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2
ских услуг е цифровой экосистеме в обеспечении устойчивого экономического развития.
Определены стратегические направления развития цифровой среды предоставления медицинских услуг вусловиях цифровизации экономических отношений, отражающие и национальные цели развития экономики государства.
Литература:
1. Цифровое здравоохранение е эпоху посгкоеи-да [Электронный ресурс]. - Режим доступа: https:/ /cipr.ru/ (дата обращения: 24.06.2021 г.). https:// www.youtube.com/wa tch?v=_l-kY2y7p7o
2. Global strategy on digital health 2020-2025 [Electronic resource]. - Available at: https:// www.who.int/docs/default-source/documen ts/ gs4dhdaa2a9f3 52b0445bafbc79ca799dce4d.pdf (date of access: 30.06.2021).
3. Аккредитация в образовании [Электронный ресурс]. - Режим доступа: https://akvobr.ru/ cifrovaya_obrazova telnaya_sreda_ehto.html (дата обращения: 26.06.2021).
4. T'iemann, Кч Annaggar, A. A framework for the theory-driven design of digital learning environments (FDDLEs) using the example of problem-solving In chemistry education [Electronic resource]// Interactive learning environments. 2020, - Available at: https://www.tandfonline.com/doi/ a bs/10.1080/10494820.2020.1826981 DOI: 10,1080/ 10494820.2020.1826981.
5. Soboleva, Elena V., Karavaev, Nikita L. Characteristics of the Project-Based Teamwork in the Case of Developing a Smait Application in a Digital Educational Environment // European journal of contemporary education. 2020. - Vol. 9. - Issue 2. -Pp. 417-433.
6. Nascimento, M.G., iorio, G.,Thome,T.G. Medeiros, A.A., et al. Covid-19: A Digital Transformation Approach to a Public Primary Healthcare Environment [Electronic resource] // Book Series: iEEE Symposium on Computers and Communications ISCC. 2020. - Pp.: 892-897. - Available at; https://easychair.org/publications/prepri nt/8gbL (date of access: 29.06.2021).
7. Da Silva, M.P., Goncalves, A.L., Dantas, M.A. A conceptual mode! for quality of experience management to provide context-aware eHealth services [Electronic resource] // Future generation computer systems - The international journal of eScience.2019.-Vol. 101.-Pp. 1041 1061.-Available at: https://www.researchgate.net/publication/ 334674887_A_concep1idjTiodel_fa_qualr^_ofjExperience_ management _to_, provi d e_ с on tex t-a wa re_e He a lth_
services (date of access: 17,05.2021}. DOI: 10.1016/ j.future.2019.07.033
8. An eHealth Context Management and Distribution Approach in AAL Environments [Electronic resource] / da Silva, M P., Nazario, D.C, Dantas, MA, Goncalves, A.L et al. // Book Series: IEEE 29th Internationa! Symposium on Computer-Based Medical Systems. - 2016,- Pp. 169-174. - Available at: https://ieeexplore.ieee.org/document/7S45978 (date of access: 14.06.2021). DOI: 10.1109/ CBMS, 2016.15.
9. Pibsof, N.P., Barrett, M.,0born, E.etal.Telemedicine Implementation in COVID-19 ¡CU: Balancing Physical and Virtual Forms of Visibility // Herd-health environments research & design journal. Article Number: 19375867211009225, DOI: 10.1177/ 19375867211009225.
10. Baker, S.B.,Xiang,W., Atkinson, I, Internet of Things for Smart Healthcare: Technologies, Challenges, and Opportunities [Electronic resource] // IEEE ACCESS. 2017. Vol. 5. - Pp. 26521-26544. - Available at: https:/ /ieeexplore.ieee.org/document/8124196 (date pf access: 17.06.2021). DOI: 10.1109/ AC CESS.2017.2775180
11.Ajana, B. Digital health and the biopolitics of the Quantified Self [Electronic resource] // Digital Health, 2017. Vol. 3. Article Number: 2055207616689509. -Available at: https-./Zjoumals.sagepub.com/doi/full/ 1 0.1 1 77/205520 7616689509 (date of access: 16.05.2021), DOI: 10.1177/2055207616689509,
12.Craig, KJ., Willis, Van C; Gruen, D. etal.The burden of the digital environment: a systematic review on organization directed workplace interventions to mitigate physician burnout // Journal of the American medical informatics association. - 2021. -Vol. ?28.- Issue5.-Pp.? 985-997.
