Economic-Mathematical Model and Mathematical Methods for Substantiating the Choice of the Company Innovation Strategy

Subject. This article discusses the development of a differentiated strategy of innovative development taking into account the distinguishing features of Russia's regions. Objectives. The article aims to improve the effectiveness of innovative development strategies for Russian regions, which vary in the level of science, technology, and innovation capacities. Methods. For the study, we used statistical, and economic and mathematical methods, normalization principle, the methods of comparative, and expert and sociological analyses, foresight techniques, and original region assessment techniques. Results. The article presents certain criteria for differentiation of Russia's regions, taking into account the level of development of scientific and technical activities, and it proposes three modifications of the regional innovation strategy, corresponding to the main types of Russian regions by scientific and technological development. Conclusions. A differentiated approach to a regional innovation strategy development can improve the efficiency and targeting of government innovation policies by making better use of available resources.

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ANALYSIS DEVELOPMENT OF AGRICULTURAL ENTERPRISES OF ECONOMIC-MATHEMATICAL METHODS USING

Intellect XXІ ◽

10.32782/2415-8801/2021-4.6 ◽

2021 ◽

Author(s):

Volodymyr Ulanchuk ◽

Olena Zharun

Keyword(s):

Mathematical Model ◽

Development Strategy ◽

Forage Production ◽

Mathematical Methods ◽

Cattle Breeding ◽

Agricultural Enterprises ◽

Sectoral Structure ◽

Production Type ◽

Regional Development Strategy ◽

Different Types

The article deals with the problems of the regional development strategy, which primarily should be aimed at increasing the soil fertility in Ukraine. Suggested concept of innovation-investment development of agriculture, which is based on the objective necessity of providing agricultural enterprises in future with investments taking into account the state of their development, the most complete use of internal opportunities and adaptation to changes in the external environment. The economic-mathematical model for setting the prospects of agricultural production development has been developed. To substantiate the development of agricultural enterprises of different types of production prospects, the task matrix includes data on production and financial activities which was collected on the basis of typical agricultural enterprises. These enterprises data was determined on the basis of processing of statistical information on agrarian formations of a certain region. The proposed economic-mathematical model of the problem is designed in such way that it is possible to introduce other variants for the determined situations, by making minor changes in the limitations of its matrix. It gives opportunities to set the need for investments for the goal achievement with the maximum predicted profit by enterprises of each separate production type and in the whole region of enterprises which are engaged in the production of agricultural products. The solution of the problem by this model will enable to determine in each production type of agricultural enterprises such a sectoral structure of production, which gives the opportunity to obtain maximum profits and the minimum terms of return on investment. Developed activities at the stage of practical realization and commercialization of innovations allow increasing income of the agricultural enterprises from the cattle breeding and plant growing sectors, to organize their own production of the required amount of cultures to ensure optimum forage production beef cattle and dairy direction, to preserve quality characteristics of cultivated of soils.

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The Emergence of Mathematical Needs in an Industrial Center

Mathematics Teacher ◽

10.5951/mt.46.1.0001 ◽

1953 ◽

Vol 46 (1) ◽

pp. 1-2

Author(s):

Arvid W. Jacobson

Keyword(s):

Mathematical Model ◽

Modern Science ◽

Order Effects ◽

Entire System ◽

Trial And Error ◽

Mathematical Methods ◽

Economic Process ◽

Operating Unit ◽

Industrial Center

The foremost feature in modern science and technology is the expanding role of mathematics. In industry and business the increasing complexity of problems and the ever-present search for better products and services, lead to the use of mathematical methods. Trial and error methods can not alone yield the information of the behavior of a physical system or a business procedure or an economic process necessary if improvement in design or function is to be achieved. To understand and evaluate the effects of small components on the behavior of a system, it must be considered as a single operating unit. The functional dependance of the entire system must be expressed in terms of all of the components, large and small. Thus a mathematical model emerges which is an abstraction of the quantitative and logical relationships of the system. Often, as further improvements are sought, the effect of a larger number of these smaller components need to be understood and weighed. It is thus the proper evaluation of the small effects or “second order effects” that determines progress.

