iosr-Jm   Volume-20 ~ Issue-4 ~ Jul. – Aug. 2024

Abstract : The purpose of this research is to bridge the disparity between the theory of mathematics and musical practice by investigating the application of finite cyclic groups to musical notations. It also provides novel approaches to long-standing problems in music representation and analysis. This work intends to further computational musicology and music theory through multidisciplinary collaboration and empirical validation, with possible applications to a variety of musical pursuits. Modulo 12, the musical notes form an additive abelian group. Knowing how......

Key words: Group theory, Cylic group, Abelian group, Musical NOTES, P-Sylow Subgroup

[1]. Ada Zhang, (2009) The framework of music theory as represented with Groups 9-11
[2]. Adam Townsend (2011). Mathematics and Music theory, A paper presentation of undergraduate Mathematics Colloquium at the University College London (http://ucl.sneffel.com) 5-8
[3]. Alissa, S. Crans, (2009). Musical Actions of Dihedral groups 479-482
[4]. Emma Rose, (2011). Mathematics and Music 5-6 H.
[5]. Wussing (2007). The Genesis of the abstract group concept: A contribution to the History of the origin of Abstract Group theory, New York: Dover Publications http://en.Wikipedia.org/wiki/Group(Mathematics)

Abstract : Hypercyclicity is the study of linear and continuous operators that possess a dense orbit. Hypercyclicity of linear operators is one of the most studied properties of linear dynamics and has become an active area of research. Hypercyclicity of various types of elementary operators including the generalised derivations, left and right multiplication operators among others has been studied and various results obtained. In this paper we present some results on hypercyclicity of the basic elementary operator......

Keywords:- Hypercyclicity , Basic elementary operator and Orbit

[1]. Ansari, S. (1995). Hyper-cyclic and cyclic vectors.J. Funct. Anal., 148:374–383.
[2]. Chan, K. (1999). Hypercyclicity of theOperator Algebra for a Separable Hilbert.J. Operator Theory,42:231–244.
[3]. Clifford, O. (2019). Dynamics of generalised derivations and elementary operators.Complex Analysis and Operator Theory, 13:257–274.
[4]. DelaRosa, M. (2022). Hypercyclicity of operators that commute with the differentiation operatoron the space of entire functions.Journal of Functional Analysis, 282:108–391.

Abstract : Résumé Contexte Il est d'impérieuse nécessité, que chaque institution de manière générale et en particulier L'Institut Supérieur des Techniques Médicales de Lubumbashi dispose en son sein un règlement disciplinaire pour garantir le maintien de la quiétude dans l'environnement scolaire. À cet effet, cette disposition pourrait contribuer à l'atteinte des objectifs éducationnels....

[1]. Bodo S. La pendule de l'éducation : le role de la discipline dans les résultats de l'apprenant et la qualité 2020 ; 19/04/2024 online
[2]. Gréhaigne JF, Poggi MP et al., ; L'enseignement et l'apprentissage des connaissances et des compétences motrices utiles en sport collectif ; https://doi.org/10.4000/ejrieps.778; 2017 ; 19/04/2024 online
[3]. Marie Michelle et al., le développement Pédagogique ; Le mirage de la classe modèle, Vol. 6, numéro 1 - septembre 2006, 2024 19/04/2024 online
[4]. Gabriel Lecompte, Satisfaction et apprentissage : s'appuyer sur le plaisir de connaitre ; 2024 19/04/2024 online
[5]. Belmihoub Soltana , (2023) ? La gestion de la classe : clés pour un environnement d'apprentissage positif. Revue des recherches éducatives et didactique. Volume: 12 / N°: 1 (2023), p971-986.

Abstract : Starting with a pebble free graph, our aim is to pebble the target vertex ....

Keywords: Kragujevac tree, reversible pebbling number, root, branch

[1]. Bhattacharjee Debjyoti, Mathias Soeken, Srijit Dutta, Anupam Chattopadhyay, and Giovanni De Micheli. "Reversible pebble games for reducing qubits in hierarchical quantum circuit synthesis."
[2]. In 2019 IEEE 49th International Symposium on Multiple-Valued Logic (ISMVL), pp. 102-107. IEEE, 2019.
[3]. Gutman Ivan. "Kragujevac trees and their energy." Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics 6, no. 2 (2014): 71-79.
[4]. Komarath Balagopal, Jayalal Sarma, and Saurabh Sawlani. "Pebbling meets coloring: Reversible pebble game on trees." arxiv:1604:05510v1 [cs.cc]19 April 2016.

Abstract : numerical change in energy will be explained through new algebra....

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Abstract : This paper examines the practical stability of the trivial solution of a nonlinear impulsive Caputo fractional differential equations with fixed moments of impulse using a class of piecewise continuous Lyapunov functions which generalizes the vector Lyapunov functions. Together with comparison results, sufficient conditions for the practical stability of the impulsive Caputo fractional order systems are established. Results obtained extends and improves on existing results.

Keywords: practical stability, Caputo derivative, impulse, vector Lyapunov functions, fractional differential equations. MSC: 34A08; 34A12; 34A37; 34D20.

[1]. R. Agarwal, D. O'Regan, and S. Hristova, "Stability of Caputo Fractional Differential Equations". Applications of Mathematics.
60, No. 6, 653-676, 2015.
[2]. R. Agarwal, S. Hristova and D. O'Regan, "Stability of Solutions of Impulsive Caputo Fractional Differential Equations,"
Electronic Journal of Differential Equations, vol. 2016, No. 58, pp. 1-22, 2016.
[3]. R. Agarwal, D. O'Regan, S. Hristova, and Cicek, M., (2017). Practical Stability with respect to Initial Time Difference for Caputo
Fractional Differential Equations. Electronic Journal of Differential Equations. Communications in Nonlinear Science and
Numerical Simulations, 42, 106, 2017, doi.org/10.1016/j.cnsns.2016.05.005.
[4]. E. P. Akpan and O. Akinyele, "On the 0  -Stability of Comparison Differential Systems." Journal of Mathematical Analysis and
Applications, 164(2), 307-324.
[5]. L. Arnold and B. Schmalfuss, "Lyapunov's Second Method for Random Dynamical Systems." Journal of Differential Equations,
177(1), 235-265..