13.Sax, M. Optimization of what? For-profit health apps as manipulative digital environments // Ethics and information technology [Electronic resource]. -Available at: https://papers.ssrn.com/sol3/papers. cfm?abstract_id=3752597(dateofac cess. 14.06.2021). DOI: 10,1007/s 10676-020-09576-6. 14.Masyuk, N., Bushueva, M., Bragina, Z. The Institutional Regulatory Environment of the Digital Ecosystem: Theoretical Approach and Russian Experience [Electronic resource] // Conference: Innovative Economic Symposium - Potential of Eurasian Economic Union (IES 2019). Book Series: ? SHS Web of Conferences. - 2019, - Vol. 73, - Article Number: 01019. - Available at: https://www, researchgate.net/publica ti on/3 3 85 51 98 9_ The J nsiitutiona LRegulatoryJnvironrnent_of_the_Dig rtal_ EcosystemJTl)ewettcal_Ap[:)roac[i_ar)d_Rus,^an_Fjqaerience (date of access: 02.06.2021). D0l:l0.1051/shsconf/ 20207301019
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ОСЕВАЯ ЛИНИЯ "РОЯ" ГЛОБАЛЬНОЙ ЭКОНОМИКИ В ПРОСТРАНСТВЕ ЭКОНОМИЧЕСКИХ ИНДЕКСОВ ЕР/, ВЦ CP! Сейдаметова За рема Сейдалиевна, доктор педагогических наук, профессор Темненко Валерий Анатольевич, кандидат физико-математических наук, доцент
Крымский инженерно-педагогический университет имени Февзи Якубова, Симферополь, Республика Крым
Цель исследования - определить понятие осевой линии роя глобальной экономики в трехмерном простран cree экономических индексов EPI, BU, СР/ и сконструировать математические выражения, определяющие форму этой линии на основе статистических данных об экономике стран мира в 2019 г. Для построения
te
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осевой линии использованы медианные точки EPI-групп глобальной экономики. В статье рассматриваются определенные предположения об асимптотическом поведении осевой линии при малых и больших значениях индекса CPL Научная новизна заключается в явном построении осевой линии глобальной экономики. Существование и форма этой линии выявляют в результате некоторый фундаментальный тренд мировой экономики, статистически связывающий на уровне EPl-rpynn состояние общества (индекс CPI), меру социальной ориентации государства (индекс ВЦ') и экономическую продуктивность (индекс EPI),
Ключевые слова; глобальная экономика; экономические индексы; ЕР ¡-группы; медианные точки EPl-rpynn; индекс восприятия коррупции СИ; индекс бюджетной нагрузки 8U; индекс экономической продуктивности ЕР%
DO! 10.24923/2222-243Х.2021-40.15
УДК 339.97:330.43 ВАК РФ 08,00,13
> Сейдаметова 3. С, 2021
> Темненко (¡ А ., 2021
SBDAMETOVA Zarema Seidatievna, DScof Pedagogical sciences, Professor
TEMNENKO Valéry AnatoHevich, PhD of Physics and Mathematical sciences, Associate Professor
Eevzi Yakubov Crimean Engineering-Pedagogical University, Simferopol, Republic of Crimea
THE AXIAL LINE OF THE GLOBAL ECONOMY "SWARM" IN THE SPACE OF ECONOMIC INDICES EPL DUr CPI
The purpose of the Study is to determine the concept of the axial line of the swarm of the global economy in the three-dimensional space of the economic indices EPl, BLI, CPI and to construct mathematical expressions that determine the shape of this line based on statistical data on the world economy. To construct the axial line the median points of the EPI-groups of the global economy were used. In the paper we discuss certain assumptions about the asymptotic behavior of the axial line at small and large values of the CPI. Scientific novelty of research lies in the explicit construction of the axial line of the global economy. The existence and shape of this line reveal as a result some fundamental trend in the world economy, statistically Unking at the level of EPI-groups the state of society (CPI), the measure of the state's social orientation (BLI) and economic productivity (EPl). Keywords; global economy; economic indices; EPI-groups; median points of EPI-groups; Corruption Perception Index CPI; Budget Loading index BU; Economic Productivity Index EPl.
