Differential calculus and equations Books

Book Synopsis Dieses vierfarbige Lehrbuch wendet sich an Studierende der Mathematik in Bachelor-Studiengängen. Es bietet in einem Band ein lebendiges Bild der mathematischen Inhalte, die üblicherweise im zweiten und dritten Studienjahr behandelt werden (mit Ausnahme der Algebra).Mathematik-Studierende finden wichtige Begriffe, Sätze und Beweise ausführlich und mit vielen Beispielen erklärt und werden an grundlegende Konzepte und Methoden herangeführt.Im Mittelpunkt stehen das Verständnis der mathematischen Zusammenhänge und des Aufbaus der Theorie sowie die Strukturen und Ideen wichtiger Sätze und Beweise. Es wird nicht nur ein in sich geschlossenes Theoriengebäude dargestellt, sondern auch verdeutlicht, wie es entsteht und wozu die Inhalte später benötigt werden.Herausragende Merkmale sind: durchgängig vierfarbiges Layout mit mehr als 350 Abbildungen prägnant formulierte Kerngedanken bilden die Abschnittsüberschriften Selbsttests in kurzen Abständen ermöglichen Lernkontrollen während des Lesens farbige Merkkästen heben das Wichtigste hervor „Unter-der-Lupe“-Boxen zoomen in Beweise hinein, motivieren und erklären Details „Hintergrund-und-Ausblick“-Boxen stellen Zusammenhänge zu anderen Gebieten und weiterführenden Themen her Zusammenfassungen zu jedem Kapitel sowie Übersichtsboxen mehr als 500 Verständnisfragen, Rechenaufgaben und Aufgaben zu Beweisen Der inhaltliche Schwerpunkt liegt auf dem weiteren Ausbau der Analysis sowie auf den Themen der Vorlesungen Numerik sowie Wahrscheinlichkeitstheorie und Statistik. Behandelt werden darüber hinaus Inhalte und Methodenkompetenzen, die vielerorts im zweiten und dritten Studienjahr der Mathematikausbildung vermittelt werden.Auf der Website zum Buch Matheweb finden Sie Hinweise, Lösungswege und Ergebnisse zu allen Aufgaben die Möglichkeit, zu den Kapiteln Fragen zu stellen Das Buch wird allen Studierenden der Mathematik ein verlässlicher Begleiter sein.Trade Review“ ... Ausführliche Erklärungen und über 400 Abbildungen verdeutlichen abstrakte Sachverhalte, kompakte Übersichten liefern zentrale Ergebnisse, Kontrollfragen ermöglichen eine fortlaufende Verständniskontrolle und Übungsaufgaben dienen der eingehenden Beschäftigung mit dem Stoff ... Der Zielgruppe als Lehrbuch und Nachschlagewerk auch neben der Studienliteratur zu den einzelnen Teilgebieten sehr dienlich.” (Philipp Kastendieck, in: ekz-Informationsdienst, Jg. 11, 2016)“... für den Autodidakt kann dieses Lehrbuch empfohlen werden, da eine Vielfalt an Beispielen , Übungsaufgaben und entsprechenden Abfragen den Einstieg im nicht immer leichten Lehrstoff erleichtert. ... kann dieses Lehrbuch für das Mathematikstudium empfohlen werden. Es beinhaltet die Grundlagen des Mathematikstudiums und hat den Vorteil ...” (La, in: Amazon.de, 10. November 2015)Table of Contents1 Mathematik – eine Wissenschaft für sich.- 2 Lineare Differenzialgleichungen – Systeme und Gleichungen höherer Ordnung.- 3 Randwertprobleme und nichtlineare Differenzialgleichungen – Funktionen sind gesucht.- 4 Qualitative Theorie – jenseits von analytischen und mehr als numerische Lösungen.- 5 Funktionentheorie – Analysis im Komplexen.- 6 Differenzialformen und der allgemeine Satz von Stokes.- 7 Grundzüge der Maß- und Integrationstheorie vom Messen und Mitteln.- 8 Lineare Funktionalanalysis – Operatoren statt Matrizen.- 9 Fredholm-Gleichungen – kompakte Störungen der Identität.- 10 Hilberträume – fast wie im Anschauungsraum.- 11 Warum Numerische Mathematik? – Modellierung, Simulation und Optimierung.- 12 Interpolation – Splines und mehr.- 13 Quadratur – numerische Integrationsmethoden.- 14 Numerik linearer Gleichungssysteme – Millionen von Variablen im Griff.- 15 Eigenwertprobleme – Einschließen und Approximieren.- 16 Lineare Ausgleichsprobleme – im Mittel das Beste.- 17 Nichtlineare Gleichungen und Systeme – numerisch gelöst.- 18 Numerik gewöhnlicher Differenzialgleichungen – Schritt für Schritt zur Trajektorie.- 19 Wahrscheinlichkeitsräume – Modelle für stochastische Vorgänge.- 20 Bedingte Wahrscheinlichkeit und Unabhängigkeit – Meister Zufall hängt (oft) ab.- 21 Diskrete Verteilungsmodelle – wenn der Zufall zählt.- 22 Stetige Verteilungen und allgemeine Betrachtungen – jetzt wird es analytisch.- 23 Konvergenzbegriffe und Grenzwertsätze – Stochastik für große Stichproben.- 24 Grundlagen der Mathematischen Statistik – vom Schätzen und Testen.

