Within this research, The problem of scheduling jobs on a single machine is the subject of study to minimize the multi-criteria and multi-objective functions. The first problem, minimizing the multi-criteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥), and the second problem, minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 +𝐸𝑚𝑎𝑥 are the problems at hand in this paper. In this study, a mathematical model is created to address the research problems, and some rules provide efficient (optimal) solutions to these problems. It has also been proven that each optimal solution for ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is an efficient solution to the problem (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥). Because these problems are NP-hard problems so it is difficult to determine the efficient (optimal) solution set for these problems so some special cases are shown and proven which find some efficient (optimal) solutions suitable for the discussed problem, and highlight the significance of the Dominance Rule (DR), which can be applied to this problem to enhance efficient solutions.
Objectives: The main objective of this study is to examine the crucial role that Russian writers and intellectuals played in catalyzing the 1905 Revolution in Russia. Specifically, the study sought to analyze how their literary works, philosophical ideas, and political writings challenged Tsarist autocracy, depicted the suffering of the masses, and inspired opposition movements. The study aimed to highlight the defiant writings that contributed to the rise of political figures and the eventual overthrow of the repressive regime. Methods: The historical narrative and analytical methods were employed, conducting a comparative analysis of prominent works by renowned authors such as Tolstoy, Gorky, and Chekhov. This analysis focused on
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All of us are indispensable for this rule (the most important and important) individuals, whether we were groups of leaders or followers of peoples or countries because the rule provides adequate guarantees for the correct positions and drawing the plan for successful decision-makers matching with the balances of Sharia without incompatibility between religious or worldly interests or legal positions and therefore in the framework of the most important appointment And distinguish it from the important from the interests or the appointment of the most important and distinguish from the important from the evils and through this rule we learn about the scientific and practical solutions t
... Show MoreThin films were prepared from poly Berrol way Ketrrukemaaih pole of platinum concentrations both Albaarol and salt in the electrolytic Alastontrel using positive effort of 7 volts on the pole and the electrical wiring of the membrane record
The concept of aesthetics is one of the postmodern propositions, and it is one of the branches of philosophy that examines beauty, its standards and theories, and it is a holistic concept that includes several concepts, including the beautiful, the ugly, and the sublime.
The concept of aesthetics dealt with several studies in general (and in the field of architecture in particular), and the problem of aesthetics is in the blurring of the relationship between aesthetics and architectural criticism, based on the research hypothesis which states that there is a relationship between aesthetics and architectural criticism. The importance of the research in accommodating aesthetic standards and bases of evaluation that increases the possi
When a person found himself in a life he did not understand، he tried to create in his imagination powers and gods that tried to protect him from his ignorance of that world، and when he was reassured internally through those fantasy creatures when he made them the greatest protector and the source of his existence and his being، he began to weave myths and myths until he created his reality that he did not have. Any hint، and when we go back to the mechanism of embodying those myths، myths and fantasias in which he lived، we will find that the first building blocks were written on the walls of the caves in which he lived during that period. And when his thought developed and thus his expressive means developed، he began to embody
... Show MoreIn this work, the occurrence conditions of both local Bifurcation and persistence were studied, Saddle-node bifurcation appears near fourth point, near the first point, the second point and the third point a transcritical bifurcation occurred but no pitchfork bifurcation happened near any of the four equilibrium points. In addition to study conditions for Hopf-bifurcation near positive stable point that is the fourth point. Besides discuss persistence occurrence as globally property of the food chain of three species include prey, first predator and top predator with impact of toxin in all species and harvesting effect on the predator’s only. Numerical results for the set of hypothe
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