Introduction
In previous studies by the authors [1], [2], [3], the existence of EPI-groups in the global economy was revealed and the position of the median points ofEPI-groups in the three-dimensional space of economic indices EPl, BLI, CPI was determined. In this regard, an attempt to construct the axial fine of the swarm of the global economy in the form of some curve passing through the median points of EPi-groups, or near these median points in the sense of the best approximation of the least square method, seems relevant. This axial line may be a first approximation to describe the hidden laws of the global economy. These laws form the general view of the swarm of the global economy and the density of distribution of countries in this swarm, containing about 170 countries, for which the economic indices EPl, 8LI, CPi are known.
The purpose of the study - building the axial line of the swarm of the global economy - structured thefollowing tasks: 1) rational construction of assumptions about the asymptotic behavior of the axial line in the area of "weak" economies (small values of CPi and EPl) and "strong" economies (large values of CPI and EPl); 2) construction of an analytical expression for the projection of the axial line on the plane of economic indices {CPI, BLI); 3) determination of the parameters of this analytical expression by the least squares method; 4} construction of the projection of the axial line on the plane of economic indices {CPI, EPi} in the form of a continuous and piecewise-smooth curve passing through the projections of the median points of the EPI-groups onto this plane.
The theoretical basis of the research was the publications [1], [2], [3], [8], [9].
The practical significance of this study is to create a basis for identifying the laws of the global economy at two levels: 1) the level of the general trend that forms the type of the axial line; 2) the level of group deviations from this trend within each EPi-groups.
Basic part
Genera/ description of terminology and statistical data. The paper [1] provides a general description of the state of the global economy in 2019 in the space of economic indices EPI, 8U, CPI. The papers [2], [3] presented a detailed description of the EPI-groups of the global economy in 2019 and introduced the idea of the median points of the EPI-groups. Table 1 shows the coordinates of the median points of EPI-groups in the three-dimensional space of economic indices.
The top line ofTable 1 contains the abbreviated names of the EPI-groups introduced by us [1 ]: LDC - Least Development Countries (EPkO.8) LC - LowCold (0.94<EPI<2.0) MC-JVliddleCold (2.2<EP!<4.4) UC - UpperCold (4.6<EPI<11.5) LW - LowWarm (12.9<EPI<17.1) UW- UpperWarm (20.1 < EPI <29.0} H - Hot (35<EPS)
Table 1. Coordinates of the median points of the EPI-groups of the global economy in 2019
The abbreviated designation W in the top line ofTable 1 denotes the "warm" zone of the global economy. This "warm" zone Is an integration of EPI-groups LowWarm and UpperWarm. For some research tasks, the "warm" zone of the global economy can be considered as one large EPI-group.
The economic indices shown i n Table 1 contain the following information:
CP! (Corruption Perception index) is an expert assessment on a 100-point scale that characterizes the level of corruption in the country: the higher the CPi index, the lower the level of corruption. The method for determining the CP! index is described in [4]. We borrowed data on the CPI index for each country from [5].
BLI (Budget Loading Index} is the ratio of government budget revenues of a given country (BR} to the Gross Domestic Product (GDP}, expressed as a percentage. We borrowed information about the BLi for each country from [6].
EPI (Economic Productivity Index) is a percentage ratio of the specific (per capita) Gross Domestic Product Per Capita (GDP/PC) of a given country In a given year to the maximum value of
this value (max (GDP/PC}), achieved in some country in the world in the same year. This champion-country with the highest GDP/PC is selected from among countries with known CPI and BLI. In 2019, Luxembourg was such a champion-country (however, as in a number of previous years). Liechtenstein and Monaco ^ usually outperform Luxembourg In terms of GDP/ rd PC, but for these two countries, data on CPI and fy BLI are not provided in [5] and [6]. The data on the value of GDP/PC of the countriesofthe world, Q-necessary for calculating EPI, we borrow from [7].
The EPI and BLI indices shown in Table 1 are expressed as a percentage. The symbol "%" in lu Table 1 is omitted. EPI and BLI indices can vary ^ from zero to one hundred percent. There are g-situatlons when in a certain country 8LI>100%, 3. The government of such a country is dependent £? on foreign financial support even for performing ^
basic government functions. We prefer not to |-
include such countries in the picture of the three-dimensional space of economic indices that we construct.
