GENERALIZ GENERALIZATION OF THE H TION OF THE HARDY CLASS FOR AN ASS FOR ANALYTIC FUNCTIONS

2021 ◽  
Vol 5 (4) ◽  
pp. 29-46
Author(s):  
Behzod Husenov ◽  
Keyword(s):  
Research Methods ◽  
Analytic Functions ◽  
Function Theory ◽  
Beltrami Equation ◽  
Analytic Solutions ◽  
Conformal Mappings ◽  
Point Of View ◽  
Hardy Class ◽  
Literature Research ◽  
Almost Everywhere

Introduction. Quoting from a well-known American mathematician Lipman Bers [1] “It would be tempting to rewrite history and to claim that quasiconformal transformations have been discovered in connection with gas-dynamical problems. As a matter of fact, however, the concept of quasiconformality was arrived at by Grotzsch [2] and Ahlfors [3] from the point of view of function theory”. The present work is devoted to the theory of analytic solutions of the Beltrami equation which directly related to the quasi-conformal mappings. The function is, in general, assumed to be measurable with almost everywhere in the domain under consideration. Solutions of equation (1) are often referred to as analytic functions in the literature. Research methods.

scholarly journals Virtual Element Method for the Laplace-Beltrami equation on surfaces

2018 ◽  
Vol 52 (3) ◽  
pp. 965-993 ◽  
Author(s):  
Massimo Frittelli ◽  
Ivonne Sgura
Keyword(s):  
Numerical Experiments ◽  
Beltrami Equation ◽  
Convergence Result ◽  
Point Of View ◽  
Polygonal Approximation ◽  
Virtual Element Method ◽  
Element Space ◽  
First Order ◽  
Virtual Element ◽  
Element Method

We present and analyze a Virtual Element Method (VEM) for the Laplace-Beltrami equation on a surface in ℝ3, that we call Surface Virtual Element Method (SVEM). The method combines the Surface Finite Element Method (SFEM) (Dziuk, Eliott, G. Dziuk and C.M. Elliott., Acta Numer. 22 (2013) 289–396.) and the recent VEM (Beirão da Veiga et al., Math. Mod. Methods Appl. Sci. 23 (2013) 199–214.) in order to allow for a general polygonal approximation of the surface. We account for the error arising from the geometry approximation and in the case of polynomial order k = 1 we extend to surfaces the error estimates for the interpolation in the virtual element space. We prove existence, uniqueness and first order H1 convergence of the numerical solution.We highlight the differences between SVEM and VEM from the implementation point of view. Moreover, we show that the capability of SVEM of handling nonconforming and discontinuous meshes can be exploited in the case of surface pasting. We provide some numerical experiments to confirm the convergence result and to show an application of mesh pasting.

scholarly journals Conditions for a Dialogue of Local Community and Genius Loci

2018 ◽  
Vol 14 (1) ◽  
pp. 70-74
Author(s):  
Vytautas Petrušonis
Keyword(s):  
Research Methods ◽  
Local Community ◽  
Semantic Analysis ◽  
Point Of View ◽  
Community Dialogue ◽  
Cultural Ecological

Abstract The research focuses on local community dialogue with genius loci as certain subjectivity of urbanized environment. The following research methods were used: abstraction, analogy, generalization, synthesis, and semantic analysis. Sets of informational units as system of genius loci symptoms, offered in this article, can be used for the presentation of genius loci. Such data figure as network of knowledge highlighted from a cultural-ecological point of view. Some traits of genius loci of Lentvaris manor park are presented.

scholarly journals Factors that affect public relations practice: in the case of Tigray Education Bureau

2020 ◽  
Vol 9 ◽  
pp. 184-194
Author(s):  
Solomon Shiwabaw Mulu
Keyword(s):  
Public Relations ◽  
Research Methods ◽  
Quantitative Research ◽  
Sampling Method ◽  
Point Of View ◽  
Disciplinary Boundaries ◽  
The Public ◽  
Tigray Region ◽  
Qualitative Research Design ◽  
Reporting Method

Public relations practice is a profitable interpretation of an organization's new and continuous relationship with stakeholders, including customers, by managing all communication relationships with the organization that creates the reputation and protects its reputation [5]. The researcher has employed mixed research methods. Mixed approaches are far more compressive than attacking a problem one point of view and allow a different type of data to be accessed from disciplinary boundaries. Employing a purposive sampling method, a total of 7 PR officers of the Tigray region education Bureau and the Public relations Manager of the respective Bureau have been selected. An interview and questionnaires have been employed to gather data. After the researcher has collected the relevant data using the mixed research methods it has been analyzed. The data which was gathered using a quantitative research method has been analyzed and interpreted in a table and report in percentage with sufficient explanation for each table result and percentages using SPSS data analyzing software. Besides, the gathered data using a qualitative research design was analyzed in the reporting method with elaboration.

