scholarly journals Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Krzysztof Gdawiec ◽  
Wiesław Kotarski ◽  
Agnieszka Lisowska
Keyword(s):  
Iteration Process ◽  
Higher Order ◽  
Point Of View ◽  
Complex Polynomials ◽  
Root Finding ◽  
Points Of View ◽  
Iteration Processes

A survey of some modifications based on the classic Newton’s and the higher order Newton-like root finding methods for complex polynomials is presented. Instead of the standard Picard’s iteration several different iteration processes, described in the literature, which we call nonstandard ones, are used. Kalantari’s visualizations of root finding process are interesting from at least three points of view: scientific, educational, and artistic. By combining different kinds of iterations, different convergence tests, and different colouring we obtain a great variety of polynomiographs. We also check experimentally that using complex parameters instead of real ones in multiparameter iterations do not destabilize the iteration process. Moreover, we obtain nice looking polynomiographs that are interesting from the artistic point of view. Real parts of the parameters alter symmetry, whereas imaginary ones cause asymmetric twisting of polynomiographs.

scholarly journals Higher-Order Root-Finding Algorithms and Their Basins of Attraction

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Amir Naseem ◽  
M. A. Rehman ◽  
Thabet Abdeljawad
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Basins Of Attraction ◽  
Higher Order ◽  
Complex Polynomials ◽  
Convergence Criteria ◽  
Root Finding ◽  
Variational Iteration ◽  
Order Root ◽  
Iteration Technique

In this paper, we proposed and analyzed three new root-finding algorithms for solving nonlinear equations in one variable. We derive these algorithms with the help of variational iteration technique. We discuss the convergence criteria of these newly developed algorithms. The dominance of the proposed algorithms is illustrated by solving several test examples and comparing them with other well-known existing iterative methods in the literature. In the end, we present the basins of attraction using some complex polynomials of different degrees to observe the fractal behavior and dynamical aspects of the proposed algorithms.

NONSENSE, ABSURDITY AND PARADOX AS LINGUISTIC AND CULTURAL CATEGORIES

2019 ◽  
Keyword(s):  
Cognitive Function ◽  
Common Sense ◽  
Point Of View ◽  
Ontological Category ◽  
Ordinary Meaning ◽  
New Meanings ◽  
Points Of View ◽  
Human Thinking

In the article the analysis of nonsense, absurdity and paradox from the standpoint of linguistics is giv-en. Different points of view on these categories in relation to the meaning are considered. An attempt is made to reveal the commonality and specificity of nonsense, absurdity and paradox. Some researchers consider nonsense and paradox as a kind of absurdity. There is a dichotomous point of view on nonsense as one of the components of absurdity. However, there are works where these categories are differentiat-ed, for example, absurdity is understood as an ontological category, and nonsense as an epistemological category. There is a view of these categories through the allocation of "non-sense", "out-sense" and 136 "counter-sense" there is also a view that in the case of nonsense we are talking about the incompatibility of representations, and in the case of absurdity-the incompatibility of objects. If there are criteria that allow us to consider the presence of this phenomenon as natural, absurdity ceases to exist. Consequently, the view is expressed that nonsense, absurdity and paradox are different categories of thinking. Paradox is a contradiction arising from the presence of two or more common sense. The absurdity can be seen as a" counter-sense» opposing common sense and putting forward the concept of active impossibility of the latter's existence. As for nonsense, it is the meaning of metaphysical level – a meaning that goes beyond the ordinary meaning and creates new meanings. It is concluded that nonsense, absurdity and paradox are independent categories of human thinking, which is a manifestation of the cognitive function of hu-man consciousness.

scholarly journals Voigt Transform and Umbral Image

2020 ◽  
Vol 25 (3) ◽  
pp. 49
Author(s):  
Silvia Licciardi ◽  
Rosa Maria Pidatella ◽  
Marcello Artioli ◽  
Giuseppe Dattoli
Keyword(s):  
Spectroscopic Studies ◽  
Higher Order ◽  
Point Of View ◽  
The Other ◽  
Pivotal Role ◽  
Umbral Calculus ◽  
Laguerre Functions ◽  
Hermite And Laguerre Functions ◽  
Higher Order Functions ◽  
Voigt Function

In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other applications, according to a new point of view, and on the other, the introduction of a Voigt transform and its possible use. Furthermore, by the same method, we point out that the Hermite and Laguerre functions, extension of the corresponding polynomials to negative and/or real indices, can be expressed through a definition in a straightforward and unified fashion. It is illustrated how the techniques that we are going to suggest provide an easy derivation of the relevant properties along with generalizations to higher order functions.