The CPI of each country is a discrete integer index, expressed in points on a 100-point 7, scale. The CP! of the median point of some EPI-groups may be half-integer.
For the purposes of economic analysis, it is permissible to neglect the mathematical difference between continuous variables (EPi and BLI) and discrete variables (CPI), We can think about the global economy as about a swarm of one hundred and seventy points (about the same number of countries each year have all three known economic indices), located in a continuous "index box" of 100 100 100. The fact of the existence of (so far not formulated) laws of the world economy is manifested in the fact that the points of this swarm cannot occupy arbitrary positions in this "box": a completely arbitrary, random combination of three economic indices is impossible. We noted earlier that the nucleus of the world economy, interpreted as a set of nuclei of the EPI-groups, occupies less than five percent of the total volume of the "index box" [81.
The purpose of this paper is to construct some central, axial line of the swarm of the global economy by the coordinates of the median points of the EPI-groups shown in table 1.
The last row in the table 1 contains a special socio-economic parameter a a,introduced earlier in [2] as follows:
EPI-groups Median point coordinates LDC LC MC UC LW W UW H
CPI 27 30 35 39 54 57 58.5 77
BLI 19.373 19.302 25.85 26.519 34.983 36.91 40.159 38.922
EPI 0.565 1.31 3.27 6.94 14.71 18.606 24.97 44.413
i 0.42 0.65 0.87 1.20 0.69 0.70 0.85 0.50
& =
so
4 ■ EPF (CPI)*'
I03
(I)
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Substituting the EPi and CPI indices for the median points of EPI-groups into formula (1), we obtain the values of the parameter a for each EPLgroup.
The origin of formula (1) is associated with the empirical fact that we established earlier [8], [9] of the statistical relationship that exists between the CPI and EPI indices at the level of the nuclei of EPi groups:
EPI = a (CPI)4.
(2)
The proportionality coefficient a, appearing in formula (2), is of the order of and varies somewhat from one EPi-group to another. However, this change is small, the largest and smallest values of a differ only by a factor of 3, The very same values of EPI and (CPI)4 for different EPI-groups differ by three orders of magnitude. Accordingly, It is convenient to look for the equation of the projection of the center line of the swarm of the global economy on the plane {CPI,EPi} in the following form
EPI = - * A(CPI) * (CPI)4 -10"s. 4
(S)
The function A in formula (3), which weakly depends on the CPI index, must be constructed as some continuous function passing in the best way (in the sense of the least squares method) through the points of table 1 & (CP!) corresponding to the median points of the EPi-groups.
The usefulness of formula (3) is as follows. Using multiplies (CPI)4, we highlight the main trend of the statistical relationship that exists in the global economy between the CPf and EPI indices. The task of constructing the axial line of the "swarm" of the global economy is reduced to constructing a low-varying function A(CPI).
We will define the axiai line of the global economy's swarm as a smooth continuous spatial curve of a certain type, which deviates least (in the mathematical sense of the standard deviation) from the set of eight median points of Table 1 in the space of economic indices EPI, 8LI, CPI. The expression "a curve of a certain type" means that the data in Table 1, we must supplement with assumptions about the behavior of the curve at very small CPis, close to zero, and, possibly, assumptions about the behavior of the curve at very large CPis, close to CPI 100,
The projection of the axial line on the plane of economic indices {CPI, BlIJ. When constructing
this axial curve, we will temporarily replace the three-letter symbols of economic indices with one-letter symbols:
CPI >x. EPI >v, BTJ -z.
This change of notation will makethe formulas describing theaxiallineofthe swarm of the global economy more compact.
The problem of choosing the type of dependence of z (e.g., Btl) from x (e.g., CPI). is somewhat difficult. Data represented in Table 1 suggest that for sufficiently large x, the value of z tends to some positive constant.
When choosing to extrapolate the data in Table 1 in the region of small r(r->0), as we believe, two different assumptions are possible.
1. As x decreases below a certain value x
mm
(x <20), z tends to zero. We'll call this theHoobes
* mm '
hypothesis. This assumption means that society is in a state of "Beilum omnium contra omnes" [TO] ("the war of all against all"), the state has no social obligations, the economy has a military-predatory nature.
