Papers by Gafurjan Ibragimov
Mathematics
We present a pursuit differential game for an infinite system of two-block differential equations... more We present a pursuit differential game for an infinite system of two-block differential equations in Hilbert space l2. The pursuer and evader control functions are subject to integral constraints. The differential game is said to be completed if the state of the system falls into the origin of l2 at some finite time. The purpose of the pursuer is to bring the state of the controlled system to the origin of the space l2, whereas the evader’s aim is to prevent this. For the optimal pursuit time, we obtain an equation and construct the optimal strategies for the players.
Symmetry
The paper considers an axisymmetric problem of filtering suspensions with the formation of a cake... more The paper considers an axisymmetric problem of filtering suspensions with the formation of a cake on the filter surface. It is supposed that the cake has elastic–plastic properties. Using the mass conservation equation and Darcy’s law, the suspension filtration equations at the elastic–plastic regime are derived, which characterize the partial irreversibility of the filtration characteristics when the system is unloaded after loading. An equation is also derived that describes the increase in the thickness of the cake. Problems of suspension filtering for the derived equations are posed and numerically solved. The role of partial irreversibility of deformation on the filtration characteristics is estimated. Distributions of compression pressure, the concentration of solid particles in the cake, relative permeability in the mode of primary and secondary loading of the system, as well as in the mode of unloading after the first loading are obtained. The growth dynamics of the cake thi...
Universiti Putra Malaysia Press, 2013
We study a control problem described by infinite system of differential equations of second order... more We study a control problem described by infinite system of differential equations of second order in the space 2 1 r l +. Control parameter is subjected to integral constraint. Our goal is to transfer the state of the system from a given initial position to the origin for finite time. We obtained necessary and sufficient conditions on the initial positions for which the problem can be solved.
International Journal of Pure and Apllied Mathematics, 2017
An evasion differential game of two pursuers and one evader in R 2 is studied. Unlike the traditi... more An evasion differential game of two pursuers and one evader in R 2 is studied. Unlike the traditional integral constraints, in the present work, integral constraints are imposed on each component of control functions of the players. By definition, evasion is said to be possible if the state of a pursuer does not coincide with that of the evader for all t ≥ 0. Sufficient conditions of evasion are obtained and then strategies for the evader are constructed.
Mathematics
A differential game of m, 3≤m≤6, pursuers and one evader is studied on an icosahedron in R3. All ... more A differential game of m, 3≤m≤6, pursuers and one evader is studied on an icosahedron in R3. All the players move only along the 1-skeleton graph of the icosahedron when the maximal speeds of the pursuers are less than the speed of the evader. Pursuit is said to be completed if the state of a pursuer coincides with the state of evader at some time. We give a sufficient condition of the completion of pursuit in the game.
Differential Pursuit-Evasion Games and Space Economy: New Research Perspectives
Mathematical and Statistical Methods for Actuarial Sciences and Finance
Journal of Dynamical and Control Systems, 2021
In this work, the null controllability problem for a linear system in ℓ2 is considered, where the... more In this work, the null controllability problem for a linear system in ℓ2 is considered, where the matrix of a linear operator describing the system is an infinite matrix with $\lambda \in \mathbb {R}$ λ ∈ ℝ on the main diagonal and 1s above it. We show that the system is asymptotically stable if and only if λ ≤− 1, which shows the fine difference between the finite and the infinite-dimensional systems. When λ ≤− 1 we also show that the system is null controllable in large. Further we show a dependence of the stability on the norm, i.e. the same system considered $\ell ^{\infty }$ ℓ ∞ is not asymptotically stable if λ = − 1.