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Book SynopsisAnimationen im Internet veranschaulichen z. B. die Wellengleichung durch eine schwingende Membran, die Wärmeleitung durch eine abnehmende Temperaturverteilung und die Potentialgleichung durch ein von der Randbelegung aufgeprägtes Potenzial. Welche Methoden verbergen sich dahinter, wie erzeugt man diese Animationen? Darauf soll der Leser eine erschöpfende Antwort geben können. Auf ausführliche, formale Beweise wird verzichtet. Die Begriffe werden mittels Beispielen und Graphiken in ihren Grundideen veranschaulicht und motiviert. Der Leser soll Hintergrundwissen und Lösungskompetenz bekommen, damit er sich nicht mit der Formelmanipulation zufrieden geben muss. Studierende sollen in die Lage versetzt werden, Probleme, die sich aus ihrer Bachelor/Masterarbeit oder aus den Anwendungen ergeben, zu bearbeiten. Table of ContentsTensoren.- Tensorfelder.- Kurven- und Flächenintegrale.- Orthogonale Systeme von Polynomen.- Lineare Differentialgleichungen im Komplexen.- Stabilität dynamischer Systeme.- Partielle Differentialgleichungen.- Gleichungen erster Ordnung.- Gleichungen zweiter Ordnung.- Wellengleichung.- Wärmeleitungsgleichung.- Potentialgleichung.

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Book SynopsisDas Buch bietet eine kompakte, grundlegende Einführung in die Theorie gewöhnlicher Differentialgleichungen aus der Perspektive der dynamischen Systeme im Umfang einer einsemestrigen Vorlesung. Über die Diskussion der Lösungstheorie und der Theorie linearer Systeme hinaus werden insbesondere einfache analytische und numerische Lösungsverfahren, Konzepte der Theorie dynamischer Systeme, Stabilität, Verzweigungen und Hamilton-Systeme behandelt. Der Stoff wird durchgängig anhand von Beispielen, Fragen, Übungsaufgaben und Computerexperimenten illustriert und vertieft.Das Buch ist besonders für das Bachelor-Studium gut geeignet, sowohl vorlesungsbegleitend zum Modul "Gewöhnliche Differentialgleichungen" als auch zum Selbststudium. Es werden nur die Grundvorlesungen in Analysis und Linearer Algebra vorausgesetzt.Table of ContentsEinführung.- Lineare Differentialgleichungen.- Lösungstheorie.- Lösungseigenschaften.- Analytische Lösungsmethoden.- Numerische Lösungsmethoden.- Gleichgewichte und ihre Stabilität.- Lyapunov-Funktionen und Linearisierung.- Spezielle Lösungen und Mengen.- Verzweigungen.- Attraktoren.- Hamiltonsche Differentialgleichungen.- Anwendungsbeispiele.- Anhänge.

