We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive...We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.展开更多
In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generate...In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.展开更多
Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and...Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and their uniqueness is proven. In previous works, the main research method for the study scalar singular integral operators and Riemann boundary value problems with Carlemann shift were operator identities, which allowed to eliminate shift and to reduce scalar problems to matrix problems without shift. In this study, the operator identities were used for the opposite purpose: to transform operators of multiplication by matrix-functions into scalar operators with Carlemann linear-fractional shift.展开更多
In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holde...In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.展开更多
This study consisted of a geochemical analysis of the Dos Carlos tailings’ deposit located in the Mining District of Pachuca-Real del Monte in the state of Hidalgo, Central Mexico. The goal of the study was to determ...This study consisted of a geochemical analysis of the Dos Carlos tailings’ deposit located in the Mining District of Pachuca-Real del Monte in the state of Hidalgo, Central Mexico. The goal of the study was to determine the potential effects of this deposit on the environment and health of the population of the metropolitan area of Pachuca. Sampling was conducted from the top to the base of two raised sections at opposite ends of the deposit, and macroscopic features (profiles A and B) of these deposits were evaluated. Subsequently, mineralogical analyses of the collected samples were performed using X-ray diffraction and physico-chemical analysis of the leachates. The results were compared with the maximum permissible limits established by different national and international standards for drinking water and hazardous waste. In addition, geochemical modeling was conducted using PHREEQC to calculate the distribution of aqueous species, ionic activities and saturation indices.(For more information, please refer to the PDF.)展开更多
文摘We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.
文摘In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.
文摘Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and their uniqueness is proven. In previous works, the main research method for the study scalar singular integral operators and Riemann boundary value problems with Carlemann shift were operator identities, which allowed to eliminate shift and to reduce scalar problems to matrix problems without shift. In this study, the operator identities were used for the opposite purpose: to transform operators of multiplication by matrix-functions into scalar operators with Carlemann linear-fractional shift.
文摘In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.
基金the Faculty Improvement Program(PROMEP)for financing through the project F-PROMEP-38/Rev-03,SEP-23-005.
文摘This study consisted of a geochemical analysis of the Dos Carlos tailings’ deposit located in the Mining District of Pachuca-Real del Monte in the state of Hidalgo, Central Mexico. The goal of the study was to determine the potential effects of this deposit on the environment and health of the population of the metropolitan area of Pachuca. Sampling was conducted from the top to the base of two raised sections at opposite ends of the deposit, and macroscopic features (profiles A and B) of these deposits were evaluated. Subsequently, mineralogical analyses of the collected samples were performed using X-ray diffraction and physico-chemical analysis of the leachates. The results were compared with the maximum permissible limits established by different national and international standards for drinking water and hazardous waste. In addition, geochemical modeling was conducted using PHREEQC to calculate the distribution of aqueous species, ionic activities and saturation indices.(For more information, please refer to the PDF.)
