Calculus and mathematical analysis Books

Book SynopsisThe Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is still open for general polarizations or more generally in extremal Kähler cases. In this book, the unsolved cases of the conjecture will be discussed.It will be shown that the problem is closely related to the geometry of moduli spaces of test configurations for polarized algebraic manifolds. Another important tool in our approach is the Chow norm introduced by Zhang. This is closely related to Ding’s functional, and plays a crucial role in our differential geometric study of stability. By discussing the Chow norm from various points of view, we shall make a systematic study of the existence problem of extremal Kähler metrics.Trade Review“The concise style of exposition likely means that this monograph is best suited for experts with background knowledge in canonical Kähler metrics. … It can be recommended also to those who would like a review of important results concerning the generalised Kähler-Einstein metrics, with various examples, and the moduli space of Lp-spaces.” (Yoshinori Hashimoto, Mathematical Reviews, May, 2023)Table of ContentsIntroduction.- The Donaldson-Futaki invariant.- Canonical Kähler metrics.- Norms for test configurations.- Stabilities for polarized algebraic manifolds.- The Yau-Tian-Donaldson conjecture.- Stability theorem.- Existence problem.- Canonical Kähler metrics on Fano manifolds.- Geometry of pseudo-normed graded algebras.- Solutions.

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Book SynopsisThis book presents original papers reflecting topics featured at the international symposium entitled “Fusion of Mathematics and Biology” and organized by the editor of the book. The symposium, held in October 2020 at Osaka University in Japan, was the core event for the final year of the research project entitled “Establishing International Research Networks of Mathematical Oncology.” The project had been carried out since April 2015 as part of the Core-to-Core Program of Japan Society for the Promotion of Science (JSPS). In this book, the editor presents collaborative research from prestigious organizations in France, the UK, and the USA. By utilizing their individual strengths and realizing the fusion of life science and mathematical science, the project achieved a combination of mathematical analysis, verification by biomedical experiments, and statistical analysis of chemical databases.Mathematics is sometimes regarded as a universal language. It is a valuable property that everyone can understand beyond the boundaries of culture, religion, and language. This unifying force of mathematics also applies to the various fields of science. Mathematical oncology has two aspects, i.e., data science and mathematical modeling, and definitely helps in the prediction and control of biological phenomena observed in cancer evolution.The topics addressed in this book represent several methods of applying mathematical modeling to scientific problems in the natural sciences. Furthermore, novel reviews are included that may motivate many mathematicians to become interested in biological research.Table of ContentsPART 1: Mathematical Modeling: D. Guan, X. Luo, and H. Gao, Constitutive Modelling of Soft Biological Tissue from Ex Vivo to In Vivo: Myocardium as an Example.- T. Colin, T. Michel, and C. Poignard, Mathematical Modeling of Gastro-intestinal Metastasis Resistance to Tyrosine Kinase Inhibitors.- Y. Tanaka and T. Yasugi, Mathematical Modeling and Experimental Verification of the Proneural Wave.- D. Kumakura and S. Nakaoka, Exploring Similarity between Embedding Dimension of Time-series Data and Flows of an Ecological Population Model.- T. Hayashi, Mathematical Modeling for Angiogenesis.- S. Collin, Corridore and C. Poignard, Floating Potential Boundary Condition in Smooth Domains in an Electroporation Context.- N. L. Othman and T. Suzuki, Free Boundary Problem of Cell Deformation and Invasion.- L. Preziosi and M. Scianna, Multi-level Mathematical Models for Cell Migration in Confined Environments.- S. Magi, Mathematical Modeling of Cancer Signaling Addressing Tumor Heterogeneity.- N. Sfakianakis and Mark A.J. Chaplain, Mathematical Modelling of Cancer Invasion: A Review.- T. Williams, A. Wilson, and N. Sfakianakis, The First Step towards the Mathematical Understanding of the Role of Matrix Metalloproteinase-8 in Cancer Invasion.- PART II: Biological Prediction: T. Ito, T. Suzuki, and Y. Murakami, Mathematical Modeling of the Dimerization of EGFR and ErbB3 in Lung Adenocarcinoma.- H. Kubota, Selective Regulation of the Insulin-Akt Pathway by Simultaneous Processing of Blood Insulin Pattern in the Liver.- D. Oikawa, N. Hatanaka, T. Suzuki, and F. Tokunaga, Mathematical Simulation of Linear Ubiquitination in T Cell Receptor-mediated NF-κB Activation Pathway.- Y. Ito, D. Minerva, S. Tasaki, M. Yoshida, T. Suzuki, and A. Goto, Time Changes in the VEGF-A Concentration Gradient Lead Neovasculature to Engage in Stair-like Growth.- N. Hatanaka, M. Futakuchi, and T. Suzuki, Mathematical Modeling of Tumor Malignancy in Bone Microenvironment.- M. Yamamoto and Jun-ichiro Inoue, Signaling Networks Involved in the Malignant Transformation of Breast Cancer.- PART III: Data Science: R. Morishita, H. Takahashi, and T. Sawasaki, Cell-free Based Protein Array Technology.- Y. Nojima and Y. Takeda, Omics Data Analysis Tools for Biomarker Discovery and the Tutorial.- M. Oyama and H. Kozuka-Hata, Integrative Network Analysis of Cancer Cell Signaling by High-resolution Proteomics.- N. Nakamura and R. Yamada, Distance-matrix-based Extraction of Motility Features from Functionally Heterogeneous Cell Populations.- S. Kawasaki, H. Hayashi, and Y. Tominaga, Data Analytic Study of Genetic Mechanism of Ovarian Carcinoma from Single Cell RNA-seq Data.