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Book SynopsisDieses essential bietet eine Einführung in die theoretischen Grundlagen und Anwendungen der verallgemeinerten Funktionen. Nach zwei typischen Anwendungen verallgemeinerter Funktionen wird die Theorie entwickelt, wobei zum besseren Verständnis nur die fundamentalen Ideen vorgestellt werden, sodass keine funktionalanalytischen Kenntnisse vorausgesetzt werden. Danach folgt eine systemtheoretische Untersuchung von LTI-Systemen unter Einbeziehung der Dirac-Distribution und die Modellierung gezupfter schwingender Saiten. Den Abschluss bildet die Modellierung technischer Rauschprozesse am Beispiel des kontinuierlichen weißen Rauschens.Table of ContentsSignalübertragung und schwingende Saite.- Darstellung von Funktionen durch Funktionale und Distributionen.- LTI-Systeme, schwache Lösungen und Rauschprozesse.

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Book SynopsisDieses Open-Access-Buch behandelt für eine breite Klasse zweidimensionaler Variationsprobleme eine Existenz- und Regularitätstheorie, die der Lösung von Randwertproblemen partieller Differentialgleichungssysteme dient. Dabei werden bekannte Ergebnisse gründlich untersucht und umfassend aufgearbeitet. Teilweise wird eine geeignete Anpassung der Voraussetzungen einiger Resultate vorgenommen. Speziell wird die Theorie auf das Plateausche Problem für Flächen vorgeschriebener mittlerer Krümmung im ℝ³ angewendet.Diese Veröffentlichung wurde aus Mitteln des Publikationsfonds für Open-Access-Monografien des Landes Brandenburg gefördert./This publication was supported by funds from the Publication Fund for Open Access Monographs of the Federal State of Brandenburg, Germany. Table of ContentsEinleitung.- Grundlagen.- Direkte Methoden der Variationsrechnung.- Regularitätstheorie zur Stetigkeit von Minimierern.- Höhere Regularität von Minimierern im Inneren.- Minimierer vom Poissonschen Typ.- Literaturverzeichnis.

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Book SynopsisThis self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix.The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition.Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.Trade Review“Every line of the book reflects that the author is the leading expert for hierarchical matrices. … Hierarchical matrices: algorithms and analysis is without a doubt a beautiful, comprehensive introduction to hierarchical matrices that can serve as both a graduate level textbook and a valuable resource for future research.” (Thomas Mach, Mathematical Reviews, April, 2017)“The book ‘Hierarchical matrices: algorithms and analysis’ is a self-contained monograph which presents an efficient possibility to handle the numerical treatment of fully populated large scale matrices appearing in scientific computations, and therefore it is of interest to scientists in computational mathematics, physics, chemistry and engineering.” (Constantin Popa, zbMATH 1336.65041, 2016)Table of ContentsPreface.- Part I: Introductory and Preparatory Topics.- 1. Introduction.- 2. Rank-r Matrices.- 3. Introductory Example.- 4. Separable Expansions and Low-Rank Matrices.- 5. Matrix Partition.- Part II: H-Matrices and Their Arithmetic.- 6. Definition and Properties of Hierarchical Matrices.- 7. Formatted Matrix Operations for Hierarchical Matrices.- 8. H2-Matrices.- 9. Miscellaneous Supplements.- Part III: Applications.- 10. Applications to Discretised Integral Operators.- 11. Applications to Finite Element Matrices.- 12. Inversion with Partial Evaluation.- 13. Eigenvalue Problems.- 14. Matrix Functions.- 15. Matrix Equations.- 16. Tensor Spaces.- Part IV: Appendices.- A. Graphs and Trees.- B. Polynomials.- C. Linear Algebra and Functional Analysis.- D. Sinc Functions and Exponential Sums.- E. Asymptotically Smooth Functions.- References.- Index.

