Results for 'Yaroslav Pushak'

45 found
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  1. Current issues of security management during martial law.Maksym Bezpartochnyi, Igor Britchenko, Olesia Bezpartochna, Kostyantyn Afanasyev, Mariia Bahorka, Oksana Bezsmertna, Olena Borschevska, Liliana Chyshynska-Hlybovych, Anna Dybała, Darya Gurova, Iryna Hanechko, Petro Havrylko, Olha Hromova, Tetiana Hushtan, Iryna Kadyrus, Yuri Kindzerski, Svіtlana Kirian, Anatoliy Kolodiychuk, Oleksandr Kovalenko, Andrii Krupskyi, Serhii Leontovych, Olena Lytvyn, Denys Mykhailyk, Oleh Nyzhnyk, Hanna Oleksyuk, Nataliia Petryshyn, Olha Podra, Nazariy Popadynets, Halyna Pushak, Yaroslav Pushak, Oksana Radchenko, Olha Ryndzak, Nataliia Semenyshena, Vitalii Sharko, Vladimir Shedyakov, Olena Stanislavyk, Dmytro Strikhovskyi, Oksana Trubei, Nataliia Trushkina, Sergiy Tsviliy, Leonid Tulush, Liudmyla Vahanova, Nataliy Yurchenko, Andrij Zaverbnyj & Svitlana Zhuravlova (eds.) - 2022 - Vysoká škola bezpečnostného manažérstva v Košiciach.
    The authors of the book have come to the conclusion that toensuring the country’s security in the conditions of military aggression, it is necessary to use the mechanisms of protection of territories and population, support of economic entities, international legal levers of influence on the aggressor country. Basic research focuses on assessment the resource potential of enterprises during martial law, the analysis of migration flows in the middle of the country and abroad, the volume of food exports, marketing and logistics (...)
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  2. Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.
    In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic both with one (...)
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  3. Independence of the Grossone-Based Infinity Methodology from Non-standard Analysis and Comments upon Logical Fallacies in Some Texts Asserting the Opposite.Yaroslav D. Sergeyev - 2019 - Foundations of Science 24 (1):153-170.
    This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...)
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  4.  74
    THE HISTORICAL SYNTAX OF PHILOSOPHICAL LOGIC.Yaroslav Hnatiuk - 2022 - European Philosophical and Historical Discourse 8 (1):78-87.
    This article analyzes the historical development of the philosophical logic syntax from the standpoint of the unity of historical and logical methods. According to this perspective, there are three types of logical syntax: the elementary subject-predicate, the modified definitivespecificative, and the standard propositional-functional. These types are generalized in the grammatical and mathematical styles of logical syntax. The main attention is paid to two scientific revolutions in elementary subject-predicate syntax, which led to the emergence of modified definitive-specific and standard propositional-functional syntaxes (...)
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  5.  37
    ANTHROPOLOGICAL SPECIFICS OF UKRAINIAN PHILOSOPHY IN THE PERSPECTIVE OF CULTURAL-PREDICATIVE ANALYSIS.Yaroslav Hnatiuk - 2022 - Ukrainian Studies 82 (1):92-105.
    The main purpose of the article is to analyze the statements of philosophical Ukrainian Studies about the anthropological specifics of Ukrainian philosophical thought by means of historicalphilosophical cultural-predicative analysis. The research methodology was determined primarily by the concept of cultural attribution and translation in the dialogue of languages of historical cultures of the Poznań Methodological School (J. Topolski, W. Wrzosek, E. Domańska) and the culturological approach in historical-philosophical Ukrainian Studies (V. Horskyi, S. Rudenko). The statements of the language of historical (...)
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  6.  55
    Силлогизм о добродетельных мудрецах.Yaroslav Slinin - 2018 - Schole 12 (1):63-71.
    The article deals with the Aristotelian doctrine of induction and its influence on the theory of induction of Al-Farabi. Inductive syllogisms of antiquity and the Middle Ages are compared with modern inferences by induction.
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  7. МЕТОДОЛОГІЧНА КОМУНІКАЦІЯ ЯК МОДУС МІЖКУЛЬТУРНОЇ КОМУНІКАЦІЇ.Yaroslav Hnatiuk - 2019 - Науковий Вісник Чернівецького Національного Університету. Серія: Філософія 806 (1):32-37.
