Books/Book Chapters/Edited Books
Permanent URI for this collectionhttp://192.168.24.11:4000/handle/123456789/237
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Item Perturbation Theory and Eigenvalue Localization for Quaternionic Matrices(Book Rivers, 2025) Istkhar Ali, Mohammad Waquas Khadim"This chapter presents a comprehensive exploration of perturbation theory and eigenvalue localization for matrices over the quaternion division algebra, addressing key theoretical and computational challenges arising from their non-commutative nature. Building on recent advances in quaternionic linear algebra, we extend classical perturbation results-such as the Bauer-Fike theorem and relative eigenvalue bounds-to the quaternionic setting, with a focus on both right and left eigenvalues, which exhibit fundamentally distinct behaviors. We derive new perturbation bounds for structured quaternionic matrices (e.g., Hermitian, unitary, and skew-Hermitian), leveraging their unique spectral properties."Item Numerical Solutions of Non-Linear Equations by Newton’s, Steffensen’s & Halley’s Method(Book Rivers, 2025) Najmuddin Ahmad"In his chapter, Numerical analysis is the study of algorithms that use numerical approximation for the problem of mathematical analysis."Item Goal Programming(Book Rivers, 2025) Quazzafi Rabbani"In this chapter, we discussed Goal Programming (GP) is the most widely and suitable technique for solving multi-objective linear problems."Item Non-linear Equations and Their Numerical Solution by Fast Convergent Methods(Book Rivers, 2025) Abdul Wadood Khan"In his chapter, Numerical analysis is the study of algorithms that use numerical approximation for the problem of mathematical analysis. These are used in solving scientific and engineering problems which has increased dramatically in modern time. Numerical methods are often used to obtain the approximate solution of such problem in which it is not possible to obtain exact solution."Item Graph Theory(Book Rivers, 2025) Shadab Ahmad Khan"In this chaper, Graph Theory is a fundamental area of discrete mathematics that studies the relationships between pairs of objects. These objects are represented as vertices (or nodes), and the connections between them are known as edges (or links). Originating Königsberg bridge problem in the 18th century, Graph Theory has since evolved into a powerful mathematical framework with broad applications."Item Comprehensive Overview of Ring Theory and Polynomial Structures(Book Rivers, 2025) Malik Rashid Jamal"This chapter offers a unified and paraphrased examination of essential concepts in ring theory, with a particular focus on polynomial rings. It introduces core algebraic definitions, explores fundamental theorems along with their rigorous proofs, and incorporates illustrative examples to clarify theoretical insights. The purpose of this chapter is to introduce and define the basic principles and preliminary concepts that are foundational for further study in ring theory. These introductory materials serve as a basis for the subject matter. The content is largely based on standard algebraic references."Item An Introduction to Approximation Theory(Book Rivers, 2025) Idrees Ahmad Khan"In this chapter, we have defined some basic ideas about the Approximation theory with their properties and applications. The approximation theory has a close relationship with other branches of mathematics (like Fourier analysis). Existence of such a relationship is explained by the fact that many important problems of the approximation theory are formulated."Item Hypersurfaces Immersed in Metallic Riemannian Manifolds(Book Rivers, 2025) Mohammad Aamir Qayyoom, Mobin Ahmad"In this chapter, we find some properties of an n- dimensional hypersurface M in a metallic Riemannian manifold ( n+1 ,g, J). The totally geodesic, minimal and umbilical hypersurface in metallic Riemannian manifolds are studied and example is presented."Item A Fuzzy Optimization Model for Multi-Item Production Planning Problem in an Uncertain Environment(Book Rivers, 2025) Ahteshamul HaqIn this chapter, we have formulated a multi-objective production planning model for a hardware firm. This firm produces different types of hardware locks and other items in its production run. The objectives of the firm aretominimize the production cost, minimize the inventory holding cost and maximize the net profit subject to theset of realistic constraints. In the past, the production planning problem of a similar type has been formulated with exact information where the input information is precisely known to the decision-maker. However, in most of the real-life situations, the input information is not precisely known. In such situations,fuzzy set theory playsa vital role in modelling of the problem where the input data have some vagueness.The proposed model of production planning also been formulated under fuzzy environment. The triangular fuzzy number has been used to present the vagueness in the input information. The equivalent crisp form of the fuzzy model has been obtained bytwo different types of defuzzificationapproaches namely ranking function and α–cut approach respectively. Henceforth, the formulated models under fuzzy environment havebeen solved by the fuzzy goal programming approach.Item Fuzzy Ideals in Ordered Semigroups(Book Rivers, 2025) Mohammad Aasim Khan"In this chaper, we discussed Ordered semigroups, which combine algebraic operations with partial order relations, form an important area of study in modern algebra."