Solving Higher-Order Graphs Method: A Linear Analytical Treatment | Chapter 7 | Recent Advances in Mathematical Research and Computer Science Vol. 5

 The composition of higher-order graphs reflecting linear relationships between variables is treated analytically. A path formalism is presented to deal with difficulties in graph theory. It is demonstrated how individual contributions to variable relationships can be tallied and represented by ordinals in a composed graph. The method allows for partial information extraction and provides an alternative to the traditional graph approach. An investigation of higher-order graphs as a powerful tool for developing algorithms for SoS, IoT, quantum communications, neuronal network models, and multiple interferometric devices is also presented.

Author(S) Details

Eusebio Bernabeu
Universidad Complutense de Madrid, Ciudad Universitaria. 28040 Madrid, Spain.

Hala Kamal
Department of Physics, Faculty of Science, Ain Shams University. 1156 Cairo, Egypt.

Alicia Larena
Universidad Politécnica de Madrid, ETSII. 28006 Madrid, Spain.

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Entropy Optimization Problems for Modified Verma Measures in Primal and Dual Spaces | Chapter 6 | Recent Advances in Mathematical Research and Computer Science Vol. 5

 The dual problem for a primal problem involving maximisation of the modified version of Verma measure of entropy [1-2] or minimization of the related measure of cross-entropy is presented in this study. In this instance, the greatest value of that entropy (or the minimum value of the associated cross-entropy, as inspired by Kullback [3]-Leibler [4]) is equal to the minimum (or maximum) value of the dual problem's objective function. When the dual problem is stated, the recovery of the primal problem is also discussed.

Author(S) Details

Rohit Kumar Verma
G.D. Rungta College of Engineering Bhilai, C.G, India.

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Review on Fractional Q-calculus with Varying Arguments | Chapter 5 | Recent Advances in Mathematical Research and Computer Science Vol. 5

 We introduce a novel subclass of analytic functions described by fractional q - calculus integral operators in this chapter. Using the concept of q-calculus, we also introduce the q-Bernadi integral operator for analytic functions. For the functions f belonging to the classes V(A, B, q, ) and K(A, B, q, ), we cover coefficient estimates, growth, distortion theorems, and many other features.

Author(S) Details

N. Ravi Kumar
Department of Mathematics, JSS College of Arts, Commerce and Science, Mysore - 570 025, India.

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Describing the Properties of Characteristic Polynomial of Marker Set and Its Laplacian | Chapter 4 | Recent Advances in Mathematical Research and Computer Science Vol. 5

 Marker set distance matrices, as well as their eigenvalues and characteristic polynomials, have a wide range of applications. In order to gain a wide range of applications, the Laplacian associated with marker set distances must also be examined in depth. These ideas have received a lot of attention in recent years. The features of characteristic polynomials of M-set distance matrices and their Laplacian are discussed in this chapter.

Author(S) Details

Medha Itagi Huilgol
Department of Mathematics, Bengaluru City University, Central College Campus, Bengaluru-560001-India.

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The Concept of Pseudoblocks of Endomorphism Algebra | Chapter 3 | Recent Advances in Mathematical Research and Computer Science Vol. 5

 Marker set distance matrices, as well as their eigenvalues and characteristic polynomials, have a wide range of applications. In order to gain a wide range of applications, the Laplacian associated with marker set distances must also be examined in depth. These ideas have received a lot of attention in recent years. The features of characteristic polynomials of M-set distance matrices and their Laplacian are discussed in this chapter.

Author(S) Details

Ahmed A. Khammash
Department of Mathematics, Umm Al-Qura University Makkah, Saudi Arabia.

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Study on Integrodifferential Evolution Systems with Nonlocal Initial Conditions | Chapter 2 | Recent Advances in Mathematical Research and Computer Science Vol. 5

 Systems of abstract integrodifferential equations with general nonlocal beginning conditions are the focus of the research. We use a vector approach based on matrices, vector-valued norms, and a vector version of Krasnoselskii's fixed point theorem for a sum of two operators to allow the nonlinear parts of the equations to behave as independently as possible. The assumptions provide for the hybridity of the system as well as the support for nonlocal beginning circumstances. Two examples are offered to show the principle.

Author(S) Details

Sylvain Koumla
Department of Mathematics, Faculty of Sciences and Technical, Adam Barka University, B.P. 1173, Abeche, Chad.

Radu Precup
Institute of Advanced Studies in Sciences and Technology, Babes–Bolyai University, 400084 Cluj-Napoca, Romania. & Tiberiu Popviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68-1, 400110 Cluj-Napocca, Romanian.

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Problem Solving Using Bayes Theorem: A Mathematical Approach | Chapter 1 | Recent Advances in Mathematical Research and Computer Science Vol. 5

 The study of Bayes' Theorem and how to apply that knowledge to actual challenges in a variety of professional disciplines. Provides a method for doing probability calculations after updating probabilities when new information is obtained in a critical stage of probability analysis. By manipulating the information in the Multiplication Rule, one can determine P(B/A) when given P(A) and P(A B). However, P(A/B) could not be calculated. Similarly, using the information in the Multiplication Rule, one can calculate P(A/B) when given P(B) and P(A B). There is now a place where Bayes' Theorem can be applied. The proof of Bayes' theorem is simple; not everyone is in the future, and you're using it to draw conclusions about the past. This is difficult for people who think in terms of causality.

Author(S) Details

Ismael Yaseen Abdulridha Alasadi
Department of Mathematics, University College of Science, Osmania University, India and University of Dhi qar, Iraq.

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