Mathematics and computer science. Volume 1.

Mathematics and computer science Volume 1. Volume 1. /

MATHEMATICS AND COMPUTER SCIENCE This first volume in a new multi-volume set gives readers the basic concepts and applications for diverse ideas and innovations in the field of computing together with its growing interactions with mathematics. This new edited volume from Wiley-Scrivener is the first...

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Detalles Bibliográficos
Otros Autores: Ghosh, Sharmistha, editor (editor)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Hoboken, NJ : John Wiley & Sons, Inc [2023]
Materias:
Computer science > Mathematics.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009757933106719
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • Chapter 1 Error Estimation of the Function by (Zrμ, r ≥1) Using Product Means (E,s)(N, pn,qn) of the Conjugate Fourier Series
  • 1.1 Introduction
  • 1.1.1 Definition 1
  • 1.1.2 Definition 2
  • 1.1.3 Definition 3
  • 1.2 Theorems
  • 1.2.1 Theorem 1
  • 1.2.2 Theorem 2
  • 1.3 Lemmas
  • 1.3.1 Lemma 1
  • 1.3.2 Lemma 2
  • 1.3.3 Lemma 3
  • 1.4 Proof of the Theorems
  • 1.4.1 Proof of the Theorem 1
  • 1.4.2 Proof of the Theorem 2
  • 1.5 Corollaries
  • 1.5.1 Corollary 1
  • 1.5.2 Corollary 2
  • 1.6 Example
  • 1.7 Conclusion
  • References
  • Chapter 2 Blow Up and Decay of Solutions for a Klein-Gordon Equation With Delay and Variable Exponents
  • 2.1 Introduction
  • 2.2 Preliminaries
  • 2.3 Blow Up of Solutions
  • 2.4 Decay of Solutions
  • Acknowledgment
  • References
  • Chapter 3 Some New Inequalities Via Extended Generalized Fractional Integral Operator for Chebyshev Functional
  • 3.1 Introduction
  • 3.2 Preliminaries
  • 3.3 Fractional Inequalities for the Chebyshev Functional
  • 3.4 Fractional Inequalities in the Case of Extended Chebyshev Functional
  • 3.5 Some Other Fracional Inequalities Related to the Extended Chebyshev Functional
  • 3.6 Concluding Remark
  • References
  • Chapter 4 Blow Up of the Higher-Order Kirchhoff-Type System With Logarithmic Nonlinearities
  • 4.1 Introduction
  • 4.2 Preliminaries
  • 4.3 Blow Up for Problem for E (0) &lt
  • d
  • 4.4 Conclusion
  • References
  • Chapter 5 Developments in Post-Quantum Cryptography
  • 5.1 Introduction
  • 5.2 Modern-Day Cryptography
  • 5.2.1 Symmetric Cryptosystems
  • 5.2.2 Asymmetric Cryptosystems
  • 5.2.3 Attacks on Modern Cryptosystems
  • 5.2.3.1 Known Attacks
  • 5.2.3.2 Side-Channel Attacks
  • 5.3 Quantum Computing
  • 5.3.1 The Main Aspects of Quantum Computing
  • 5.3.2 Shor's Algorithm
  • 5.3.3 Grover's Algorithm.
  • 5.3.4 The Need for Post-Quantum Cryptography
  • 5.4 Algorithms Proposed for Post-Quantum Cryptography
  • 5.4.1 Code-Based Cryptography
  • 5.4.2 Lattice-Based Cryptography
  • 5.4.3 Multivariate Cryptography
  • 5.4.4 Hash-Based Cryptography
  • 5.4.5 Supersingular Elliptic Curve Isogeny Cryptography
  • 5.4.6 Quantum-Resistant Symmetric Key Cryptography
  • 5.5 Launching of the Project Called "Open Quantum Safe"
  • 5.6 Algorithms Proposed During the NIST Standardization Procedure for Post-Quantum Cryptography
  • 5.7 Hardware Requirements of Post-Quantum Cryptographic Algorithms
  • 5.7.1 NTRUEncrypt
  • 5.7.1.1 Polynomial Multiplication
  • 5.7.1.2 Hardware to Accelerate NTRUEncrypt
  • 5.7.2 Hardware-Software Design to Implement PCQ Algorithms
  • 5.7.3 Implementation of Cryptographic Algorithms Using HLS
  • 5.8 Challenges on the Way of Post-Quantum Cryptography
  • 5.9 Post-Quantum Cryptography Versus Quantum Cryptography
  • 5.10 Future Prospects of Post-Quantum Cryptography
  • References
  • Chapter 6 A Statistical Characterization of MCX Crude Oil Price with Regard to Persistence Behavior and Seasonal Anomaly
  • 6.1 Introduction
  • 6.2 Related Literature
  • 6.3 Data Description and Methodology
  • 6.3.1 Data
  • 6.3.2 Methodology
  • 6.3.2.1 Characterizing Persistence Behavior of Crude Oil Return Time Series Using Hurst Exponent
  • 6.3.2.2 Zipf Plot
  • 6.3.2.3 Seasonal Anomaly in Oil Returns
  • 6.4 Analysis and Findings
  • 6.4.1 Persistence Behavior of Daily Oil Stock Price
  • 6.4.2 Detecting Seasonal Pattern in Oil Prices
  • 6.5 Conclusion and Implications
  • References
  • Appendix
  • Chapter 7 Some Fixed Point and Coincidence Point Results Involving Gα-Type Weakly Commuting Mappings
  • 7.1 Introduction
  • 7.2 Definitions and Mathematical Preliminaries
  • 7.2.1 Definition: G-metric Space (G-ms)
  • 7.2.2 Definition: t-norm.
