Applied mathematics Books

Book SynopsisThis open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book.It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas.Table of ContentsChapter 1. Preparatory knowledge.- Chapter 2. The basis of code theory.- Chapter 3. Shannon theory.- Chapter 4. Cryptosystem and authentication system.- Chapter 5. Prime test.- Chapter 6. Elliptic curve.- Chapter 7. Lattice-based cryptography.

Read more less

Book SynopsisThis open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book.It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas.Table of ContentsChapter 1. Preparatory knowledge.- Chapter 2. The basis of code theory.- Chapter 3. Shannon theory.- Chapter 4. Cryptosystem and authentication system.- Chapter 5. Prime test.- Chapter 6. Elliptic curve.- Chapter 7. Lattice-based cryptography.

Read more less

Book SynopsisThis open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random analysis tools, there is a problem of "ambiguity" in both definition and algorithm. The greatest feature of this book is to use probability distribution to carry out rigorous mathematical definition and mathematical demonstration for various unclear or imprecise expressions, so as to make it a rigorous theoretical system for classroom teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic lattice, ideal lattice and generalized NTRU cryptography.This book is used as a professional book for graduate students majoring in mathematics and cryptography, as well as a reference book for scientific and technological personnel engaged in cryptography research.Table of ContentsChapter 1. Gauss lattice theory.- Chapter 2. Reduction principle of Ajtai.- Chapter 3. Learning with errors.- Chapter 4. LWE cryptosystem.- Chapter 5. Cyclic lattice and Ideal lattice.- Chapter 6. Fully Homomorphic Encryption.- Chapter 7. General NTRU cryptosystem.

Read more less

Book SynopsisThis open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random analysis tools, there is a problem of "ambiguity" in both definition and algorithm. The greatest feature of this book is to use probability distribution to carry out rigorous mathematical definition and mathematical demonstration for various unclear or imprecise expressions, so as to make it a rigorous theoretical system for classroom teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic lattice, ideal lattice and generalized NTRU cryptography.This book is used as a professional book for graduate students majoring in mathematics and cryptography, as well as a reference book for scientific and technological personnel engaged in cryptography research.Table of ContentsChapter 1. Gauss lattice theory.- Chapter 2. Reduction principle of Ajtai.- Chapter 3. Learning with errors.- Chapter 4. LWE cryptosystem.- Chapter 5. Cyclic lattice and Ideal lattice.- Chapter 6. Fully Homomorphic Encryption.- Chapter 7. General NTRU cryptosystem.

