3 research outputs found
βMean Field Gamesβ as Mathematical Models for Control and Optimization of Business Activity
The article is a review of modern mathematical economic models with the βMean Field Gamesβ structure. They are currently used for the predictive modelling under given control conditions or for optimizing control actions to achieve the desired result. The mathematical model is a pair of parabolic partial differential equations with a set of initial and boundary conditions for optimizing a given target functional. For them, the discretization is applied to obtain systems of nonlinear algebraic equations which are solved by computer in an iterative way to get the best instant benefit for each agent. This mathematical apparatus is used for the quantitative modelling of the distribution or the use of alternative resources, environmental problems, optimization of wages and insurance, network sales, and other economic activities to predict the aggregate behavior of the great mass of agents looking for instant personal benefit
Β«ΠΠ³ΡΡ ΡΡΠ΅Π΄Π½Π΅Π³ΠΎ ΠΏΠΎΠ»ΡΒ» ΠΊΠ°ΠΊ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΈ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ
The article is a review of modern mathematical economic models with the βMean Field Gamesβ structure. They are currently used for the predictive modelling under given control conditions or for optimizing control actions to achieve the desired result. The mathematical model is a pair of parabolic partial differential equations with a set of initial and boundary conditions for optimizing a given target functional. For them, the discretization is applied to obtain systems of nonlinear algebraic equations which are solved by computer in an iterative way to get the best instant benefit for each agent. This mathematical apparatus is used for the quantitative modelling of the distribution or the use of alternative resources, environmental problems, optimization of wages and insurance, network sales, and other economic activities to predict the aggregate behavior of the great mass of agents looking for instant personal benefitΠ‘ΡΠ°ΡΡΡ ΠΏΠΎΡΠ²ΡΡΠ΅Π½Π° ΠΎΠ±Π·ΠΎΡΡ ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ
Π² ΡΠ΅ΡΠΌΠΈΠ½Π°Ρ
ΡΠ΅ΠΎΡΠΈΠΈ βMean Field Gameβ. Π Π½Π°ΡΡΠΎΡΡΠ΅Π΅ Π²ΡΠ΅ΠΌΡ ΡΠ°ΠΊΠΈΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ Π΄Π»Ρ ΠΏΡΠΎΠ³Π½ΠΎΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΈ Π·Π°Π΄Π°Π½Π½ΡΡ
ΡΡΠ»ΠΎΠ²ΠΈΡΡ
ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΈΠ»ΠΈ
Π΄Π»Ρ ΠΏΠΎΠΈΡΠΊΠ° ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΠΎΠΉ Π΄Π»Ρ Π΄ΠΎΡΡΠΈΠΆΠ΅Π½ΠΈΡ ΠΆΠ΅Π»Π°Π΅ΠΌΠΎΠ³ΠΎ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°. ΠΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΠ΅Ρ ΡΠΎΠ±ΠΎΠΉ ΠΏΠ°ΡΡ ΠΏΠ°ΡΠ°Π±ΠΎΠ»ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ Π² ΡΠ°ΡΡΠ½ΡΡ
ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΡ
Ρ Π½Π°ΡΠ°Π»ΡΠ½ΡΠΌΠΈ ΠΈ Π³ΡΠ°Π½ΠΈΡΠ½ΡΠΌΠΈ ΡΡΠ»ΠΎΠ²ΠΈΡΠΌΠΈ Π΄Π»Ρ
ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ Π·Π°Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΡΠ΅Π»Π΅Π²ΠΎΠ³ΠΎ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»Π°. ΠΠ»Ρ Π½ΠΈΡ
ΠΏΡΠΈΠΌΠ΅Π½ΡΠ΅ΡΡΡ Π΄ΠΈΡΠΊΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡ
Ρ ΡΠ΅Π»ΡΡ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΈΡΡΠ΅ΠΌΡ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ
Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ΅ΡΠ°ΡΡΡΡ Π½Π° ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ΅ ΠΈΡΠ΅ΡΠ°ΡΠΈΠΎΠ½Π½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ Π΄Π»Ρ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ Π½Π°ΠΈΠ±ΠΎΠ»ΡΡΠ΅Π³ΠΎ ΡΠ΅ΠΊΡΡΠ΅Π³ΠΎ Π²ΡΠΈΠ³ΡΡΡΠ° ΠΊΠ°ΠΆΠ΄ΡΠΌ Π°Π³Π΅Π½ΡΠΎΠΌ. ΠΠ°Π½Π½ΡΠΉ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ Π°ΠΏΠΏΠ°ΡΠ°Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΡΡΡ Π΄Π»Ρ
ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΈΠ»ΠΈ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π°Π»ΡΡΠ΅ΡΠ½Π°ΡΠΈΠ²Π½ΡΡ
ΡΠ΅ΡΡΡΡΠΎΠ², ΡΠ΅ΡΠ΅Π½ΠΈΡ ΡΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΠ±Π»Π΅ΠΌ, ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ Π·Π°ΡΠ°Π±ΠΎΡΠ½ΠΎΠΉ ΠΏΠ»Π°ΡΡ ΠΈ ΡΡΡΠ°Ρ
ΠΎΠ²Π°Π½ΠΈΡ, ΡΠ΅ΡΠ΅Π²ΡΡ
ΠΏΡΠΎΠ΄Π°ΠΆ ΠΈ Π΄ΡΡΠ³ΠΈΡ
Π²ΠΈΠ΄ΠΎΠ² ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π΄Π΅ΡΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ Π΄Π»Ρ ΠΏΡΠ΅Π΄ΡΠΊΠ°Π·Π°Π½ΠΈΡ
Π°Π³ΡΠ΅Π³Π°ΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ ΠΎΠ³ΡΠΎΠΌΠ½ΠΎΠΉ ΠΌΠ°ΡΡΡ Π°Π³Π΅Π½ΡΠΎΠ², ΠΈΡΡΡΠΈΡ
ΡΠΎΠ±ΡΡΠ²Π΅Π½Π½ΡΡ Π²ΡΠ³ΠΎΠ΄
Π‘Π°ΠΌΠΎΡΠ±ΠΎΡΠΊΠ° ΡΡΡΡΠΊΡΡΡ, ΡΠΎΡΡΠΎΡΡΠΈΡ ΠΈΠ· ΡΡΠ΅Ρ Π½Π°Π½ΠΎΡΠ°ΡΡΠΈΡ, Ρ Π·Π°ΡΠ°Π½Π΅Π΅ Π·Π°Π΄Π°Π½Π½ΠΎΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΠ΅ΠΉ ΠΏΠΎΠ΄ Π΄Π΅ΠΉΡΡΠ²ΠΈΠ΅ΠΌ ΠΊΠ²Π°Π·ΠΈΡΠ΅Π·ΠΎΠ½Π°Π½ΡΠ½ΠΎΠ³ΠΎ Π»Π°Π·Π΅ΡΠ½ΠΎΠ³ΠΎ ΠΈΠ·Π»ΡΡΠ΅Π½ΠΈΡ
In the paper a dynamic model of self-assembly of nanoparticles under laser field is proposed for research
the possibility of a step-by-step assembly of a structure consisting of three particles with different form.
The possibility of forming such structures with a predetermined geometry from a preformed pair of par-
ticles is consideredΠ ΡΠ°ΠΌΠΊΠ°Ρ
Π΄Π°Π½Π½ΠΎΠΉ ΡΠ°Π±ΠΎΡΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π° Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ°ΠΌΠΎΡΠ±ΠΎΡΠΊΠΈ Π½Π°Π½ΠΎΡΠ°ΡΡΠΈΡ Π² ΠΏΠΎΠ»Π΅ Π»Π°Π·Π΅Ρ-
Π½ΠΎΠ³ΠΎ ΠΈΠ·Π»ΡΡΠ΅Π½ΠΈΡ Ρ ΡΠ΅Π»ΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΏΠΎΡΡΠ°ΠΏΠ½ΠΎΠΉ ΡΠ±ΠΎΡΠΊΠΈ ΡΡΡΡΠΊΡΡΡΡ, ΡΠΎΡΡΠΎΡΡΠ΅ΠΉ
ΠΈΠ· ΡΡΠ΅Ρ
ΡΠ°ΡΡΠΈΡ, Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΠΎΠΉ ΡΠΎΡΠΌΠΎΠΉ. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½ ΠΏΡΠΎΡΠ΅ΡΡ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ°ΠΊΠΈΡ
ΡΡΡΡΠΊΡΡΡ Ρ Π·Π°Π΄Π°Π½Π½ΠΎΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΠ΅ΠΉ Π² Π²Π°ΡΠΈΠ°Π½ΡΠ΅ ΠΏΡΠΈΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΡ ΠΊ Π·Π°ΡΠ°Π½Π΅Π΅ ΡΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΠΏΠ°ΡΠ΅ ΡΠ°ΡΡΠΈΡ ΡΡΠ΅ΡΡΠ΅ΠΉ
ΡΠ°ΡΡΠΈΡ