    Засобами логіки комунікації історичних логік і методології історико-філософської міжкультурної комунікації аналізується культурна предикація як концепт історико-філософського дискурсу. Звертається увага на функціювання культурної предикації в контексті методологічної комунікації як інформаційної взаємодії конкуруючих методологій, їхніх інструментів і стратегій. Здійснюється конкретний аналіз ситуації застосування методологічної комунікації в межах історико-філософської комунікації як різновиду міжкультурної комунікації. В результаті методологічний і процесуальний дискурси історії філософії постають складниками специфічного історико-філософського комплексу.
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  8.  44
    КОНСТРУКТИВІСТСЬКА ФУНКЦІЯ КУЛЬТУРНОЇ ПРЕДИКАЦІЇ В ІСТОРИЧНОМУ ДИСКУРСІ.Yaroslav Hnatiuk - 2019 - EVROPSKÝ FILOZOFICKÝ A HISTORICKÝ DISKURZ 5 (2):98-104.
    The article analyzes cultural constructivism as one of the ways of a conceptual representation of historical reality. The connection between cultural constructivism as an epistemological position and cultural predication as a procedure of historical discourse is substantiated. The main focus is on the constructive function of cultural prediction in historical discourse. Constructivism as the position, behind which reality is the construction of consciousness is opposed to realism – the position in which thought or language reflect objectively existing and independent of (...)
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  9.  25
    ПАРАДИГМАЛЬНІ МЕТОДОЛОГІЧНІ МОЖЛИВОСТІ ІСТОРИКО-ФІЛОСОФСЬКОЇ НАУКИ.Yaroslav Hnatiuk - 2020 - VROPSKÝ FILOZOFICKÝ A HISTORICKÝ DISKURZ 6 (1):146-153.
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  10.  19
    АНАЛІЗ ІСТОРИКО-ФІЛОСОФСЬКОГО ДИСКУРСУ ЗАСОБАМИ ІСТОРІЇ ФІЛОСОФСЬКИХ ПОНЯТЬ.Yaroslav Hnatiuk - 2019 - Гілея (Науковий Вісник) 155 (5):10-13.
    Досліджуються методологічні можливості історії понять та її зв'язок з історією філософських понять і дискурс-аналізом філософських текстів. Окреслюються їхні функції у процесі культурної предикації. Наголошується на їхньому значенні при забезпеченні адекватного перекладу з мови історичної на мову актуальної культури.
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  11.  18
    РЕКОНСТРУКЦІЯ КОРДОЦЕНТРИЧНОЇ ПАРАДИГМИ В УКРАЇНСЬКІЙ КЛАСИЧНІЙ ФІЛОСОФІЇ: ПОСТАНОВКА ПРОБЛЕМИ І ТЕРМІНОЛОГІЧНІ ПОЯСНЕННЯ.Yaroslav Hnatiuk - 2000 - Збірник Наукових Праць: Філософія, Соціологія, Психологія. – Івано-Франківськ: Вид-Во Andquot;Плай" Прикарпатського Ун-Ту 4 (1):207-215.
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  12.  18
    СТРАТЕГІЇ РЕДУКЦІЇ ІСТОРІЇ ФІЛОСОФІЇ ДО ФІЛОСОФСЬКОЇ ЛОГІКИ Й ФІЛОСОФСЬКОЇ ЕВРИСТИКИ.Yaroslav Hnatiuk - 2013 - Вісник Прикарпатського Університету. Філософські І Психологічні Науки 17 (1):8-13.
    У статті аналізуються джерела активності та розвитку історії філософії. Головна увага звертається на Світовий дух – суб’єкт історії філософії як логіки поняття та концептуальний персонаж – суб’єкт історії філософії як логіки смислу, філософську логіку та філософську евристику. Обґрунтовується діалектичний зв’язок між Світовим духом як абсолютним чи універсальним суб’єктом і концептуальним персонажем як індивідуальним суб’єктом.