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OPTIMIZATION OF USE OF MANUFACTURING RESOURCES BY ENTERPRISES OF THE AGRICULTURAL SECTOR

Economic Analysis ◽

10.35774/econa2018.04.225 ◽

2018 ◽

pp. 225-234

Author(s):

Svitlana Nuzhna ◽

Nataliia Samarets

Keyword(s):

Mathematical Model ◽

Economic Efficiency ◽

Economic Activity ◽

Agricultural Sector ◽

Raw Materials ◽

Mathematical Methods ◽

Forage Crops ◽

Resource Potential ◽

Agricultural Enterprises ◽

Microsoft Office

The article deals with the main aspects of the stages of development and construction of an optimization of the economic and mathematical model of agricultural enterprises' resources for identifying reserves of resource potential, its rational use and increase of the economic efficiency of economic activity. Some economic indicators of functioning and development of agricultural enterprises that can be taken into account when compiling an optimization model are analysed. The basic stages of construction of the economic and mathematical model and their characteristic features are revealed. Applied testing of mathematical calculations has been carried out for the agricultural enterprise LLC UM-Vatutino, which wants to optimize the structure of its production in order to ensure maximum overall profitability. The developed economic and mathematical model provides the main activities of the UM-Vatutino LLC. They are the cultivation of grain and forage crops, cows of various productivity. Such a model can be used to analyse and identify the reserves of resource potential of enterprises of any form of ownership, at different periods of time, as well as to identify features of strategies for improving the economic efficiency of economic activity of the enterprise itself and its individual units. In addition, the constructed model can be modified both structurally and substantively. The analysis results are processed by means of one of the office programs of Microsoft Office Excel spreadsheets. Data analysis has been performed with the use of the "Solver" tool in spreadsheets. It allows finding an optimization solution with a large number of variables. As a result, it has been confirmed that the application of economic and mathematical methods is very effective in assessing not only the resource potential of agricultural enterprises, but also optimizing the volumes of sales of products, feeds, raw materials for another. The process of modelling in the activities of agricultural enterprises gives the opportunity to make managerial decisions at various stages of the operation and development of the enterprise.

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Modelling of hydrogen diffusion in the retina

ANZIAM Journal ◽

10.21914/anziamj.v61i0.14995 ◽

2020 ◽

Vol 61 ◽

pp. C119-C136

Author(s):

Wafaa Mansoor ◽

Graeme Hocking ◽

Duncan Farrow

Keyword(s):

Mathematical Model ◽

Blood Flow ◽

Oxygen Transport ◽

Hydrogen Diffusion ◽

Theoretical Models ◽

Retinal Blood Flow ◽

Inert Gas ◽

Mathematical Methods ◽

Physiol Heart Circ ◽

Hydrogen Clearance

A simple mathematical model for diffusion of hydrogen within the retina has been developed. The model consists of three, well-mixed, one dimensional layers that exchange hydrogen via a diffusion process. A Fourier series method is applied to compute the hydrogen concentration. The effect of important parameters is examined and discussed. The results may contribute to an understanding of the hydrogen clearance technique to estimate blood flow. A two dimensional numerical method for the hydrogen diffusion is also presented. It is shown that the predominant features of the process are captured quite well by the simpler model. References V. A. Alder, D. Y. Yu, S. J. Cringle and E. N. Su. Experimental approaches to diabetic retinopathy. Asia-Pac. J. Ophthalmol. 4:20–25, 1992. J. C. Arciero, P. Causin and F. Malgoroli. Mathematical methods for modeling the microcirculation. AIMS Biophys. 4:362–399, 2017. doi:10.3934/biophy.2017.3.362 D. E. Farrow, G. C. Hocking, S. J. Cringle and D.-Y. Yu. Modeling Hydrogen clearance from the retina. ANZIAM J. 59:281–292, 2018. doi:10.1017/S1446181117000426 A. B. Friedland. A mathematical model of transmural transport of oxygen to the retina. Bull. Math. Biol. 40:823–837, 2018; doi:10.1007/BF02460609 D. Goldman. Theoretical models of microvascular oxygen transport to tissue. Microcirculation 15:795–811, 2008. doi:10.1080/10739680801938289 A. C. Hindmarsh. ODEPACK, A Systematized Collection of ODE Solvers. In Scientific Computing, R. S. Stepleman, et al., Eds., pp. 55-64. North-Holland, Amsterdam, 1983. S. S. Kety. The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol. Rev. 3:1–41, 1951. http://pharmrev.aspetjournals.org/content/3/1/1 B. P. Leonard. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19:59–98, 1979. doi:10.1016/0045-7825(79) 90034-3 S. L. Mitchell. Coupling transport and chemistry: numerics, analysis and applications. PhD thesis, University of Bath, UK, 2003. https://researchportal.bath.ac.uk/en/studentTheses/coupling-transport-and-chemistry-numerics-analysis-and-applicatio G. A. Winchell. Mathematical model of inert gas washout from the retina: evaluation of hydrogen washout as a means of determining retinal blood flow in the cat. Master\textquoteright s Thesis, Northwestern University, Evanston, USA, 1983. https://search.library.northwestern.edu/permalink/f/5c25nc/01NWU_ALMA21563278530002441 D. Y. Yu, V. A. Alder and S. J. Cringle. Measurement of blood flow in rat eyes by hydrogen clearance. Am. J. Physiol. (Heart Circ. Physiol.) 261:H960–H968, 1991. doi:10.1152/ajpheart.1991.261.3.H960 D. Y. Yu, S. J. Cringle, V. A. Alder, E. N. Su, and P. K. Yu, Intraretinal oxygen distribution and choroidal regulation in the avascular retina of guinea pigs. Am. J. Physiol. (Heart Circ. Physiol.) 270:H965-H973, 1996. doi:10.1152/ajpheart.1996.270.3.H965 S. Cringle, D.-Y. Yu, V. Alder, E.-N. Su, and P. Yu. Choroidal regulation of oxygen supply to the guinea pig retina. In A. G. Hudetz, and D. F. Bruley (Eds.), Oxygen Transport to Tissue XX, pp. 385–389. Springer, 1998. doi:10.1007/978-1-4615-4863-8