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Book SynopsisDieses Lehrbuch gibt eine Einführung in die partiellen Differenzialgleichungen. Wir beginnen mit einigen ganz konkreten Beispielen aus den Natur-, Ingenieur und Wirtschaftswissenschaften. Danach werden elementare Lösungsmethoden dargestellt, z.B. für die Black-Scholes-Gleichung aus der Finanzmathematik. Schließlich wird die analytische Untersuchung großer Klassen von partiellen Differenzialgleichungen dargestellt, wobei Hilbert-Raum-Methoden im Mittelpunkt stehen. Numerische Verfahren werden eingeführt und mit konkreten Beispielen behandelt. Zu jedem Kapitel finden sich Übungsaufgaben, mit deren Hilfe der Stoff eingeübt und vertieft werden kann. Dieses Buch richtet sich an Studierende im Bachelor oder im ersten Master-Jahr sowohl in der (Wirtschafts-)Mathematik als auch in den Studiengängen Informatik, Physik und Ingenieurwissenschaften.Die 2. Auflage ist vollständig durchgesehen, an vielen Stellen didaktisch weiter optimiert und um die Beschreibung variationeller Methoden in Raum und Zeit für zeitabhängige Probleme ergänzt.Stimme zur ersten AuflageAuf dieses Lehrbuch haben wir gewartet.Prof. Dr. Andreas Kleinert in zbMATHTable of Contents1 Modellierung, oder wie man auf eine Differenzialgleichung kommt 1.1 Modellierung mit Differenzialgleichungen 1.2 Transport-Prozesse 1.3 Diffusion 1.4 Die Wellengleichung 1.5 Die Black-Scholes-Gleichung 1.6 Jetzt wird es mehrdimensional 1.7 Es gibt noch mehr 1.8 Klassifikation partieller Differenzialgleichungen 1.9 Aufgaben 2 Kategorisierung und Charakteristiken 2.1 Charakteristiken von Anfangswertproblemen auf R 2.2 Gleichungen zweiter Ordnung 2.3 Anfangs- und Randwerte 2.4 Nichtlineare Gleichungen zweiter Ordnung 2.5 Gleichungen höherer Ordnung und Systeme 2.6 Aufgaben 3 Elementare Lösungsmethoden 3.1 Variablentransformation für die Transportgleichung 3.2 Trennung der Variablen am Beispiel der Wellengleichung 3.3 Fourier-Reihen 3.4 Die Laplace-Gleichung 3.5 Die Wärmeleitungsgleichung 3.6 Die Black-Scholes-Gleichung 3.7 Integral-Transformationen 3.8 Aufgaben 4 Hilbert-Räume 4.1 Unitäre Räume 4.2 Orthonormalbasen 4.3 Vollständigkeit 4.4 Orthogonale Projektionen 4.5 Linearformen und Bilinearformen 4.6 Schwache Konvergenz 4.7 Stetige und kompakte Operatoren 4.8 Der Spektralsatz 4.9 Aufgaben 5 Sobolev-Räume und Randwertaufgaben in einer Dimension 5.1 Sobolev-Räume in einer Variablen 5.2 Randwertprobleme auf einem Intervall 5.3 Aufgaben 6 Sobolev-Räume und Hilbert-Raum-Methoden für elliptische Gleichungen 6.1 Regularisierung 6.2 Sobolev-Räume 6.3 Der Raum H1 6.4 Die Poisson-Gleichung mit Dirichlet-Randbedingungen 6.5 Sobolev-Räume und Fourier-Transformation 6.6 LokaleRegularität 6.7 Die Poisson-Gleichung mit inhomogenen Dirichlet-Randbedingungen 6.8 Das Dirichlet-Problem 6.9 Elliptische Gleichungen mit Dirichlet-Randbedingung 6.10 H2-Regularität 6.11 Kommentare zu Kapitel 6 6.12 Aufgaben 7 Elliptische Gleichungen mit Neumann- und Robin-Randbedingungen 7.1 Der Satz von Gauß 7.2 Beweis des Satzes von Gauß 7.3 Die Fortsetzungseigenschaft 7.4 Die Poisson-Gleichung mit Neumann-Randbedingungen 7.5 Der Spursatz und Robin-Randbedingungen 7.6 Kommentare zu Kapitel 7 7.7 Aufgaben 8 Spektralzerlegung und Evolutionsgleichungen 8.1 Ein vektorwertiges Anfangswertproblem 8.2 Die Wärmeleitungsgleichung mit Dirichlet-Randbedingungen 8.3 Die Wärmeleitungsgleichung mit Robin-Randbedingungen 8.4 Die Wellengleichung 8.5 Aufgaben 9 Numerische Verfahren 9.1 Finite Differenzen 9.2 Finite Elemente 9.3 Ergänzungen und Erweiterungen 9.4 Parabolische Probleme 9.5 Aufgaben 10 Maple, oder manchmal hilft der Computer 10.1 Maple® 10.2 Aufgaben