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  13.  17
    ПРОБЛЕМИ ЛОГІКИ У ФІЛОСОФІЇ МИСЛИТЕЛІВ ЗАХІДНОЇ УКРАЇНСЬКОЇ ДІАСПОРИ.Yaroslav Hnatiuk - 2008 - Науковий Вісник Чернівецького Національного Університету Імені Юрія Федьковича 412 (1):90-94.
    Аналізується специфіка та характер логіки як науки, основні логічні форми й закони, логічні основи наукової методології. Обґрунтовується роль логіки в підготовці до філософського та наукового мислення.
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  14.  17
    АНАЛІТИКА ФІЛОСОФСЬКИХ МІРКУВАНЬ.Yaroslav Hnatiuk - 2015 - Вісник Прикарпатського Університету. Філософські І Психологічні Науки 19 (1):48-54.
    У статті розглядається логіка філософії, її структури і метафори. Головна увага звертається на SP-структури метафізичної логіки і DS-структури діалектичної логіки, метафоричний стиль метафізики і діалектики.
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  15.  17
    ДІАЛОГІЧНІ ДЕФІНІЦІЇ ЛОГІКИ КОМУНІКАЦІЇ ІСТОРИЧНИХ ЛОГІК.Yaroslav Hnatiuk - 2016 - Вісник Прикарпатського Університету. Філософські І Психологічні Науки 20 (1):82-89.
    У статті досліджуються структурні елементи діалогічних дефініцій. Обґрунтовується можливість застосування діалогічних дефініцій в інтерпретативних моделях філософського тексту.
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  16.  13
    ЛОГІКА І МЕТАЛОГІКА ДМИТРА ЧИЖЕВСЬКОГО.Yaroslav Hnatiuk - 2008 - Науковий Вісник Чернівецького Національного Університету Імені Юрія Федьковича 410 (1):49-53.
    Досліджуються логічні ідеї Д. Чижевського, співвідношення предметної логіки й металогіки у його логіко-філософській концепції. Основна увага зосереджена на логічних теоріях поняття, судження й виводу та їх філософських інтерпретаціях.
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  17.  12
    УКРАЇНСЬКА ФІЛОСОФІЯ НА ШЛЯХАХ КОНЦЕПТУАЛІЗАЦІЇ.Yaroslav Hnatiuk - 2013 - In Гуцуляк О.Б (ed.), Історія філософії як школа думки. Збірник на пошану професора С.М. Возняка (до 85-річчя з дня народження). Івано-Франківськ, Івано-Франківська область, Україна, 76000: pp. 429-443.
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  18.  12
    ДОГМАТИЗМ У ЛОГІЦІ ТА ЙОГО ПОДОЛАННЯ ЗАСОБАМИ ЛОГІКИ КОМУНІКАЦІЇ ІСТОРИЧНИХ ЛОГІК.Yaroslav Hnatiuk - 2019 - Науковий Вісник Чернівецького Національного Університету. Серія: Філософія 811 (1):56-61.
    Логіка комунікації історичних логік є відповіддю на онтологічну проблему логічного синтаксису, засобомїї розв’язання і способом звільнення від догматизму в логіці. Суть цієї проблеми в тому, що, відповідно допануючих і конкуруючих між собою догматичних уявлень і переконань, право на існування має лише якась однаверсія логічного синтаксису – суб’єктно - предикативний синтаксис Аристотеля, дефінітивно - специфікативнийсинтаксис Ґ. Геґеля чи пропозиційно - функціональний синтаксис Г. Фреґе. Логіка комунікації історичних логік,пропонуючи розв’язання цієї проблеми, обґрунтовує інформаційну взаємодію між існуючими історичнимитипами логічного синтаксису за правилами побудови (...)
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  19.  11
    АНАЛІТИЧНІ ІНТЕРПРЕТАЦІЇ В ІСТОРІЇ ФІЛОСОФІЇ.Yaroslav Hnatiuk - 2010 - Вісник Прикарпатського Університету. Філософські І Психологічні Науки 13 (1):3-7.
    У статті розглядаються базові моделі основних тем історії філософії. Значна увага приділяється проблемі наступності й прогресу, взаємодії особистого й колективного в історії філософії.