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A new formula to calculate the medicine dosage in function of the weight

Research Society and Development ◽

10.33448/rsd-v10i7.16594 ◽

2021 ◽

Vol 10 (7) ◽

pp. e30110716594

Author(s):

Dyecika Souza-Couto ◽

Amanda Barcelos-Faria ◽

Emmanuel Freitas-Ferreira ◽

Tales Alexandre Aversi-Ferreira

Keyword(s):

Mathematical Model ◽

Elderly People ◽

The Elderly ◽

Mathematical Methods ◽

New Formula

A problem in relation to medicine concentration is linked to difference of age of the patients when the medicine was formulated for a pattern age, for instance, for adults. The use of this kind of medicine for children must be calculate correctly and some formulas based in the empirical mathematical methods were suggested and they are used nowadays; however, patients form a same pattern age but with different weight shows a different biotype and requires a different concentration of medicines, as well as the children and the elderly people. According, in this work, based on the mechanical mathematical model using the relation area/volume, a more exact calculus including the metabolism, was proposed to generate a more accuracy formula to calculate the medicine concentration for children and for people of different weight.

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THE NONLINEAR MODEL OF BEHAVIOR OF TWO COMPETITIVE FIRMS

BULLETIN OF CHERNIVTSI INSTITUTE OF TRADE AND ECONOMICS ◽

10.34025/2310-8185-2021-1.81.08 ◽

2021 ◽

Vol I (81) ◽

pp. 115-128

Author(s):

Bohdan Drin ◽

◽

Iryna Drin ◽

Svitlana Drin ◽

◽

...

Keyword(s):

Mathematical Model ◽

Differential Equations ◽

Mathematical Description ◽

Information Technologies ◽

Dynamic Models ◽

Nonlocal Problem ◽

Variable Coefficients ◽

Economic Behavior ◽

Algebraic Equations ◽

Mathematical Methods

The practical task of economics lies in applying the methods of substantiating its decisions. For economics, the main method is the modeling of economic phenomena and processes and, above all, mathematical modeling, which has been stipulated by the presence of stable MATHEMATICAL METHODS, MODELS AND INFORMATION TECHNOLOGIES IN ECONOMY Issue I (81), 2021 117 quantitative patterns and the possibility of a formalized description of many economic processes. The economic-mathematical model contains a system of equations of linear and nonlinear units that promote a mathematical description of economic processes and phenomena, consists of a set of variables and parameters and serves to study these processes and control them. Dynamic models of the economy describe it in development, as well as provide a detailed description of technological methods of production. Mathematical description of dynamic models is carried out with the use of a system of differential equations (in models with continuous time), difference equations (in models with discrete time), as well as systems of algebraic equations. It is important that the investigation of various economic issues has led to the development of the mathematical apparatus. In linear algebra, productive matrices are caused by the studies of intersectoral balance, whereas mathematical programming arose in the course of researching the optimal plan for the distribution of limited resources. In a similar way, there emerged the theory of economic indices and econometrics, the theory of production functions and the theory of consumption, the theory of general economic balance and social welfare, the theory of optimal economic growth. The paper under studies deals with the dynamic economic behavior of two competing objects, whose mathematical model is a nonlinear nonlocal problem for a system of ordinary differential equations with variable coefficients and argument deviation. The dynamic mathematical model is based on the assumption that the volume of output of both firms is determined by such factors on which output depends linearly. The model under discussion includes nonlinear factors, which describe the level of distrust of the competitors and depend on the time of observations and production volumes in previous moments, because the latter significantly affect the production activities of the firm. Such mathematical models are called time-delayed models.