scholarly journals On the Relation between a Cluster set Introduced by Constantinescu and Cornea, and the Fine Cluster set of Cartan, Brelot, and Naïm

1965 ◽  
Vol 8 (1) ◽  
pp. 59-71
Author(s):  
H. L. Jackson
Keyword(s):  
Analytic Function ◽  
Holomorphic Function ◽  
Limit Theorems ◽  
Function Theory ◽  
Angular Limit ◽  
Boundary Limit ◽  
Cluster Set ◽  
Almost Everywhere ◽  
Bounded Holomorphic Function ◽  
Bounded Holomorphic

The field of boundary limit theorems in analytic function theory is usually considered to have begun about 1906, with the publication of Fatou's thesis [8]. In this remarkable memoir a theorem is proved, that now bears the author's name, which implies that any bounded holomorphic function defined on the unit disk possesses an angular limit almost everywhere (Lebesgue measure) on the frontier. Outstanding classical contributions to this field can be attributed to F. and M. Riesz, R. Nevanlinna, Lusin, Privaloff, Frostman, Plessner, and others.

XXIV.—The Solution of a Functional Equation

1952 ◽  
Vol 63 (4) ◽  
pp. 336-345
Author(s):  
A. H. Read
Keyword(s):  
Functional Equation ◽  
Recurrence Relation ◽  
Unknown Function ◽  
Analytic Functions ◽  
Analytic Solutions ◽  
Sequence Of Functions

SynopsisAnalytic solutions of the functional equation f[z, φ{g(z)}] = φ(z), in which f(z, w) and g(z) are given analytic functions and φ(z) is the unknown function, are investigated in the neighbourhood of points ζ such that g(ζ) = ζ. Conditions are established under which each solution φ(z) may be given as the limit of a sequence of functions φn(z), defined by the recurrence relation φn+1(Z) = ƒ[z, φn{g(z)}], the function φn(z) being to a large extent arbitrary.

scholarly journals Scientific methods of public administration in migration research

2020 ◽  
Vol 68 (2) ◽  
pp. 109-122
Author(s):  
András László Szabó
Keyword(s):  
Public Administration ◽  
Research Methods ◽  
Methodological Approach ◽  
Point Of View ◽  
Scientific Methods ◽  
Migration Research ◽  
Independent Field ◽  
The Subject ◽  
The Given ◽  
Insight Into

In my study, I list the directions of migration research, all from the point of view of public administration science. The emergence of migration research as an independent field is necessitated by the growth of migration. Researchers are researching the phenomenon of migration from their own field. Public administration uses a multidisciplinary, i.e. methodological approach of several disciplines, all of which is determined by the knowledge and nature of the subject of the given research. In the following, I review and evaluate the methodological directions of the research, which can provide an answer to a segment of the phenomenon of migration. The study gives an insight into research methods for migration research. It is not intended to present specific examples and procedures. At the end of the study, in possible directions, beyond the science of public administration, I list the organizations and faculties that are able to use the methodology of migration research.

scholarly journals Free Function Theory Through Matrix Invariants

2017 ◽  
Vol 69 (02) ◽  
pp. 408-433 ◽  
Author(s):  
Igor Klep ◽  
Špela Špenko
Keyword(s):  
Power Series ◽  
Analytic Functions ◽  
Function Theory ◽  
Rational Functions ◽  
Generalized Polynomials ◽  
Direct Sums ◽  
Real Analytic Functions ◽  
Power Series Expansions ◽  
Noncommutative Polynomials ◽  
Free Function

Abstract This paper concerns free function theory. Freemaps are free analogs of analytic functions in several complex variables and are defined in terms of freely noncommuting variables. A function of g noncommuting variables is a function on g-tuples of square matrices of all sizes that respects direct sums and simultaneous conjugation. Examples of such maps include noncommutative polynomials, noncommutative rational functions, and convergent noncommutative power series. In sharp contrast to the existing literature in free analysis, this article investigates free maps with involution, free analogs of real analytic functions. To get a grip on these, techniques and tools from invariant theory are developed and applied to free analysis. Here is a sample of the results obtained. A characterization of polynomial free maps via properties of their finite-dimensional slices is presented and then used to establish power series expansions for analytic free maps about scalar and non-scalar points; the latter are series of generalized polynomials for which an invarianttheoretic characterization is given. Furthermore, an inverse and implicit function theorem for free maps with involution is obtained. Finally, with a selection of carefully chosen examples it is shown that free maps with involution do not exhibit strong rigidity properties enjoyed by their involutionfree counterparts.

