iosr-Jm   Volume-19 ~ Issue-4 ~ July – Aug. 2023

Abstract : In recent years, the internet plays a vital role in education, business and other industries. Tons of data are transferred using the internet. This results in a number of concerns, including data confidentiality, user authenticity, non-repudiation and so on. To address this issue, more research on digital signatures should be conducted in order to increase the data security and authenticity of transferred data. Digital Signature is an electronic signature that can be used to authenticate the identity of the sender. It ensures that the content of the message or document that has been sent is unchanged. In this study, a new digital signature method is mathematically modelled using the Elliptic Curve Digital Signature Algorithm (ECDSA) and Rabin encryption technique. It provides features like confidentiality, non-repudiation and authenticity.

Keywords: Digital Signature, ECDSA, Rabin encryption technique

[1]. Asbullah, M. A., Ariffin, M. R. K. (2016). "Algebraic Analysis Of A Rabin-Like Cryptosystem And Its Countermeasures". Indian Journal Of Science And Technology, 9(1), 1-5.
[2]. Asbullah, M. A., & Ariffin, M. R. K. (2016). "Design Of Rabin-Like Cryptosystem Without Decryption Failure". Malaysian Journal Of Mathematical Sciences, 10, 1-18.
[3]. Benjamin K. (2017). "Elliptic Curve Digital Signatures And Their Application In The Bitcoin Crypto-Currency Transactions", International Journal Of Scientific And Research Publications (IJSRP), Volume 7, Issue 11, ISSN 2250-3153.
[4]. Budiman, M. A., Rachmawati, D., & Utami, R. (2019, June). "The Cryptanalysis Of The Rabin Public Key Algorithm Using The Fermat Factorization Method". In Journal Of Physics: Conference Series (Vol. 1235, No. 1, P. 012084). IOP Publishing.
[5]. Don J., Alfred M., Scott V. (2001). "The Elliptic Curve Digital Signature Algorithm (ECDSA)", International Journal Of Information Security 1, No. 1, Pp.36-63..

Abstract : The inventory model (IM) for products with inventory-dependent demand levels (IDDL) was considered in the study. In this model, wear time was assumed to follow a modified three-parameter Weibull distribution while the demand rate (DR) was a quadratic function (QF) with shortages permitted and no backlog. The model was examined under the presumption that the deficit is manageable and has only partially accrued. To reduce the cost of inventory every cycle, the study addresses the ideal replenishment strategy in terms of the number of goods and the duration of storage. The three-parameter Weibull Hazard Index illustrates the effect of both obsolete and potentially....

Keywords: Inventory; Optimal, Stock-dependent; Modified Three-parameter Weibull, EOQ

[1]. Sanni, S. S. And Chukwu, W.I.E. (2016). An Inventory Model With Three-Parameter Weibull Deterioration, Quadratic Demand Rate And Short-Ages, American Journal Of Mathematical And Management Sciences, 35(2): 159-170.
[2]. Ouyang, L-Y., Wu, K-S., Cheng, M-C. (2005).An Inventory Model For Deteriorating Items With Exponential Declining Demand And Partial Backlogging, Yugoslav Journal Of Operations Re-Search, 15(2): 277-288.
[3]. Sanni, S. S. And Chukwu, W.I.E. (2013). An Economic Order Quantity Model For Items With Three-Parameter Weibull Distribution Deterioration, Ramp-Type Demand And Shortages, Applied Mathematical Modeling, 37: 9698-9706.
[4]. Kumar, S. And Rajput, U.S. (2014). A Two Warehouse Inventory Model For Non-Instantaneous Deteriorating Items With Time-Dependent Demand And Partial Backlogging, International Journal Of Applied Engineering Re-Search, 9(11): 1347-1356.
[5]. Tyagi, R. And Chouhan, P. (2015). An Inventory Model For Non-Instantaneous Deteriorating Items With Partial Backlogging And Stock-Dependent Demand, International Journal Of Mathematics And Computer Applications Research, 5(1): 1-6.

Abstract : In This Article, The Collection.....

Keywords: Integer Sequence, Diophantine 4-Tuples

[1]. Diophantus Of Alexandria, "Arithmetics And The Book Of Polygonal Numbers", I. G. Bashmakova, Ed., 1974, 85-86. [2]. Ezra Brown, "Sets In Which Xy+ K Is Always A Square", Mathematics Of Computation, 1985,45, 172, 613-620.
[3]. A. Dujella, "Some Polynomial Formulas For Diophantine Quadruples", 1996.
[4]. Eran Assaf And Shay Gueron, "Characterization Of Regular Diophantine Quadruples", Elemente Der Mathematik, 2001,56(2), 71-81.
[5]. A. Dujella, "There Are Only Finitely Many Diophantine Quintuples", 2004,183-214.
[6]. Alan Filipin And Yasutsugu Fujita, "Any Polynomial D (4) - Quadruple Is Regular", Mathematical Communications, 13(1), 2008, 45-55...