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Book SynopsisThis first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone–Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the concepts leading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.Trade Review“With an encyclopedic range of topics and terse exposition, Basic Topology 1 may make a reasonable reference for self-motivated learners … .” (Timothy Clark, MAA Reviews, March 20, 2023)Table of Contents1. Prerequisites: Sets, Algebraic Systems, and Classical Analysis.- 2. Metric Spaces and Normed Linear Spaces.- 3. Topological Spaces and Continuous Maps.- 4. Separation Axioms.- 5. Compactness and Connectedness.- 6. Real-valued Continuous Functions.- 7. Countability, Separability and Embedding.- 8. Brief History of General Topology.

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Book SynopsisThis third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.Table of Contents1. Prerequisite Concepts of Topology, Algebra and Category Theory.- 2. Homotopy Theory: Fundamental and Higher Homotopy Groups.- 3. Homology and Cohomology Theories: An Axiomatic Approach with Consequences.- 4. Topology of Fiber Bundles.- 5. Homotopy Theory of Bundles.- 6. Some Applications of Algebraic Topology.- 7. Brief History on Algebraic Topology and Fiber Bundles.

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Book SynopsisThis second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.Table of Contents1. Background on Topology, Analysis and Algebra.- 2. Topological Groups.- 3. Topology of Manifolds.- 4. Lie Groups and Lie Algebra.- 5. Brief History of Topological Groups, Manifold and Lie Groups.

