Prevalence and morphology of multiple roots, root canals and C-shaped canals in mandibular premolars from cone-beam computed tomography images in a Thai population [PDF]
Journal of Dental Sciences, 2021 Background/purpose: Variations in root and root canal morphology of mandibular premolars of Thais has not been reported, and understanding these variations enhances endodontic success.
Raweewan Arayasantiparb +1 more
doaj +2 more sources
A Complete Review of the General Quartic Equation with Real Coefficients and Multiple Roots
Mathematics, 2022 This paper presents a general analysis of all the quartic equations with real coefficients and multiple roots; this analysis revealed some unknown formulae to solve each kind of these equations and some precisions about the relation between these ones ...
Mauricio Chávez-Pichardo +4 more
doaj +3 more sources
Basins of attraction for family of Popovski’s methods and their extension to multiple roots
Journal of Numerical Analysis and Approximation Theory, 2022 In this paper we revisit Popovski’s family of methods for simple roots. We compare several members using basins of attraction visually and qualitatively by comparing the run-time on several examples, the average number of iterations and the number of ...
Beny Neta
doaj +1 more source
An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros
Mathematics, 2021 In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α
Ramandeep Behl +3 more
doaj +1 more source
Parametric Iterative Method for Addressing an Embedded-Steel Constitutive Model with Multiple Roots
Mathematics, 2023 In this paper, an iterative procedure to find the solution of a nonlinear constitutive model for embedded steel reinforcement is introduced. The model presents different multiplicities, where parameters are randomly selected within a solvability region ...
José J. Padilla +4 more
doaj +1 more source
Mathematics, 2023 High-order iterative techniques without derivatives for multiple roots have wide-ranging applications in the following: optimization tasks, where the objective function lacks explicit derivatives or is computationally expensive to evaluate; engineering ...
Sunil Kumar +2 more
doaj +1 more source
Memorizing Schröder’s Method as an Efficient Strategy for Estimating Roots of Unknown Multiplicity
Mathematics, 2021 In this paper, we propose, to the best of our knowledge, the first iterative scheme with memory for finding roots whose multiplicity is unknown existing in the literature.
Alicia Cordero +2 more
doaj +1 more source
A Derivative Free Fourth-Order Optimal Scheme for Applied Science Problems
Mathematics, 2022 We suggest a new and cost-effective iterative scheme for nonlinear equations. The main features of the presented scheme are that it does not involve any derivative in the structure, achieves an optimal convergence of fourth-order factors, has more ...
Ramandeep Behl
doaj +1 more source
Information, 2021 This article numerically analyzes the distribution of the zeros of Riemann’s zeta function along the critical line (CL). The zeros are distributed according to a hierarchical two-layered model, one deterministic, the other stochastic. Following a complex
Michel Riguidel
doaj +1 more source
Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions
Mathematics, 2021 There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence ...
Ramandeep Behl +3 more
doaj +1 more source