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Book SynopsisThis book provides a clear and easy-to-understand introduction to higher mathematics with numerous examples. The author shows how to solve typical problems in a recipe-like manner and divides the material into short, easily digestible learning units.Have you ever cooked a 3-course meal based on a recipe? That generally works quite well, even if you are not a great cook. What does this have to do with mathematics? Well, you can solve a lot of math problems recipe-wise: Need to solve a Riccati's differential equation or the singular value decomposition of a matrix? Look it up in this book, you'll find a recipe for it here. Recipes are available for problems from the· Calculus in one and more variables,· linear algebra,· Vector Analysis,· Theory on differential equations, ordinary and partial,· Theory of integral transformations,· Function theory.Other features of this book include:· The division of Higher Mathematics into approximately 100 chapters of roughly equal length. Each chapter covers approximately the material of a 90-minute lecture.· Many tasks, the solutions to which can be found in the accompanying workbook.· Many problems in higher mathematics can be solved with computers. We always indicate how it works with MATLAB®.For the present 3rd edition, the book has been completely revised and supplemented by a section on the solution of boundary value problems for ordinary differential equations, by the topic of residue estimates for Taylor expansions and by the characteristic method for partial differential equations of the 1st order, as well as by several additional problems.Table of ContentsPreface.- 1 Ways of speaking, symbols and quantities.- 2 The natural, whole and rational numbers.- 3 The real numbers.- 4 Machine numbers.- 5 Polynomials.- 6 Trigonometric functions.- 7 Complex numbers - Cartesian coordinates.- 8 Complex numbers - Polar coordinates.- 9 Systems of linear equations.- 10 Calculating with matrices.- 11 LR-decomposition of a matrix.- 12 The determinant.- 13 Vector spaces.- 14 Generating systems and linear (in)dependence.- 15 Bases of vector spaces.- 16 Orthogonality I.- 17 Orthogonality II.- 18 The linear balancing problem.- 14 The linear balancing problem. 14 Generating systems and linear (in)dependence.- 15 Bases of vector spaces.- 16 Orthogonality I.- 17 Orthogonality II.- 18 The linear compensation problem.- 19 The QR-decomposition of a matrix.- 20 Sequences.- 21 Computation of limit values of sequences.- 22 Series.- 23 Illustrations.- 24 Power series.- 25 Limit values and continuity.- 26 Differentiation.- 27 Applications of differential calculus I.- 28 Applications of differential calculus I.- 28 Applications of differential calculus II.- 28 Applications of differential calculus I.- 28 Applications of differential calculus II. 28 Applications of differential calculus II.- 29 Polynomial and spline interpolation.- 30 Integration I.- 31 Integration II.- 32 Improper integrals.- 33 Separable and linear differential equations of the 1st order.- 34 Linear differential equations with constant coefficients.- 35 Some special types of differential equations.- 36 Numerics of ordinary differential equations I.- 37 Linear mappings and representation matrices.- 38 Basic transformation.- 39 Diagonalization - Eigenvalues and eigenvectors.- 40 Numerical computation of eigenvalues and eigenvectors.- 41 Quadrics.- 42 Schurzdecomposition and singular value decomposition.- 43 Jordan normal form I.- 44 Jordan normal form II.- 45 Definiteness and matrix norms.- 46 Functions of several variables.- 47 Partial differentiation - gradient, Hessian matrix, Jacobian matrix.- 48 Applications of partial derivatives.- 49 Determination of extreme values.- 50 Determination of extreme values under constraints.- 51 Total differentiation, differential operators.- 52 Implicit functions.- 53 Coordinate transformations.- 54 Curves I.- 55 Curves II.- 56 Curve integrals.- 57 Gradient fields.- 58 Domain integrals.- 59 The transformation formula.- 60 Areas and area integrals.- 61 Integral theorems I.- 62 Integral theorems II.- 63 General about differential equations.- 64 The exact differential equation.- 65 Systems of linear differential equations I.- 66 Systems of linear differential equations II.- 67 Systems of linear differential equations II.- 68 Boundary value problems.- 69 Basic concepts of numerics.- 70 Fixed point iteration.- 71 Iterative methods for systems of linear equations.- 72 Optimization.- 73 Numerics of ordinary differential equations II.- 74 Fourier series - Calculation of Fourier coefficients.- 75 Fourier series - Background, theorems and application.- 76 Fourier transform I.- 77 Fourier transform II.- 78 Discrete Fourier transform.- 79 The Laplacian transform.- 80 Holomorphic functions.- 81 Complex integration.- 82 Laurent series.- 83 The residue calculus.- 84 Conformal mappings.- 85 Harmonic functions and Dirichlet's boundary value problem.- 86 Partial differential equations 1st order.- 87 Partial differential equations 2nd order - General.- 88 The Laplace or Poisson equation.- 89 The heat conduction equation.- 90 The wave equation.- 91 Solving pDGLs with Fourier and Laplace transforms.- Index.