Read more less

Book SynopsisThis book contains select papers presented at the International Conference on Applied Mathematics and Computational Intelligence (ICAMCI-2020), held at the National Institute of Technology Agartala, Tripura, India, from 19–20 March 2020. It discusses the most recent breakthroughs in intelligent techniques such as fuzzy logic, neural networks, optimization algorithms, and their application in the development of intelligent information systems by using applied mathematics. The book also explains how these systems will be used in domains such as intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and complicated problems in optimization. The book publishes new developments and advances in various areas of type-3 fuzzy, intuitionistic fuzzy, computational mathematics, block chain, creak analysis, supply chain, soft computing, fuzzy systems, hybrid intelligent systems, thermos-elasticity, etc. The book is targeted to researchers, scientists, professors, and students of mathematics, computer science, applied science and engineering, interested in the theory and applications of intelligent systems in real-world applications. It provides young researchers and students with new directions for their future study by exchanging fresh thoughts and finding new problems.Table of ContentsA. Bajpai and P. Kumar Sharma, Free Vibration Analysis of Generalized Thermoelastic Homogeneous Isotropic plate with Two Temperatures.- Premkumar P.S., Nadaraja Pillai S., Arunvinthan S., and S. Teja, Analysis of Heat Transfer Coefficients and Pressure Drops in Surface Condenser with Different Baffle Spacing.- U.M. Pirzada, S. Rama Mohan, Fuzzy Form of Euler Method to Solve Fuzzy Differential Equations and its Application.- K. Bhattacharya and S. Kumar De, Intuitionistic Fuzzy Metrics and its Application.- H Singh, Complex Structure of Number in Language Processing.- A. George, S. Rukhande, and D. Pillai, Digital Newspaper using Augmented Reality.- Dimplekumar N. Chalishajar and R. Ramesh, Nonlocal Fuzzy Solutions for Abstract Second-Order Differential Equations.- J. Grover and S. Singhal, Performance Assessment of Routing Protocols in Cognitive Radio Vehicular ad-hoc Networks.- T. Jalal and I. A. Malik, Infinite System of Second-Order Differential Equations in Banach Space c0.- B. HemaSundar Raju, Fourth-Order Computations of Mixed Convection Heat Transfer Past a Flat Plate for Liquid Metals in Elliptical Cylindrical Coordinates.- D. Dey and R. Borah, Steady and Unsteady Solutions of Free Convective Micropolar Fluid Flow Near the Lower Stagnation Point of a Solid Sphere.- I. Agrawal, T. Sharma and N. K. Verma, Low-Light Image Restoration using Dehazing based Inverted Illumination Map Enhancement.- A. Venkatesh and R. Gomathi Bhavani, Mathematical Modelling of Probability and Profit of Single Zero Roulette to Enhance Understanding of Bets.- M. Mohan and L. Pattabiraman, Application of Blockchain in Food Safety.- T. Sen, Non-linear Computational Crack Analysis of Flexural Deficit Carbon and Glass FRP Wrapped Beams.- R. Mitra, S. Gope, A. Goswami, P. K. Tiwari, Economic Benefit Analysis by Integration of Different Comparative Methods for FACTS Devices.- A. K. Mondal, S. Pareek, A. Bera and B. Sarkar, Optimal Pricing with Servicing Effort in Two Remanufacturing Scenarios of a Closed-Loop Supply Chain.- F. Valdez, O. Castillo, and P. Melin, A Review on Type-2 Fuzzy Systems in Robotics and Prospects for Type-3 Fuzzy.- O. Castillo, P. Melin and Juan R. Castro, A Proposal for Interval Type-3 Fuzzy Sets Mathematical Definitions.- Z. Jankova, P. Dostal, D. K. Jana, S. Roy, S. Bhattacharjee and B. Bej, Optimization of Solubilization of Palm Oil Mill Effluent (POME) by using Interval Imprecise Data Set.

Read more less

Book SynopsisOlympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics.In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate number of test questions is available for reader's practice and testing purpose. Their detailed solutions are also conveniently provided.The examples are not very complicated so that readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions are from many countries, e.g. China, Russia, USA, Singapore, etc. In particular, the reader can find many questions from China, if he is interested in understanding mathematical Olympiad in China. This book serves as a useful textbook of mathematical Olympiad courses, or as a reference book for related teachers and researchers.Table of ContentsVolume 1: Operations on Rational Numbers; Linear Equations of Single Variable; Multiplication Formulae; Absolute Value and Its Applications; Congruence of Triangles; Similarity of Triangles; Divisions of Polynomials; Solutions to Testing Questions; Volume 2: Congruence of Integers; Decimal Representation of Integers; Pigeonhole Principle; Viete's Theorem and Its Applications; Linear Inequalities and System of Linear Inequalities; Inequalities with Absolute Values; Geometric Inequalities; Fundamental Properties of Circles; Solutions to Testing Questions; and other chapters.

Read more less

Book SynopsisOlympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics.In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate number of test questions is available for reader's practice and testing purpose. Their detailed solutions are also conveniently provided.The examples are not very complicated so that readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions are from many countries, e.g. China, Russia, USA, Singapore, etc. In particular, the reader can find many questions from China, if he is interested in understanding mathematical Olympiad in China. This book serves as a useful textbook of mathematical Olympiad courses, or as a reference book for related teachers and researchers.Table of ContentsVolume 1: Operations on Rational Numbers; Linear Equations of Single Variable; Multiplication Formulae; Absolute Value and Its Applications; Congruence of Triangles; Similarity of Triangles; Divisions of Polynomials; Solutions to Testing Questions; Volume 2: Congruence of Integers; Decimal Representation of Integers; Pigeonhole Principle; Viete's Theorem and Its Applications; Linear Inequalities and System of Linear Inequalities; Inequalities with Absolute Values; Geometric Inequalities; Fundamental Properties of Circles; Solutions to Testing Questions; and other chapters.