THE CONCEPT AS THE OBJECT OF STUDY OF LINGUISTICS

2020 ◽  
Vol 72 (2) ◽  
pp. 236-242
Author(s):  
K. Galiyeva ◽  
◽  
S. Isakova ◽  
Keyword(s):  
Cognitive Linguistics ◽  
Point Of View ◽  
Subject Areas ◽  
The Subject ◽  
Basic Concepts ◽  
Points Of View ◽  
Definition Of ◽  
Object Of Study ◽  
Linguistic Phenomenon ◽  
Scientific Fields

The article is devoted to the definition of concept in modern linguistics. Various points of view and definitions of the basic concepts are considered: "concept", "conceptual sphere", "content". The aim of the article is to describe and explain such a complex unit as a concept from the point of view of linguistics. The object of research is studied in its various manifestations, the combination of verbal and nonverbal means of information expression in the conceptual sphere is revealed. the relevance of this topic is due to the need for a detailed consideration of the concept of concept based on the works of prominent scientists and linguists. Researchers treat the concept as a cognitive, psycholinguistic, linguocultural, cultural and linguistic phenomenon. The concept is an umbrella term because it "covers" the subject areas of several scientific fields: primarily cognitive psychology and cognitive linguistics.

Jules Verne’s ‘Around the World in 80 Days’: Multilingualism, Multiculturalism and Symbols

2021 ◽  
Vol 2021 ii (15) ◽  
pp. 146-182
Author(s):  
Haroula Hatzimihail ◽  
Ioannis Pantelidis
Keyword(s):  
Key Words ◽  
Age Groups ◽  
Literary Work ◽  
Point Of View ◽  
Social Classes ◽  
Jules Verne ◽  
The World ◽  
Semiotic Systems ◽  
Points Of View ◽  
Different Cultures

In this announcement, the various –linguistic and non-linguistic- symbols used in the literary work 'Around the world in 80 days', written by Jules Verne, are examined from an intertemporal and contemporary point of view. The references through these points of view, in matters of multiculturalism and multilingualism, are becoming classical in nature: they concern the necessity of the applied ability to communicate between individuals who belong to different social classes and age groups, speak the same or different languages, come from different cultures, with rights and obligations in their various areas of life, etc. Key-words: linguistics, multilingualism, multiculturalism, semiotics, semiotic systems, symbols

LEGAL STATUS OF THE SOLE EXECUTIVE BODY OF A LIMITED LIABILITY COMPANY

2021 ◽  
Author(s):  
Yulia Fanilevna Aitova ◽  
Keyword(s):  
General Theory ◽  
Legal Status ◽  
Limited Liability ◽  
Point Of View ◽  
Limited Liability Company ◽  
Points Of View ◽  
Theory Of Law ◽  
The Individual ◽  
Executive Body

The article analyzes the issue of determining the legal status of the individual management body of a limited liability company. The author begins his research with the concept of legal status existing in the general theory of law, and then proceeds to consider the issue from the point of view of philosophical categories. In addition, the work explores the diversity of points of view existing in the doctrine regarding the legal status of the individual management body of economic societies.

UNEXPECTED BEHAVIOR IN THE CROSSING OF MICROWAVE AND OPTICAL BEAMS

2005 ◽  
Vol 19 (27) ◽  
pp. 1403-1410 ◽  
Author(s):  
E. ALLARIA ◽  
R. MEUCCI ◽  
D. MUGNAI ◽  
A. RANFAGNI ◽  
C. RANFAGNI
Keyword(s):  
Lorentz Invariance ◽  
Point Of View ◽  
Experimental Results ◽  
Light Velocity ◽  
Broken Lorentz Invariance ◽  
Points Of View ◽  
Optical Beams ◽  
Definite Solution ◽  
Unexpected Behavior

The question of the superluminal speed of information was stopped at crossroads in the last few years. According to one point of view, this speed must be limited to the light velocity in vacuum, whereas a different point of view is more open in this respect and, under specific conditions, this limit is considered surmountable. Very recently, a third approach (based on the hypothesis of a local broken Lorentz-invariance) was proposed and, if confirmed, would go beyond the controversy of the two points of view mentioned above. It is therefore worthwhile to recall attention to this problem, which is far from having a definite solution. The present paper reports some experimental results (similar to those of Ref. 1) which can contribute to these discussions, and also considers the fact that they seem to give some support to the aforesaid third approach, although revised in terms of decaying waves.