  • 7.2.3 Definition: t-norm of Hadžić type (H-type)
  • 7.2.4 Definition: G-fuzzy metric space (G-fms)
  • 7.2.5 Definition
  • 7.2.6 Lemma
  • 7.2.7 Lemma
  • 7.2.8 Definition
  • 7.2.9 Definition
  • 7.2.10 Definition: Φ-Function
  • 7.2.11 Definition: Ψ-Function
  • 7.2.12 Lemma
  • 7.2.13 Definition
  • 7.2.14 Definition
  • 7.2.15 Definition
  • 7.2.16 Definition
  • 7.2.17 Definition
  • 7.2.18 Remarks
  • 7.2.19 Lemma
  • 7.3 Main Results
  • 7.3.1 Theorem
  • 7.3.2 Theorem
  • 7.3.3 Definition Ψ-Function
  • 7.3.4 Theorem
  • 7.3.5 Theorem
  • 7.3.6 Corollary
  • 7.3.7 Corollary
  • 7.3.8 Example
  • 7.3.9 Example
  • 7.3.10 Example
  • 7.3.11 Example
  • 7.4 Conclusion
  • 7.5 Open Question
  • References
  • Chapter 8 Grobner Basis and Its Application in Motion of Robot Arm
  • 8.1 Introduction
  • 8.1.1 Define Orderings in K[y1, ..., yn]
  • 8.1.2 Introducing Division Rule in K[y1, ..., yn]
  • 8.2 Hilbert Basis Theorem and Grobner Basis
  • 8.3 Properties of Grobner Basis
  • 8.4 Applications of Grobner Basis
  • 8.4.1 Ideal Membership Problem
  • 8.4.2 Solving Polynomial Equations
  • 8.5 Application of Grobner Basis in Motion of Robot Arm
  • 8.5.1 Geometric Elucidation of Robots
  • 8.5.2 Mathematical Representation
  • 8.5.3 Forward Kinematic Problem
  • 8.5.4 Inverse Kinematic Problem
  • 8.6 Conclusion
  • References
  • Chapter 9 A Review on the Formation of Pythagorean Triplets and Expressing an Integer as a Difference of Two Perfect Squares
  • 9.1 Introduction
  • 9.2 Calculation of Triples
  • 9.2.1 Calculation for Odd Numbers
  • 9.2.2 Calculation for Even Numbers
  • 9.2.3 Code Snippet
  • 9.2.4 Observation
  • 9.3 Computing the Number of Primitive Triples
  • 9.3.1 Calculation for Odd Numbers
  • 9.3.2 Calculation for Even Numbers
  • 9.3.3 Code Snippet
  • 9.3.4 Observation
  • 9.4 Representation of Integers as Difference of Two Perfect Squares
  • 9.4.1 Calculation for Odd Numbers.