Abstract : The solutions of differential equations can be obtained using different analytical methods. Many transform methods have been applied to differential equations and results were obtained. Coupled systems of linear ordinary differential equations often occur in context where two or three different variables are expected to interact. Context such as in population models, mechanical systems, and in electrical engineering. This study showcases the applicability of the new integral transform, Kamal transform, to coupled systems of linear ordinary differential equations by solving three different coupled systems of linear ordinary differential equations..

Keywords: Kamal transform, Ordinary differential equation, Coupled systems, Mechanical systems, Intergral transform

[1]. Abdelilah Kamal H. Sedeeg (2016). The New Integral Transform "Kamal Transform".
[2]. Advances in Theoretical and Applied Mathematics. ISSN 0973 – 4554 Volume 11, Number 4, pp 45 – 48
[3]. Abdelilah Hassan Sedeeg and Zahra I. Adam Mahamoud (2017). The Use of Kamal Transform for Solving Partial Differential
equations. Advances in Theoritical and Applied Mathematics. ISSN 0973 – 4554 Volume 12, No 1, pp 7-13
[4]. Anjana Gupta, Sudhaushu Aggarwal and Deeksha Agrawal (2018). Solution of Linear Partial Integro-Differential Equations Using
Kamal Transform.
[5]. Antony Raj Aruldass, Divyakumari Pachaiyappan, and Choonkil Park (2021). Kamal Transform and Ulam Stability of Differential
Equations. Journal of Applied Analysis & Computation. 11(3): 1631-1639.

Abstract : Deficiencies in intercultural insight amongst American youth have led to an increased focus on globalization within institutions of higher education.To remedy this need amongst undergraduates, which has been exacerbated since the pandemic, short-term study abroads have been developed with the goal of enhancing these skillsets through application-based curriculum. New pedagogies have resulted so that students can be adequately exposed to true intercultural experiences along with tools to quantify this learning. This study identified and assessed intercultural learning gaps during a recent trip abroad.

Keywords-intercultural competencies, American expatriate, intercultural development inventory, global awareness, short-term study abroad

[1]. Alt, D., & Raichel, N. (2021). Equity and Formative Assessment in Higher Education.1st edition. New York, NY: Springer
Publishing.
[2]. Anderson, P., Lawton, L., Rexeisen, R., & Hubbard, A. (2006). Short-term Study Abroad and Intercultural Sensitivity: A pilot
study. International Journal of Intercultural Relations, 30(4), 457-469.
[3]. Anderson, P., & Lawton, L. (2011). Intercultural Development: Study Abroad vs. On-campus study. Frontiers: The
Interdisciplinary Journal of Study Abroad, 21, 86–108.
[4]. Badstübner, T., &Ecke, P.(2009, Spring). Student Expectations, Motivations, Target Language Use, and Perceived Learning
Progress in a Summer Study Abroad Program in Germany. Die Unterrichtspraxis/Teaching German, 42(1), 41-49.
[5]. Baratti, L. (2021, August). How Gen Z, Millennials, Gen X Are Approaching Post-Pandemic Travel. Travel Pulse. Retrieved
from: https://www.travelpulse.com/News/Features/How-Gen-Z-Millennials-Gen-X-Are-Approaching-Post-Pandemic-Travel

Abstract : This article deals with mathematical connection. This connectivity is related to the ability of learners and learners to connect between one concept and another in learning activities in the classroom. In mathematics learning, this activity is called mathematical connection. Mathematical connection is one of the important abilities possessed by a learner. The importance of having mathematical connection skills is included in one of the objectives of learning mathematics in secondary school which is still used by most secondary schools in Indonesia. Mathematics consists of various topics that are interconnected. These connections are not only contained within the field of mathematics, but also in relation to other disciplines, as well as the relationship of mathematics to real life.

Keywords: mathematical connection, math learning

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https://journal.upgris.ac.id/index.php/JIPMat/issue/view/168
[3]. Suprihatin A. Peningkatan kemampuan koneksi matematis melalui pembelajaran tematik. Jurnal Sains dan Pendidikan Matematika, 2013; 1(2) https://e-journal.iain-palangkaraya.ac.id/index.php/edusains/article/view/11/0 [4]. Kusumah, Y. S. Konsep, Pengembangan dan Implementasi Computer-Based Learning dalam Peningkatan Kemampuan High-Order Mathematical Thinking. Disampaikan pada pidato pengukuhan guru besar. Bandung: UPI. 2008.
https://scholar.google.co.id/citations?user=diiZoeIAAAAJ&hl=en
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https://jonedu.org/index.php/joe/article/view/68

Abstract : In this chapter, we investigate non-invariant submanifolds of almost para-contact Riemannian manifolds, we establish a necessary and sufficient condition for a sub manifold immersed in an almost Para contact Riemannian manifold to be invariant and show further properties of invariant sub manifolds in almost paracontact Riemannian manifolds.
Now we shall recollect an almost r-para-contact Riemannian manifold and treat the relations between this manifold and an almost product Riemannian manifold. Next, we study an invariant sub manifold immersed in an almost r-para contact Riemannian manifold and show that there exist the invariant sub manifolds of the three types in the almost r-para contact Riemannian manifold.

