Cenário do Surgimento e o Impacto do Teorema da Incompletude de Gödel na Matemática

2018 ◽  
Vol 10 (3) ◽  
pp. 198
Author(s):  
Rosemeire De Fatima Batistela ◽  
Maria Aparecida Viggiani Bicudo ◽  
Henrique Lazari
Keyword(s):  
Mathematical Community ◽  
Incompleteness Theorem ◽  
Axiomatic Method ◽  
Mathematical Discussions ◽  
The Impact

Este artigo trata do panorama das discussões matemáticas mantidas entre os matemáticos à época em que Gödel apresentou à comunidade matemática seu teorema da incompletude. Argumenta-se que o Teorema da Incompletude de Gödel (TIG) é um teorema mais para a alma do que para as mãos dos matemáticos. Afirma-se ser ele importante porque mostra que a Matemática não pode comunicar (provar) todas as suas verdades. Porém, as provas de que a aritmética básica dos naturais é incompleta e incompletável e da impossibilidade de demonstrar a sua não contradição não impossibilita que a Matemática continue sendo produzida. A linha de argumentação exposta segue apresentando: o cenário matemático vigente no momento da publicação do TIG; o ponto de incidência deste resultado na Matemática, o impacto deste teorema nesta ciência, bem como, como ele foi compreendido e acolhido pelos matemáticos.Palavras-chave: Teorema da Incompletude de Gödel (TIG). Problema da Compatibilidade da Aritmética. Programa de Hilbert. Método Axiomático.AbstractThis article deals with the panorama of the mathematical discussions held among mathematicians at the time when Gödel introduced his incompleteness theorem to the mathematical community. It is argued that Gödel’s Incompleteness Theorem (TIG) is a more theorem for the soul than for the hands of mathematicians. It is said to be important because it shows that Mathematics can’t communicate (prove) all its truths. However, evidence that the basic arithmetic of the natural is incomplete and incomplete and that it is impossible to demonstrate its non-contradiction does not preclude mathematics from being produced. The line of argument exposed continues presenting: the mathematical scenario in force at the time of the publication of the TIG; The point of incidence of this result in Mathematics, the impact of this theorem on this science, as well as how it was understood and welcomed by mathematicians.Keywords: Gödel’s Incompleteness Theorem. Hilbert’s Second Problem. Hibert’s Program. Axiomatic Method.

scholarly journals Institutional genesis of kleptocratic economy and its formation in Ukraine

2020 ◽  
pp. 180-187
Author(s):  
R Pustoviit ◽  
O Kuklin ◽  
N Azmuk ◽  
I Yakushyk ◽  
V Gunko
Keyword(s):  
Research Methods ◽  
Political Violence ◽  
Institutional Environment ◽  
Institutional Arrangement ◽  
Axiomatic Method ◽  
Economic Science ◽  
Theoretical Knowledge ◽  
Business And Society ◽  
The European Union ◽  
The Impact

Purpose. To analyze the kleptocratic economy as an institutional arrangement that is focused on the key function of generating sources of income for the ruling pseudo-elite by introducing corrupt non-market transaction costs for firms and households, which are based on administrative, bureaucratic and political violence. Methodology. In the proposed scientific research, we distinguish three types of research methods: firstly, inherent in cognition as a whole (general logical) methods such as analysis, synthesis, abstraction, generalization, induction, deduction, analogy; secondly, general scientific, primarily empirical, research methods, namely observation, description, measurement; thirdly, the theoretical methods of cognition used by the economic science, in particular: idealization, formalization; the axiomatic method for constructing theoretical knowledge; a hypothetical-deductive method for constructing and developing theoretical knowledge. Findings. The socio-economic structure of Ukraine is analyzed from the point of view of the factors that are determined by the impact of formal and informal institutions in kleptocratic economy and affect corruption risks. Recommendations are provided for modernization of the institutional environment in Ukraine in the context of the modern methodological paradigm of searching for points of contact within the interaction of government, business and society. Originality. The proposed study carried out a comprehensive analysis of the institutional environment of the Ukrainian economy, which provides convincing grounds to characterize it as kleptocratic, and such where the fundamental modernization proposed in the work has yet to be implemented, accounting for the European integration prospects. In contrast to previously proposed studies, the presented approach focuses on the correlation between key performance indicators of institutions, GDP per capita, and corruption indices in Ukraine and in the studied countries of the European Union. Practical value. The research results can be used by specialized experts when forming the institutional requirements for creating an effective system for preventing corruption.