Read more less

Book SynopsisThis book collects select papers presented at the 7th International Arab Conference on Mathematics and Computations (IACMC 2022), held from 11–13 May 2022, at Zarqa University, Zarqa, Jordan. These papers discuss a new direction for mathematical sciences. Researchers, professionals and educators will be exposed to research results contributed by worldwide scholars in fundamental and advanced interdisciplinary mathematical research such as differential equations, dynamical systems, matrix analysis, numerical methods and mathematical modelling. The vision of this book is to establish prototypes in completed, current and future mathematical and applied sciences research from advanced and developing countries. The book is intended to make an intellectual contribution to the theory and practice of mathematics. This proceedings would connect scientists in this part of the world to the international level.Table of ContentsA. S. Salama and R. Abu Gdair: Generalized Neighborhood Systems Approach for Information Retrieval Systems.- Emad A. Kuffi, E. S. Abbas and S. F. Maktoof: Applying “Emad–Sara” Transform on Partial Differential Equations.- A. Al-Swaftah, A. Burqan and M. Khandaqji: Estimations of the Bounds for the Zeros of Polynomials Using Matrices.- B. Ghazal, R. Saadeh and G. Gharib: Applications on Formable Transform in Solving Integral Equations.- O. Tug: On the Eigenvalue of a Norlund Type Matrix as an Operator on the Sequence Spaces L1 and bv.- N. Tahat, Obaida M. Al-hazaimeh and S. Shatnawi: A New Authentication Scheme Based on Chaotic Maps and Factoring Problems.- R. B. Albadarneh, A. M. Adawi, Sa'ud Al-Sa'di, I. M. Batiha and S. Momani: A pro rata Definition of the Fractional-order Derivative.- S. Ibrahim, M. Muhammed Al-Kassab and M. Qasim Al-Awjar: Investigating Multicollinearity in Factors Affecting Number of Born Children in Iraq.- T. Alkharabsheh, K. shebrawi and M. Abu-sSaleem: Hilbert–Schmidt Numerical Radius Inequalities For Certain 2 x 2 Operator Matrices.- Y. A. Sabawi, Mardan A. Pirdawood, Hemn M. Rasool and S. Ibrahim: Model Reduction and Implicit–Explicit Runge–Kutta Schemes for Nonlinear Stiff Initial-value Problems.- G. M. Gharib, Maha S. Alsauodi, A. Guiatni, Mohammad A. Al-Omari and A. Al-Rahman M. Malkawi: Using Atomic Solution Method to Solve the Fractional Equations.- S. Ramadan: Analysis in the Algebra A(E).- S. rasem, A. Dababneh and Ma’mon Abu Hammad: Applications of Conformable Fractional Weibull Distribution.- O. Ramadan: Stable Second-order Explicit Runge–Kutta Finite Difference Time Domain Formulations for Modeling Graphene Nano-material Structures.- Ali Shehab, Ahmed M. R. El-Baz and A. M. Elmarhomy: Hydrodynamic Analysis and CFD Modeling of PAWEC Interacted with Regular Waves Using CFX.- M. Muhammed Al-Kassab and S. Ibrahim: Using Ridge Regression to Estimate Factors Affecting the Number of Births: A Comparative Study.- T. Hamadneh, J. Merker and G. Schuldt: Discrete Maximum Principle and Positivity Certificates for the Bernstein Dual Petrov–Galerkin Method.- A. Burqan, A. Sarhan and R. Saadez: Analytical Solutions of the Fractional Riccati Differential Equations Using Laplace Residual Power Series Method.- D. Andrica and O. Bagdasa: On the Dynamic Geometry of Kasner Triangles with Complex Parameter.- D. Amr and Ma’mon Abu Hammad: Application of Conformable Fractional Nakagami Distribution.- Rawya Al-deiakeh, Maha S. Alsauodi, S. Momani, Gharib M. Gharib and T. B. Salameh: Application of Laplace Residual Series Method for Solving Time-fractional Fisher Equation.- M. Hassen Eid Abu-Sei'leek: Self-consistent Single-particle Spectra with Delta Excitations.- I. M. Batiha, N. Djenina, A. Ouannas and T. E. Oussaeif: Fractional-order SEIR Covid-19 Model: Discretization and Stability Analysis.