[1]. Adati, T. : Suibmanifolds Of An Almost Product Riemannian Manifold, Kodai Math., J., 4 (1981), 327-343.
[2]. Adati, T. : Conditions For Invariant Submanifolds Of An Almost Para Contact Riemannian Manifold, Tensor, N.S. 38 (1982), 41-
52.
[3]. Adati, T. And Miyazawa, T. : On Paracontact Riemannian Manifolds, TRU Math., 13-2 (1977), 27-30.
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641-646.
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Abstract : This paper solves the perpetual problem of Reimann's hypothesis that has remained unsolved till date and has intrigued scientists for ages, centuries. Concrete proof along with mathematical equations is used to show that the hypothesis is wrong and that the values and assumptions suggested by Reimann is incorrect.

[1]. Bombieri, Enrico (2000), The Riemann Hypothesis – Official Problem Description (PDF), Clay Mathematics Institute, Retrieved 2008-10-25 Reprinted In (Borwein Et Al. 2008).
[2]. Borwein, Peter; Choi, Stephen; Rooney, Brendan; Weirathmueller, Andrea, Eds. (2008), The Riemann Hypothesis: A Resource For The Afficionado And Virtuoso Alike, CMS Books In Mathematics, New York: Springer, Doi:10.1007/978-0-387-72126-2, ISBN 978-0-387-72125-5
[3]. Borwein, Peter; Ferguson, Ron; Mossinghoff, Michael J. (2008), "Sign Changes In Sums Of The Liouville Function", Mathematics Of Computation, 77 (263): 1681–1694, Bibcode:2008macom..77.1681B, Doi:10.1090/S0025-5718-08-02036-X, MR 2398787
[4]. Connes, Alain (2000), "Noncommutative Geometry And The Riemann Zeta Function", Mathematics: Frontiers And Perspectives, Providence, R.I.: American Mathematical Society, Pp. 35–54, MR 1754766
[5]. Connes, Alain (2016), "An Essay On The Riemann Hypothesis", In Nash, J. F.; Rassias, Michael (Eds.), Open Problems In Mathematics, New York: Springer, Pp. 225–257, Arxiv:1509.05576, Doi:10.1007/978-3-319-32162-2_5

Abstract : There is an existing theorem showing that not every group has a minimal generating set, by relying on a claim that all Proper Subgroups of infinitecoincide......

Keywords: Semigroup, Minimal Generating Set, Maximal Generating Set, Independent Set, Generating set, Ordering, Cyclic Group, p-primary Group, additive semigroup

[1] Bukh, Boris. Math Studies Algebra: Axiom Of Choice∗ (2019), Pages 21 – 237.
Http://Www.Borisbukh.Org/Mathstudiesalgebra1718/Notes_Ac.Pdf.
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[3] Halbeisen, L., Hamilton, M. & Růžička, P. Minimal Generating Sets Of Groups, Rings, And Fields. Quaestiones Mathematicae(2007), Volume 30 - Issue 3.
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Abstract : In this article, we have constructed an iterative method of third order for solving polynomial equations with multiple polynomial zeros. We have combined two well known third order methods Chebyshev and Halley for this construction purpose. We have proposed some local convergence theorems of this C-H Combined Mean Method to establish the computation of a polynomial with known multiple zeros. For the establishment of this local convergence theorem, the main role is performed by a function, termed as the function of initial conditions. Here the initial conditions uses the information only at the initial point. We have used the notion of......

Keywords: Local convergence; Halley method; Chebyshev method; Initial conditions; Multiple zeros; Normed field. MSC: 65H04, 12Y05

....

Abstract : This paper explores the application of Dirichlet averages and fractional calculus in analyzing the function dynamics within generalized K4 structures in graph theory. By extending the classical K4 complete graph, this study introduces a framework that incorporates fractional derivatives, enabling the capture of more nuanced behavior and complex relationships within the generalized K4 system. The Dirichlet average, a powerful tool in functional analysis, is applied to examine the behavior of node interactions under fractional derivatives, revealing insights into the stability, convergence, and distribution of values across graph nodes. Results indicate that the combination of Dirichlet averages with fractional derivatives provides a robust approach to examining generalized graphs, offering potential applications in network analysis, mathematical physics, and applied mathematics.....

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