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  20. КОМУНІКАТИВНИЙ ПОТЕНЦІАЛ КУЛЬТУРНОЇ ПРЕДИКАЦІЇ.Yaroslav Hnatiuk - 2019 - Івано-Франківськ, Івано-Франківська область, Україна, 76000:
    У монографії аналізуються методологічні можливості культурної предикації, що має теоретичний статус міжкультурної комунікації і дефінітивної специфікації. Вони слугують основами культурно-предикативного аналізу як гуманітарно-наукової методології. Культурно-предикативний аналіз узагальнює окремі методології гуманітарних наук. Серед них – методологія історії, методологія логіки і методологія історії філософії, в якій методології історії і логіки поєднуються на підставі принципу єдності історичного і логічного. Монографія адресована фахівцям з філософії і методології гуманітарних наук, методології історії, логіки та історії філософії, метафілософії і комунікативістики.
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  21. УКРАЇНСЬКИЙ КОРДОЦЕНТРИЗМ У КОНФЛІКТІ МІФОЛОГІЙ ТА ІНТЕРПРЕТАЦІЙ.Yaroslav Hnatiuk - 2010 - Івано-Франківськ, Івано-Франківська область, Україна, 76000:
    Українська академічна спільнота, незважаючи на значний теоретичний масив інформації, й далі перебуває у полоні ілюзій, шаблонів сприйняття та некоректних тлумачень концепта «український кордоцентризм». Філософська дискусія навколо цього концепта є конфліктом міфологій – протистоянням між міфом про унікальний етноментальний феномен та міфом про ілюзію наукової уяви. Водночас вона є конфліктом інтерпретацій – протистоянням між міфічною інтерпретацією класичної доби української філософії та її метафілософською інтерпретацією. Пропонована монографія ознайомлює із філософською позицією автора концепта «український кордоцентризм», його оцінкою цих конфліктів.
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  22. Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems.Yaroslav Sergeyev - 2017 - EMS Surveys in Mathematical Sciences 4 (2):219–320.
    In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than the (...)
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  23. Solving ordinary differential equations by working with infinitesimals numerically on the Infinity Computer.Yaroslav Sergeyev - 2013 - Applied Mathematics and Computation 219 (22):10668–10681.
    There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer is (...)
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  24. The Olympic medals ranks, lexicographic ordering and numerical infinities.Yaroslav Sergeyev - 2015 - The Mathematical Intelligencer 37 (2):4-8.
    Several ways used to rank countries with respect to medals won during Olympic Games are discussed. In particular, it is shown that the unofficial rank used by the Olympic Committee is the only rank that does not allow one to use a numerical counter for ranking – this rank uses the lexicographic ordering to rank countries: one gold medal is more precious than any number of silver medals and one silver medal is more precious than any number of bronze medals. (...)
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  25. The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area.Yaroslav Sergeyev - 2016 - Communications in Nonlinear Science and Numerical Simulation 31 (1-3):21–29.
    The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowing one to execute numerical computations with infinities and infinitesimals is applied to study the Koch snowflake at infinity. Numerical computations with actual infinite and infinitesimal numbers can be executed on the Infinity Computer being a new supercomputer patented in USA and (...)
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  26. UN SEMPLICE MODO PER TRATTARE LE GRANDEZZE INFINITE ED INFINITESIME.Yaroslav Sergeyev - 2015 - la Matematica Nella Società E Nella Cultura: Rivista Dell’Unione Matematica Italiana, Serie I 8:111-147.
    A new computational methodology allowing one to work in a new way with infinities and infinitesimals is presented in this paper. The new approach, among other things, gives the possibility to calculate the number of elements of certain infinite sets, avoids indeterminate forms and various kinds of divergences. This methodology has been used by the author as a starting point in developing a new kind of computer – the Infinity Computer – able to execute computations and to store in its (...)
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  27.  28
    Lower and Upper Estimates of the Quantity of Algebraic Numbers.Yaroslav Sergeyev - 2023 - Mediterranian Journal of Mathematics 20:12.
    It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ①-based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is countable (...)
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  28. Higher order numerical differentiation on the Infinity Computer.Yaroslav Sergeyev - 2011 - Optimization Letters 5 (4):575-585.
