Volume-3 Issue-1, April 2023 – Indian Journal of Advanced Mathematics (IJAM)

A1144043123

IJAM Journal — Tue, 19 Dec 2023 11:27:17 +0000

The Indian Journal of Advanced Mathematics (IJAM) has ISSN 2582-8932 (online), an open-access, peer-reviewed, periodical half-yearly international journal, which is published by Lattice Science Publication (LSP) in April and October. The journal aims to publish high-quality peer–reviewed original articles in the area of Mathematics that covers Applied Mathematics, Arithmetic, Algebra, Calculus and Analysis, Geometry and Topology, Trigonometry, Combinatorics, Logic, Number Theory, Numerical Analysis, Dynamical Systems, Differential Equations, Mathematical Physics, Information Theory and Signal Processing, Probability and Statistics, Game Theory, Operations Research, Discrete Mathematics, Business Mathematics and Financial Mathematics. #Applied Mathematics #Arithmetic #Algebra #Calculus and Analysis #Geometry and Topology #Trigonometry #Combinatorics #Logic #Number Theory #Numerical Analysis #Dynamical Systems #Differential Equations #Mathematical Physics #Information Theory and Signal Processing #Probability and Statistics #Game Theory #Operations Research #Discrete Mathematics #Business Mathematics and Financial Mathematics #PhD ademic #Scopus #SCI #LatticeScience #Springer, #ScienceDirect #IEEE #Mendeley #Research #Scholarship #UGC #SSRN #LatticeScience #ESCI #Science #Journal #Conference #SSRN #PubLons

Derivation and Implementation of a Fifth Stage Fourth Order Explicit Runge-Kutta Formula using 𝑓(𝑥,𝑦) Functional Derivatives
Esekhaigbe Aigbedion Christopher

Esekhaigbe Aigbedion Christopher, Department of Statistics, Federal Polytechnic, Auchi, Edo State, Nigeria.

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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: This paper is aimed at using 𝒇(𝒙,𝒚) functional derivatives to derive a fifth stage fourth order Explicit Runge-Kutta formula for solving initial value problems in Ordinary Differential Equations. The 𝒇(𝒙,𝒚) functional derivatives from the general Runge-Kutta scheme will be compared with the 𝒇(𝒙,𝒚) functional derivatives from the Taylor series expansion to derive the method. The method will be implemented on some initial value problems, and results compared with results from the classical fourth order method. The results revealed that the method compared favorably well with the existing classical fourth order method.

Keywords: Initial Value Problems, Comparison, explicit, 𝒇(𝒙,𝒚) partial derivatives, Explicit Runge-Kutta Methods, Linear and non- linear equations, Taylor series expansion
Scope of the Article: Numerical Analysis

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A1148043123

IJAM Journal — Fri, 24 Mar 2023 08:09:41 +0000

Pseudo Number 0.999…
Sumit Gehlot

Sumit Gehlot, Student, Srijan Manav Shiksha Avam Kalyan Sansthan, Jodhpur (Rajasthan), India.

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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: As we know that the number 0.999… is a rational number and mathematicians, teachers and students of mathematics generally wonder whether the number 0.999… and the number 1 are really equal or not. This problem is one of the ancient problems of mathematics and is generally the most asked problem. While trying to solve the above problem, a new fact is found that the number 0.999… is not a real problem and with this a satisfactory solution of the above problem is obtained. In this paper, we do analysis about the existence of the number 0.999… on the real number line and prove that the number 0.999… is only a virtual number.

Keywords: Number System, Mathematical Reasoning.
Scope of the Article: Arithmetic

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A1147043123

IJAM Journal — Sat, 18 Mar 2023 05:53:18 +0000

Partial Group Representations on Semialgebras
Meenakshi¹, R. P. Sharma²

¹Dr. Meenakshi, Srinivasa Ramanujan Department of Mathematics Central University of Himachal Pradesh Shahpur, Kangra India.

²Prof. R.P. Sharma, Department of Mathematics and Statistics Himachal Pradesh University Summerhill, Shimla, India.

