scholarly journals On the Moment Problem and Related Problems

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2289
Author(s):  
Octav Olteanu
Keyword(s):  
Moment Problem ◽  
Borel Measure ◽  
Truncated Moment Problem ◽  
Regular Borel Measure ◽  
The Subject ◽  
Markov Moment ◽  
The Moment ◽  
Adjoint Operators ◽  
Classical Moment Problem ◽  
Unknown Solution

Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence (yj)j∈ℕn  of real numbers and a closed subset F⊆ℝn, n∈{1,2,…}, find a positive regular Borel measure μ on F such that ∫Ftjdμ=yj, j∈ℕn. This is the full moment problem. The existence, uniqueness, and construction of the unknown solution μ are the focus of attention. The numbers yj, j∈ℕn are called the moments of the measure μ. When a sandwich condition on the solution is required, we have a Markov moment problem. Secondly, we study the existence and uniqueness of the solutions to some full Markov moment problems. If the moments yj are self-adjoint operators, we have an operator-valued moment problem. Related results are the subject of attention. The truncated moment problem is also discussed, constituting the third aim of this work.

scholarly journals New Results on Markov Moment Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Octav Olteanu
Keyword(s):  
Moment Problem ◽  
Sufficient Conditions ◽  
Linear Operators ◽  
Moment Problems ◽  
Finite Dimensional ◽  
Integrable Functions ◽  
Truncated Moment Problem ◽  
Markov Moment ◽  
The Moment ◽  
Necessary And Sufficient

The present work deals with the existence of the solutions of some Markov moment problems. Necessary conditions, as well as necessary and sufficient conditions, are discussed. One recalls the background containing applications of extension results of linear operators with two constraints to the moment problem and approximation by polynomials on unbounded closed finite-dimensional subsets. Two domain spaces are considered: spaces of absolute integrable functions and spaces of analytic functions. Operator valued moment problems are solved in the latter case. In this paper, there is a section that contains new results, making the connection to some other topics: bang-bang principle, truncated moment problem, weak compactness, and convergence. Finally, a general independent statement with respect to polynomials is discussed.

scholarly journals On the Truncated Multidimensional Moment Problems in Cn

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Sergey Zagorodnyuk
Keyword(s):  
Integral Representation ◽  
Finite Subset ◽  
Moment Problem ◽  
Complex Numbers ◽  
Moment Problems ◽  
Linear Functionals ◽  
Truncated Moment Problem ◽  
The Moment ◽  
Multidimensional Moment Problem ◽  
Multidimensional Moment Problems

We consider the problem of finding a (non-negative) measure μ on B(Cn) such that ∫Cnzkdμ(z)=sk, ∀k∈K. Here, K is an arbitrary finite subset of Z+n, which contains (0,…,0), and sk are prescribed complex numbers (we use the usual notations for multi-indices). There are two possible interpretations of this problem. Firstly, one may consider this problem as an extension of the truncated multidimensional moment problem on Rn, where the support of the measure μ is allowed to lie in Cn. Secondly, the moment problem is a particular case of the truncated moment problem in Cn, with special truncations. We give simple conditions for the solvability of the above moment problem. As a corollary, we have an integral representation with a non-negative measure for linear functionals on some linear subspaces of polynomials.

Crimes against marriage and family before Criminal Code 1968

2020 ◽  
Vol 15 (1-3) ◽  
pp. 44-59
Author(s):  
Lidia Peneva
Keyword(s):  
Criminal Code ◽  
Point Of View ◽  
Marriage And Family ◽  
Historical Method ◽  
Legal Method ◽  
The Subject ◽  
The Republic ◽  
Criminal Groups ◽  
The Moment ◽  
Structural Point

Crimes against marriage and family are a particular group of social relation­ships that the law has defended properly in view of the high public significance and value they enjoy. At the moment they are regulated in Chapter VI, Section I, of the specific part of the Penal Code the Repub­lic of Bulgaria. The subject matter of this Statement will, however, be the legisla­tive provisions concerning these criminal­ized acts in retrospect. The purpose of the study is to show by historical method and through the comparatively legal method the development of these criminal groups during the periods of various criminal laws in Bulgaria. This will also provide a basis for reflection on possible de lege ferenda proposals. This report from a structural point of view will be divided into three distinct points, marking each of the penal laws in the Republic of Bulgaria, which were in force before 1968.

scholarly journals Cartilage Injuries and Posttraumatic Osteoarthritis in the Wrist: A Review

Cartilage ◽  
2021 ◽  
pp. 194760352110219
Author(s):  
Jonny K. Andersson ◽  
Elisabet Hagert ◽  
Mats Brittberg
Keyword(s):  
Literature Review ◽  
Radius Fractures ◽  
Osteochondral Autograft ◽  
Posttraumatic Osteoarthritis ◽  
Osteochondral Repair ◽  
Chondrocyte Implantation ◽  
Cartilage Injuries ◽  
The Subject ◽  
The Moment ◽  
And Cartilage