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Book SynopsisIn this book, for the first time, a hitherto unknown general solution of the reliably known stress conditions is presented. This general solution forms a reliable and new starting point to get further in stress calculations than before. In this way, approximately realistic solutions can be found despite a recurring problem: the information deficits that are unavoidable due to the difficulty of exploring glaciers. This issue is demonstrated by the example of stagnating glaciers. For horizontally isotropic homogeneous tabular iceberg models, even mathematically exact unambiguous solutions of all relevant conditions are presented. All calculations use only elementary arithmetic operations, differentiations and integrations. The mathematical fundamentals are presented in detail and explained in many application examples. The integral operators specific to calculations of stresses facilitate the mathematical considerations. The stand-alone text allows the reader to understand what is involved even without considering the formulas. The author Peter Halfar is a theoretical physicist. He also developed a model of the movement of large ice caps (1983), which is still in use today.Table of ContentsI Introduction and fundamentals. Introduction.- Balance and boundary conditions.- Integral operators.- Forces and torques on surfaces.- Special solutions of balance conditions.- Weightless stress tensor fields.- II The general solution of balance and boundary conditions. Weightless stress tensor fields with boundary conditions.- The general solution of balance and boundary conditions.- Models and model selection. III Applications and examples. Land glaciers.- Floating glaciers.- IV Appendix. Bibliography.- Explanation and list of symbols.

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Book SynopsisDas Buch vermittelt Lösungsverfahren für partielle Riccati-Differenzialgleichungen (DGL). Diese DGL appliziert man zur mathematischen Beschreibung der Funktion von Faraday-Effekt-Stromsensoren. Ausgehend vom allgemeinen Lösungsverhalten erfolgt die Definition des individuellen sowie kollektiven Lösungsverhaltens einer beliebigen Gleichung. Reiner Thiele erklärt den Unterschied zwischen Individual- und Partiallösungen. Außerdem kreiert er Simulationsdiagramme und zeigt, dass es sich bei der Hardware um Regelkreise handelt. Table of ContentsEinleitung.- 2 Partielle Typ1-Riccati-DGL.- 3 Partielle Typ2-Riccati-DGL.- 4 Zusammenfassung.

