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EN
In the present paper, we investigate the Gompertz function, which is commonly used, mostly as diffusion model, in economics and management. Our approach is based on indicating in a given time series, presumably with a Gompertz trend, some characteristic points corresponding to zeroes of successive derivatives of this function. This allows us to predict the saturation level of a phenomenon under investigation, by using only the early values of the time series. We also give an example of applications of this method.
EN
Sustainable development means the shift towards the use of sustainable renewable Energy sources. The development of wind energy is certainly one of the most successful examples of how to do this. Wind power engineering is the fastest developing branch of the global Energy industry. In 2014, the world reached the highest level of new wind turbines installed, a capacity more than 51 GW. This means that the share of wind in total electricity production is increasing, reaching, in some countries, outstanding values (for example, 39% of total electricity consumption in Denmark in 2014). The total capacity of a new wind turbine is comparable with the biggest traditional electrical power plants and the total installed capacity of the energy system. However, it causes specific problems of interconnection, operation, and putting such installations in traditional energy systems with traditional energy sources. There are good chances that the Kaliningrad region energy system in the nearest future would have to go into isolate operation because of the disconnection of Lithuanian, Latvian, and Estonian energy systems from Russian networks. If that is the case, the development of wind energy in the Kaliningrad region could become one of the most attractive options for a sustainable future of power engineering.
EN
The article suggests a mathematical model of the multicriteria problem of formation of production tasks and operational-calendar plans at food companies, taking into account their specific features. The research was carried out, the bat algorithm and its modifications were adjusted and tested. The choice of the bat algorithm based on the Levy flight random search strategy is substantiated. This approach provides the formation of new and alternative plans for orders fulfillment at a food company, taking into account the proposed mathematical model.
EN
Research background: Project portfolio optimization isa  demanding process in the case of considering a large number of project intentions and has so far been the subject of research by many authors, especially foreign authors. However, the issue of project portfolio optimization is an area that is not sufficiently addressed by Slovak authors. This was the main impulse to create a specific mathematical model of integer programming with bivalent variables to optimize the company's project portfolio with the intention to reflect the specific requirements of Slovak companies. Purpose of the article: The aim of the article is to propose a mathematical model of integer programming with bivalent variables to optimize the project portfolio with a focus on Slovak companies. Methods: In accordance with the aim of the article, a questionnaire survey was carried out with the intention of identifying the criteria that are perceived by the managers of Slovak companies as important in the optimization of the project portfolio. These criteria were subsequently reflected in the mathematical model design using the mathematical programming method. Findings & Value added: Based on a literature review aimed at the project portfolio optimization, we have found a gap in considering the compliance of project intentions and strategic objectives of the company within the optimization of the project portfolio. Based on the results of the questionnaire survey, the significance of the mutual compliance of project intentions with the strategic objectives of the company was confirmed from the point of view of Slovak companies. Given the fact that our aim was to create an innovative integer programming model with bivalent variables orientated to the conditions of Slovak companies, we included in the resulting model the criteria that were not considered within the scope of existing research in this area, and which are perceived as important by the Slovak companies.
EN
DEMATEL technique is a graphical representation method to deal with complex systems. The final analyzed cause and effect categorization would be fundamentally dependent on the threshold value setting. This research is intended to present some mathematical models for calculating the threshold value in the DEMATEL method. The min(max) operator has been intentionally used for considering three equations to identify the threshold value. Additionally, the proposed mathematical equations are gradually developed to gain more useful data to yield a threshold value as well. Particularly, the expert’s initial scoring for building the primary matrix would also be applied in one equation. Results show eliciting an expert’s opinions regarding the value of a threshold value determination leads to setting relatively high thresholds. But, there would be an equation which takes advantage of more data derived from the total influence matrix T. Moreover, a span of different threshold values is gained by making use of the Hamacher t-conorms operator which especially would cause better complexity management of the final total matrix T based on expert’s opinions. As a contribution to this research, threshold value determination is developed mathematically by making use of the direct data gained by the total matrix T. Besides combining data derived from total matrix T, the initial influence direct matrix given by experts, a simpler aggregating procedure and no need for statistical information compared to special Lenth’s method hints at this research’s novelty as well.
