We obtain converse Marcinkiewicz-Zygmund inequalities such as k P kLp[ 1;1] C 0@ n X j=1 j jP (tj)j 1A1=p for polynomials P of degree n 1, under general conditions on the points ftjgj=1 and on the function . The weights f jgj=1 are appropriately chosen. We illustrate the results by applying them to extended Lagrange interpolation for exponential weights on [ 1; 1].

A new iterative technique is employed to solve a system of nonlinear fractional partial differential equations. This new approach requires neither Lagrange multiplier like variational iteration method VIM nor polynomials like Adomian’s decomposition method ADM so that can be more easily and effectively established for solving nonlinear fractional differential equations, and will overcome the li...

In this paper, we propose a modified Lagrange type interpolation operator to approximate functions in Sobolev spaces by continuous piecewise polynomials. In order to define interpolators for "rough" functions and to preserve piecewise polynomial boundary conditions, the approximated functions are averaged appropriately either on dor (d 1 )-simplices to generate nodal values for the interpolatio...

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. N...

The purpose of this paper is to provide a counterexample to a conjecture of Carl de Boor [2], that every ideal projector is a limit of Lagrange projectors. The counterexample is based on a construction of A. Iarrobino [9] pointed to in this context by G. Ellingsrud (as mentioned in de Boor’s paper [2]). We also show that the conjecture is true for polynomials in two variables.

Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that this polynomial has integer coefficients, and made various conjectures. Recently, Śniady has proved Biane’s conjectured explicit form for the first family of nontrivial terms in this polynomial. In this paper, we give an...

In this paper, to improve the uniform convergence of the known Lagrange interpolation polynomials, a new triangle interpolation operator of Bernstein type is constructed by using the method of two revised nodes. It is proved that the constructed operator converges uniformly to arbitrary continuous functions with period on the whole axis. The best approximation order of the operator is then obta...

In this paper, we prove some approximation results in statistical sense and establish some direct theorems for the positive linear operators constructed by the means Lagrange type polynomials. We compute error estimation by using modulus of continuity with the help of Matlab and give its algorithm. Furthermore, we show graphically the convergence of our operators to various functions. AMS Subje...

Abstract The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the Maxwell-Boltzmann distribution. The ranges of flow velocity and temperature providing positive valued distributions vary with regulating discrete v...