Quantitative analysis of the economic potential on the example of the Upper Silesian Metropolis

Purpose: The aim of the article is to show the modified method of calculating the economic potential on the example of territorial units of the Upper Silesian Metropolis. Design/methodology/approach: Economic potential is a measure of a region's strength compared to other regions. In economics, potential is a substitute for socio-economic development. The methodology of calculating the modified economic potential of territorial units was discussed in the first part of the article, and an empirical example is presented in the second part. Findings: As a result of the research, strong regions were identified and the self-potential of the regions and their surroundings were compared. Research limitations/implications: The proposed modified method of potentials can be used for a comparative analysis of any territorial units. The metric that is used to measure the distance between territorial units is important. Practical implications: On the basis of the presented method, any regions or countries can be compared in terms of socio-economic development. Social implications: The method makes it possible to compare the socio-economic development of regions in terms of income and population. Originality/value: The article compares selected communes of the Silesian Voivodeship in terms of income, population and socio-economic development. A modified measure of economic potential was used

Solving a two-step continuous-discrete optimal split-distribution problem with fuzzy parameters

The theory of optimal set partitioning from an n-dimensional Euclidean space En is an important part of infinite-dimensional mathematical programming. The mostly reason of high interest in development of the theory of optimal set partitioning is that its results can be applied to solving the classes of different theoretical and applied optimization problems, which are transferred into continuous optimal set partitioning problem. This paper investigates the further development of the theory of optimal set partitioning from En in the case of a two-stage continuous-discrete problem of optimal partitioningdistribution with non-determined input data, which is frequently appear in solving practical problems. The two-stage continuous-discrete problem of optimal partition-distribution under constraints in the form of equations and determined position of centers of subsets is generalized by proposed continuous-discrete problem of optimal partition-distribution in case if some parameters are presented in incomplete, inaccurate or unreliable form. These parameters can be represented as linguistic variables and the method of neurolinguistic identification of unknown complex, nonlinear dependencies can be used in purpose to recovery them. A method for solving the two-stage continuous-discrete optimal partitioning-distribution problem with fuzzy parameters in target functional which based on usage of neurolinguistic identification of unknown dependencies for recovering precise values of fuzzy parameters, methods of the theory of optimal set partitioning and the method of potentials for solving a transportation problem is proposed.

Green matrices and continuity of the weak solutions for the elliptic systems with lower order terms

In this paper, we consider the second-order elliptic systems with lower order terms coefficients belonging to Kato–Stummel type classes in a bounded domain [Formula: see text], where [Formula: see text]. We establish the existence, global pointwise estimates and [Formula: see text] estimates for Green matrices. Based on these estimates, we are able to show the continuity of weak solutions for the general elliptic systems by using method of potentials. We also obtain the optimal Schauder estimates for weak solutions.