ROA-CONS: Raccoon Optimization for Job Scheduling
<jats:p>High-performance computing comprises thousands of processing powers in order to del... more <jats:p>High-performance computing comprises thousands of processing powers in order to deliver higher performance computation than a typical desktop computer or workstation in order to solve large problems in science, engineering, or business. The scheduling of these machines has an important impact on their performance. HPC's job scheduling is intended to develop an operational strategy which utilises resources efficiently and avoids delays. An optimised schedule results in greater efficiency of the parallel machine. In addition, processes and network heterogeneity is another difficulty for the scheduling algorithm. Another problem for parallel job scheduling is user fairness. One of the issues in this field of study is providing a balanced schedule that enhances efficiency and user fairness. ROA-CONS is a new job scheduling method proposed in this paper. It describes a new scheduling approach, which is a combination of an updated conservative backfilling approach further optimised by the raccoon optimisation algorithm. This algorithm also proposes a technique of selection that combines job waiting and response time optimisation with user fairness. It contributes to the development of a symmetrical schedule that increases user satisfaction and performance. In comparison with other well-known job scheduling algorithms, the simulation assesses the effectiveness of the proposed method. The results demonstrate that the proposed strategy offers improved schedules that reduce the overall system's job waiting and response times.</jats:p>
Game with Slow Pursuers on the Edge Graphs of Regular Simplexes
Trends in Mathematics, 2021
On modelling parallel programmes for static mapping: a comparative study
Heterogeneous parallel architecture (HPA) are inherently more complicated than their homogeneous ... more Heterogeneous parallel architecture (HPA) are inherently more complicated than their homogeneous counterpart. HPAs allow composition of conventional processors, with specialised processors that target particular types of task. However, this makes mapping and scheduling even more complicated and difficult in parallel applications. Therefore, it is crucial to use a robust modelling approach that can capture all the critical characteristics of the application and facilitate the achieving of optimal mapping. In this study, we perform a concise theoretical analysis as well as a comparison of the existing modelling approaches of parallel applications. The theoretical perspective includes both formal concepts and mathematical definitions based on existing scholarly literature. The important characteristics, success factors and challenges of these modelling approaches have been compared and categorised. The results of the theoretical analysis and comparisons show that the existing modelling...
A Differential Game Problem of Many Pursuers and One Evader in the Hilbert Space $$\ell_2$$
Differential Equations and Dynamical Systems, 2020
In this paper, we investigate a differential game problem of multiple number of pursuers and a si... more In this paper, we investigate a differential game problem of multiple number of pursuers and a single evader with motions governed by a certain system of first-order differential equations. The problem is formulated in the Hilbert space $$\ell_2,$$ with control functions of players subject to integral constraints. Avoidance of contact is guaranteed if the geometric position of the evader and that of any of the pursuers fails to coincide for all time t. On the other hand, pursuit is said to be completed if the geometric position of at least one of the pursuers coincides with that of the evader. We obtain sufficient conditions that guarantees avoidance of contact and construct evader’s strategy. Moreover, we prove completion of pursuit subject to some sufficient conditions. Finally, we demonstrate our results with some illustrative examples.
Pursuit Differential Game of Many Pursuers with Integral Constraints on Compact Convex Set
Bulletin of the Malaysian Mathematical Sciences Society, 2019
We study a pursuit differential game of many pursuers and one evader in the plane. We are given a... more We study a pursuit differential game of many pursuers and one evader in the plane. We are given a compact convex subset of $${\mathbb {R}}^2$$ R 2 , and the pursuers and evader move in this set. They cannot leave this set during the game. Control functions of players are subject to coordinate-wise integral constraints. If the state of a pursuer coincides with that of evader at some time, then we say that pursuit is completed. Pursuers try to complete the pursuit, and the aim of the evader is opposite. We obtain some conditions under which pursuit can be completed from any positions of the players in the given set. Moreover, we construct strategies for the pursuers. Also, we prove some properties of convex sets.
Taiwanese Journal of Mathematics, 2015
We study a differential game of optimal approach of finite or countable number of pursuers with o... more We study a differential game of optimal approach of finite or countable number of pursuers with one evader in the Hilbert space l 2. On control functions of the players integral constraints are imposed. Such constraints arise in modeling the constraint on energy. The duration of the game θ is fixed. The payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the payoff functional, and the evader tries to maximize it. In this paper, we find formula for the value of the game and construct explicitly optimal strategies of the players. Important point to note is that the energy resource of any pursuer needs not be greater than that of the evader.
Journal of Physics: Conference Series, 2018
The present paper considers a pursuit game problem of an infinite system of 1storder differential... more The present paper considers a pursuit game problem of an infinite system of 1storder differential equations in the space l 2. In the game, the player's control functions satisfy both geometric and integral constraints. The pursuer's action is to force the state of the system to coincides with another state for a finite time and the evader's action is to retrieve this. In each case, we obtain a condition for the completion of the game for which the pursuer's strategy is explicitly constructed. In addition, we study a control problem.
