scholarly journals A Generic Family of Optimal Sixteenth-Order Multiple-Root Finders and Their Dynamics Underlying Purely Imaginary Extraneous Fixed Points

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 562 ◽  
Author(s):  
Min-Young Lee ◽  
Young Ik Kim ◽  
Beny Neta
Keyword(s):  
Fixed Points ◽  
Multiple Root ◽  
Weight Functions ◽  
Computational Results ◽  
Special Cases ◽  
Extraneous Fixed Points ◽  
Free Parameters ◽  
Future Work ◽  
Generic Family ◽  
Selection Of

A generic family of optimal sixteenth-order multiple-root finders are theoretically developed from general settings of weight functions under the known multiplicity. Special cases of rational weight functions are considered and relevant coefficient relations are derived in such a way that all the extraneous fixed points are purely imaginary. A number of schemes are constructed based on the selection of desired free parameters among the coefficient relations. Numerical and dynamical aspects on the convergence of such schemes are explored with tabulated computational results and illustrated attractor basins. Overall conclusion is drawn along with future work on a different family of optimal root-finders.

scholarly journals Developing an Optimal Class of Generic Sixteenth-Order Simple-Root Finders and Investigating Their Dynamics

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 8 ◽  
Author(s):  
Young Hee Geum ◽  
Young Ik Kim ◽  
Beny Neta
Keyword(s):  
Global Convergence ◽  
Real World ◽  
Simple Root ◽  
Weight Functions ◽  
Root Finding ◽  
Special Cases ◽  
Attraction Basins ◽  
Visual Description ◽  
Future Work ◽  
Real World Problems

Developed here are sixteenth-order simple-root-finding optimal methods with generic weight functions. Their numerical and dynamical aspects are investigated with the establishment of a main theorem describing the desired optimal convergence. Special cases with polynomial and rational weight functions have been extensively studied for applications to real-world problems. A number of computational experiments clearly support the underlying theory on the local convergence of the proposed methods. In addition, to investigate the relevant global convergence, we focus on the dynamics of the developed methods, as well as other known methods through the visual description of attraction basins. Finally, we summarized the results, discussion, conclusion, and future work.

scholarly journals Regulating the Regulators: Mechanisms of Substrate Selection of the O-GlcNAc Cycling Enzymes OGT and OGA

Glycobiology ◽  
2021 ◽  
Author(s):  
Hannah M Stephen ◽  
Trevor M Adams ◽  
Lance Wells
Keyword(s):  
Nutrient Sensing ◽  
Substrate Selection ◽  
Disease States ◽  
Dynamic Modification ◽  
Selection For ◽  
Outstanding Question ◽  
Glcnac Transferase ◽  
Future Work ◽  
Partner Proteins ◽  
Selection Of

Abstract Thousands of nuclear and cytosolic proteins are modified with a single β-N-acetylglucosamine on serine and threonine residues in mammals, a modification termed O-GlcNAc. This modification is essential for normal development and plays important roles in virtually all intracellular processes. Additionally, O-GlcNAc is involved in many disease states, including cancer, diabetes, and X-linked intellectual disability. Given the myriad of functions of the O-GlcNAc modification, it is therefore somewhat surprising that O-GlcNAc cycling is mediated by only two enzymes: the O-GlcNAc transferase (OGT), which adds O-GlcNAc, and the O-GlcNAcase (OGA), which removes it. A significant outstanding question in the O-GlcNAc field is how do only two enzymes mediate such an abundant and dynamic modification. In this review, we explore the current understanding of mechanisms for substrate selection for the O-GlcNAc cycling enzymes. These mechanisms include direct substrate interaction with specific domains of OGT or OGA, selection of interactors via partner proteins, posttranslational modification of OGT or OGA, nutrient sensing, and localization alteration. Altogether, current research paints a picture of an exquisitely regulated and complex system by which OGT and OGA select substrates. We also make recommendations for future work, toward the goal of identifying interaction mechanisms for specific substrates that may be able to be exploited for various research and medical treatment goals.

scholarly journals Extensions in graph normal form

2020 ◽  
Author(s):  
Michał Walicki
Keyword(s):  
Normal Form ◽  
Fixed Points ◽  
Propositional Logic ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Special Cases

Abstract Graph normal form, introduced earlier for propositional logic, is shown to be a normal form also for first-order logic. It allows to view syntax of theories as digraphs, while their semantics as kernels of these digraphs. Graphs are particularly well suited for studying circularity, and we provide some general means for verifying that circular or apparently circular extensions are conservative. Traditional syntactic means of ensuring conservativity, like definitional extensions or positive occurrences guaranteeing exsitence of fixed points, emerge as special cases.

scholarly journals A Qualitative Study of COVID-19 Distress in University Students

2021 ◽  
pp. 216769682110251
Author(s):  
Samantha G. Farris ◽  
Mindy M. Kibbey ◽  
Erick J. Fedorenko ◽  
Angelo M. DiBello
Keyword(s):  
University Students ◽  
Undergraduate Students ◽  
Mental Health Problems ◽  
Financial Strain ◽  
Public Response ◽  
Viral Spread ◽  
Future Work ◽  
The Impact ◽  
Viral Outbreak ◽  
Selection Of

The psychological effect of the pandemic and measures taken in response to control viral spread are not yet well understood in university students; in-depth qualitative analysis can provide nuanced information about the young adult distress experience. Undergraduate students ( N = 624) in an early US outbreak “hotspot” completed an online narrative writing about the impact and distress experienced due to the COVID-19 pandemic. Data were collected April-May 2020. A random selection of 50 cases were sampled for thematic analysis. Nine themes were identified: viral outbreak distress, fear of virus contraction/transmission, proximity to virus, dissatisfaction with public response, physical distancing distress, social distancing distress, academic and school-related distress, disruptive changes in health behavior and routines, financial strain and unemployment, worsening of pre-existing mental health problems, and social referencing that minimizes distress. Future work is needed to understand the persistence of the distress, in addition to developing methods for assessment, monitoring, and mitigation of the distress.

