Much work is going into securing the public key infrastructure (PKI). Various models for trust exist; Pretty Good Privacy (PGP) and the Progressive-Constraint Trust model are examples.[3] These models describe how to protect and ensure the interrelationships of their certificate based structures; however, vulnerabilities may arise when structures based on certificate authorities (CAs) are invol...

Two third order methods for finding multiple zeros of nonlinear functions are developed. One method is based on Chebyshev’s third order scheme (for simple roots) and the other is a family based on a variant of Chebyshev’s which does not require the second derivative. Two other more efficient methods of lower order are also given. These last two methods are variants of Chebyshev’s and Osada’s sc...

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially dete...

Let N be a positive integer. In this paper we shall study the special values of multiple polylogarithms atNth roots of unity, called multiple polylogarithm values (MPVs) of levelN . These objects are generalizations of multiple zeta values and alternating Euler sums, which was studied by Euler, and more recently, many mathematicians and theoretical physicists.. Our primary goal in this paper is...

Recently, a new treatment based on Taylor’s expansion to give the estimate of the convergence radius of iterative method for multiple roots has been presented. It has been successfully applied to enlarge the convergence radius of themodified Newton’s method and Osada’s method for multiple roots. This paper re-investigates the convergence radius of Halley’s method under the condition that the de...

In the literature, recently, some three-step schemes involving four function evaluations for the solution of multiple roots of nonlinear equations, whose multiplicity is not known in advance, are considered, but they do not agree with Kung–Traub’s conjecture. The present article is devoted to the study of an iterative scheme for approximating multiple roots with a convergence rate of eight, whe...

This paper argues for a distinction between word formation from roots and word formation from existing words. Focusing on Hebrew, it is shown that words made of roots may be assigned multiple and varied interpretations, while words made of existing words must depend semantically and phonologically on the word from which they are derived. To account for this difference, a locality constraint on ...

introduction: the purpose of this study was to investigate the root and canal morphology of maxillary first molars with regards to patients’ age and gender with cone-beam computed tomography (cbct). methods and materials: a total of 149 cbct scans from 92 (67.1%) female and 57 (31.3%) male patients with mean age of 40.5 years were evaluated. tooth length, presence of root fusion, number of the ...

PURPOSE Nerve root traction injuries induce spinal cord inflammation and lead to neuronal death within days. In the present study, we examined the inflammatory response one week after multiple cervical root transections. METHODS In the transection group, the left cervical roots (C6-8) of rats were cut at the spinal cord junction. In the repair group, transected roots were repaired with nerve ...

We define motivic multiple polylogarithms and prove the double shuffle relations for them. We use this to study the motivic fundamental group π 1 (Gm −μN ), where μN is the group of all N -th roots of unity, and relate the structure of π 1 (Gm − μN ) to the geometry and topology of modular varieties Xm(N) := Γ1(m;N)\GLm(R)/R ∗ + ·Om for m = 1, 2, 3, 4, .... We get new results about the action o...