Review of Methods, Applications and Publications on the Approximation of Piecewise Linear and Generalized Functions

Aliukov, Sergei; Alabugin, Anatoliy; Осинцев, К. В.

doi:10.3390/math10163023

Cited by 5 publications

(2 citation statements)

References 47 publications

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“…The difference lies in the fact that trigonometric expressions in the developed methods have the form of nested, recursive functions [45][46][47][48]. The methods were further developed in [49,50] and many other scientific papers.…”

Section: Description Of the Methodsmentioning

confidence: 99%

Modeling of Rapidly Changing Macroeconomic Processes Based on the Analysis of Jump and Generalized Functions

Aliukov

2023

Mathematics

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In recent years, the economies of many countries around the world have been in a situation of intense, rapidly changing, abrupt processes. The current situation urgently requires a change in the economic paradigm in the near future, which leads to the need to develop new conceptual models. The purpose of the article is to develop basic theoretical principles and practical approaches to modeling macroeconomic processes based on the analysis of jump and generalized functions. The objectives of the study are the following: (1) describe the main types of impulse and jump functions using examples from economic theory and practice; (2) perform an analytical representation of impulse and jump functions; (3) select macroeconomic characteristics to analyze rapidly changing processes in the economy; and (4) create models and mechanisms for forecasting impulsive and abrupt changes in the macroeconomy. The approaches to the development of macroeconomic theory and its methods proposed in the article are not associated with the use of evolutionary continuous functions; for example, power functions, which is typical for many canonical macroeconomic models. These approaches do not include management decisions to achieve optimal values of given target functions, which is typical for recursive macroeconomic models of dynamic programming. This article is about formulating the main provisions of macroeconomic theory and its methods, which, with varying degrees of accuracy, could give a forecast about the upcoming possibility of sudden changes (impulse, shock, spasmodic, and others) in the macroeconomic situation. The research methodology is statistical analysis, special methods developed by the author for studying impulse, and jump processes. As a result of this study, the basic principles of modeling macroeconomic theory based on rapid impulse and abrupt changes were formulated, approaches to constructing the tools of this theory were outlined, and problems and tasks for further research were identified.

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Section: Description Of the Methodsmentioning

confidence: 99%

Modeling of Rapidly Changing Macroeconomic Processes Based on the Analysis of Jump and Generalized Functions

Aliukov

2023

Mathematics

Self Cite

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show abstract

“…The difference lies in the fact that trigonometric expressions in the developed methods have the form of nested, recursive functions [30][31][32][33]. The methods were further developed in [34,35] and many other scientific papers.…”

Section: Description Of the Methodsmentioning

confidence: 99%

Theoretical Foundations of Macroeconomics with Impulse and Jump Characteristics

Aliukov

2023

Preprint

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In recent years, the economies of many countries of the world are in a situation of intense shock processes. The current situation urgently needs to change the economic paradigm in the near future, which objectively requires the development of new conceptual models. The purpose of the paper is to develop the basic theoretical provisions of a new macroeconomics based on impulse and jump processes. Research problems are the following: 1) to describe the main types of impulse and jump functions with examples from economic theory and practice; 2) to perform an analytical representation of impulse and jump functions; 3) to select macroeconomic characteristics for the analysis of rapidly changing processes in the economy; 4) to create models and mechanisms for predicting impulsive and abrupt changes in macroeconomics. The approaches to the development of macroeconomic theory and its methods proposed in the article are not associated with the use of evolutionary continuous functions, for example, power functions, which is typical for many canonical macroeconomic models. These approaches do not include management decisions to achieve optimal values of given target functions, which is typical for recursive macroeconomic models of dynamic programming. This article is about formulating the foundations of macroeconomic theory and its methods, which, with some degree of accuracy, could give a forecast about the impending possibility of abrupt changes (impulse, shock, jump, stepwise and others) in the macroeconomic situation. The research methodology is statistical analysis, special methods for studying impulse and jump processes developed by the author. As a result of the study, the main provisions of the macroeconomic theory based on rapid impulse and spasmodic changes were formulated, approaches were outlined for constructing the tools of this theory, problems and tasks for further research were identified.

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Multiple Exciton Generation Solar Cells: Numerical Approaches of Quantum Yield Extraction and Its Limiting Efficiencies

Lee¹,

Ahn

2023

Energies

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Multiple exciton generation solar cells exhibit low power conversion efficiency owing to non-radiative recombination, even after the generation of numerous electron and hole pairs per incident photon. This paper elucidates the non-idealities of multiple exciton generation solar cells. Accordingly, we present mathematical approaches for determining the quantum yield to discuss the non-idealities of multiple exciton generation solar cells by adjusting the delta function. We present the use of the Gaussian distribution function to present the occupancy status of carriers at each energy state using the Dirac delta function. Further, we obtained ideal and non-ideal quantum yields by modifying the Gaussian distribution function for each energy state. On the basis of this approach, we discuss the material imperfections of multiple exciton generations by analyzing the mathematically obtained quantum yields. Then, we discuss the status of radiative recombination calculated from the ratio of radiative to non-radiative recombination. Finally, we present the application of this approach to the detailed balance limit of the multiple exciton generation solar cell to evaluate the practical limit of multiple exciton generation solar cells.

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Review of Methods, Applications and Publications on the Approximation of Piecewise Linear and Generalized Functions

Cited by 5 publications

References 47 publications

Modeling of Rapidly Changing Macroeconomic Processes Based on the Analysis of Jump and Generalized Functions

Modeling of Rapidly Changing Macroeconomic Processes Based on the Analysis of Jump and Generalized Functions

Theoretical Foundations of Macroeconomics with Impulse and Jump Characteristics

Multiple Exciton Generation Solar Cells: Numerical Approaches of Quantum Yield Extraction and Its Limiting Efficiencies

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