This state of society, governance and economy can hardly be adequately described by some point in the three-dimensional index space. In countries affected by long-term armed conflicts, the CPI may indeed be less than 20, in such conditions, statistics on GOP/PC and BLI cause some distrust: how can you accumulate and control data flows in an armed conflict? Is it appropriate to use economic terminology at all? Another assumption seems to be somewhat more plausible:
2, As x decreases below a certain value, z asymptotically tends to a certain positive value. We will call this assumption the "optimistic hypothesis" or the "humanitarian hypothesis". Within the framework of this hypothesis, we assume that the governance continues to function even with a very poor state of society (low CPI values) and economy (low EPI values).
Within the framework of this "optimistic hypothesis", a convenient approximation of the dependence z{x) is, in our opinion, a four-parameter expression containing the error function:
z = Z(x) = a + (- aX-), (4/
where
1>,
(5)
and
2 f a
Erf(v) = -j= I e 1 dx (error function).
(6)
The necessary information about the error function can be found, for example, in the reference books [It],[12].
Function (4} ensures the "correct" behavior of Zfx) for x«xg Z(x)« a = const and x»Xg Z(x) sb a + p — const.
Function (4) may seem excessively cumbersome to describe economic phenomena. However, there seems to be some managerial and economic sense in this formula. This function shows that the intention to increase budget spending z white improving the state of society -and the strength of this intention is measured by the derivative dZ/'dx-XHi intention is described by a normal (Gaussian) probability distribution with center x0 and variance a2.
The four parameters a,p,x0 and a included in formula (4) are determined from the condition of minimizing the sum of squares of deviations of curve (4) from the points of Tabie 1:
a
S = - Z(a, p, x0,a; X0)2
W
k-i
In expression (7), the index k numbers the points in the Table -is the CP I index k-th point, 2, - is the BU index of the k-th point in Table 1.
We have constructed a projection of the axial line of the swarm of the global economy onto the coordinate piane of economic indices CP! BU in the form of a curve of the form (4), (5), containing the error function (6), it can be noted that this is not a difficult task: the error function is a standard Microsoft Excel function and it is quite possible to construct a curve of the form (4) without knowing what the "integral of probabilities" is (and, perhaps, not even knowing what the "integral" is}.
A series of preliminary calculations on a fairly coarse grid of parameters in the four-dimensional space of parameters a,p,x0, and determined the optima! values of the parameters a,p and
CL = 18,P = 21,x0 - 40.
(8)
. o i.
|Dfl I I 104
iq.B ii .a
Fig, 1, The sum of the squares of the deviations of the median points of the EPI-groups from the curve of the form (2) as a function of variance a = i8.p - 2i,x0 - 40
Hot
r
For the values of parameters (8), a graph of the function S- -S(o) was plotted (Fig. 1}, where S is the sum of squares of deviations from a curve of the form (4) in the CPI x BU plane. The optimal variance value was determined from this graph:
CU
o
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-0 Q-LQ Os
X uu O
o
m
ai 2
s
a = 9.95.
№
Fig, 2. Projection of the axial line of the swarm of the global economy onto the plane of the economic indices CPI EPl, Legend: • - median points of EPI-groups; □ - boundaries
of the nuclei of EPI-groups;....... - axial line
of the swarm of the global economy
Fig, 2 shows the projection of the axial curve of the swarm of the global economy onto the coordinate piane of economic indices CPI BLI, built in the form of a curve of the form (4), (5), (6) with the optimal parameters (8) and (9), providing the minimum value of the sum of squares of deviations curve from the projection of the median points of the EPi-groups on this plane. The same figure shows the median points of the EPi-groups themselves, as well as the boundaries of the nuclei of the EPI-groups. The name is Indicated on!y for the EPI-group "Hot". The names of the remaining EPi-groups are not shown in this figure, since in the CPI x BLI plane, the nuclei of the EPI-groups partially overlap each other.
The projection of the axial line on the plane of economic indices {CPI, EPl}. When constructing projections of the axial fine onto the piane of economic indices {CP!,EPl}, we will present in table 2 a different form of the part of table 1 we need. In this view, instead of the names of EPI-groups, there are their numbers assigned in ascending order of the EPI-index of the EPI-groups median points. "Combined" EPI-group "Warm", which is a
81
union of EPI-groups LowWarm and UpperWarm, in table 2 does not appear.