EN
To create an astronomical software, one should use the most effective method to produce the quickest hardware calculation. However, the not so effective object oriented paradigm seems to have bigger influence on the astronomical domain. We discuss the status quo of its methodology. The traditional, Turing computation model does not have so distinct influence on knowledge creation because it is hardware-oriented. An object oriented programming language is more influential on discovery, because it works directly in the scientific domain.
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MAZĀS UZŅĒMĒJDARBĪBAS STĀVOKLIS LATVIJĀ

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EN
Small business is currently vital for the development of any country. In the article, the term “small entrepreneurship” is an umbrella term that includes both small and micro enterprises. These two types of small enterprises, according to EU Regulation 364/2004, differ by several indicators, which given in the article. In Latvia, - just like, for example, in the USA, - small business employs about half of the workforce. The review of publications - including those of the SCOPUS database - by Latvia’s scientists and researchers shows that not enough attention paid to small business in Latvia. At the same time, in other regions of the world, for example, in Southeast Asia, where small business is also widely spread, more attention is devoted to it in scientific research. Therefore, the theme of the article is topical for Latvia. The object of the research: micro and small enterprises in the Latvia’s economy. The goal of the research: based on the analysis of the country’s socio-economic system, to test the hypothesis about the presence in the system of factors that impede the successful development of small business in Latvia, to identify and rank the most acute problems. Research methods: system analysis, expert assessment of the importance of the problems faced by enterprises, and modern mathematical methods for processing the results of the examination. A well-developed small business sector contributes to the growth of employment. The development of micro and small entreprises in Latvia is in line with global trends. However, Latvia is still lagging behind the highly developed EU countries. The socio-economic system that includes these enterprises is only partially balanced and is not stable enough. This shown in the article using mathematical model. Micro and small enterprises that differ in the number of employees have accordingly different problems. The problems are largely associated with insufficient state support for small business and an unstable tax policy. Due to the significant labour migration of young people to other EU countries, the search for qualified employees is an acute problem for all enterprises. The state programme aimed at helping the people return home, who have left their homeland to work abroad, is still ineffective. It is advisable to simplify the provision of loans by start-up entrepreneurs, to organise special courses for them, following the example of other countries.
EN
DEMATEL technique is a graphical representation method to deal with complex systems. The final analyzed cause and effect categorization would be fundamentally dependent on the threshold value setting. This research is intended to present some mathematical models for calculating the threshold value in the DEMATEL method. The min(max) operator has been intentionally used for considering three equations to identify the threshold value. Additionally, the proposed mathematical equations are gradually developed to gain more useful data to yield a threshold value as well. Particularly, the expert’s initial scoring for building the primary matrix would also be applied in one equation. Results show eliciting an expert’s opinions regarding the value of a threshold value determination leads to setting relatively high thresholds. But, there would be an equation which takes advantage of more data derived from the total influence matrix T. Moreover, a span of different threshold values is gained by making use of the Hamacher t-conorms operator which especially would cause better complexity management of the final total matrix T based on expert’s opinions. As a contribution to this research, threshold value determination is developed mathematically by making use of the direct data gained by the total matrix T. Besides combining data derived from total matrix T, the initial influence direct matrix given by experts, a simpler aggregating procedure and no need for statistical information compared to special Lenth’s method hints at this research’s novelty as well.
EN
The theoretical questions of mathematical modeling of agricultural production processes are described. Production of agricultural goods and foodstuffs is modeled except for the production of forage and involvement of equipment and techniques, buildings, infrastructure etc. The model is based on a division of economic and technological processes in agriculture into four stages specific for agribusiness. A mathematical description of four stages in used production functions is provided.