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Book SynopsisThis book collects original peer-reviewed contributions presented at the "International Conference on Mathematical Analysis and Applications (MAA 2020)" organized by the Department of Mathematics, National Institute of Technology Jamshedpur, India, from 2–4 November 2020. This book presents peer-reviewed research and survey papers in mathematical analysis that cover a broad range of areas including approximation theory, operator theory, fixed-point theory, function spaces, complex analysis, geometric and univalent function theory, control theory, fractional calculus, special functions, operation research, theory of inequalities, equilibrium problem, Fourier and wavelet analysis, mathematical physics, graph theory, stochastic orders and numerical analysis. Some chapters of the book discuss the applications to real-life situations. This book will be of value to researchers and students associated with the field of pure and applied mathematics.Table of ContentsG. K. Srinivasan, A note on isolated removable singularities of harmonic functions.- O. Chadli, Ram N. Mohapatra, B. K. Sahu, Equilibrium Problems and Variational Inequalities: a Survey of Existence Results.- O. Chadli, Ram N. Mohapatra, G. Pany, Nonlinear evolution equations by a Ky Fan minimax inequality approach.- L. A. Wani and A. Swaminathan, Sufficient Conditions Concerning the Unified Class of Starlike and Convex Functions.- S. Menchavez and I. Mae Antabo, One Dimensional Parametrized Test Functions Space of Entire Functions.- D. Raghavan and S. Nagarajan, Extremal mild solutions of Hilfer fractional Impulsive systems.- B. Roy and S. N. Bora, On existence of integral solutions for a class of mixed Volterra-Fredholm integro fractional differential equations.- P. Kumar, A. Kumar, R. Kumar Vats and A. Kumar, Trajectory Controllability of Integro-differential Systems of Fractional Order γ ∈ (1, 2] in a Banach Space with Deviated Argument.- A. S. Kelil and A. Rao Appadu, Shehu-Adomian Decomposition Method for dispersive KdV-type Equations.- A. S. Kelil, A. R. Appadu and S. Arjika, On certain properties of perturbed Freud-type weight: a revisit.- A. K. Singh, Complex chaotic systems and its complexity.- M. Incesu, S. Y. Evren and O. Gursoy, On the bertrand pairs of open non uniform B-spline curves.- M. Verma, P. Sharma and N. Gupta, Convergence analysis of a sixth-order method under weak continuity condition with First-order Frechet derivative.- B. Kour and S. Ram, (m, n)-paranormal composition operators.- T. Yaying, On the domain of q-Euler matrix in c0 and c.- N. Sarkar and M. Sen, Study on some particular class of non linear integral equation with a hybridized approach.- D. Saha, M. Sen and S. Roy, Investigation of the existence criteria for the solution of the functional integral equation in the Lp space.- S. Das and K. Mehrez, Functional Inequalities for the Generalized Wright Functions.- S. Dutta and P. Guha, An Information Theoretic Entropy Related to Ihara $\zeta$ Function and Billiard Dynamics.- S. Baskaran, G. Saravanan and K. Muthunagai, On a new subclass of Sakaguchi type functions using (p;q)- derivative operator.- N. K. Jangid, S. Joshi and S. D. Purohit, Some Double integral Formulae Associated with Q Function and Galue Type Struve Function.- M. Jain, M. Singh and R. K. Meena, Time-dependent analytical and computational study of an M/M/1 queue with disaster failure and multiple working vacations.- M. Datta and N. Gupta, Usual stochastic ordering results for series and parallel systems with components having Exponentiated Chen distribution.

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Book SynopsisThis book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.Table of Contents1. Sets, Functions and Cardinality.- 2. The Real Numbers.- 3. Sequence and Series of Numbers.- 4. Analysis on R.- 5. Topology of the Real Line.- 6. Metric Spaces.- 7. Continuity and Differentiability.- 8. Sequences and Series of Functions.- 9. Lebesgue Integration.- 10. Fourier Series.

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Book SynopsisThis book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.Table of Contents1. Sets, Functions and Cardinality.- 2. The Real Numbers.- 3. Sequence and Series of Numbers.- 4. Analysis on R.- 5. Topology of the Real Line.- 6. Metric Spaces.- 7. Continuity and Differentiability.- 8. Sequences and Series of Functions.- 9. Lebesgue Integration.- 10. Fourier Series.

