scholarly journals On one interpolating rational process of Fejer – Hermite

2020 ◽  
Vol 56 (3) ◽  
pp. 263-274
Author(s):  
Ya. A. Rouba ◽  
K. A. Smatrytski ◽  
Ya. V. Dirvuk
Keyword(s):  
Numerical Analysis ◽  
Continuous Function ◽  
Approximation Theory ◽  
Complex Variable ◽  
Arbitrary Function ◽  
Rational Functions ◽  
New Approach ◽  
Definition Of ◽  
Rational Process ◽  
Made In

In this paper, a new approach to the definition of the interpolating rational process of Fejer – Hermite with first-type Chebyshev – Markov nodes on a segment is studied and some of its approximating properties are described. In the introduction a brief analysis of the results on the topic of the research is carried out. Herein, the methods of the construction of interpolating processes, in particular, Fejer – Hermite processes, in the polynomial and rational approximation are analysed. A new method to determine the interpolating rational Fejer – Hermite process is proposed. One of the main results of this paper is the proof of the uniform convergence of this process for an arbitrary function, which is continuous on the segment, under some restrictions for the poles of approximating functions. This result is preceded by some auxiliary statements describing the properties of special rational functions. The classic methods of mathematical analysis, approximation theory, and theory of functions of a complex variable are used to prove the results of the work. Moreover, we present the numerical analysis of the effectiveness of the application of the constructed interpolating Fejer – Hermite process for the approximation of a continuous function with singularities. The choice of parameters, on which the nodes of interpolation depend, is made in several standard ways. The obtained results can be applied to further study the approximating properties of interpolating processes.

scholarly journals On one generalization of the Hermite quadrature formula

2021 ◽  
Vol 57 (3) ◽  
pp. 319-329
Author(s):  
Y. A. Rouba ◽  
K. A. Smatrytski ◽  
Y. V. Dirvuk
Keyword(s):  
Numerical Analysis ◽  
Approximation Theory ◽  
Complex Variable ◽  
Jacobi Polynomials ◽  
Rational Functions ◽  
Quadrature Formulas ◽  
New Approach ◽  
Rational Chebyshev ◽  
Rational Type ◽  
Made In

In this paper we propose a new approach to the construction of quadrature formulas of interpolation rational type on an interval. In the introduction, a brief analysis of the results on the topic of the research is carried out. Most attention is paid to the works of mathematicians of the Belarusian school on approximation theory – Gauss, Lobatto, and Radau quadrature formulas with nodes at the zeros of the rational Chebyshev – Markov fractions. Rational fractions on the segment, generalizing the classical orthogonal Jacobi polynomials with one weight, are defined, and some of their properties are described. One of the main results of this paper consists in constructing quadrature formulas with nodes at zeros of the introduced rational fractions, calculating their coefficients in an explicit form, and estimating the remainder. This result is preceded by some auxiliary statements describing the properties of special rational functions. Classical methods of mathematical analysis, approximation theory, and the theory of functions of a complex variable are used for proof. In the conclusion a numerical analysis of the efficiency of the constructed quadrature formulas is carried out. Meanwhile, the choice of the parameters on which the nodes of the quadrature formulas depend is made in several standard ways. The obtained results can be applied for further research of rational quadrature formulas, as well as in numerical analysis.

A New Approach for the Geotechnical Zoning of the Rights of Way

2019 ◽  
Author(s):  
Julian Chaves Agudelo ◽  
Jaime Aristizabal Ceballos ◽  
Carlos Motta Tierradentro ◽  
Juan Alvarado Franco
Keyword(s):  
Land Use ◽  
Natural Hazards ◽  
National Scale ◽  
Technical Literature ◽  
New Approach ◽  
Technological Tools ◽  
Definition Of ◽  
Made In

Abstract Usually, the definition of geotechnically homogeneous zones is established through the analysis of information on a regional (and even national) scale of those characteristics that define the topographic, geological, climatic, and land use conditions by categorizing them and applying algorithms of interaction between these variables. However, in technical literature and in technical reports of state entities that manage natural hazards, new advances are being made in the determination of other aspects or variables that detail the condition of geotechnical susceptibility; at the same time, nowadays there are technological tools for the massive analysis of information and its spatialization. This article presents a new approach to the definition of geotechnically homogeneous zones using these technological tools. A comparison is made against the conventional definition.

scholarly journals A new approach to the notion of political risk: concept and definition

Moldoscopie ◽  
2021 ◽  
Author(s):  
Tatiana Alymova ◽  
Keyword(s):  
Political Risk ◽  
Investment Climate ◽  
New Approach ◽  
The Face ◽  
Ancient Times ◽  
Points Of View ◽  
Definition Of ◽  
Political Actions ◽  
Time Information ◽  
Made In

Since the ancient times we found the references on risk, starting from the Greek tragedies that narrate about risk as a phenomenon which is accompanied by uncertainty in decision-making process. In the Renaissance era when people dropped many inhibitions and questioned old beliefs and points of view then a serious study of problem starts. This article is about the theoretical analysis of political risk. Points of view of Russian and other foreign researches are included in this article. The article contains the definition of political risk by different representatives, of the political risk influence on investment climate, of likelihood of adverse consequences in political decisions that were made in the face of uncertainty, when recourses are scarce, (in time, information and other), which leads to prejudice for the members of political actions and leads to unwanted events. In the conclusion, the author tries to give its own definition of political risk.