Abstract: Let A bean additively cancellative semialgebra over an additively cancellative semifield K as defined in [9]. For a given partial action α of a group G on an algebra, the associativity of partial skew group ring together with the existence and uniqueness of enveloping (global) action were studied by M. Dokuchaev and R. Exel [2] which were extended for semialgebras with some restriction by Sharma et. al. using the ring of differences. In a similar way, we extend the results of [2,3] for semialgebras regarding partial representations.

Keywords: Semialgebras; partial group actions; partial representations. AMS Subject Classification: 22E46, 53C35, 57S20
Scope of the Article: Algebra

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A1141043123

IJAM Journal — Sat, 11 Feb 2023 11:36:09 +0000

Algebraizations of Propositional Logic and Monadic Logic
Adel Mohammed Al-Odhari

Adel Mohammed Al-Odhari, Department of Mathematics, Faculty of Education, Humanities and Applied Sciences (Khwalan), Sana’a University, Sana’a, Yemen.

Manuscript received on 13 January 2023 | Revised Manuscript received on 11 February 2023 | Manuscript Accepted on 15 April 2023 | Manuscript published on 30 April 2023 | PP: 12-19 | Volume-3 Issue-1, April 2023 | Retrieval Number: 100.1/ijam.A1141043123 | DOI: 10.54105/ijam.A1141.043123

Abstract: In this paper, we introduce the language systems of propositional logic (LSPL), which involves no variables, and monadic predicate logic (LSMPL), which consists of predicates applied to single variables. We review the validity and dedication related to (LSPL) and (LSMPL) with their properties. After that, we investigate the connection between Boolean algebras with (LSPL) and (LSMPL) to make algebraizations methods out of logic.

Keywords: Propositional and Monadic Logic, Validity, Deduction, Boolean Algebra, Algebraizations of Propositional and Monadic Logic.
Scope of the Article: Logic

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A1142043123

IJAM Journal — Sat, 04 Feb 2023 13:20:23 +0000

On the Results of Coffy and Moli
Anand G Puranik

Anand G Puranik, Department of Mathematics, Government Science College, Chitradurga (Karnataka), India.

Manuscript received on 14 January 2023 | Revised Manuscript received on 04 February 2023 | Manuscript Accepted on 15 April 2023 | Manuscript published on 30 April 2023 | PP: 8-11 | Volume-3 Issue-1, April 2023 | Retrieval Number: 100.1/ijam.A1142043123 | DOI: 10.54105/ijam.A1142.043123

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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: The primary aim of this article is Generalization leading to search of integrals of the type∫ 𝒍𝒐𝒈𝑷 𝒍𝒐𝒈𝑸 𝒅𝒙 = ∫ 𝑭𝑮 𝒏𝒅𝒙 where both P, Q are functions of x only and also verification of results by using new trend. In this direction of verification, converting integrals into ordinary differential equations and finding the solutions, has significant trend and fresh impetus in the recent years. In this paper, along with the generalization of integrals, formation of ordinary differential equations and their solutions were also listed. Here in this article we obtained significant differential equations based on integrals of Russell [1], type. In the first part, generalizations of preliminary lemmas along with new integrals of logarithmic integrand were evaluated on the lines Mark Coffy [4]. Then first order linear differential equations were obtained for such integrals, to verify the truth of the solutions.

Keywords: Beta-functions, Definite Integrals, First order linear Differential Equations. Gamma-functions, Taylor Series, Ordinary Differential Equations.
Scope of the Article: Calculus and Analysis

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A1137043123

IJAM Journal — Sat, 03 Dec 2022 12:19:56 +0000

Proofs of Beal’s Conjecture, Fermat’s Conjecture, Collatz Conjecture and Goldbach Conjecture
Nishad T M¹, Mohamed M Azzedine²

¹Nishad T M, Research Scholar, Rajah Serfoji Government College, Thanjavur, (Affiliated to Bharathidasan University, Tiruchirappalli), Tamil Nadu, India.

²Dr. Mohamed M Azzedine, Member of Mathematical Association of America.

Abstract: In this article the elementary mathematical methods are used to prove Beal’s Conjecture, Fermat’s Conjecture, Collatz Conjecture and Goldbach Conjecture.

Keywords: Beal’s Conjecture, Fermat’s Conjecture, Collatz Conjecture, Goldbach Conjecture
Scope of the Article: Number Theory

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