We derive a new deterministic algorithm for the computation of a sparse Legendre expansion f of degree N with M N nonzero terms from only 2M function resp. derivative values f (1), j = 0, . . . , 2M − 1 of this expansion. For this purpose we apply a special annihilating filter method that allows us to separate the computation of the indices of the active Legendre basis polynomials and the evalu...

aim: the aim of this study was to compare cusp deflection, infraction and fracture in teeth filled with three temporary filling materials. materials & method: forty five extracted human premolar teeth were chosen. after root canal therapy and mesio-occluso-distal cavity preparation, samples were randomly divided into three groups , each contained 15 teeth and filled with three temporary filling...

The   ) ( exp    -expansion method is a promising method for finding exact traveling wave solutions to nonlinear evolution equations in physical sciences. In this article, we use the   ) ( exp    -expansion method to find the exact solutions for the nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation and the good Boussinesq equations. Many solitary wave solutions are formally d...

Nowadays NLEEs have been the subject of allembracing studies in various branches of nonlinear sciences. Most of the phenomena in real world can be described using non-linear equations. A nonlinear phenomenon plays a vital role in applied mathematics, physics and engineering branches. Many complex nonlinear phenomenons in plasma physics, fluid dynamics, chemistry, biology, mechanics, elastic med...

The exact traveling wave solutions of the nonlinear variable coefficients Burgers-Fisher equation and the generalized Gardner equation with forced terms can be found in this article using the generalized ( ′ G )-expansion method. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. When these parameters are taken special values, the solitary wave ...

Background: In vitro model studies are becoming increasingly popular for experimental research designs. They include isolation and expansion of cells of a particular tissue, such as the nervous tissue which contributes to understanding the underlying mechanisms in many pathologies. It enables  the scrutinization of intracellular signaling pathways responsible for cell death. OBJECTIVES: In the ...

Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity corresponding effective field theories. Despite past efforts in computing perturbative corrections to tree-level action, neither systematic approach nor unified framework has emerged yet. We make progress this direction, focusing on moduli dependence 4D sc...

if the polynomial has no roots in [−1, 1]. If the inverse polynomial is decomposed into partial fractions, the an are linear combinations of simple functions of the polynomial roots. If the first k of the coefficients an are known, the others become linear combinations of these with expansion coefficients derived recursively from the bj ’s. On a closely related theme, finding a polynomial with ...

We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free boundaries. The low-temperature series expansions of the correlation functions are presented when the spin-spin couplings are the same in both directions. The exact ...