Table 2. Data on the values of the indices x and à for EPi-groups of the global economy in 2019
n (EPI-group number) 1 2 3 4 5 6 7
X 27 30 35 39 54 58.5 77
s 0.42 0.65 0.87 1.20 0.69 0.85 0.50
tC
s
LU
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o
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=r
s X o
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Formula (3) can be represented as
y=--A(r).(r)M0-!\
(10)
where >>=EPi,x=CPI.
The slowly varying function A/x) should be
constructed so that for the values xrx_ (r = 1,7), appearing in table 2, the function A(xt) should be equal to the values q ., presented in this table.
For the function AM only one a priori upper estimate is possible for r= 100:
A(100) < 0.4.
m
The estimate (11) follows from the trivial condition
v < 100.
(12)
The inequality (12) follows from the definition of the index EPS.
Fig. 3 shows the set of points fx,, a,) from table 2 and a continuous but nonsmooth approximating curve A(x) passing through them. This curve is constructed as follows.
A(x)=b+k.-x. (14)
3} For .*6 100:
A(x)=b6+c6*(l00-xf. (15)
The choice of A(x) in the form (13) (for c9>0) guarantees that the function A/x) has a minimum at r=0. The lower bound for the parameter p is determined by the condition b0 > 0.
The choice of A(x) in the form (15) guarantees that the function A(x) has a minimum at r=lOO (for c6>0).
Linear functions A(x) (14) are the simplest local approximations of the unknown function A(x), which can be proposed in the absence of any economic theory capable of predicting the form of this function.
In relations (13), (14) and (15) the coefficients
b„ cn, b„ c, n bk. 2<i<5 are constants
0 0 6 6 t f
determined from the condition of the passage of the broken continuous line A/x) through the points presented in table 2. From this condition, it is easy to obtain explicit expressions for all these coefficients:
gs-fli , _â1A2"-â1
C0 - 2t> 2n > 0 ~
2p _ Ip > l2
(16)
where A = x2/xi -1.1111 for i = 27$:
/
(
J
/
* : 4- 1 X,
Xf*i Xi
aA - a7
cfi =
£>6 =
(*7-*6)(200-(x6 + x7))'
q7(100 - x6)z - a6C100-x7y (x7 - X6)(200- (X6 + X7))
(17)
(18)
Substituting in (17) and (18) the data of table 2, we find the numerical values of the coefficients:
Fig, 3, The approximating function A(x) constructed according to the data in table 2 on the median points of EPI-groups (2019)
1) For 0 < a < x2'
A(x) = b0 +c„ -x2p
m
where p - some mode! parameter, the choice of which is specified below (p > pmili « 3).
2) For xi < x e jc,+1j, 2 < t < 5*
k2 = 0.044 k3 = 0.0825 fe4 = -0.034 fc5 = 0.03S6 CfL = 2.93- 10"4
b2 - -0.67 b2 = -2.0175 b4 = 2.526 b5 = -1.23 b6 = 0.345
¡19)
From formula (15) it follows that
A(100)=b6. (20)
It follows from (19) and (20) that inequality (11) is satisfied.
The parameters eg arid bg for the curve A(x) we are looking for depend on the model parameter p.
We will subject the choice of the parameter p to the following condition:
кт=к <21>
Substituting condition (21) into the formula forhjip) (16) and solving the resulting equation for the parameter p, we find that
1 1 , fa2-b6\
orp=6.657255l13.
The parameter eg in accordance with (16) is equal to 6.56378-1021.
The economic meaning of condition (21) is quite simple. This condition means that the factor A(x} in formula (10), which defines the relationship between the CPS and EPi indices for the axial line, has the same limiting minimum values as r->0 andr->l00. Function^ix) has a maximum in the UpperCold EPi-group and possibly also a secondary maximum in the UpperWarm EPl-group.
It can be said that condition (21) is generated by Occam's razor principle: "entities should not be multiplied without necessity" ("Numquam ponenda est pluraiitas sine necessitate") [13].
