On the convergence of iterative processes for the solution of simultaneous equations in several variables

1960 ◽  
Vol 56 (3) ◽  
pp. 286-289 ◽  
Author(s):  
W. F. Bodmer
Keyword(s):  
Detailed Analysis ◽  
Iterative Process ◽  
Order Of Convergence ◽  
Simultaneous Equations ◽  
Iterative Processes ◽  
Several Variables ◽  
The Subject ◽  
Newton Raphson

The notion of the order of convergence of iterative processes may well have been known to Gauss or even Newton, but to the author's knowledge it was first considered in detail in 1870 by Schröder(5). The subject was later investigated independently by Hartree(4) and Bodewig(1). Hartree alone mentions, briefly, the extension from one to several variables, but gives no detailed analysis. Domb and Fisher(2) consider a particular type of iterative process in several variables, which they call ‘degenerate’, in which all the variables tend to the same value. We shall follow essentially Hartree's treatment, in considering the solution of r simultaneous equations in r variables and applications to a generalization of the Newton-Raphson process.

Meet fractal curves with 1C:MathKit

2020 ◽  
pp. 38-48
Author(s):  
O. M. Korchazhkina
Keyword(s):  
Methodological Approach ◽  
Fractal Curve ◽  
Iterative Processes ◽  
Geometric Figures ◽  
Modern Natural ◽  
Geometric Objects ◽  
Ict Tools ◽  
Subject Areas ◽  
The Subject ◽  
And Mathematics

The article presents a methodological approach to studying iterative processes in the school course of geometry, by the example of constructing a Koch snowflake fractal curve and calculating a few characteristics of it. The interactive creative environment 1C:MathKit is chosen to visualize the method discussed. By performing repetitive constructions and algebraic calculations using ICT tools, students acquire a steady skill of work with geometric objects of various levels of complexity, comprehend the possibilities of mathematical interpretation of iterative processes in practice, and learn how to understand the dialectical unity between finite and infinite parameters of flat geometric figures. When students are getting familiar with such contradictory concepts and categories, that replenishes their experience of worldview comprehension of the subject areas they study through the concept of “big ideas”. The latter allows them to take a fresh look at the processes in the world around. The article is a matter of interest to schoolteachers of computer science and mathematics, as well as university scholars who teach the course “Concepts of modern natural sciences”.

Re-appraising and Re-classifying: a New Look at the Corpus of Miniature Socketed Axes from Britain

2020 ◽  
Vol 75 (1) ◽  
pp. 1-27
Author(s):  
Alex Bliss
Keyword(s):  
Spatial Distribution ◽  
Data Collection ◽  
Detailed Analysis ◽  
Significant Proportion ◽  
Direct Result ◽  
Object Type ◽  
England And Wales ◽  
Extensive Data ◽  
Metal Artefacts ◽  
The Subject

The advent of the Portable Antiquities Scheme (PAS) has added a great deal to our understanding of prehistoric metal artefacts in England and Wales, namely in expanding enormously the corpuses of objects previously thought to be quite scarce. One such artefact type is the miniature socketed 'votive' axe, most of which are found in Wiltshire and Hampshire. As a direct result of developing such recording initiatives, reporting of these artefacts as detector finds from the early 2000s onwards has virtually trebled the number originally published by Paul Robinson in his 1995 analysis. Through extensive data-collection, synthesising examples recorded via the PAS with those from published excavations, the broad aims of this paper (in brief) are as follows: firstly, produce a solid typology for these artefacts; secondly, investigate their spatial distribution across England and Wales. As a more indirect third aim, this paper also seeks to redress the imbalance of focus and academic study specifically applying to Hampshire finds of this object type, which despite producing a significant proportion of the currently known corpus have never been the subject of detailed analysis.

Features of optative modality in Macedonian language (with emphasis on the functionalities of independent da-construction)

2020 ◽  
pp. 301-323
Author(s):  
Natalya I. Kikilo ◽  
Keyword(s):  
Detailed Analysis ◽  
Present Article ◽  
Literary Language ◽  
Natural Context ◽  
Wide Range ◽  
Verb Forms ◽  
Text Types ◽  
The Future ◽  
The Subject ◽  
Ritual Context

