scholarly journals Economic complexity and inclusion of regional economies

2021 ◽  
Vol 106 ◽  
pp. 01003
Author(s):  
Mikhail Afanasiev ◽  
Aleksander Kudrov
Keyword(s):  
Existence And Uniqueness ◽  
Traditional Approach ◽  
Value Chains ◽  
Regional Economies ◽  
Internal Markets ◽  
Explanatory Variables ◽  
Economic Complexity ◽  
The Matrix ◽  
Uniqueness Of The Solution ◽  
Aggregated Nesting

The paper presents a probabilistic interpretation of the elements of the matrix, which is used to assess the economic complexity in accordance with the traditional approach. Their properties are given, on the basis of which aggregate indicators are introduced that characterize the nesting of the structures of strong sectors of regional economies. It is shown that aggregate nesting indicators are statistically significant explanatory variables for economic complexity. It is proved that the used procedure for calculating the economic complexity is correct in the sense of the existence and uniqueness of the solution. It is shown that the data that are used to assess the economic complexity in accordance with the author’s approach allow to reflect the formation of value chains and groups of related sectors focused on both the external and internal markets. For this economic complexity, calculated on regional data, its high values correspond to large values of the aggregated nesting indicators. Low values of economic complexity correspond to low values of nesting indicators.

Economic complexity and embedding of regional economies’ structures

2021 ◽  
Vol 57 (3) ◽  
pp. 67
Author(s):  
Mikhail Afanasiev
Keyword(s):  
Economic Activity ◽  
Traditional Approach ◽  
Expert Assessment ◽  
Potential Contribution ◽  
Regional Economies ◽  
Economic Diversification ◽  
Economic Complexity ◽  
The Past ◽  
The Matrix ◽  
Strong Sector

 The research focuses on the development of localized specialization and economic diversification theories. Our task is forecasting of the emergence of new strong sectors in the region. On the basis of probabilistic and statistical modeling the model which allows estimating the probability of appearing a new strong sector in the region taking into account characteristics of economic structure is constructed. The possibility of building such a model is based on the assumption that the emergence and development of sectors is largely determined by the evolution of past economic activity. The model uses the indicators of embedding structures of the strong sectors in the regional economies is introduced by the authors. These indicators are based on the probabilistic interpretation and properties of the elements of the matrix, by which economic complexity is estimated following the traditional approach. The probability of originating a strong sector in the structure for each region is estimated. Based on sorting the sectors according to the value of these probabilities and assessments of their potential contribution to socio-economic development expert assessment of the feasibility of developing a new strong sector in the region can be made. The results show that sectors’ introduction and generation in the regional economy is largely due to the evolution of the past economic activity.    

scholarly journals Forecast of the appearance of new strong sectors in the regional economy based on a probabilistic model

2021 ◽  
Vol 106 ◽  
pp. 01006
Author(s):  
Mikhail Afanasiev ◽  
Aleksander Kudrov
Keyword(s):  
Traditional Approach ◽  
Expert Assessment ◽  
Potential Contribution ◽  
Regional Economies ◽  
Matrix Elements ◽  
Occurrence Probability ◽  
Economic Diversification ◽  
Economic Complexity ◽  
The Matrix ◽  
Strong Sector

The problem of forecasting the appearance of new strong sectors in the region shall be considered. Based on the methods of probabilistic and statistical modeling, a model has been built that makes it possible to assess the occurrence probability of a new strong sector in the region, taking into account the characteristics of the structure of the economy. The possibility of building such a model is based on the assumption that the appearance and development of sectors are largely due to the evolution of past economic activity. The model uses the indicators of nesting of structures of strong sectors of regional economies entered by the authors. These values are based on the probabilistic interpretation and properties of the matrix elements, which assesses the economic complexity, in accordance with the traditional approach. The condition for the appearance of a certain strong sector in the structure of the economy of a particular region with a probability exceeding 0.5 shall be obtained. This condition used to form a list of sectors recommended for priority development in the region. For each region in its structure, the occurrence probability of a specific sector as a strong one was estimated. On the basis of ordering the sectors by the value of these probabilities and assessing their potential contribution to socio-economic development, an expert assessment of the feasibility of developing a new strong sector in the region can be given. Research is focused on the development of theories of localized specialization and economic diversification.

scholarly journals On the weighted boundary value problem for systems of degenerate ordinary differential equations

2010 ◽  
Vol 51 ◽  
Author(s):  
Stasys Rutkauskas ◽  
Igor Saburov
Keyword(s):  
Singular Point ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Linear Equations ◽  
System Of Equations ◽  
The Matrix ◽  
Uniqueness Of The Solution ◽  
Weighted Boundary ◽  
Well Posed

A system of ordinary second order linear equations with a singular point is considered. The aim of this work is such that the system of eigenvectors of the matrix that couples the system of equations is not complete. That implies a matter of the statement of a weighted boundary value problem for this system. The well-posed boundary value problem is proposed in the article. The existence and uniqueness of the solution is proved.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

scholarly journals Correctness conditions for high-order differential equations with unbounded coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kordan N. Ospanov
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Order Linear Differential Equation ◽  
Unbounded Coefficients ◽  
Weighted Norms ◽  
Uniqueness Of The Solution ◽  
Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

scholarly journals On Existence Theorems to Symmetric Functional Set-Valued Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1219
Author(s):  
Marek T. Malinowski
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Theorems ◽  
Type Theorem ◽  
Integral Representations ◽  
Uniqueness Of The Solution ◽  
Nonempty Compact ◽  
Picard Type Theorem ◽  
Convex Subsets

In this paper, we consider functional set-valued differential equations in their integral representations that possess integrals symmetrically on both sides of the equations. The solutions have values that are the nonempty compact and convex subsets. The main results contain a Peano type theorem on the existence of the solution and a Picard type theorem on the existence and uniqueness of the solution to such equations. The proofs are based on sequences of approximations that are constructed with appropriate Hukuhara differences of sets. An estimate of the magnitude of the solution’s values is provided as well. We show the closeness of the unique solutions when the equations differ slightly.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

scholarly journals ON STOCHASTIC GENERALIZED FUNCTIONS

2011 ◽  
Vol 14 (02) ◽  
pp. 237-260 ◽  
Author(s):  
PEDRO CATUOGNO ◽  
CHRISTIAN OLIVERA
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Generalized Functions ◽  
Uniqueness Of The Solution ◽  
Stochastic Cauchy Problem

In this work we introduce a new algebra of stochastic generalized functions. The regular Hida distributions in [Formula: see text] are embedded in this algebra via their chaos expansions. As an application, we prove the existence and uniqueness of the solution of a stochastic Cauchy problem involving singularities.

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