    There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of information. In this paper, a new way to do this is presented for a new kind of a computer - the Infinity Computer - able to work numerically with finite, infinite, and infinitesimal number. It is proved that the Infinity Computer is able (...)
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  29. A new applied approach for executing computations with infinite and infinitesimal quantities.Yaroslav D. Sergeyev - 2008 - Informatica 19 (4):567-596.
    A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework. The (...)
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  30.  9
    The Bulletin of Yaroslav Mudryi National Law University. Series: philosophy, philosophy of law, political science, sociology. Trebin, Blikhar & Trebin Mykhailo Petrovych - 2022 - The Bulletin of Yaroslav Mudryi National Law University. Series: Philosophy, Philosophy of Law, Political Science, Sociology : The Collection of Scientific Papers 240:204-217.
    The article examines the peculiarities of state-church relations that are formed in the process of legitimizing civil society. It is substantiated that the 21st century, like the last 20th century, forces us to search for a new format of state-church relations in the context of international relations, modern globalization challenges, and the development of the latest communication and information space. This, of course, prompts a new assessment of the status of religion and the church in the modern political system and (...)
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  31. Interpretation of percolation in terms of infinity computations.Yaroslav Sergeyev, Dmitri Iudin & Masaschi Hayakawa - 2012 - Applied Mathematics and Computation 218 (16):8099-8111.
    In this paper, a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use Cantor’s ideas and describes infinite and infinitesimal numbers in accordance with the principle ‘The part is less than the whole’. It gives a possibility to work with finite, infinite, and infinitesimal quantities numerically by using a new kind of a compute - the Infinity Computer – introduced recently in [18]. The new approach does not (...)
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  32. Some paradoxes of infinity revisited.Yaroslav Sergeyev - 2022 - Mediterranian Journal of Mathematics 19:143.
    In this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirah ̃a, working with only three numerals (one, two, many) can help us to change our perception (...)
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  33. Numerical infinities applied for studying Riemann series theorem and Ramanujan summation.Yaroslav Sergeyev - 2018 - In AIP Conference Proceedings 1978. AIP. pp. 020004.
    A computational methodology called Grossone Infinity Computing introduced with the intention to allow one to work with infinities and infinitesimals numerically has been applied recently to a number of problems in numerical mathematics (optimization, numerical differentiation, numerical algorithms for solving ODEs, etc.). The possibility to use a specially developed computational device called the Infinity Computer (patented in USA and EU) for working with infinite and infinitesimal numbers numerically gives an additional advantage to this approach in comparison with traditional methodologies studying (...)
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  34.  59
    Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains.Yaroslav Sergeyev - 2009 - Nonlinear Analysis Series A 71 (12):e1688-e1707.
    The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical world around us. These numbers have a strong practical advantage with respect to traditional approaches: they are representable at a new kind (...)
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  35. Using blinking fractals for mathematical modelling of processes of growth in biological systems.Yaroslav Sergeyev - 2011 - Informatica 22 (4):559–576.
    Many biological processes and objects can be described by fractals. The paper uses a new type of objects – blinking fractals – that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that both traditional and blinking fractals can be successfully studied by a recent approach allowing one to work numerically with infinite and infinitesimal numbers. It is shown that blinking fractals can be applied for modeling complex processes of growth of biological systems including their (...)
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  36. Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers.Yaroslav Sergeyev - 2007 - Chaos, Solitons and Fractals 33 (1):50-75.
    The paper considers a new type of objects – blinking fractals – that are not covered by traditional theories studying dynamics of self-similarity processes. It is shown that the new approach allows one to give various quantitative characteristics of the newly introduced and traditional fractals using infinite and infinitesimal numbers proposed recently. In this connection, the problem of the mathematical modelling of continuity is discussed in detail. A strong advantage of the introduced computational paradigm consists of its well-marked numerical character (...)
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  37. Single-tape and multi-tape Turing machines through the lens of the Grossone methodology.Yaroslav Sergeyev & Alfredo Garro - 2013 - Journal of Supercomputing 65 (2):645-663.