Objective: Focal cartilage injuries, and posttraumatic osteoarthritis (OA) in the wrist are likely common and a cause of wrist pain. To estimate the incidence of cartilage lesions and to understand the pathomechanisms leading to wrist cartilage injuries and OA, a literature review on the subject was performed combined with a presentation of one of the authors’ own experience. Design: This study includes a literature review of the topic. As a comparison to the review findings, the observations of one of the authors’ consecutive 48 wrist arthroscopies, were assessed. PubMed, Scholar, and Cochrane databases were searched using the keywords “cartilage injury AND wrist AND treatment” and “wrist AND cartilage AND chondral AND osteochondral AND degenerative OA.” :Result A total of 11 articles, including 9 concerning chondral and osteochondral repair and treatment and 2 regarding posttraumatic OA, were retrieved. The cartilage repair treatments used in these articles were drilling, osteochondral autograft, juvenile articular cartilage allograft, and chondrocyte implantation. One article displayed concomitant cartilage injuries in displaced distal radius fractures in 32% of the patients. The review of our findings from a 1-year cohort of wrist arthroscopies showed 17% cartilage injuries. Conclusion: There is a lack of knowledge in current literature on cartilage injuries and treatment, as well as posttraumatic OA in the wrist. Cartilage injuries appear to be common, being found in 17% to 32% of all wrist arthroscopies after trauma, but no guidelines regarding conservative or surgical treatment can be recommended at the moment. Larger prospective comparative studies are needed.

The moment problem on perfect hypergroups

2016 ◽  
Vol 29 (2) ◽  
pp. 232-236
Author(s):  
A. S. Okb El Bab ◽  
Hossam A. Ghany
Keyword(s):  
Moment Problem ◽  
The Moment

scholarly journals On the moment problem for a finite interval

1932 ◽  
Vol 38 (4) ◽  
pp. 269-271 ◽  
Author(s):  
T. H. Hildebrandt
Keyword(s):  
Moment Problem ◽  
Finite Interval ◽  
The Moment

scholarly journals The multidimensional truncated moment problem: Carathéodory numbers

2018 ◽  
Vol 461 (2) ◽  
pp. 1606-1638
Author(s):  
Philipp J. di Dio ◽  
Konrad Schmüdgen
Keyword(s):  
Moment Problem ◽  
Truncated Moment Problem

Social capital in the theory and research of LIS professionals in the light of the literature on the subject. Review of current knowledge

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Maja Dorota Wojciechowska
Keyword(s):  
Social Capital ◽  
Current Knowledge ◽  
Future Research ◽  
Content Type ◽  
Individual Social Capital ◽  
Rural Libraries ◽  
The Subject ◽  
The Moment ◽  
The Impact

Purpose The purpose of the paper is to present the latest scholarly trends in the field of social capital in libraries, to review research concepts published by LIS professionals and to suggest further research possibilities in this area. Design/methodology/approach This paper presents a review and critical analysis of literature associated with research on social capital in libraries to highlight its importance for the development of LIS and its impact on the functioning of environments linked with various types of libraries. The goal of literature analysis was to determine the current condition of research on social capital in libraries. The main trends were identified and the need for further qualitative analyses, which are missing at the moment, was confirmed. Findings It was determined that, so far, LIS professionals have focussed mainly on the role of municipal libraries in developing social capital, the problem of building trust, especially in immigrant circles and the impact of libraries on promoting a civil society. Academic libraries, rural libraries, organisational capital in libraries and individual social capital of librarians were a much less frequent subject of research. The role of libraries in developing social capital in educational (primary and secondary education) and professional (non-university professionals) circles is practically non-existent in research, and it will require in-depth studies and analyses in the coming years. Originality/value This paper constitutes a synthetic review of the latest research concepts concerning social capital in libraries. It identifies the most important research trends and areas that so far have not been explored and suggests research methods to help LIS professionals design future research in this area more effectively.

To the Matter of Procedural and Legal Problems of Detaining a Person on Suspicion of Committing a Crime

2021 ◽  
Author(s):  
E.V. Bolshakov ◽  
◽  
I.D. Nazarov ◽  
Keyword(s):  
Russian Federation ◽  
Criminal Procedure ◽  
Criminal Case ◽  
Judicial Practice ◽  
Procedure Code ◽  
Legal Nature ◽  
The Status ◽  
The Subject ◽  
The Russian Federation ◽  
The Moment

The subject of the research within the framework of the article is the criminal procedure institute for the detention of a person on suspicion of committing a crime. The legal nature of this institution is analyzed, and comments are given on the normative legal acts and judicial practice regulating the issues of detention. The theoretical basis of the research is based on the publications of the last two decades on this problem, in particular, reflecting the discussion of the process scientists S. A. Shafer, S. B. Rossinsky and A. A. Tarasov, the subject of which was the issue of the legal nature of a suspect detention in a criminal case. In the paper, the authors ask the following questions: What is the detention of a person on suspicion of committing a crime in accordance with the legislation of the Russian Federation? From what moment does the detained person acquire the status of a suspect? Is it possible to detain a person before initiating a criminal case? The study concludes that a person acquires the actual status of a suspect from the moment of direct detention, that is, before documenting this status and, as a result, before initiating a criminal case. Amendments to the articles of the Criminal Procedure Code of the Russian Federation are proposed, and the authors` versions of the definitions of the concepts «detention of a suspect», «the moment of actual detention» and «pre-trial proceedings» are given.

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