10
63%
EN
A distributed-coding model incorporating lateral inhibition in a simulated nerve network has been successful in accounting for many properties of backward masking (Bridgeman, 1971, 1978), linking modeling with neurophysiology and psychophysics. Metacontrast is a variety of backward masking that is of particular interest in uncovering properties of visual coding because target and mask do not overlap in time or space, and it is the first stimulus that is reduced in visibility, not the second. The lateral inhibitory model can also simulate common-onset masking, where a target and mask appear simultaneously but the mask disappears after a variable delay, and it can reproduce qualitatively the effects of attention on object substitution by varying the time interval over which sensory codes are analyzed.
PL
Przedstawiono model matematyczny wiążący obwód talii (lt) z obwodem w biodrach i masą tłuszczu w talii (mt). Ów model jest oparty o podstawowe zależności geometryczne dla pierścienia kulistego oraz wyniki badań doświadczalnych polegających na pośrednim pomiarze całkowitej masy tłuszczu i masy tłuszczu wisceralnego metodą bioimpedancji oraz pomiaru obwodu talii (lt) i obwodu w biodrach (lb) przy pomocy ergonomicznej taśmy mierniczej do pomiaru obwodów. Wyniki obliczeń obwodu talii (lt) wykonane na podstawie tego modelu są zgodne w 4% korytarzu błędu z wynikami pomiarów dla mężczyzny uczestniczącego w eksperymencie polegającym na redukcji masy ciała w oparciu o dietę niskocukrową. Wyniki badań są istotne z biomedycznego punktu widzenia.
EN
A mathematical model that correlates waist circumference (lt) with fat mass (mt) was presented. This model is based on basic geometrical dependencies for spherical ring and the results of experimental studies involving the indirect measurement of peripheral fat mass by bioimpedance method and measurement of waist circumference by means of an ergonimic measure used for circuit measurements. The calculated waist circumference (lt) based on this model significantly correlated with the results of waist circumference measurement using an ergonomic circumferential measuring ruler for four participants that followed a low-sugar diet in a weight reduction experiment.
12
63%
PL
Obok powszechnie znanej odmiany formalnego modelowania zjawisk biologicznych, szczególnie ewolucyjnych, rozwijanej w postaci matematycznej, warto byłoby podjąć także próby modelowania formalnego zjawisk organicznych przy użyciu współczesnej logiki. Dotyczy to w szczególności kolektywnego (w mereologii) lub dystrybutywnego (w teorii mnogości) rozumienia klas lub zbiorów wielu przedmiotów, np. organizmów żywych, ich populacji i gatunków, a także składników organicznych właściwych poszczególnym organizmom (molekuły, komórki, organy). Ujęcie kolektywne odnosiłoby się do stanu owych zbiorów lub klasy, o ile są one warunkowane obiektywnie w samej przyrodzie. Natomiast ujęcie dystrybutywne dotyczyłoby językowo–badawczego przybliżania się wiedzy biologicznej do adekwatnego ujmowania owych zależności przyrodniczych.
EN
Two formal types of models of living processes, especially evolutionary ones, may be distinguished: the well-known mathematical type and the less-known logical one. The latter applies the terms “class” or “set”; both the terms are understood either in a collective sense (in mereology) or in a distributive sense (in set theory). These formal terms may be used among others to such organic multiplicities as populations or species of organisms, and to organic constituents (molecules, cells, organs) of living organism. Collective concepts refer to objects existing in nature, whereas distributive concepts refer to the linguistic and research constructions of models of natural objects, developed to cognitively grasp natural regularities.