scholarly journals THE IMPACT OF THE COVID-19 PANDEMIC ON THE FILLING OF LOCAL BUDGETS

2020 ◽  
pp. 86-94
Author(s):  
Pavlina Fugelo ◽  
Svitlana Savitska
Keyword(s):  
Theoretical Research ◽  
Axiomatic Method ◽  
Monitoring Methods ◽  
Negative Effects ◽  
Excise Tax ◽  
Measurement Monitoring ◽  
Tax Legislation ◽  
Local Budget ◽  
Government Body ◽  
The Impact

Introduction. The topical matter is defined due to the need of the COVID-19 pandemic’s impact assessment and legislative innovations aimed at counteracting it, to change the volume and structure of local budget revenues. Methods. The methodological basis of the study are methods of empirical research (comparison, measurement, monitoring); methods of theoretical research (ascent from the abstract to the concrete, idealization, deductive and axiomatic method); general methods used both at the empirical and theoretical level of research (abstraction and concretization, analysis, synthesis, induction, deduction, analogy). Results. The article deals with detailed changes to the Tax Law book, as tax revenues are the main source of filling local budgets. In particular, changes are related to personal income tax, local taxes and fees (including real estate tax, land fees, unified tax). The moratorium impact on the application of penalties and inspections on the filling of local budgets is noted. The decision’s influence of the local self-government body regarding the reduction of unified tax rates for I and II groups of unified taxpayers on local budget revenues has been studied. The dynamics and structure of owned revenues of Kamianets-Podilskyi for 2017-2019 is analyzed. The amounts of possible shortcomings of local budgets due to the initiation of quarantine measures are calculated. The reasons for reduction of revenues from excise tax, land tax, unified tax, tourist tax, from the application of fines and other sanctions are explained. Discussion. The outlook for further research is to outline the ways to overcome negative effects of the COVID-19 pandemic and the resulting quarantine measures for local budgets. Keywords: local budget revenues, pandemic, budget legislation, tax legislation, budget deficit.

scholarly journals Gymnastics exercises as a way of improving the health of students

2021 ◽  
pp. 90-94
Author(s):  
Mykola Puzdymir ◽  
Iuliia Chekhivska ◽  
Kateryna Tsymbaliuk
Keyword(s):  
Physical Education ◽  
Self Control ◽  
Axiomatic Method ◽  
Systematic Analysis ◽  
Test Standards ◽  
Good Physical Condition ◽  
Relevant Today ◽  
Theoretical Generalization ◽  
Education Of Students ◽  
The Impact

The system of physical education of students is aimed only at solving current problems - drawing up control and test standards, which does not contribute to the development of their desire for self-improvement, aims to educate obedient performers focused on compliance with the requirements of the physical education program. The purpose of the article: to determine the impact of gymnastic exercises on health, as well as to provide practical recommendations to students. Research methods: theoretical generalization, systematic analysis of data from the scientific literature, axiomatic method. The article substantiates the importance of physical education classes that promote the development of strength qualities in students, as the development of these qualities provides good physical condition and readiness for creative activity. Over the last decade, the situation in Ukraine has been alarming: the health and fitness of student youth has deteriorated sharply. According to medical research centers, up to 90% of pupils and students have health problems, 30-50% of them - unsatisfactory physical fitness. The recommended set of exercises for daily gymnastics to improve the health of students is given. Describes the basic tips that students should follow during gymnastics. The essence of self-control over the state of health of young men during training is revealed. The problem of physical improvement of student youth is relevant today and requires from scientists, coaches and teachers of physical education further scientific and practical research in improving health, physical development and improvement of physical qualities.