Seeing, imagined, and lived

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Anandi Silva Knuppel
Keyword(s):  
Sensory Experience ◽  
Religious Practices ◽  
Daily Lives ◽  
New Approach ◽  
Theories Of Practice ◽  
Sources Of Authority ◽  
Definition Of

Scholarship on Hindu traditions and practices proposes the practice of darshan as fundamental to Hindu traditions, particularly in temple worship, observing that devotees seek out images of deities primarily to see them and “receive” their darshan. These works typically gloss the definition of darshan with a sentence or two about seeing, exchanging glances, and/or receiving blessings. In this paper, I focus on the ways in which darshan is ideally imagined in conjunction with other bodily sensory practices through sources of authority, such as texts and senior devotees, to create a specific sensory experience and expectation in the transnational Gaudiya Vaishnava community. I then look to the lived realitiesof darshan in this tradition, specifically how devotees negotiate the structures created through sources of authority in their daily lives. Through this juxtaposition of idealized and lived darshan, I argue that we need a new approach towards theories of practice to take into account the complexities of darshanic moments in this and other religious practices.

Need of Human Rights as a Better Way of Life

Think India ◽  
2019 ◽  
Vol 22 (3) ◽  
pp. 72-83
Author(s):  
Tushar Kadian
Keyword(s):  
Human Rights ◽  
Basic Needs ◽  
Research Paper ◽  
Human Being ◽  
Way Of Life ◽  
Labour Unions ◽  
The People ◽  
The Subject ◽  
Definition Of ◽  
Made In

Actually, basic needs postulates securing of the elementary conditions of existence to every human being. Despite of the practical and theoretical importance of the subject the greatest irony is non- availability of any universal preliminary definition of the concept of basic needs. Moreover, this becomes the reason for unpredictability of various political programmes aiming at providing basic needs to the people. The shift is necessary for development of this or any other conception. No labour reforms could be made in history till labours were treated as objects. Its only after they were started being treating as subjects, labour unions were allowed to represent themselves in strategy formulations that labour reforms could become a reality. The present research paper highlights the basic needs of Human Rights in life.

scholarly journals A dominated convergence theorem for Eisenstein series

2021 ◽  
Author(s):  
Johann Franke
Keyword(s):  
Fourier Series ◽  
Dirichlet Series ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Convergence Theorem ◽  
Rational Functions ◽  
New Approach ◽  
Series Representations ◽  
Dominated Convergence ◽  
Generalized Dirichlet

AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.

Defining hormesis: the necessary tool to clarify experimentally the low dose–response relationship

2002 ◽  
Vol 21 (2) ◽  
pp. 103-104 ◽  
Author(s):  
G Carelli ◽  
I Iavicoli
Keyword(s):  
Dose Response ◽  
Low Dose ◽  
Experimental Models ◽  
Assessment Criteria ◽  
Response Relationship ◽  
Dose Response Relationship ◽  
Specific Context ◽  
Definition Of ◽  
Time Specific ◽  
Made In

The authors comment on Calabrese and Baldwin's paper ‘Defining Hormesis’, which, to date, is the first attempt to provide a definition of hormesis that goes beyond the different interpretations of this phenomenon reported in the literature. While appreciating the effort made in this study to place hormesis in a general and at the same time specific context, the authors believe some clarifications are needed as regards the quantitative features of this phenomenon. In this connection, they speculate on whether Calabrese and Baldwin think it appropriate to include hormesis assessment criteria in the document, referring in particular to those reported in a previous paper. The authors share Calabrese and Baldwin's conclusion that future experimental models designed to study hormetic phenomena must necessarily include the time factor, which not only guarantees this phenomenon will be detected, but is also able to detect the specific type of hormesis.

The construction of units in conversational talk

2000 ◽  
Vol 29 (4) ◽  
pp. 477-517 ◽  
Author(s):  
MARGRET SELTING
Keyword(s):  
Conversation Analysis ◽  
Activity Type ◽  
Seminal Work ◽  
Conversational Context ◽  
Linguistic Unit ◽  
Definition Of ◽  
Made In

The notion of Turn-Constructional Unit (TCU) in Conversation Analysis has become unclear for many researchers. The underlying problems inherent in the definition of this notion are here identified, and a possible solution is suggested. This amounts to separating more clearly the notions of TCU and Transition Relevance Place (TRP). In this view, the TCU is defined as the smallest interactionally relevant complete linguistic unit, in a given context, that is constructed with syntactic and prosodic resources within their semantic, pragmatic, activity-type-specific, and sequential conversational context. It ends in a TRP unless particular linguistic and interactional resources are used to project and postpone the TRP to the end of a larger multi-unit turn. This suggestion tries to spell out some of the assumptions that the seminal work in CA made in principle, but never formulated explicitly.

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