Higher-Order Multilevel Solvers for the EHL Line and Point Contact Problem

1994 ◽  
Vol 116 (4) ◽  
pp. 741-750 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Contact Problem ◽  
Computing Time ◽  
Point Contact ◽  
Higher Order ◽  
Second Order ◽  
Point Of View ◽  
First Order ◽  
Fundamental Point ◽  
Numerical Solver ◽  
Circular Contact

This paper addresses the development of efficient numerical solvers for EHL problems from a rather fundamental point of view. A work-accuracy exchange criterion is derived, that can be interpreted as setting a limit to the price paid in terms of computing time for a solution of a given accuracy. The criterion can serve as a guideline when reviewing or selecting a numerical solver and a discretization. Earlier developed multilevel solvers for the EHL line and circular contact problem are tested against this criterion. This test shows that, to satisfy the criterion a second-order accurate solver is needed for the point contact problem whereas the solver developed earlier used a first-order discretization. This situation arises more often in numerical analysis, i.e., a higher order discretization is desired when a lower order solver already exists. It is explained how in such a case the multigrid methodology provides an easy and straightforward way to obtain the desired higher order of approximation. This higher order is obtained at almost negligible extra work and without loss of stability. The approach was tested out by raising an existing first order multilevel solver for the EHL line contact problem to second order. Subsequently, it was used to obtain a second-order solver for the EHL circular contact problem. Results for both the line and circular contact problem are presented.

scholarly journals Estimation of Influence of Explosive Characteristics of Emulsion Explosives on Shotpile Width

2018 ◽  
Vol 56 ◽  
pp. 01003
Author(s):  
Victor Sinitsyn ◽  
Pavel Menshikov ◽  
Vyacheslav Kutuev
Keyword(s):  
Detonation Velocity ◽  
Dynamic Compression ◽  
Point Of View ◽  
Head Part ◽  
Detonation Pressure ◽  
Emulsion Explosives ◽  
Clastic Rocks ◽  
Total Magnitude ◽  
Efficient Type ◽  
Points Of View

The article deals with the question of the effect of explosive characteristics of emulsion explosives on the shotpile width. Currently, there are two main points of view to select an efficient type of explosive, which contributes to the qualitative destruction (fragmentation) of coarse clastic rocks. The first is based on the assumption that the detonation velocity of explosives must correspond to the break-down point of the rock (dynamic compression). Another point of view is that the detonation pressure of explosives determines only the head part of the pulse, on which the rock fragmentation is dependent only near the charge, in the contact zone around the borehole. The fragmentation of the entire rock volume within a given borehole array depends on the total magnitude of the explosion pulse, determined not by the detonation velocity, but by the total energy reserve of the explosive charge. Experimental explosions with some of the most common industrial explosives have been carried out in the current conditions of blasting of borehole charges by various types of industrial explosives from the point of view to select the most important parameter, which determines its influence on the shotpile width The investigations have been carried out according to the data obtained to establish that the energy properties of explosives (heat of explosive transformation and density of explosives) determine the decisive influence on the shotpile width, and the operability, the volume of the released gases, the detonation velocity for the change in the shotpile width have very little effect and may not be taken into account in calculations for the prediction of the shotpile.

scholarly journals Gauss law, minimal coupling and fermionic PEPS for lattice gauge theories

2020 ◽  
Author(s):  
Patrick Emonts ◽  
Erez Zohar
Keyword(s):  
Gauge Theories ◽  
Point Of View ◽  
Lattice Gauge ◽  
Hamiltonian Lattice ◽  
Tensor Network ◽  
Network Methods ◽  
Matter Theory ◽  
Lattice Gauge Theories ◽  
Points Of View ◽  
The One

In these lecture notes, we review some recent works on Hamiltonian lattice gauge theories, that involve, in particular, tensor network methods. The results reviewed here are tailored together in a slightly different way from the one used in the contexts where they were first introduced. We look at the Gauss law from two different points of view: for the gauge field, it is a differential equation, while from the matter point of view, on the other hand, it is a simple, explicit algebraic equation. We will review and discuss what these two points of view allow and do not allow us to do, in terms of unitarily gauging a pure-matter theory and eliminating the matter from a gauge theory, and relate that to the construction of PEPS (Projected Entangled Pair States) for lattice gauge theories.

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