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Book SynopsisThis unique book provides a new and well-motivated introduction to calculus and analysis, historically significant fundamental areas of mathematics that are widely used in many disciplines. It begins with familiar elementary high school geometry and algebra, and develops important concepts such as tangents and derivatives without using any advanced tools based on limits and infinite processes that dominate the traditional introductions to the subject. This simple algebraic method is a modern version of an idea that goes back to René Descartes and that has been largely forgotten. Moving beyond algebra, the need for new analytic concepts based on completeness, continuity, and limits becomes clearly visible to the reader while investigating exponential functions.The author carefully develops the necessary foundations while minimizing the use of technical language. He expertly guides the reader to deep fundamental analysis results, including completeness, key differential equations, definite integrals, Taylor series for standard functions, and the Euler identity. This pioneering book takes the sophisticated reader from simple familiar algebra to the heart of analysis. Furthermore, it should be of interest as a source of new ideas and as supplementary reading for high school teachers, and for students and instructors of calculus and analysis.Table of ContentsTangents and Double Points; Derivatives by Algebra; Exponential Functions; Completeness of Real Numbers; The Base of the Natural Exponential and Logarithm Functions; Continuity of Functions; Differentiability; Chain Rule and Other Rules for Derivatives; Derivatives of Trigonometric Functions; Mean Value Inequality and Theorem; Basic Differential Equations; Motion with Constant Acceleration; Linear and Higher Order Approximations; The Antiderivative Problem; Definite Integrals; Fundamental Theorem of Calculus; Integrability of Monotonic Functions; Integrability of Functions with Bounded Derivative; Substitution; Integration by Parts; Taylor's Theorem; Analytic Functions; The Euler Identity;

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Book SynopsisBackground in Potential Theory.- Fundamentals of Fine Potential Theory.- Further Developments.- Fine Complex Potential Theory.

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Book Synopsis

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Book SynopsisChapter 1 The System of Real Numbers.- Chapter 2 Real Sequences.- Chapter 3 Infinite Series of Numbers.- Chapter 4 Limits, Continuity and Differentiability.- Chapter 5 Metric Spaces.

