Journal of Advanced Research in Applied Mathematics and Statistics

Review and Applications of Brahmagupta’s Formula: A Priceless Morsel in Ancient Indian Mathematics

2026-07-15T12:15:07+00:00

Among the great mathematicians of India, there is a renowned name “Brahmagupta”. Brahmagupta’s formula is the well-known
result in geometry. This paper is based on the ancient Indian mathematics, and their work, which mainly focuses on Brahmagupta formula. The formulae enunciated by Brahmagupta for the area of a cyclic quadrilateral is proved with an easier method. In addition, various formulas for the area of different types of quadrilaterals are derived using the Brahmagupta’s formula. The applications of Brahmagupta formula, and its relevance in modern era, have also been discussed in the paper. In this entire review, we give a detailed overview of Brahmgupta formulas, particularly, we describe how we can use this formula to
obtain area of different geometrical shapes that have been widely used in the school mathematics.

How to cite this article:
Kaushik R, Purwar K, Singh R B, Review and
Applications of Brahmagupta’s Formula: A
Priceless Morsel in Ancient Indian Mathematics,
Vol 11, Issue 3&4, 2026: Pg. No. 1-13.

DOI: https://doi.org/ 10.24321/2455.7021.202605

An Introduction to HP-Algebras: Axiomatic Foundations and Basic Theory

2026-07-04T10:29:35+00:00

This research introduces Algebras, a novel algebraic framework defined by a set and a binary operation that adheres to the principles of Asymmetry, Transitive Difference, and Left Identity/Dominance. The study systematically develops Subalgebras as closed subsets, showing that they uphold all the axioms of Algebras and that their non-empty intersections also constitute subalgebras. This concept leads to the notion of a uniquely smallest generated subalgebra. Moreover, the study introduces Normal Sub algebras, a specific type of sub algebra that exhibits a "Left Absorption Property," meaning that for any element x from the main algebra and n from the normal sub algebra, indicating strong left-invariance. Additionally, Isomorphisms are defined as bijective mappings that preserve operations between Algebras. Theorems demonstrate that these isomorphisms maintain all fundamental axioms and the subalgebra structure. It is also established that the inverse of an Isomorphism is itself an Isomorphism, confirming algebraic equivalence. This foundational research aims to classify and understand the structural relationships within Algebras.

How to cite this article:

Perarasan, M. Vasuki, Mishra A k , B. Mohamed Harif, A. Dinesh Kumar, Celestin M, An Introduction to HP-Algebras: Axiomatic Foundations and Basic Theory, J Adv Res Appl Math Stat, Vol 11, Issue 1&2 2026: Pg. No. 14-25.

DOI : https://doi.org/10.24321/2455.7021.202606

Stylometric Feature Analysis for Authorship Identification Using Data Mining Classification Techniques

2026-08-01T08:55:51+00:00

Identification of authorship is one of the most important applications in Natural Language Processing (NLP), digital forensics and literature studies, wherein an anonymous or disputed document is identified by its author based on writing style analysis. In this paper, study present an authorship identification framework based on a set of stylometric features using supervised data mining classification techniques. A balanced literary corpus containing 100 documents authored by four Indian English authors has been used, with the analysis performed on sixteen stylometric features encompassing structure, lexical, vocabulary richness, readability, punctuation and function word properties. Performance of five classifiers, including Decision Tree, Random Forest, Naïve Bayes, K-Nearest Neighbour and Support Vector Machine, has been investigated for authorship classification. Experimental results reveal that the proposed authorship identification framework successfully differentiates between the authors based on their unique writing styles, with the Support Vector Machine having attained the best classification accuracy of 95.24%, whereas Random Forest shows better robustness during cross-validation.

How to cite this article:
Sharma T, Singh V. Stylometric Feature Analysis for Authorship Identification Using Data Mining Classification Techniques. J Adv Res Appl Math Stat, Vol 11, Issue 3&4 2026: Pg. No. 26-46.

DOI: https://doi.org/10.24321/2455.7021.202608

Application of Anuj Transform for Solving Improper Integrals whose Kernels Contain Bessel Functions of First Kind

2026-08-11T03:56:05+00:00

Improper integrals play a crucial role in both pure and applied mathematics, especially in problems involving unbounded functions or infinite intervals. These integrals arise naturally in the solutions of the problems of gravitational fields, heat conduction, electromagnetic theory, and probability distributions. However, determining the value of improper integrals is often challenging task due to the presence of infinite limits or singularities within the interval of integration. Motivated by these challenges, this study focuses on the development and application of the Anuj transform as an effective tool for handling improper integrals whose kernels contain Bessel functions of the first kind. The Anuj transform is employed to reformulate complex integrals into more tractable forms, thereby facilitating their analytical evaluation. By applying this approach, the study demonstrates a significant reduction in computational burden, alongside acceleration in the overall process of integral evaluation. The findings presented in this paper indicate that the Anuj transform has not only significantly accelerated the overall process of evaluation of improper integrals but has also substantially reduced the associated computational burden. This reduction in computational load reinforces the potential of the Anuj transform for practical uses within engineering applications and other related fields, showcasing its promise as a powerful tool in mathematical analysis and applied science. Future investigations may explore its integration with numerical schemes and its adaptability to other classes of special functions.

How to cite this article:

Aggarwal S. Application of Anuj Transform for Solving Improper Integrals whose Kernels Contain Bessel Functions of First Kind. J Adv Res Appl Math Stat, Vol 11, Issue 3&4 2026: Pg. No. 47-54.

DOI: https://doi.org/10.24321/2455.7021.202609