We can describe the assumed form of the unknown smooth function A(x) in this way. This function behaves in the same way for smaii CPI (r->0) and Sarge CP! (r->100), demonstrating a global trend in the relationship between the CPI and EPI indices:
EPI-CPE
In the middle zone of CP! change, the function A(x> has a maximum (possibly two maximums). In this area, the EPI along the axiai line of the swarm of the global economy, as a function of the CPi, grows faster as the CP! rises. The approximating function A fx) shown in fig. 3 is the simplest mathematical approximation compatible with the data in table 2.
Fig. 4 shows the projection of the axiai line of the 2019 swarm of the global economy on the plane of the CPi x EPi economic indices. This projection was constructed according to formula (3) (or according to formula (10)) using the approximating function A(x> shown in fig. 3.
Axial lines of the swarm of the global economy as a spatial curve. Two equations of the form y=y(x) and z=z(x) define some spatial curve - the axial line of the swarm of the globai economy.
Fig. 5 shows this spatial curve immersed in the 2019 swarm of the global economy.
/
/
/
/
X /
• U 1* H « M « ft at K >4
en
Fig. 4, Projection of the axial l ine of the 2019 swarm of the global economy on the plane of the CPI x EPI economic indices. ■ - positions of median points of EPI groups
Fig, 5, Spatial curve of the axial line of the swarm of the global economy
Conclusions
Th us, accord i n g to the results of the resea rch, the following conciusions were formulated
1. The definition of the axial iine of the swarm of the global economy in the space of economic indices EPi, BLI, CPi was introduced in the paper.
2. An analytical expression is obtained for the axial iine equation. The parameters of this equation are determined by the location of the median points of the EPI-groups of the global economy according to the statistics of 2019,
3. Possibie direction for further research would be studying the distribution of deviations of the swarm points from the axial line of the global economy.
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ORGANIZATION OF ACCOUNTING FOR TRANSACTION COSTS AT A MANUFACTURING ENTERPRISE
Starukhin Vitatii Anatolievich, Postgraduate student. Department of Finance and Management, Tula State University,
Tula
The purpose of the study is to present the author's accounting mechanisms in relation to the transaction costs of a manufacturing enterprise in relation to the financial, managerial and strategic aspects of this process. The scientific novelty of the research lies in the fact that the paper systematizes views on the existing accounting and analytical support in relation to transaction costs, offers various options for constructing accounting, management and strategic accounting of transaction costs, depending on the assessment available for reflection. As a result, the recommended accounting approaches using accounting, management and strategic accounting of transaction costs are presented on the example of an industrial company. Since transaction costs occupy a significant share in the cost structure of business units engaged in production, it is necessary to organize their reflection using modern accounting principles. The complexity of the monetary assessment of such costs causes the complexity of the management process associated with their accounting. This publication is devoted to the problems of accounting, management and strategic accounting of transaction costs ata manufacturing enterprise. The use of an integrated approach based on accounting principles makes it possible to ensure control over transaction costs for solving urgent tasks of management and owners.
Keywords: transaction costs; transactions; expenses; cost price; structured work chart of accounts; aaccounting; management accounting; strategic accounting; ac counting and analytical support; manufacturing enterprise.
DOI 10.24923/2222-243X.2021-40.1 б
ОРГАНИЗАЦИЯ УЧЕТА ТРАНСАКЦИОННЫХИЗДЕРЖЕК НА ПРОИЗВОДСТВЕННОМ ПРЕДПРИЯТИИ
Цель исследования состоит в авторском представлении учётных механизмов в отношении трансакционных издержек производственного предприятия применительно к финансовому, управленческому и стратегическому аспектам этого процесса. Научная новизна исследования заключается в том, что в работе систематизированы взгляды в отношении существующегоучетно-ана-литического обеспечения в отношении трансакционных издержек, предложены различные варианты построения бухгалтерского, управленческого и стратегического учета трансакционных издержек в зависимости от доступной для отражения оценки. В результате представлены рекомендуемые учетные подходы с использованием бухгалтерского, управленческого и стратегического учёта трансакционных издержек на примере промышленной компании. Поскольку трансакционные издержки занимают значительную долю в структуре затрат бизнес-единиц, занимающихся производством, необходимо организо вать их отражение с использованием современных учётных принципов. Слож-
УДК338 ВАК РФ 08,00,05
& Старухин В.А., 2021