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Book SynopsisThe emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).Trade ReviewFrom the reviews:“The authors consider the problem of constructing closed-form and approximate solutions to nonlinear partial differential equations with the help of computer algebra systems. … The book will be useful for readers who want to try modern methods for solving nonlinear partial differential equations on concrete examples without bothering too much about the mathematics behind the methods. Thus it is mainly of interest for applied scientists. Mathematicians may use it in connection with more theoretical works; some references are given throughout the book.” (Werner M. Seiler, Zentralblatt MATH, Vol. 1233, 2012)Table of Contents1 Introduction 1.1 Basic Concepts 2 Algebraic Approach 2.1 Point Transformations 2.2 Contact Transformations 2.3 Transformations Relating Differential Equations 2.4 Linearizing and Bilinearizing Transformations 2.5 Reductions of Nonlinear PDEs 2.6 Separation of Variables 2.7 Transformation Groups 2.8 Nonlinear Systems 3 Geometric-Qualitative Approach 3.1 Method of Characteristics 3.2 Generalized Method of Characteristics 3.3 Qualitative Analysis 4 General Analytical Approach. Integrability 4.1 Painlevé Test and Integrability 4.2 Complete Integrability. Evolution Equations 4.3 Nonlinear Systems. Integrability Conditions 5 Approximate Analytical Approach 5.1 Adomian Decomposition Method 5.2 Asymptotic Expansions. Perturbation Methods 6 Numerical Approach 6.1 Embedded Numerical Methods 6.2 Finite DifferenceMethods 7 Analytical-Numerical Approach 7.1 Method of Lines 7.2 Spectral Collocation Method; A Brief Description of Maple A.1 Introduction A.2 Basic Concepts A.3 Maple Language B Brief Description of Mathematica B.1 Introduction B.2 Basic Concepts B.3 Mathematica Language; References, Index

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Book SynopsisThis book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.Table of ContentsFrom differential equations to structured population dynamics.- Adaptive dynamics; an asymptotic point of view.- Population balance equations: the renewal equation.- Population balance equations: size structure.- Cell motion and chemotaxis.- General mathematical tools.

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Book Synopsis"Numerik", in zwei Bänden, ist eine Einführung in die Numerische Mathematik anhand von Differenzialgleichungsproblemen. Gegliedert nach elliptischen, parabolischen und hyperbolischen Differenzialgleichungen, erläutert sie zunächst jeweils die Diskretisierung solcher Probleme. Als Diskretisierungstechniken stehen Finite-Elemente-Methoden im Raum und (partitionierte) Runge-Kutta-Methoden in der Zeit im Vordergrund. Die diskretisierten Gleichungen motivieren die Diskussion von Methoden für endlichdimensionale (nicht)lineare Gleichungen, die anschließend als eigenständige Themen behandelt werden. Ein in sich geschlossenes Bild.Table of Contents1 Einleitung.- 2 Ein erstes Beispiel einer Variationsformulierung.- 3 Der Satz von Lax-Milgram.- 4 Die Galerkin-Methode.- 4.1 Ein Beispiel einer Finite-Elemente-Methode.- 4.2 Der Diskretisierungsfehler.- 5 Lineare Gleichungssysteme.- 5.1 Kondition des Problems.- 5.2 Konditionszahl der Steifigkeitsmatrix.- 6 Das Gaußsche Eliminationsverfahren.- 6.1 Der Algorithmus.- 6.2 Numerische Stabilität des Algorithmus.- 7 Erweiterung auf lineare mehrdimensionale Randwertprobleme.- 8 Iterative Verfahren für lineare Gleichungssysteme.- 8.1 Das Richardson-Verfahren.- 8.2 Das Gradientenverfahren.- 8.3 Das Verfahren der konjugierten Gradienten.- 8.4 Präkonditionierung.- 9 Erweiterung auf nichtlineare Randwertprobleme.- 10 Das Newton-Verfahren.

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Book SynopsisTamara G. Stryzhak researches the stability of solutions of the system of linear difference equations with random Markovian coefficients. She also deals with Lyapunov functions which were used to receive the necessary and sufficient conditions of the stability of the solutions in the average quadratic mean. As an example, Stryzhak discusses the stability of solutions of a single difference equation with one random Markovian coefficient which takes on two values. The series on Modern Mathematics for Engineers is addressed to upper-course University students in Mathematics specialties, to graduate students and to researchers who apply Mathematics in different spheres.

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Book SynopsisThsi book is a concise presentation of the basic concepts used in evolving numerical methods with special emphasis on developing computional algorithms for solving problems in algebra and calculus on a computer.

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Book SynopsisStudy of first-order and first-degree differential equations, including separable, homogeneous, linear, and exact equations. Also covers equations not of first degree, singular solutions, orthogonal trajectories, and linear equations with constant coefficients.