An Application of Base-Three Numeration

1967 ◽  
Vol 60 (8) ◽  
pp. 858-859
Author(s):  
John L. Ginther
Keyword(s):  
Function Theory ◽  
Point Of View ◽  
Elementary Level ◽  
Numeration System ◽  
Potential Benefits

From a pedagogical point of view, it is desirable to be able to show a subtle relationship between two pieces of mat hematics that are seemingly unrelated. When such a relationship can be shown at a rather elementary level and when the “marriage” helps to analyze still another interesting question, the potential benefits to the teacher are great. Such a situation will be described in this paper. It involves the use of the base-three positional numeration system in analyzing some topics from function theory.

scholarly journals I’jaz Al-Qur’an Ditinjau dari Aspek Ilmu Bahasa

2021 ◽  
Vol 18 (2) ◽  
pp. 116
Author(s):  
Sulaiman Sulaiman
Keyword(s):  
Research Methods ◽  
Point Of View ◽  
Library Research ◽  
The People ◽  
Stylistic Elements ◽  
Linguistic Dimension

Scholars have used various approaches to understand the Qur'an because of its two main dimensions: the linguistic dimension and its content. Those are a great combination that cannot be matched by anyone, even though all have gathered to match it. One such approach is the stylistic approach. Al-Qur'an has a high uslub/style of language so that it becomes one of its miraculous elements. This study aim to reviewing Surah al-'Ādiyāt using a stylistic approach with library research methods. Surah al-'Ādiyāt, from the point of view of the balaghah holds a myriad of secrets, which can be classified into beautiful uslub. Likewise, from a stylistic point of view, although only in a few lines, the stylistic elements can be obtained beautifully. People who oppose the Qur'an from the polytheists or the People of the Book can slowly be conquered by the beauty of the language of the Qur'an. This is one of the methods of preaching the Prophet Muhammad SAW by prioritizing the elements of beauty.ABSTRAKBerbagai pendekatan telah digunakan oleh para ilmuan untuk memahami al-Qur’an, karena dua dimensi utamanya yaitu dimensi kebahasaan dan kandungannya adalah sebuah perpaduan yang sangat agung yang tak dapat ditandingi oleh siapapun, walaupun semuanya berkumpul untuk menandinginya. Salah satu pendekatan tersebut adalah pendekatan stilistika. al-Qur’an memilki uslub/gaya bahasa yang tinggi sehingga menjadi salah satu unsur kemu’jizatannya. Dalam mengkaji Surah al-‘Ādiyāt dengan menggunakan pendekatan Stilistika, penulis menggunakan metode penelitian kepustakaan (library research). Surah al-‘Ādiyāt, dari sudut pandang balaghah menyimpan segudang rahasia, yang dapat digolongkan ke dalam uslub yang indah. Demikian juga dari sudut pandang stilistika, walaupun hanya dalam beberapa baris saja, namun elemen-elemen stilistika telah dapat didapatkan dengan indahnya. Orang-orang yang menentang al-Qur’an dari golongan musyrikin atau Ahlil Kitab, secara pelan-pelan dapat ditaklukkan oleh keindahan bahasa al-Qur’an. Inilah salah satu metode dakwah Rasulullah Saw. dengan mengedepankan unsur-unsur keindahan

scholarly journals ARTIFICIAL INTELLIGENCE VERSUS PUBLIC ADMINISTRATION: LIMITATIONS OF APPLICATION

2019 ◽  
Vol 7 (3) ◽  
pp. 516-520
Author(s):  
Petr M. Morkhat ◽  
Igor V. Ponkin ◽  
Marina V. Markhgeym ◽  
Vladimir K. Botnev ◽  
Aidyn O. Turganbayev
Keyword(s):  
Artificial Intelligence ◽  
Public Administration ◽  
Research Methods ◽  
System Analysis ◽  
The State ◽  
Point Of View ◽  
Existing Problems ◽  
The Future ◽  
Long Time ◽  
Systemic Problems

Purpose of Study: The present study was designed to study possibilities, conditions, grounds and limitations regarding the use of technologies and units of artificial intelligence in public administration. Determinants of the need to use such technologies in public administration were also considered. In this study, directions of realizable engagement which is already implemented, as well as directions of the possible use of artificial intelligence units in the future for public administration were investigated to ensure the functioning of system of state executive bodies. Methodology: The present research carried out based on the application of research methods such as system analysis, synthesis, and classification. Using these research methods, the concepts of describing conditions, possibilities, modes and functional-target load of using technologies and units of artificial intelligence in public administration, as well as limitations of its application in public administration were developed. Results: It was found that the use of artificial intelligence by the state for performing its various own tasks is highly relevant as it might lead to finding many positive approbations. However, despite the fact that technologies and artificial intelligence units have been developed for a relatively long time, and some of them are already widely used, it is still impossible to talk about the integrated, fully tested and properly regulated implementation of this kind of technology and units for management, therefore, it is suggested to further investigate on this issue from a theoretical (prognostic) point of view, taking into account potential directions and possibilities regarding    the use of such technology and units. Implications/Applications: The use of technologies and units of artificial intelligence does not necessarily take into account as a panacea for solving the problems and may not lead to solving some systemic problems in public administration, but, on the contrary, may even aggravate some existing problems in public administration and contribute to the emergence of new problems and risks.

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