In the Macedonian literary language the analytic da-construction used in an independent clause has a wide range of possible modal meanings, the most common of which are imperative and optative. The present article offers a detailed analysis of the semantics and functions of the Macedonian optative da-construction based on fiction and journalistic texts. The first part of the article deals with the specificities of the optative as a category which primarily considers the subject of a wish. In accordance with the semantic characteristics of this category, optative constructions are used in those discourse text types where the speakers are explicitly designated (the most natural context for the optative is the dialogue). The analysis of the Macedonian material includes instances of atypical usage of the optative da-construction, in which the wish of the subject is not apparent and thereby produces new emotional tonalities perceptible to the reader of a fiction/journalistic text. The study describes Macedonian constructions involving two different verb forms: 1) present tense form (da + praes) and 2) imperfective form (da + impf). These constructions formally designate the hypothetical and counterfactual status of the optative situation, respectively. Thus, the examples in the analysis are ordered according to two types of constructions, which reflect the speaker’s view on the probability of the realisation of his/her wish. Unrealistic wishes can be communicated through the present da-construction, while the imperfective construction denotes situations in which the wish can be realised in the future. The second part of the article is devoted to performative optative da-constructions, which express formulas of speech etiquette, wishes and curses. The analysis demonstrates that these constructions lose their magical functions, when used outside of the ritual context, and begin to function as interjections.

scholarly journals Fractional Newton–Raphson Method Accelerated with Aitken’s Method

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 47
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz ◽  
U. Iturrarán-Viveros ◽  
R. Caballero-Cruz
Keyword(s):  
Fractional Derivative ◽  
Iterative Methods ◽  
Fractional Integral ◽  
Order Of Convergence ◽  
Fractional Operators ◽  
Speed Of Convergence ◽  
Newton Raphson ◽  
Raphson Method

In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order α of the derivative is different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.

scholarly journals Immigrants in Finland as a Problem Discussed in Leena Lehtolainen’s Minne Tytöt Kadonneet

2014 ◽  
Vol 16 (1) ◽  
pp. 66-76
Author(s):  
Martyna Kokotkiewicz
Keyword(s):  
Detailed Analysis ◽  
Social Issues ◽  
Crime Fiction ◽  
The Novel ◽  
Main Subject ◽  
Racial Hatred ◽  
The Subject ◽  
Different Cultures

Abstract Leena Lehtolainen belongs to the most appreciated Finnish authors of crime fiction. One of the significant features of her works is that she discusses some most alarming social issues in them. The problem concerning immigration and its different aspects can definitely be considered as an example of such an issue. Since the problem of cultural antagonisms, racial hatred and xenophobia has been widely discussed by many other Scandinavian authors of crime fiction as well, it is worth analyzing how Lehtolainen herself approaches the problem. The aim of this article is to discuss some aspects concerning the problems of immigrant societies in Finland, basing on one of Leena Lehtolainen’s novels, Minne tytöt kadonneet, which main subject could be described as a collision of two completely different cultures and attitudes to the reality. Its aim is not, however, to discuss any formal aspects of the text, since such a kind of detailed analysis cannot be the subject of one article only. That is why the article concentrates on the plot of the novel and its possible relations to some actual problems the Finnish society faces. Taking it all into consideration it may be seen as an introduction to a wider analysis of Leena Lehtolainen’s works.

scholarly journals Spanish Renaissance High Culture in Soviet Historiography: Interdisciplinary Aspect

2017 ◽  
Vol 6 (5) ◽  
pp. 256
Author(s):  
Alexander A. Zaitsev ◽  
Natalia V. Antonova
Keyword(s):  
Detailed Analysis ◽  
Present Article ◽  
Soviet Period ◽  
High Culture ◽  
Developmental Patterns ◽  
Research Areas ◽  
Renaissance Studies ◽  
The Subject ◽  
Interdisciplinary Interaction ◽  
Soviet Historiography

<p>The tradition of studying Spanish Renaissance in Russia is quite a complicated phenomenon, which requires a detailed analysis. The main questions which arise when referring to the issue are those of developmental patterns and interdisciplinary aspect of the letter. Spanish Renaissance culture is traditionally the subject to scrutiny for historians, philologists and art historians. The present article aims to outline a preliminary picture of interdisciplinary interaction, which gained momentum in the Soviet period of Russian Hispanism. Special attention is paid to the imminent figures of Spanish Renaissance historiography, as well as their ideas and concepts. The evolution of Spanish Renaissance studies is described against the background of the principal research areas. The present paper will be of interest to both intellectual historians and scholars investigating Renaissance and medieval history.</p>

scholarly journals HUNTING RIGHTS IN POLAND

2018 ◽  
Vol 32 (1) ◽  
pp. 63-81
Author(s):  
Witold Daniłowicz
Keyword(s):  
Detailed Analysis ◽  
Legal Issues ◽  
Legal Institution ◽  
Legal Nature ◽  
The Subject ◽  
Polish Law