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Book SynopsisZ. Bartosiewicz, Systems on time scales: theory and applications in modeling.- R. Deb, A. K. Das, Complementarity problem with Nekrasov Z tensor.- S. Debnath, Conformal ?-Einstein soliton on (LCS)n-manifold.- A. Gunn and S. Smith, How Much Variability Can an Impulsive Threshold Maintain Before the Outcome Switches?.- T. Ghosh, S. Ghosh, and E. Schwartz, P. Kumar Roy, Mathematical Overview of Bio-Chemical and Physical Interactions Considering Reverse Transcriptase and Integrase Enzymes to Explore HIV Progression: A Control Theoretic Approach.- T. Mondal, S. Ghosh, S. Mukherjee and A. Dénes, Mathematical Modeling of Leprosy Examining the Effect of Awareness Programs in the Disease Transmission: An optimal Control Approach.- S. Kushary, P. Kumar Roy, X. Cao, Introducing MSC Therapy to Inhibit ?Th?_1 and Th?_17 Mediated Cytokines: A Mathematical Study to Regulate Psoriasis.- H. Bose, S. Mukherjee, Xue- Zhi Li, Ratio-Dependent Vector-Host Model on Cutaneous Leishmaniasis - A Mathematical Study Based on Caputo-Fabrizio Fractional Derivative.- X. Cao, T. Ghosh, S. Ghosh.- Mathematical Modelling to Exhibit the Influence of Latently Infected Schwann cells in Leprosy: An Optimal Control-based Study.- Mst Sebi Khatun, Pritha Das, Dynamical behaviour of an SIR epidemic model with Holling type III treatment function and media control.- S. Majee1, S. Jana, and T. Kumar Kar, Dynamical study of the spread of monkeypox including optimal vaccination and treatment with cost-effectiveness.- S. Mukherjee, T. Ghosh, S. Ghosh, Impact of Stem Cell Therapy in Leprosy Pathogenesis through Mathematical Study: An Impulsive Control based Treatment Design.- P. Samui and Jayanta Mondal, Determining pathogenic behaviors of chronic HCV Infection in presence of incubation delay.- P. Das, M. S. Khatun, and K. B. Mahato, Dynamics of a stochastic prey-predator model with Allee effect and fear-dependent prey refuge function.- Amit Kumar Bag, and Amar Nath Chatterjee, The role of screening programs in cervical cancer prevention: A mathematical study.- I. Schreiber and  J. Cerveny, Reaction network based model for carbon-nitrogen metabolism and ultradian rhythms in cyanobacteria.- Sanju Sardar, Priti Kumar Roy, Subhankar Kushary, and David Greenhalgh, Mathematical insight of Methanol Toxicity Management using Charcoal and Folinic Acid.- Sk Mosaraf Ahammed1, Priti Kumar Roy1, and Shu Wang, Effect of Ultrasound Technique for Production of Biodiesel using Enzyme as Catalyst: A Mathematical Study.- Ujjwal Kumar Deb, Temperature effects on microalgae cell growth in an outdoor HLTP.- A. Kumar Paul and M. H. A. Biswas, A Mathematical Theory for Studying and Controlling the Disinformation System Dynamics.- S. Aktar, F. Rahaman, Thin accretion disks around traversable wormholes of Teo class.- P. Baidya1, S.K. Panja and S.C. Mandal, Stress Intensity factor of two co-linear rigid strips under impact load.- Amrita Bhattacharya , Discussion on strong field lensing by wormholes as black hole foils.- P. Mukherjee and S. Kumar Sardar, On a canonical multiplicative semigroup related with the C^*-algebra of a digraph.-  Narendranath Mitra, Generalization of Ramanujan's Famous Nested Radicals to the nth Root and their Evaluation.- Shipan Chandra Deb Nath1, Rajib Karmaker2*, Ujjwal Kumar Deb, Comparison of Iron and Steel Helical Suspension Springs for Mechanical Load Management using Finite Element Method.- Marina Lallallawmzuali1, Sundararajan Muniyan, Analysis of Rainfall Trend and Its Pattern in Uttarakhand Using Appropriate Probability Distributive Functions.- Manojit Das, Shariful Alam, Strategic product launch and pricing: Maximizing profitability in a dynamic consumer market.- Amit K. Ghosh*, Lopamudra Roy and Stuti Saxena, Mathematical attributes applicable on the evolution of life forms and their adaptation with changing climate in the geologic past.- K. Lalnunsiami1, M. Sundararajan and J.K. Pandey, Dispersion Pattern of PM10, PM2.5 and PM1.0 in and around an Opencast Coal Mine Using Statistical and Gaussian Emission Models.- Divya Sharma1, Deepti Kaur and R. K. Mohanty, Bi-parametric compact sixth-order two-stage BGE iteration method for two-dimensional Helmholtz equation.- B.S. Mahapatra , S. Golui , M.K. Mondal, M.B. Bera, and G.S. Mahapatra, Fuzzy TOPSIS method for resource planning selection  incorporating correlation measure.- S. Naskar,  Shariful Alam,  A. Garai, A study on closed-loop dual-channel supply chain with advertising level of online products.

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Table of Contents 1.2 Review of Algebra and Trigonometry 1.3 The Limit of a Function 1.4 Calculating Limits 1.5 Continuity 1.6 Limits Involving In¬finity 2.1 Derivatives and Rates of Change 2.2 The Derivative of a Function 2.3 Basic Differentiation 2.4 Product and Quotient Rules 2.5 Chain Rule 2.6 Differentiation of Implicit Functions 2.7 Related Rates 2.8 Linear Approximation and Differentials 3R Exponential, Logarithmic, and Inverse Functions 3.1 Exponential Functions 3.2 Logarithmic Functions 3.3 Derivatives of Exponential and Logarithmic Functions 3.4 Exponential Growth and Decay 3.5 Inverse Trigonometric Functions 3.7 Indeterminate Forms and L’Hopital’s Rule 4.1 Maximum and Minimum Values 4.2 The Mean Value Theorem 4.3 Derivatives and the Shape of Graphs 4.4 Curve Sketching 4.5 Optimization 4.6 Newton’s Method 4.7 Antiderivatives

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