scholarly journals Mathematics in the interwar period in Central-Eastern Europe. The report on an international research project for the years 2018–2020

2021 ◽  
Vol 20 ◽  
pp. 895-937
Author(s):  
Martina Bečvářová ◽  
Stanisław Domoradzki
Keyword(s):  
International Research ◽  
Mathematical Community ◽  
Research Project ◽  
Team Members ◽  
Central Eastern Europe ◽  
Book Fairs ◽  
Definition Of ◽  
The Impact ◽  
Scientific Questions ◽  
International Research Project

In the article, we will show the main important results of the international research project The impact of WWI on the formation and transformation of the scientific life of the mathematical community. It was supported by the Czech Science Foundation for the years 2018–2020 and brought together ten scientists from five countries (Czech Republic, Poland, Slovakia, USA, and Ukraine) and used the collaboration with historians of mathematics and mathematicians from many other European countries. We will discuss our motivation for the creation of the project, our methodological and professional preparations which profited from the international composition of the team and its longtime collaborations, profound specializations and experiences of the team members, and their deep and long-term studies of many archival sources and basic published works. We will present our choice of the general research trends, our definition of the scientific questions, and our determination of the main topics of our studies. We will describe our most important results (books, articles, visiting lectures, presentations at national and international conferences, seminars and book fairs, exhibitions, popularizations of the results between students, teachers, mathematicians, historians of sciences, and people who love mathematics and its history). We will analyze the new benefit that the project created for the future, for example, good platforms for future international research and cooperation, the discovery of many new interesting research questions, problems, and plans.

scholarly journals The enterprise capital structure management model

2021 ◽  
pp. 110-115
Author(s):  
K Bagatska ◽  
T Batrakova ◽  
H Silakova ◽  
N Klymash ◽  
O Vialets
Keyword(s):  
Mathematical Model ◽  
Capital Structure ◽  
Management Practice ◽  
Scientific Work ◽  
Axiomatic Method ◽  
Homogeneous Groups ◽  
Analysis And Synthesis ◽  
External Borrowing ◽  
The Impact ◽  
The Capital Structure

Purpose. To create management algorithms for the enterprises capital structure and mathematical formalization of optimization of this structure. To investigate the dynamics of changes in the share of profitable enterprises to assess, analyze and forecast changes in the capital structure of homogeneous groups of enterprises. Methodology. Both empirical and theoretical methods of cognition are used to conduct the research. Methods of scientific observation and comparison are used to form the topic of scientific work, goals and objectives of the study. Methods of analysis and synthesis, induction and deduction, abstraction are used to determine the essential features of capital structure management. Methods of system structuring and modeling are used to create a mathematical model. The analogy method is used to find the weight factor of the objective function. The axiomatic method and the method of convergence from the abstract to the concrete were used for the practical application of the mathematical model, in particular, to analyze the dynamic index of related companies, stratified by size, industry, and so on. Findings. The dynamics of the preconditions for changing the capital structure is studied, the regularities of this change for groups of homogeneous enterprises are revealed. The uneven influence of the crisis on the approaches to the formation of capital structure in groups of homogeneous enterprises is revealed, and the reasons for this are investigated. The similarity of tendencies of formation of capital structure in groups of inhomogeneous enterprises is pointed out. A correlation was found between the decrease in the share of equity and a significant prevalence of external borrowing with an increase in net loss. Moreover, it is established that enterprises, whose total amount of equity and current liabilities is stable and comparable in size with external borrowing, show a decrease in losses. Originality. Algorithms for capital structure management and a mathematical model for optimizing capital structure are proposed. A method of comparative analysis of changes in capital structure for homogeneous groups of enterprises has been introduced, which provides an opportunity to assess the impact of external risks and crisis factors in the past and predict the necessary changes in capital structure during both the new crisis and after the crisis. Practical value. The developed algorithms and mathematical model can be used in research and management practice to manage capital structure. Useful for different categories of professionals are approaches to the analysis of capital structure, the results of the analysis of the causes of change, the study on trends and their consequences for homogeneous enterprises.