    The paper investigates how the mathematical languages used to describe and to observe automatic computations influence the accuracy of the obtained results. In particular, we focus our attention on Single and Multi-tape Turing machines which are described and observed through the lens of a new mathematical language which is strongly based on three methodological ideas borrowed from Physics and applied to Mathematics, namely: the distinction between the object (we speak here about a mathematical object) of an observation and the instrument (...)
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  38.  72
    Observability of Turing Machines: a refinement of the theory of computation.Yaroslav Sergeyev & Alfredo Garro - 2010 - Informatica 21 (3):425–454.
    The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the relativity of mathematical languages used to describe the Turing machines. A deep investigation is performed on the interrelations between mechanical computations and their mathematical descriptions emerging when a human (the researcher) starts to describe a Turing machine (the object of the study) by (...)
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  39.  53
    Numerical methods for solving initial value problems on the Infinity Computer.Yaroslav Sergeyev, Marat Mukhametzhanov, Francesca Mazzia, Felice Iavernaro & Pierluigi Amodio - 2016 - International Journal of Unconventional Computing 12 (1):3-23.
    New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial condition are proposed. They are designed for work on a new kind of a supercomputer – the Infinity Computer, – that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods described in this paper are able to work (...)
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  40.  99
    The difficulty of prime factorization is a consequence of the positional numeral system.Yaroslav Sergeyev - 2016 - International Journal of Unconventional Computing 12 (5-6):453–463.
    The importance of the prime factorization problem is very well known (e.g., many security protocols are based on the impossibility of a fast factorization of integers on traditional computers). It is necessary from a number k to establish two primes a and b giving k = a · b. Usually, k is written in a positional numeral system. However, there exists a variety of numeral systems that can be used to represent numbers. Is it true that the prime factorization is (...)
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  41.  91
    Counting systems and the First Hilbert problem.Yaroslav Sergeyev - 2010 - Nonlinear Analysis Series A 72 (3-4):1701-1708.
    The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their elements) with different (...)
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  42.  49
    Lagrange Lecture: Methodology of numerical computations with infinities and infinitesimals.Yaroslav Sergeyev - 2010 - Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.
    A recently developed computational methodology for executing numerical calculations with infinities and infinitesimals is described in this paper. The approach developed has a pronounced applied character and is based on the principle “The part is less than the whole” introduced by the ancient Greeks. This principle is applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The point of view on infinities and infinitesimals (and in general, on Mathematics) presented in this paper (...)
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  43.  68
    Evaluating the exact infinitesimal values of area of Sierpinski's carpet and volume of Menger's sponge.Yaroslav Sergeyev - 2009 - Chaos, Solitons and Fractals 42: 3042–3046.
    Very often traditional approaches studying dynamics of self-similarity processes are not able to give their quantitative characteristics at infinity and, as a consequence, use limits to overcome this difficulty. For example, it is well know that the limit area of Sierpinski’s carpet and volume of Menger’s sponge are equal to zero. It is shown in this paper that recently introduced infinite and infinitesimal numbers allow us to use exact expressions instead of limits and to calculate exact infinitesimal values of areas (...)
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  44. Computation of higher order Lie derivatives on the Infinity Computer.Felice Iavernaro, Francesca Mazzia, Marat Mukhametzhanov & Yaroslav Sergeyev - 2021 - Journal of Computational and Applied Mathematics 383:113135.
    In this paper, we deal with the computation of Lie derivatives, which are required, for example, in some numerical methods for the solution of differential equations. One common way for computing them is to use symbolic computation. Computer algebra software, however, might fail if the function is complicated, and cannot be even performed if an explicit formulation of the function is not available, but we have only an algorithm for its computation. An alternative way to address the problem is to (...)
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  45. Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm.Marco Cococcioni, Massimo Pappalardo & Yaroslav Sergeyev - 2018 - Applied Mathematics and Computation 318:298-311.
    Numerous problems arising in engineering applications can have several objectives to be satisfied. An important class of problems of this kind is lexicographic multi-objective problems where the first objective is incomparably more important than the second one which, in its turn, is incomparably more important than the third one, etc. In this paper, Lexicographic Multi-Objective Linear Programming (LMOLP) problems are considered. To tackle them, traditional approaches either require solution of a series of linear programming problems or apply a scalarization of (...)
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