PL
Artykuł stanowi formę oryginalnego podejścia badającego problematykę relacji zachodzą-cych pomiędzy zjawiskami ekonomicznymi a zjawiskami politycznymi. Celem szerszym artykułu jest unifikacja teorii stosunków międzynarodowych na płaszczyźnie ekonomicznej. Cel ogólny jest realizowany w oparciu o cele szczegółowe, jednym z tych celów – czego dotyczy artykuł – jest przeprowadzenie procesu badawczego analizującego relacje zachodzące pomiędzy aktywnością militarną USA a poziomem osiąganego przez to państwo wzrostu gospodarczego (w szerszym aspekcie – całego cyklu koniunkturalnego gospodarki USA). Metodologia badawcza stosowana w całym procesie badawczym jest analogicznie tożsama metodologii stosowanej na gruncie ścisłej ekonomii. Tym samym istota procesu badawczego realizowana jest w oparciu o idee pozytywistyczne, behawioralne i scjentyczne filozofii nauk. Ujmując bardziej ściśle: w procesie badawczym wykorzystywane są w sposób abstrakcyjny ele-menty matematyki deterministycznej (dedukcyjnej), jak również określona jest przestrzeń do zastosowania matematyki stochastycznej (indukcyjnej). Aczkolwiek, w pewnym zakresie, uwi-dacznia się wada neopozytywistycznej filozofii nauk (zbyt mała ilość nadmiernie ogólnej wiedzy) i z tego względu poszczególne elementy w sposób subtelny uzupełnione zostały aspektami aprio-rycznymi fenomenologicznego podejścia do kwestii poznania. Wnioski płynące z przeprowadzonego procesu badawczego są obfite, w wielkim skrócie stwierdzić można wysoki poziom korelacji zmiennych procesów ekonomicznych ze zmiennymi procesów polityki.
EN
Article is a form of the original approach, examining the issue of relations between economic phenomena and political phenomena. The purpose of this article is to unify the broader theory of international relations at the economic level. The overall aim is realized on the basis of objectives, one of the goals of what the article is to carry out the research process, analyzing the relationships between the U.S. military activity and the level of economic growth achieved, or in a broader aspect of the business cycle, the economy of the state. Research methodology used throughout the research process is the same as the methodology used similarly on the basic strict economy. Thus, the essence of the research process is carried out based on the ideas of positivist, behavior sciences and philosophy scientists. Put more precisely, the research process used in the abstract elements of deterministic mathematics (deductive) and is determined to used the space of stochastic mathemat-ic (induction). However, to same extent reflected the neo-positivist philosophy of since defect (to little and to general knowledge), and therefore the individual elements are complemented by a subtle aspect of a priori phenomenological approach to knowledge. Conclusions of a researches process are plentiful, in a nutshell, you can find a high level of correlation variables of economics process of policy process variables.
EN
The aim of the article is to build a model describing the relationship between the economic growth and military activity of the USA. The model is a proposition of a formal, abstract and deductive approach towards the abovementioned relationship between war and economic growth, based on the example of the USA. The research is based on the results of previous empirical investigations. The inconclusiveness of empirical research suggests a need for an interpretation in a wider context of social reality.
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2019
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vol. 67
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issue 1
5-18
PL
Przedstawiony jest nowy model Boga, a raczej relacji Bóg-człowiek, używający modelu płaszczyzny rzutowej. Ilustruje on dobrze koncepcje Martina Bubera, którego sformułowania zainspirowały ten model. Następnie pokazane jest użycie tego modelu do wizualizacji w trakcie żydowskiej modlitwy zawierającej werset „Słuchaj Izraelu…”. Po wskazaniu zalet opisanej konstrukcji następuje krytyczna dyskusja adekwatności tego modelu i w ogóle modeli matematycznych w teologii.
EN
In the paper a new model of God, or rather of the relation man-God, is presented. It uses the model of the projective plane. The resulting picture illustrates Martin Buber’s conception, and in fact his statements inspired the construction presented here. Further, it is shown how to apply this model to visualization in the course of the Jewish prayer involving the verse “Hear, oh Israel…”. Having indicated the merits of the model, the author critically analyses its adequacy, and, more generally, the suitability of mathematical models in theology.
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