Modified gravity theory is known to violate Birkhoff’s theorem. We explore a key consequence of this violation, the effect of distant matter in an Einstein-de Sitter universe on the motion of test particles. We find that when a particle is accelerated, a force is experienced that is proportional to the particle’s mass and acceleration and acts in the direction opposite to that of the accelerati...

In this paper, we prove that Newton’s method for convex best interpolation is locally q-quadratically convergent, giving an answer to a question of Irvine, Marine and Smith [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. A damped Newton-type method is presented which has global q-quadratic convergence. Analogous results are obtained for the convex smoothin...

Modified gravity theory is known to violate Birkhoff’s theorem. We explore a key consequence of this violation, the effect of distant matter in the universe on the motion of test particles. We find that when a particle is accelerated, a force is experienced that is proportional to the particle’s mass and acceleration and acts in the direction opposite to that of the acceleration. We identify th...

By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial coefficients and an odd power of a natural number. For example, we prove that for all positive integers n1, . . . , nm, nm+1 = n1, and any nonnegative integer...

Several optimal eighth order methods to obtain simple roots are analyzed. The methods are based on two step, fourth order optimal methods and a third step of modified Newton. The modification is performed by taking an interpolating polynomial to replace either f ðznÞ or f ðznÞ. In six of the eight methods we have used a Hermite interpolating polynomial. The other two schemes use inverse interpo...

Probability weighting function (PWF) is the psychological probability of a decision-maker for objective probability, which reflects and predicts risk preferences in behavioral decisionmaking. The existing approaches to PWF estimation generally include parametric methodologies construction nonparametric elicitation PWF. However, few them explores combination approximate To describe quantitativel...

This paper develops a computational model for nonlinear bending analysis of functionally graded (FG) plates using a four-node quadrilateral element SQ4T within the context of the first order shear deformation theory (FSDT). In particular, the construction of the nonlinear geometric equations are based on Total Lagrangian approach in which the motion at the present state compared with the initia...

Time-Delay-Estimation (TDE) has been a topic of interest in many applications in the past few decades. The emphasis of this work is on the application of model-based estimation (MBE) for TDE of ultrasonic signals used in ultrasonic thickness gaging. Ultrasonic thickness gaging is based on precise measurement of the time difference between successive echoes which reflect back from the back wall ...

Abstract Solar energy has attracted a lot of attention because it is clean and no pollution. However, due to the partially shaded condition, photovoltaic array cannot work uniformly at maximum power point, resulting in large loss. To improve this problem, research point tracking (MPPT) algorithm discussed by scholars. In paper, an improved particle swarm optimization (PSO) proposed achieve goal...