Although hunting rights constitute the key element of Polish hunting law, so far they have not been subject to detailed analysis in legal writings devoted to the subject. This is most likely due to the fact, that the term itself is not used in the hunting legislation. The article fills this gap. It analyzes the legal nature of hunting rights under Polish law as well as examines legal issues most closely related to this legal institution, namely hunting preserve and hunting lease. Also analyzed is the ownership of game at large, game carcass, hunting trophies and shed antlers.

scholarly journals ASPECTS OF NARRATIVE IN THE PROSE OF WRITER PETRO MARKO

2019 ◽  
Vol 2 (2) ◽  
pp. 1-4
Author(s):  
Antela Voulis
Keyword(s):  
Detailed Analysis ◽  
Narrative Analysis ◽  
Subject Matter ◽  
Creative Work ◽  
The Novel ◽  
Social Equality ◽  
Critical Studies ◽  
Prose Style ◽  
Poetic Expression ◽  
The Subject

Petro Marko is considered by critics as one of the founders of modern Albanian prose. Scientific assessments of Petro Markos’s creativity are mainly based on long and short prose, in the form of genuine critical studies, short predictions, comments and analysis. There are papers of this nature written by scholars such as: Floresha Dado, Adriatik Kallulli, Bashkim Kuçuku, Ali Aliu, Robert Elsie and many others. The subject matter of these articles varies from simple information to moments of writer’s life, to genuine studies and analysis regarding interpretation and explanation of different elements of the structure of his literary works. In this case, we would like to highlight an article written by the author Bashkim Kuçuku, namely the novel “A name on four streets”. In this particular paper, Kucuku discusses the symbolism of the novel’s title, that even in its metaphorical form didn’t escape the punishment of dictatorship censure, closely connected with the tragic fate that followed Petro Marko. And by doing so the researcher gives us a detailed insight of the connection between his work and a broader background of Marco’s biography. In this context, together with the detailed analysis of the novel’s title, we will find the key point that paves the way for penetrating the original metaphor and symbolism of the story. According to Kuçuku, Petro Marko is a dignified, idealist, as well a stoic writer for justice and social equality. It is precisely this book, “A name in four ways”, that distinctly portrays the aforementioned author as one of the leading writers of prose in Albania and this work is one of his most distinguished among all the others. It is the aim of this study to harmonize the internal narrative analysis of the prose style with the poetic expression of all Petro Mario’s creative work.

A summary review of mechanical properties prediction methods for textile reinforced polymer composites

2005 ◽  
Vol 219 (2) ◽  
pp. 91-109 ◽  
Author(s):  
J J Crookston ◽  
A C Long ◽  
I A Jones
Keyword(s):  
Mechanical Properties ◽  
Detailed Analysis ◽  
Polymer Composites ◽  
Numerical Models ◽  
Textile Composites ◽  
Prediction Methods ◽  
Reinforced Polymer ◽  
Mechanical Properties Prediction ◽  
The Subject

The use of textile reinforcements for polymer composite components has become a common practice due to the favourable material costs and labour requirements compared with traditional unidirectional prepreg composites, and the high stiffness and strength compared with the use of randomly orientated reinforcements. As a result, determination of both elastic properties and failure behaviour of textile composites has been the subject of substantial research in recent years. This paper presents a review of some of the analytical and numerical models pertaining to the mechanics of textile composites which have been published in the literature. Particular consideration is given to the suitability of models for the analysis of non-orthogonal weave structures such as those which have been deformed in shear during component manufacture. The intention of the paper is not to provide a detailed analysis of the underlying mathematics of the models discussed, but rather to provide an overview of the work conducted in order to direct further reading.

The Local Economic Impact of Construction Projects in a Small and Relatively Self-contained Economy

1997 ◽  
Vol 12 (2) ◽  
pp. 146-159 ◽  
Author(s):  
H. W. Armstrong ◽  
J. Darrall ◽  
R. Grove-White
Keyword(s):  
Detailed Analysis ◽  
Economic Impact ◽  
Construction Projects ◽  
Economic Impacts ◽  
Capital Projects ◽  
Intensive Research ◽  
Simplifying Assumptions ◽  
Local Construction ◽  
The Subject ◽  
Capital Construction

Whilst the local multiplier impacts of the annual operation of universities has been the subject of intensive research, the economic impacts of capital construction projects have been almost completely ignored. This paper presents the results of detailed analysis of capital projects at Lancaster University in 1993- The reasons for the radically different annual operation and construction multipliers estimated in the Lancaster study are examined. Despite the smaller size of construction multipliers it is argued that it is a serious mistake to estimate local construction multipliers by making simplifying assumptions on the size of the key parameters in the multiplier equations.

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