Formation of Lunar Craters and Bright Rays as a Result of Meteorite Impacts

1962 ◽  
Vol 14 ◽  
pp. 415-418
Author(s):  
K. P. Stanyukovich ◽  
V. A. Bronshten
Keyword(s):  
Explosive Charge ◽  
The Moon ◽  
Meteorite Impacts ◽  
The Earth ◽  
Lunar Craters ◽  
The Impact

The phenomena accompanying the impact of large meteorites on the surface of the Moon or of the Earth can be examined on the basis of the theory of explosive phenomena if we assume that, instead of an exploding meteorite moving inside the rock, we have an explosive charge (equivalent in energy), situated at a certain distance under the surface.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

Organic Syntheses During the Impact of a Comet with a Gaseous Planet

1997 ◽  
Vol 161 ◽  
pp. 189-195
Author(s):  
Cesare Guaita ◽  
Roberto Crippa ◽  
Federico Manzini
Keyword(s):  
Polymeric Material ◽  
Molecular Form ◽  
Parent Compound ◽  
Blue Filter ◽  
Organic Syntheses ◽  
The Impact

AbstractA large amount of CO has been detected above many SL9/Jupiter impacts. This gas was never detected before the collision. So, in our opinion, CO was released from a parent compound during the collision. We identify this compound as POM (polyoxymethylene), a formaldehyde (HCHO) polymer that, when suddenly heated, reformes monomeric HCHO. At temperatures higher than 1200°K HCHO cannot exist in molecular form and the most probable result of its decomposition is the formation of CO. At lower temperatures, HCHO can react with NH3 and/or HCN to form high UV-absorbing polymeric material. In our opinion, this kind of material has also to be taken in to account to explain the complex evolution of some SL9 impacts that we observed in CCD images taken with a blue filter.

Hydrogen Cyanide Polymers from the Impact of Comet P/Shoemaker-Levy 9 on Jupiter

1997 ◽  
Vol 161 ◽  
pp. 179-187
Author(s):  
Clifford N. Matthews ◽  
Rose A. Pesce-Rodriguez ◽  
Shirley A. Liebman
Keyword(s):  
Amino Acids ◽  
Solar System ◽  
Hydrogen Cyanide ◽  
Nitrogen Heterocycles ◽  
Laboratory Studies ◽  
Heterogeneous Solids ◽  
The Many ◽  
Comet Halley ◽  
The Impact ◽  
By Products

AbstractHydrogen cyanide polymers – heterogeneous solids ranging in color from yellow to orange to brown to black – may be among the organic macromolecules most readily formed within the Solar System. The non-volatile black crust of comet Halley, for example, as well as the extensive orangebrown streaks in the atmosphere of Jupiter, might consist largely of such polymers synthesized from HCN formed by photolysis of methane and ammonia, the color observed depending on the concentration of HCN involved. Laboratory studies of these ubiquitous compounds point to the presence of polyamidine structures synthesized directly from hydrogen cyanide. These would be converted by water to polypeptides which can be further hydrolyzed to α-amino acids. Black polymers and multimers with conjugated ladder structures derived from HCN could also be formed and might well be the source of the many nitrogen heterocycles, adenine included, observed after pyrolysis. The dark brown color arising from the impacts of comet P/Shoemaker-Levy 9 on Jupiter might therefore be mainly caused by the presence of HCN polymers, whether originally present, deposited by the impactor or synthesized directly from HCN. Spectroscopic detection of these predicted macromolecules and their hydrolytic and pyrolytic by-products would strengthen significantly the hypothesis that cyanide polymerization is a preferred pathway for prebiotic and extraterrestrial chemistry.

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