(b)) may increase exponentially if the symbol b has very strong zeros on the unit circle T = fz 2 C : jzj = 1g, for example, if b vanishes on some...

v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...

The goal of the next two talks is to (1) discuss a class of integrable connections associated to root systems (2) describe their monodromy in terms of quantum groups These connections come in two forms: • Rational form leading to representations of braid groups (this week) • Trigonometric form leading to representations of affine braid groups (next week) The relevance of these connections is th...

However, we cannot easily control the curve locally. That is, any change to an individual control point will cause changes in the curve along its full length. In addition, we cannot create a local cusp in the curve, that is, we cannot create a sharp corner unless we create it at the beginning or end of a curve where it joins another curve. Finally, it is not possible to keep the degree of the B...

We discuss Fσ filters and show that the minimum size of a filter base generating an undiagonalizable filter included in some Fσ filter is the better known bounded evasion number eubd. An application to N -sets from trigonometric series is given by showing that if A is an N -set and B has size less eubd, then A ∪ B is again an N -set.