Journal of Mathematics Research, 2011
Existence of a limit cycle for the dynamical system well-known as the Prigogine brusselator model... more Existence of a limit cycle for the dynamical system well-known as the Prigogine brusselator model is proved when parameters of the system take concrete values. The proof is conducted by the new method called discrete numerical (DN) tracking of trajectory combined with the Poincare-Bendickson theorem.
Taiwanese Journal of Mathematics, 2015
We study a differential game of optimal approach of finite or countable number of pursuers with o... more We study a differential game of optimal approach of finite or countable number of pursuers with one evader in the Hilbert space l 2. On control functions of the players integral constraints are imposed. Such constraints arise in modeling the constraint on energy. The duration of the game θ is fixed. The payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the payoff functional, and the evader tries to maximize it. In this paper, we find formula for the value of the game and construct explicitly optimal strategies of the players. Important point to note is that the energy resource of any pursuer needs not be greater than that of the evader.
We study a differential game of many pursuers and single evader in nonempty closed bounded convex... more We study a differential game of many pursuers and single evader in nonempty closed bounded convex subset of Rn. In this game, all players cannot leave the given set. Control parameters of all players are subjected to geometric constraints. Maximum speeds of all players are equal to 1. Pursuit is said to be completed if geometric position of at least one pursuer coincides with that of the evader. Pursuers try to complete the pursuit. Problem is to find estimate for guaranteed pursuit time. To solve the problem, first, we study the same problem in an n-dimensional cube. Then, we reduce the main problem to the game in the cube. To this end, we use method of fictitious pursuers. In this paper, we improve the estimate for guaranteed pursuit time from O(n3) to O(n2).
Based on the Bertrand and Cournot economic models, we develop an evasion game model for a duopoly... more Based on the Bertrand and Cournot economic models, we develop an evasion game model for a duopoly market with two players competing on price and quantity. We show that if the total financial strength of first mover is greater than that of the second mover, and the first mover observes the second mover perfectly, our proposed optimal strategy can be followed by the first mover to remain the market leader ahead of all competition.
International Journal on Advanced Science, Engineering and Information Technology
Nowadays fast and accurate positioning of assets and people is as a crucial part of many business... more Nowadays fast and accurate positioning of assets and people is as a crucial part of many businesses, such as, warehousing, manufacturing and logistics. Applications that offer different services based on mobile user location gaining more and more attention. Some of the most common applications include location-based advertising, directory assistance, point-to-point navigation, asset tracking, emergency and fleet management. While outdoors mostly covered by the Global Positioning System, there is no one versatile solution for indoor positioning. For the past decade Wi-Fi fingerprinting based indoor positioning systems gained a lot of attention by enterprises as an affordable and flexible solution to track their assets and resources more effectively. The concept behind Wi-Fi fingerprinting is to create signal strength database of the area prior to the actual positioning. This process is known as a calibration carried out manually and the indoor positioning system accuracy highly depends on a calibration intensity. Unfortunately, this procedure requires huge amount of time, manpower and effort, which makes extensive deployment of indoor positioning system a challenging task. approach of constructing signal strength database from a minimal number of measurements using Chebyshev wavelets approximation. The main objective of the research is to minimize the calibration workload while providing high positioning accuracy. The field tests as well as computer simulation results showed significant improvement in signal strength prediction accuracy compared to existing approximation algorithms. Furhtermore, the proposed algorithm can recover missing signal values with much smaller number of on-site measurements compared to conventional calibration algorithm.
Differential Game of Optimal Pursuit for an Infinite System of Differential Equations
Bulletin of the Malaysian Mathematical Sciences Society
We study an optimal pursuit differential game problem in the Hilbert space $$l_{r+1}^2$$lr+12. Th... more We study an optimal pursuit differential game problem in the Hilbert space $$l_{r+1}^2$$lr+12. The game is described by an infinite system of the first-order differential equations whose coefficients are negative. The control functions of players are subjected to integral constraints. If the state of the system coincides with the origin of the space $$l_{r+1}^2$$lr+12, then game is considered completed. We obtain an equation to find the optimal pursuit time. Moreover, we construct the optimal strategies for players.
Uploads
Papers by Gafurjan Ibragimov