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The algorithm under this name, together with the variants, is a method that solves the problems of optimal flow and costs. Examples of such problems are planning and procurement, scheduling by contractors, distribution and supply systems, transport on the road or rail network, electricity transmission, computer and telecommunications networks, pipe...
Contexts in source publication
Context 1
... network representation of the flow of the problem is shown in Figure 1, where three numbers next to each branch indicate the lower and upper limits of the allowed flow and the cost that should be associated with the flow of one unit in that branch. Since in this case there are 31 students requiring projects, a flow of 31 must be achieved between Node 1 and Node 104. ...
Context 2
... along these branches need not be associated with costs. The diagram (Figure 1) is simplified for clarity, but the ranking branches of Student 2's project are drawn as an illustration. For his first five rankings, he chose, in descending order, Projects 37, 45, 40, 39, and 46. ...
Context 3
... network representation of the flow of the problem is shown in Figure 1, where three numbers next to each branch indicate the lower and upper limits of the allowed flow and the cost that should be associated with the flow of one unit in that branch. Since in this case there are 31 students requiring projects, a flow of 31 must be achieved between Node 1 and Node 104. ...
Context 4
... along these branches need not be associated with costs. The diagram (Figure 1) is simplified for clarity, but the ranking branches of Student 2's project are drawn as an illustration. For his first five rankings, he chose, in descending order, Projects 37, 45, 40, 39, and 46. ...
Context 5
... network representation of the flow of the problem is shown in Figure 1, where three numbers next to each branch indicate the lower and upper limits of the allowed flow and the cost that should be associated with the flow of one unit in that branch. Since in this case there are 31 students requiring projects, a flow of 31 must be achieved between Node 1 and Node 104. ...
Citations
... The Runge-Kutta method, although it requires more computing resources, shows superior accuracy compared to the Q Euler-Maruyama method. Increasing accuracy in solving stochastic differential equations is important for the analysis of real systems, where accuracy can have a significant impact on decision-making [27][28][29]. ...
The research focuses on the optimization of numerical solutions of neutral stochastic differential equations with time delay. Analyzing approaches such as Euler-Maruyama, backward Euler and θ-Euler-Maruyama methods, the goal is to investigate the characteristics of approximate solutions, especially stability and boundedness. This study contributes to the understanding of the complexity of stochastic processes, offering a perspective for further mathematical modeling and optimization. The study of the characteristics of approximate solutions includes a detailed analysis of their stability and limitations, providing insight into the system's behavior in dynamic conditions. This analysis lays the foundations for the improvement of numerical methods and more precise modeling of stochastic processes with a time delay. The aforementioned approaches, such as the Euler-Maruyama, backward Euler and θ-Euler-Maruyama methods, provide tools for understanding and solving complex mathematical challenges. Through an interdisciplinary approach, this study sheds light on the field of optimization of numerical solutions, encouraging further development of theoretical and practical aspects of stochastic differential equations.
In this paper, we investigate a new approach to irregular integrals through the theory of generalized functions. Traditional approaches to irregular integrals are often limited to certain classes of functions or require special techniques to solve singularities. However, through the application of the theory of generalized functions, we open the door to the integration of a wider range of functions that are not strictly defined or have singularities. In our research, we develop new definitions of irregular integrals based on the principles of the theory of generalized functions. Using this approach, we demonstrate the possibility of integrating functions that were previously beyond the reach of traditional methods. Furthermore, we explore applications of these new definitions in various fields, including mathematics, physics, and engineering. Our results indicate the potential advantages of this new approach, including greater flexibility when solving problems with singularities, as well as the possibility of application in complex integration problems. Through this work, we open new perspectives in the study of irregular integrals and encourage further research in this area.
In this paper, we investigate a new approach to irregular integrals through the theory of generalized functions. Traditional approaches to irregular integrals are often limited to certain classes of functions or require special techniques to solve singularities. However, through the application of the theory of generalized functions, we open the door to the integration of a wider range of functions that are not strictly defined or have singularities. In our research, we develop new definitions of irregular integrals based on the principles of the theory of generalized functions. Using this approach, we demonstrate the possibility of integrating functions that were previously beyond the reach of traditional methods. Furthermore, we explore applications of these new definitions in various fields, including mathematics, physics, and engineering. Our results indicate the potential advantages of this new approach, including greater flexibility when solving problems with singularities, as well as the possibility of application in complex integration problems. Through this work, we open new perspectives in the study of irregular integrals and encourage further research in this area.
This paper investigates performance optimization of Gaussian mixture algorithms in the context of mathematical analysis. Using advanced optimization methods, adapted to the specific requirements of mathematical problems, we investigate how to improve the efficiency and precision of Gaussian mixture algorithms. Through experimental results and analyses, we demonstrate the benefits of these optimizations on various applications of mathematical analysis. In addition, we focus on developing new techniques to address challenges arising from the application of Gaussian mixture algorithms in mathematical analysis, such as overlearning and scalability problems. Through detailed experiments on different data sets and mathematical analysis problems, we provide deeper insight into the performance and applicability of the optimized algorithms. Our work also highlights the importance of the adaptability of algorithms in different contexts of mathematical analysis and the need for continuous improvement of optimization methodologies in order to adequately respond to the dynamic demands of the research community..
This paper investigates performance optimization of Gaussian mixture algorithms in the context of mathematical analysis. Using advanced optimization methods, adapted to the specific requirements of mathematical problems, we investigate how to improve the efficiency and precision of Gaussian mixture algorithms. Through experimental results and analyses, we demonstrate the benefits of these optimizations on various applications of mathematical analysis.
In addition, we focus on developing new techniques to address challenges arising from the application of Gaussian mixture algorithms in mathematical analysis, such as overlearning and scalability problems. Through detailed experiments on different data sets and mathematical analysis problems, we provide deeper insight into the performance and applicability of the optimized algorithms. Our work also highlights the importance of the adaptability of algorithms in different contexts of mathematical analysis and the need for continuous improvement of optimization methodologies in order to adequately respond to the dynamic demands of the research community..
