In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations in curvature form. The transformation relations of a variable are established with the help basis transformations quaternion algebra. We deduced covariant derivative that explains how components vary scalar and vector fields.The metric tensor geodesic equation also discussed line element curved ...

A two–step Christoffel function based solution is proposed to distribution regression problem. On the first step, to model distribution of observations inside a bag, build Christoffel function for each bag of observations. Then, on the second step, build outcome variable Christoffel function, but use the bag’s Christoffel function value at given point as the weight for the bag’s outcome. The ap...

Central, standard, and Christoffel words are three strongly interrelated classes of binary finite words which represent a finite counterpart of characteristic Sturmian words. A natural arithmetization of the theory is obtained by representing central and Christoffel words by irreducible fractions labeling respectively two binary trees, the Raney (or Calkin-Wilf) tree and the Stern-Brocot tree. ...

The flow structure about two bluff cylinders placed one after another in hypersonic viscous flow has been studied. The grid equations approximated the Navier-Stokes equations were solved numerically by application of the implicit monotonized scheme of second-order accuracy, the modified Newton's method, and the Christoffel-Schwarz grid-transformation technique. The similarity conditions of deve...

Abstract It is well known that Sobolev-type orthogonal polynomials with respect to measures supported on the real line satisfy higher-order recurrence relations and these can be expressed as a (2N + 1)-banded symmetric semi-infinite matrix. In this paper, we state connection between matrices Jacobi associated three-term relation satisfied by standard sequence of orthonormal 2-iterated Christoff...

We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel numbers of polynomials orthogonal on the real line. This leads to a simple and fast algorithm for the estimation of frequencies. We also provide a new method, faster than th...

We establish asymptotics for Christoffel functions associated with multivariate orthogonal polynomials. The underlying measures are assumed to be regular on a suitable domain in particular this is true if they are positive a.e on a compact set that admits analytic parametrization. As a consequence, we obtain asymptotics for Christoffel functions for measures on the ball and simplex, under far m...