scholarly journals Computational Bifurcations Occurring on Red Fixed Components in the λ-Parameter Plane for a Family of Optimal Fourth-Order Multiple-Root Finders under the Möbius Conjugacy Map

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 763
Author(s):  
Young Hee Geum ◽  
Young Ik Kim
Keyword(s):  
Fourth Order ◽  
Polynomial Function ◽  
Multiple Root ◽  
Parameter Plane ◽  
Connected Components ◽  
Computational Results ◽  
Boundary Equation ◽  
Chaotic Orbits ◽  
Bifurcation Phenomena

Optimal fourth-order multiple-root finders with parameter λ were conjugated via the Möbius map applied to a simple polynomial function. The long-term dynamics of these conjugated maps in the λ -parameter plane was analyzed to discover some properties of periodic, bounded and chaotic orbits. The λ -parameters for periodic orbits in the parameter plane are painted in different colors depending on their periods, and the bounded or chaotic ones are colored black to illustrate λ -dependent connected components. When a red fixed component in the parameter plane branches into a q-periodic component, we encounter geometric bifurcation phenomena whose characteristics determine the desired boundary equation and bifurcation point. Computational results along with illustrated components support the bifurcation phenomena underlying this paper.

Exploring the Fourth Order

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Barend KLITSIE ◽  
Rebecca PRICE ◽  
Christine DE LILLE
Keyword(s):  
Action Research ◽  
Fourth Order ◽  
Subject Matter ◽  
Action Research Project ◽  
Research Project ◽  
Building Trust ◽  
Current Business

Companies are organised to fulfil two distinctive functions: efficient and resilient exploitation of current business and parallel exploration of new possibilities. For the latter, companies require strong organisational infrastructure such as team compositions and functional structures to ensure exploration remains effective. This paper explores the potential for designing organisational infrastructure to be part of fourth order subject matter. In particular, it explores how organisational infrastructure could be designed in the context of an exploratory unit, operating in a large heritage airline. This paper leverages insights from a long-term action research project and finds that building trust and shared frames are crucial to designing infrastructure that affords the greater explorative agenda of an organisation.

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

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 in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

scholarly journals ON A GENERAL CLASS OF OPTIMAL FOURTH-ORDER MULTIPLE-ROOT FINDERS

2013 ◽  
Vol 26 (3) ◽  
pp. 657-669
Author(s):  
Young Ik Kim
Keyword(s):  
Fourth Order ◽  
General Class ◽  
Multiple Root

An optimal class of fourth-order multiple-root finders of Chebyshev-Halley type and their basins of attraction

2021 ◽  
Vol 14 (1) ◽  
pp. 17
Author(s):  
Raj Bala ◽  
Munish Kansal ◽  
Vinay Kanwar
Keyword(s):  
Fourth Order ◽  
Multiple Root ◽  
Basins Of Attraction

scholarly journals Statistics and Analysis of the Relations between Rainstorm Floods and Earthquakes

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Baodeng Hou ◽  
Yongxiang Wu ◽  
Jianhua Wang ◽  
Kai Wu ◽  
Weihua Xiao
Keyword(s):  
Climate Change ◽  
Input Data ◽  
Computational Results ◽  
Occurrence Time ◽  
The Past ◽  
The Earth ◽  
Water Vapors ◽  
Transmission Zone ◽  
Chinese Scholars

The frequent occurrence of geophysical disasters under climate change has drawn Chinese scholars to pay their attention to disaster relations. If the occurrence sequence of disasters could be identified, long-term disaster forecast could be realized. Based on the Earth Degassing Effect (EDE) which is valid, this paper took the magnitude, epicenter, and occurrence time of the earthquake, as well as the epicenter and occurrence time of the rainstorm floods as basic factors to establish an integrated model to study the correlation between rainstorm floods and earthquakes. 2461 severe earthquakes occurred in China or within 3000 km from China and the 169 heavy rainstorm floods occurred in China over the past 200+ years as the input data of the model. The computational results showed that although most of the rainstorm floods have nothing to do with the severe earthquakes from a statistical perspective, some floods might relate to earthquakes. This is especially true when the earthquakes happen in the vapor transmission zone where rainstorms lead to abundant water vapors. In this regard, earthquakes are more likely to cause big rainstorm floods. However, many cases of rainstorm floods could be found after severe earthquakes with a large extent of uncertainty.

Stability and Bifurcations of Nonlinear Multibody Systems

1993 ◽  
Vol 46 (11S) ◽  
pp. S156-S159
Author(s):  
Edwin J. Kreuzer
Keyword(s):  
Multibody Systems ◽  
Qualitative Behavior ◽  
State Behavior ◽  
Bifurcation Phenomena ◽  
Nonlinear Mathematical Models ◽  
Mechanical Models ◽  
Stability And Bifurcations ◽  
Local And Global Bifurcations ◽  
Dynamics Problems

Many technical systems are adequately described only by means of nonlinear mathematical models. Multibody systems became the most important mechanical models for analyzing engineering dynamics problems. The long-term or steady-state behavior of such systems can have a periodic, quasi-periodic, or chaotic character. Changes of the qualitative behavior are characterized by local and global bifurcations. This paper deals with stability problems in multibody system dynamics and explains different bifurcation phenomena as well as methods for analyzing them. Results from a simple oscillator prove the applicability of the methods.

scholarly journals A New Biparametric Family of Two-Point Optimal Fourth-Order Multiple-Root Finders

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Young Ik Kim ◽  
Young Hee Geum
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Multiple Root ◽  
Multiple Roots ◽  
Asymptotic Error ◽  
Error Constant ◽  
Asymptotic Error Constant

We construct a biparametric family of fourth-order iterative methods to compute multiple roots of nonlinear equations. This method is verified to be optimally convergent. Various nonlinear equations confirm our proposed method with order of convergence of four and show that the computed asymptotic error constant agrees with the theoretical one.

scholarly journals Posterior Maxillary Prosthetic Treatment with Molar Hemisection – A case report

2018 ◽  
Vol 1 (1) ◽  
pp. 22
Author(s):  
Abil Kurdi ◽  
Hanoem Eka Hidayati
Keyword(s):  
Case Report ◽  
Healing Process ◽  
Multiple Root ◽  
Bridge Abutment ◽  
Infected Root ◽  
Alternative Treatment Option ◽  
Molar Teeth ◽  
Selection Of Patients ◽  
Selection Of

Background: Hemisection is an alternative treatment option for maintaining tooth with multiple root that indicated for extraction. Purpose: To reported tooth with multiple root indicated by extraction to be used as a fixed-fixed bridge abutment by extracting the infected root and maintain the healthy one. Case: A 53-year-old woman with caries in upper 1st molar teeth in mesiobuccally root that can’t be maintained. Patients refuse the teeth to be extracted. Case Management: Hemisection treatment was performed on 26 mesiobuccal root, with the addition of bone graft. After the healing process, fixed-fixed bridges were made on 25, 26, 27, 28, with PFM on 25, 26, 27 and full cast crowns on 28 as the material. Discussion: Hemisection as a conservative treatment, can be an option for multiple  root teeth that has been indicated for extraction but still have root that can be maintained. Conclusion: Teeth performed by hemisection treatments can be used as abutments with attention to the selection of patients to achieve long-term success.

An optimal class of fourth-order multiple-root finders of Chebyshev-Halley type and their basins of attraction

2021 ◽  
Vol 14 (1) ◽  
pp. 17
Author(s):  
Vinay Kanwar ◽  
Raj Bala ◽  
Munish Kansal
Keyword(s):  
Fourth Order ◽  
Multiple Root ◽  
Basins Of Attraction
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