  • 9.4.2 Calculation for Even Numbers
  • 9.4.3 Corollaries
  • 9.4.4 Code Snippet
  • 9.4.5 Output
  • 9.5 Conclusion
  • References
  • Chapter 10 Solution of Matrix Games With Pay.Offs of Single-Valued Neutrosophic Numbers and Its Application to Market Share Problem
  • 10.1 Introduction
  • 10.2 Preliminaries
  • 10.3 Matrix Games With SVNN Pay-Offs and Concept of Solution
  • 10.4 Mathematical Model Construction for SVNNMG
  • 10.4.1 Algorithm for Solving SVNNMG
  • 10.5 Numerical Example
  • 10.5.1 A Market Share Problem
  • 10.5.2 The Solution Procedure and Result Discussion
  • 10.5.3 Analysis and Comparison of Results With Li and Nanfs Approach
  • 10.6 Conclusion
  • References
  • Chapter 11 A Novel Score Function-Based EDAS Method for the Selection of a Vacant Post of a Company with q-Rung Orthopair Fuzzy Data
  • 11.1 Introduction
  • 11.2 Preliminaries
  • 11.3 A Novel Score Function of q-ROFNs
  • 11.3.1 Some Existing q-ROF Score Functions
  • 11.3.2 A Novel Score Function of q-ROFNs
  • 11.4 EDAS Method for q-ROF MADM Problem
  • 11.5 Numerical Example
  • 11.6 Comparative Analysis
  • 11.7 Conclusions
  • Acknowledgments
  • References
  • Chapter 12 Complete Generalized Soft Lattice
  • 12.1 Introduction
  • 12.2 Soft Sets and Soft Elements.Some Basic Concepts
  • 12.3 gs-Posets and gs-Chains
  • 12.4 Soft Isomorphism and Duality of gs-Posets
  • 12.5 gs-Lattices and Complete gs-Lattices
  • 12.6 s-Closure System and s-Moore Family
  • 12.7 Complete gs-Lattices From s-Closure Systems
  • 12.8 A Representation Theorem of a Complete gs-Lattice as an s-Closure System
  • 12.9 gs-Lattices and Fixed Point Theorem
  • References
  • Chapter 13 Data Representation and Performance in a Prediction Model
  • 13.1 Introduction
  • 13.1.1 Various Methods for Predictive Modeling
  • 13.1.2 Problem Definition
  • 13.2 Data Description and Representations
  • 13.3 Experiment and Result.
  • 13.4 Error Analysis
  • 13.5 Conclusion
  • References
  • Chapter 14 Video Watermarking Technique Based on Motion Frames by Using Encryption Method
  • 14.1 Introduction
  • 14.2 Methodology Used
  • 14.2.1 Discrete Wavelet Transform
  • 14.2.2 Singular-Value Decomposition
  • 14.3 Literature Review
  • 14.4 Watermark Encryption
  • 14.5 Proposed Watermarking Scheme
  • 14.5.1 Watermark Embedding
  • 14.5.2 Watermark Extraction
  • 14.6 Experimental Results
  • 14.7 Conclusion
  • References
  • Chapter 15 Feature Extraction and Selection for Classification of Brain Tumors
  • 15.1 Introduction
  • 15.2 Related Work
  • 15.3 Methodology
  • 15.3.1 Contrast Enhancement
  • 15.3.2 K-Means Clustering
  • 15.3.3 Canny Edge Detection
  • 15.3.4 Feature Extraction
  • 15.3.5 Feature Selection
  • 15.3.5.1 Genetic Algorithm for Feature Selection
  • 15.3.5.2 Particle Swarm Optimization for Feature Selection
  • 15.4 Results
  • 15.5 Future Scope
  • 15.6 Conclusion
  • References
  • Chapter 16 Student's Self-Esteem on the Self-Learning Module in Mathematics 6
  • 16.1 Introduction
  • 16.1.1 Research Questions
  • 16.1.2 Scope and Limitation
  • 16.1.3 Significance of the Study
  • 16.2 Methodology
  • 16.2.1 Research Design
  • 16.2.2 Respondents of the Study
  • 16.2.3 Sampling Procedure
  • 16.2.4 Locale of the Study
  • 16.2.5 Data Collection
  • 16.2.6 Instrument of the Study
  • 16.2.7 Validation of Instrument
  • 16.3 Results and Discussion
  • 16.4 Conclusion
  • 16.5 Recommendation
  • References
  • Chapter 17 Effects on Porous Nanofluid due to Internal Heat Generation and Homogeneous Chemical Reaction
  • Nomenclature
  • 17.1 Introduction
  • 17.2 Mathematical Formulations
  • 17.3 Method of Local Nonsimilarity
  • 17.4 Results and Discussions
  • 17.5 Concluding Remarks
  • References
  • Chapter 18 Numerical Solution of Partial Differential Equations: Finite Difference Method
  • 18.1 Introduction.
  • 18.2 Finite Difference Method.

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