Application of a Genetic Algorithm to Concept Variant Selection

2006 ◽  
Author(s):  
Ryan S. Hutcheson ◽  
Robert L. Jordan ◽  
Robert B. Stone ◽  
Janis P. Terpenny ◽  
Xiaomeng Chang
Keyword(s):  
Genetic Algorithm ◽  
Product Development ◽  
Solution Space ◽  
Variant Selection ◽  
Functional Modeling ◽  
Detailed Design ◽  
Modeling Techniques ◽  
Break Even Point ◽  
Future Work ◽  
Selection Of

This paper outlines a framework for applying a genetic algorithm to the selection of component variants between the conceptual and detailed design stages of product development. A genetic algorithm (GA) is defined for the problem and an example is presented that demonstrates its application and usefulness. Functional modeling techniques are used to formulate the design problem and generate the chromosomes that are evaluated with the algorithm. In the presented example, suitable GA parameters and the break-even point where the GA surpassed an enumerated search of the same solution space were found. Recommend uses of the GA along with limitations of the method and future work are presented as well.

scholarly journals Final coalgebras as greatest fixed points in ZF set theory

1999 ◽  
Vol 9 (5) ◽  
pp. 545-567 ◽  
Author(s):  
LAWRENCE C. PAULSON
Keyword(s):  
Fixed Points ◽  
Set Theory ◽  
Theorem Prover ◽  
Infinite Length ◽  
Special Cases ◽  
Definition Of ◽  
Recursive Definitions ◽  
Ordered Pairs

A special final coalgebra theorem, in the style of Aczel (1988), is proved within standard Zermelo–Fraenkel set theory. Aczel's Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel's solution and substitution lemmas are proved in the style of Rutten and Turi (1993). The approach is less general than Aczel's, but the treatment of non-well-founded objects is simple and concrete. The final coalgebra of a functor is its greatest fixedpoint.Compared with previous work (Paulson, 1995a), iterated substitutions and solutions are considered, as well as final coalgebras defined with respect to parameters. The disjoint sum construction is replaced by a smoother treatment of urelements that simplifies many of the derivations.The theory facilitates machine implementation of recursive definitions by letting both inductive and coinductive definitions be represented as fixed points. It has already been applied to the theorem prover Isabelle (Paulson, 1994).

scholarly journals PHOTOGRAMMETRIC PROCESSING OF OSIRIS-REX IMAGES OF ASTEROID (101955) BENNU

2020 ◽  
Vol V-3-2020 ◽  
pp. 587-594
Author(s):  
K. L. Edmundson ◽  
K. J. Becker ◽  
T. L. Becker ◽  
C. A. Bennett ◽  
D. N. DellaGiustina ◽  
...  
Keyword(s):  
Control Process ◽  
Laser Altimeter ◽  
Shape Models ◽  
Spectral Interpretation ◽  
Global Mapping ◽  
Resource Identification ◽  
Imaging Sensors ◽  
Future Work ◽  
Selection Of ◽  
Reconnaissance Surveys

Abstract. The principal objective of the Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer (OSIRIS-REx) mission is to retrieve a sample of the asteroid (101955) Bennu and return it to Earth. OSIRIS-REx arrived at Bennu in December 2018. Images of the asteroid by the OSIRIS-REx Camera Suite (OCAMS) were photogrammetrically controlled to produce a global basemap and site-specific image mosaics essential to the selection of a primary and backup sample site, which were announced in December 2019. In the control process, OCAMS images were registered to shape models created from OSIRIS-REx Laser Altimeter (OLA) data and from the process of stereophotoclinometry. This paper summarizes the photogrammetric control to date of images collected at Bennu. We briefly review the mission and the OCAMS imaging sensors. We then describe the photogrammetric control process for the global mapping campaign and targeted reconnaissance surveys of candidate sample sites. Finally, we discuss ongoing and future work.

scholarly journals Void and Moisture Content of Fiber Reinforced Composites

2021 ◽  
Vol 87 (3) ◽  
pp. 78-93
Author(s):  
Nurul Zuhairah Mahmud Zuhudi ◽  
Afiq Faizul Zulkifli ◽  
Muzafar Zulkifli ◽  
Ahmad Naim Ahmad Yahaya ◽  
Nurhayati Mohd Nur ◽  
...  
Keyword(s):  
Moisture Content ◽  
Short Review ◽  
Fiber Reinforced Composites ◽  
Moisture Determination ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Mechanical Performances ◽  
Future Work ◽  
Selection Of

In this paper, a short review on the void and moisture content studies of fiber reinforced composites for both, synthetic and natural based fibers are presented. The review summarized the research papers in which include experimental and theoretical works that related to the void and moisture content studies. In addition to that, this review paper highlighting a few research studies conducted in literature on the effects of the void and moisture on the mechanical performances of the composite. Few common measurement methods used for the void and moisture determination are discussed here. The aims of this short review, mainly to capture the trend ranging from the recent five years back and summarize the various studies and also to compare and conclude the most common method for the determination of the void and moisture content. This paper is mainly providing a baseline in the selection of the methods for the future work of the author’s work with regard to the reduction of the presence of voids and moisture occur during the impregnation process of fiber reinforced composites, especially when using natural-based fiber.

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