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An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions
Get PDFAn initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are
concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICTinSES)”, contract No DO1–205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria
A Guide to Special Functions in Fractional Calculus
Get PDFDedicated to the memory of Professor Richard Askey (1933-2019) and to pay tribute to the Bateman Project. Harry Bateman planned his project (accomplished after his death as Higher Transcendental Functions, Vols. 1-3, 1953-1955, under the editorship by A. Erdelyi) as a "Guide to the Functions". This inspired the author to use the modified title of the present survey. Most of the standard (classical) Special Functions are representable in terms of the Meijer G-function and, specially, of the generalized hypergeometric functions pFq. These appeared as solutions of differential equations in mathematical physics and other applied sciences that are of integer order, usually of second order. However, recently, mathematical models of fractional order are preferred because they reflect more adequately the nature and various social events, and these needs attracted attention to "new" classes of special functions as their solutions, the so-called Special Functions of Fractional Calculus (SF of FC). Generally, under this notion, we have in mind the Fox H-functions, their most widely used cases of the Wright generalized hypergeometric functions pΨq and, in particular, the Mittag-Leffler type functions, among them the "Queen function of fractional calculus", the Mittag-Leffler function. These fractional indices/parameters extensions of the classical special functions became an unavoidable tool when fractalized models of phenomena and events are treated. Here, we try to review some of the basic results on the theory of the SF of FC, obtained in the author's works for more than 30 years, and support the wide spreading and important role of these functions by several examples
Constructive Noncommutative Invariant Theory
Get PDFThe problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.ELKH Alfréd Rényi Institute of Mathematic
Seventieth Anniversary of Professor Vesselin Stoyanov Drensky
No full textThis article provides a short description of the life and the activities of the outstanding Bulgarian mathematician Vesselin Stoyanov Drensky. It has been written in connection with his seventieth anniversary.Тази статия е кратко описание на живота и дейностите на изтъкнатия български математик Веселин Стоянов Дренски. Написана е във връзка със 70-годишнината от неговото раждане
ИКТ инструментариум за иновативни методи и приложения в образователния процес
Get PDFИМИ-БАН, 25.02.2021 г., присъждане на образователна и научна степен "доктор" на Орлин Иванов Кузов. [Kuzov Orlin Ivanov; Кузов Орлин Иванов
Предложни наречия
Get PDFНаречията са една от най-интересните категории на езика по състав, морфологична характеристика, синтактична функция, произход, употреба и други. Погледът към тях с оглед на правописа и на значението им показва, че има редица противоречия. В работата се разглеждат сложните според българските граматики наречия, образувани с предлозипредставки НА, ОТ, ДО в пет речника на българския език и се изказват препоръки относно писането им. Изследването е базирано върху 20 наречия, извадени от Официалния правописен речник на българския език (ОПРБЕ), допълнени с някои други, свързани с нашата цел.Adverbs are one of the most intriguing categories of language in terms of composition, morphological characteristics, syntactic function, origin, usage and others. When we look at the spelling and meanings closely, number of contradictions are found. The paper examines compound adverbs in Bulgarian grammar which are formed with particularly prepositional prefix such as "НА; ОТ; ДО". The examination was carried out according to five dictionaries of the Bulgarian language and based on 20 adverbs from the Official Spelling Bulgarian Dictionary (ОПРБЕ) additionally including other adverbs related to the final goal
Регистриране и обработка на фотоплетизмографски сигнали
Get PDFHeart rate variability (HRV) is a non-invasive indicator of the condition of the cardiovascular system. To calculate HRV, the time between two adjacent R peaks of the electrocardiogram of the individual is used, i.e. between two heartbeats. This method requires the placement of electrodes in certain places on the body of the individual. An alternative way to measure heart rate is to use the change in blood volume in the blood vessels, through optical method, so-called photoplethysmography. It is based on the measurement of the change in light absorption depending on the amount of blood in the blood vessels. This article discusses ways to capture photoplethysmographic signals and convert them into data suitable for further processing. Graphs of the data from experimental studies at different stages of their processing are presented.Научното изследване е проведено като част от проекта „Изследване на приложението на нови математически методи за анализ на кардиологични данни“ № КП-06-Н22/5 от 07.12.2018г., финансиран от Фонд „Научни Изследвания“
Изследване на достъпността на някои често използвани среди за разработка на програмно осигуряване
Get PDFThe object of this article is to discuss some problems, that hav low vision developers using some frequently use rapid application development environments. Particular attention is payd to those of them, that have free versions or are use by high schools and special secondary schools. Accessibility level of main menu, submenus, settings dialog boxes, text edit tools, diagnostic and debugging addressed interface are measure.
Made reference, that summary accessibility level of development environment DEV-C++ does not allow effective work by using screen readers and braille displays. As better is estimated accessibility level of Microsoft Visual Studio, but, mention may here be made of some important components (related to creating GUI and database projects) are fully inaccessible. So, blind developer can without somebody else help create console applications only. Development environment C++ Builder is closely discussed, because by working with it using screen readers and braille displays problems mentioned before does not exist. The circumstance, that this development environment is out-of-date, is not omitted, so it have not any contrivances to develop 64 bit applications and applications for Android.
The article says, that software tools for developers has low level of accessibility, then applications addressed to generally use.Изследването е частично финансирано по проект „Дигитална достъпност за хора със специални потребности: методология, концептуални модели и иновативни екосистеми“ чрез договор №КП-06-Н42/4 от 08.12.2020 г. с фонд „Научни изследвания“ на Република България
Създаване на модели на сериозни образователни игри с приложение в медицинското обучение
Get PDFThe report presents the serious educational games in the field of medicine and their advantages in the medical education of the scientific community, medical professionals, teachers, researchers, trainers, decision makers, training companies, students, gamers and others. Research and analysis of innovative, technological methods and tools for creating semantically based knowledge for the purposes of training in medicine has been conducted. Research and analysis of innovative methods and tools for modeling and creating computer-based medical educational resources have been made. Attention is paid to the methods for creating computer-based resources in the field of medical education. The report presents videos and a serious educational game that are used in medical universities in medical education.This work was supported by the Bulgarian Ministry of Education and Science under the National Research Programme “Young scientists and postdoctoral students” approved by DCM # 577/17.08.201
Local Time Machines as a Model for Presentation of Cultural Information in Models of Smart Cities
No full textReport published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, November, 2020Публикацията прави кратък преглед на интелигентните градове като сравнително нова концепция. Основният интерес в тази работа е как моделите на интелигентните градове могат да представят данни за културно-историческото наследство. Установено е, че до момента няма установени практики да се използва наличното дигитализирано съдържание в галерии, библиотеки, архиви и музеи при създаването на модели на интелигентни градове. Като един вдъхновяващ пример за такава симбиоза разглеждаме т.нар. местни машини на времето и се надяваме, че повече дигитални модели на градове в бъдеще ще включат културно-исторически слой, който ще се изгражда с вече наличното дигитално културно съдържание.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Plovdiv University "Paisii Hilendarski