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Математична модель антени з нелінійними характеристиками для розрахунку елект-ромагнітного поля у зоні Френеля

RADIOELECTRONIC AND COMPUTER SYSTEMS ◽

10.32620/reks.2021.4.04 ◽

2021 ◽

pp. 46-58

Author(s):

Дмитро Вячеславович Грецьких ◽

Василь Олександрович Алєксєєв ◽

Андрій Володимирович Гомозов ◽

Віктор Олександрович Катрич ◽

Михайло Васильович Нестеренко

Keyword(s):

Mathematical Model ◽

Electromagnetic Compatibility ◽

Phase Distribution ◽

Mutual Influence ◽

Fresnel Zone ◽

Nonlinear Effects ◽

Arbitrary Field ◽

Mathematical Methods ◽

Nonlinear Characteristics ◽

Transmitting Antenna

The paper presents a mathematical model of radio-electronic systems (RES), which include antennas and their excitation paths with nonlinear characteristics. The model provides acceptable accuracy of RES quality indicator analysis and electromagnetic compatibility (EMC) for further practical design. General purpose: the development of a mathematical model of a transmitting multi-input radiating structure with nonlinear characteristics under the Fresnel zone. Objective: choice justification of a structural schema of a radiating multi-input system with a radiator that has a distributed nonlinear surface impedance; obtaining the nonlinear integral equations (NIE) related to the current density for radiators with distributed nonlinearity, excited by an arbitrary field distribution for solving the general analysis problem; obtaining a ratio for calculating focused electromagnetic fields (EMF) created by multi-input radiating structures with nonlinear characteristics in the Fresnel zone. The methods used in the paper are mathematical methods of electrodynamics and antennas theory with nonlinear elements (ANE), theory of microwave circuits, and multipoles. The following results were obtained. An electrodynamics approach is proposed to analyze the entire set of nonlinear effects arising in transmitting multi-input radiating structures with nonlinear characteristics. It allows considering the mutual influence of the transmitting and receiving antennas with nonlinear characteristics in the system itself and the electrodynamics interaction of the transmitting antenna with nonlinear characteristics with RES for other purposes. Component equations (NIE) of multi-input radiating structures that establish the relationship of amplitude-phase distribution at the inputs of radiators with distributed nonlinearity and amplitude-phase distribution on their surfaces are obtained. A mathematical model of multi-input radiator structures with nonlinear characteristics in the Fresnel zone for analysis purposes has been produced. Conclusions. The scientific novelty of the obtained results is as follows: a generalized theory of transmitting antennas of arbitrary configuration with nonlinear characteristics in the Fresnel zone, which makes it possible to analyze the characteristics of these antennas considering the positive and negative (beneficial and adverse) nonlinear effects that arise in them.

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TAMING COVID-19 EPIDEMIC IN SÃO PAULO WITH A LOGISTIC MODEL AND NON-PHARMACEUTICAL MEASURES

10.1101/2020.05.06.20093666 ◽

2020 ◽

Author(s):

Marcelo Marchesin

Keyword(s):

Mathematical Model ◽

Intensive Care ◽

Logistic Model ◽

Sao Paulo ◽

São Paulo ◽

Mathematical Methods ◽

Hospital Beds ◽

Seriously Ill Patients ◽

Simple Logistic ◽

Seriously Ill

Abstract.In this paper I use the simple logistic mathematical model to represent the development of COVID-19 epidemic in São Paulo city under quarantine regime and I estimate the total amount of time it is necessary to decrease the number of seriously ill patients in order to reduce the demand for hospital beds of Intensive Care Units (ICU) to tolerable levels. Clearly the same reasoning and mathematical methods used in here can be used for any other city in similar conditions of social isolation.

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