We have developed a two-point iterative scheme for multiple roots that achieves fifth order convergence by using two function evaluations and derivative each iteration. Weight approach is utilized to frame the scheme. The weight named as R(?t) used, which of ?t, ?t ?t, i.e., ?t=?t1+a?t, where real number ?t=g(yt)g(xt)1m˜ multi-valued function. consistency newly generated methods ensured numeric...

human mandibular premolars have earned the reputation for having an extremely complex root and root canal morphology. the incidence of multiple roots and canals in mandibular second premolars is lower than those in mandibular first premolars. mandibular second premolars with three root canals and separate foramina are very rare. in this case report, endodontic management of a three-rooted mandi...

A problem concerning the shift of roots of a system of algebraic equations is investigated. Its conservation and decomposition of a multiple root into simple roots are discussed.

abstract  hypercementosis is identified by an excessive, non-neoplastic deposition of radicular cementum and is mostly presented as a solitary lesion or in rare cases as a multiple type. it usually occurs in the premolar and molar region of mandible with no sex predilection. in this paper, we reported a 57-year-old female patient with multiple radiopaque lesions affecting right maxillary second...

This paper deals with the problem of determining the multiple roots of nonlinear equations, where the multiplicity of the roots is known. The paper contains some remarks on the optimality of the recently published methods [B. Liu, X. Zhou, A new family of fourth-order methods for multiple roots of nonlinear equations, Nonlinear Anal. Model. Control, 18(2):143–152, 2013] and [X. Zhou, X. Chen, Y...

Studying development and physiology of growing roots is challenging due to limitations regarding cellular and subcellular analysis under controlled environmental conditions. We describe a microfluidic chip platform, called RootChip, that integrates live-cell imaging of growth and metabolism of Arabidopsis thaliana roots with rapid modulation of environmental conditions. The RootChip has separat...

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

Human mandibular premolars have earned the reputation for having an extremely complex root and root canal morphology. The incidence of multiple roots and canals in mandibular second premolars is lower than those in mandibular first premolars. Mandibular second premolars with three root canals and separate foramina are very rare. In this case report, endodontic management of a three-rooted mandi...