- A. Alsoboh and M. Darus: A q-Starlike Class of Harmonic Meromorphic Functions Defined by q-Derivative Operator.- J. Oudetallah, Z. Chebana, Taki-Eddine Oussaeif, A. Ouannas and I. M. Batiha: Theoretical Study of Explosion Phenomena for a Semi-parabolic Problem.- L. Szala: Explicit Formulae of Linear Recurrences.- R. Abu Sallik, J. Al Jaraden: The Influence of S-quasinormal Subgroups on the Structure of Finite Groups.- S. J. Ansari and V. R. Lakshmi Gorty: Two-sided Clifford Wavelet Function in Cl(p, q).- L. Nemeth and L. Szalay: Generalizations of the Fibonacci Sequence with Zig-zag Walks.- D. Wafula Waswa and M. Muhammed Al-Kassab: Mathematics Learning Challenges and Difficulties: A Students’ Perspective.- V.R. Ibrahimov, G.Yu. Mehdiyeva, Xiao-Guang Yue and M.N. Imanova: Finding Solution to the Initial Value Problem for ODEs First and Second Order by One and the Same Method.- Doaa Al-Saan: On Symmetric Matrices with One Positive Eigenvalue and the Interval Property of Some Matrix Classes.- N. Anakira, A. Hioual, A. Ouannas, Taki-Eddine Oussaeif and Iqbal M. Batiha: Global Asymptotic Stability for Discrete-time SEI Reaction-diffusion Model.- G. Eid, I. Jebril, Ma’mon Abu Hammad and D. AbuJudeh: Atomic Solution of Euler Equation.- Worood A. AL-hakim, Maha S. Alsauodi, Gharib M. Gharib, Fatima Alqasem and May Abu Jalbosh: Solving Nonlinear Fractional Coupled Burgers Equation by Sub-equation Method.- S. M. Alshorm: Groups in which the Commutator Subgroup is Cyclic.- M. A. Amleh: On Point Prediction of New Lifetimes under a Simple Step-stress Model for Censored Lomax Data.- Tareq M. Al-shami and Radwan Abu-Gdairi: Infra Soft B-open Sets and Their Applications on Infra Soft Topological Spaces.- Raed M. Khalil: An Algorithm of the Prey and Predator Struggle to Survive as a Random Walk Simulation Case Study.- W. Beghami, B. Maayah and S. Bushnaq: Numerical Study of a Nonlinear Fractional Mathematical Model of the Tumor Cells Chemotherapy Effect.- O. Ababneh and K. Al-Boureeny: New Modification Methods for Finding Zeros of Nonlinear Function.- Ioan-Lucian Popa, T. Ceausu, L. Elena Biris and A. Zada: On Tempered Exponential Trisplitting for Random Semi-Dynamical Systems.- H. El-Metwally, F. M. Masood, R. Abu-Gdairi and Tareq M. Al-shami: On q-Laplace Transforms.- N. R. Anakira, G.F. Bani-Hani and O. Ababneh: An Effective Procedure for Solving Linear and Non-linear Volterra Integro-differential Equations.- S. Alkhalely, A. Burqan and M. Muhammed Al-Kassab: New Estimations for Zeros of Polynomials Using Numerical Radius and Similarity of Matrices.- J. Jawdat: Strong Coproximinal Subspaces in Köthe Function Spaces.- E. Savas: A New Paranormed Sequence Spaces and Invariant Means.

Read more less

Book SynopsisThis book provides a clear understanding of quantum mechanics (QM) by developing it from fundamental postulates in an axiomatic manner, as its central theme. The target audience is physics students at master's level. It avoids historical developments, which are piecemeal, not logically well knitted, and may lead to misconceptions. Instead, in the present approach all of QM and all its rules are developed logically starting from the fundamental postulates only and no other assumptions. Specially noteworthy topics have been developed in a smooth contiguous fashion following the central theme. They provide a new approach to understanding QM. In most other texts, these are presented as disjoint separate topics. Since the reader may not be acquainted with advanced mathematical topics like linear vector space, a number of such topics have been presented as mathematical preliminary. Standard topics, viz. derivation of uncertainty relations, simple harmonic oscillator by operator method,boun

Read more less

Book Synopsis

Read more less