iosr-Jm   Volume-18 ~ Issue-6 ~ Nov. – Dec. 2022

Abstract : In the course of the iteration of a function of a complex variable, the resulting family of iterates provide a surprising occurrence. This paper carefully investigates this occurrence and provides a general characterization for obtaining the Fatou sets for a class of polynomials. The contrast in the nature of these sets for different classes is then illustrated using computer programming techniques and graphics and the results are consistent with what obtains in the literature.

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[3]. Jian Hua, Z., Sheng, W., & Zhi Gang, H., (2002). Some properties of Fatou and Julia sets of transcendental meromorphic functions. Bulletin. American Mathematical Society, 66(1), 1-8
[4]. Fatou, P., (1919). Sur l'iteration des fonctions trancendentes entieres, Acta Mathmatica 47, 161 -271
[5]. Fatou, P., (1920). Sur les, equationelles fonctionelles. Bulletin, Societe Mathematique de France, 48, 208-314

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Abstract In this paper, we investigate the relationship between some classes of operators and their spectral and numerical gaps. We characterize these gaps for equivalent operators. 2020 Mathematics Subject Classification: Primary 47A10, 47A12; Secondary 47B20, 47N20

Keywords and phrases: spectral gap, spectral radius, numerical gap, numerical radius, similar, metrically equivalent

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Abstract :This article addresses an assignment problem that employs a branching approach and a lower bound. To address the assignment problem, we provide a novel approach. The approach uses branch and bound decisional problem versions to solve the problem using column creation.First, a generalized assignment problem that is currently solved by a Hungarian approach using row generation is solved in this study by using column generation, and the best solution is produced, which is quite comparable to the original Hungarian solution.For the purpose of determining the lower bound, bound tree column generation is carried out at each node of the branch.

[1]. Basirzadeh, H. (2012). Ones assignment method for solving assignment problems. Applied Mathematical Sciences, 6 (47), 2345-2355.
[2]. Wulan, E. R., Pratiwi, A., & Zaqiah, Q. Y. (2020, September). The Analysis of Unbalanced Assignment Problems Using the Kotwal-Dhope Method to Develop A Massive Open Online Course. In 2020 6th International Conference on Wireless and Telematics (ICWT) (pp. 1-5). IEEE.
[3]. Burkard, R., Dell'Amico, M., & Martello, S. (2012). Assignment problems: revised reprint. Society for Industrial and Applied Mathematics.
[4]. Geetha, S., & Nair, K. P. K. (1993). A variation of the assignment problem. European Journal of Operational Research, 68 (3), 422-426.
[5]. Caramia, M., Dell'Olmo, P., & Italiano, G. F. (2008). Novel local-search-based approaches to university examination timetabling. INFORMS Journal on Computing, 20 (1), 86-99..