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Book SynopsisThis book contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010. The contributors, Nicola Fusco, Tristan Rivière and Reiner Schätzle, provide three updated and extensive introductions to various aspects of modern Regularity Theory concerning: mathematical modelling of thin films and related free discontinuity problems, analysis of conformally invariant variational problems via conservation laws, and the analysis of the Willmore functional. Each contribution begins with a very comprehensive introduction, and is aimed to take the reader from the introductory aspects of the subject to the most recent developments of the theory.Table of ContentsErnst Kuwert and Reiner Schätzle, The Willmore functional.- Tristan Rivière, The Role of Conservation Laws in the Analysis of Conformally Invariant Problems.- B. De Maria and N. Fusco, Equilibrium configurations of epitaxially strained elastic films.

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Book SynopsisThis book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.Table of ContentsN. Alikakos: On the structure of phase transition maps for three or more coexisting phases.- S. Amato, G. Bellettini, M. Paolini: The nonlinear multidomain model: a new formal asymptotic analysis.- A. Chambolle, M. Goldman, M. Novaga: Existence and qualitative properties of isoperimetric sets in periodic media.- A. Chambolle, M. Morini, M. Ponsiglione: Minimizing movements and level set approach to geometric flow of nonlocal perimeters.- S. Choi, I. Kim: Homogenization with oscillatory Neumann boundary data in general domain.- D. Christodoulou: The Analysis of Shock Formation in 3-Dimensional Fluids.- L. Dupaigne, A. Farina, B. Sirakov: Regularity of the extremal solutions for the Liouville system.- M.-H. Giga, Y. Giga, A. Nakayasu: On general existence results for one-dimensional singular diffusion equations with spatially inhomogeneous driving force.- Y. Giga, G. Pisante: On representation of boundary integrals involving the mean curvature for mean-convex domains.- A. Lemenant, Y. Sire: Elliptic problem in nonsmooth domain, Reifenberg-flat domains, Regularity.- A. Pisante: Maximally localized wannier functions: existence and exponential localization.- A. Stancu: Flows by powers of centro-affine curvature.

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Book SynopsisThis book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.Table of ContentsIntroduction.- Fine regularity results for Mumford-Shah minimizers: porosity, higher integrability and the Mumford-Shah conjecture.- Variational models for epitaxial growth.- Local and global minimality results for an isoperimetric problem with long-range interactions.

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Book SynopsisThese lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary. The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.Table of ContentsIntroduction.- The problem studied in this monograph.- Functional analytical setting.- Existence of a minimal solution and proof of Theorem 2.2.2.- Regularity and positivity of the solution.- Existence of a second solution and proof of Theorem 2.2.4.

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Book SynopsisThe first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.​Table of ContentsAn overview on flows of vector fields and on optimal transport.- Maximal regular flows for non-smooth vector fields.- Main properties of maximal regular flows and analysis of blow-up.- Lagrangian structure of transport equations.- The continuity equation with an integrable damping term.- Regularity results for very degenerate elliptic equations.- An excess-decay result for a class of degenerate elliptic equations.- The Vlasov-Poisson system.- The semigeostrophic system.

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Book SynopsisThe Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations. Trade Review`I recommend Adomian's new book to all researchers in the area of mathematical modeling and solving complex dynamical systems.' Foundations of Physics, 1994 Table of ContentsPreface. Foreword. 1. On Modelling Physical Phenomena. 2. The Decomposition Method for Ordinary Differential Equations. 3. The Decomposition Method in Several Dimensions. 4. Double Decomposition. 5. Modified Decomposition. 6. Applications of Modified Decomposition. 7. Decomposition Solutions for Neumann Boundary Conditions. 8. Integral Boundary Conditions. 9. Boundary Conditions at Infinity. 10. Integral Equations. 11. Nonlinear Oscillations in Physical Systems. 12. Solution of the Duffing Equation. 13. Boundary-Value Problems with Closed Irregular Contours or Surfaces. 14. Applications in Physics. Appendix I: Padé and Shanks Transform. Appendix II: On Staggered Summation of Double Decomposition Series. Appendix III: Cauchy Products of Infinite Series. Index.

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Book SynopsisMethod of Variation of Parameters for Dynamic Systems presents a systematic and unified theory of the development of the theory of the method of variation of parameters, its unification with Lyapunov's method and typical applications of these methods. No other attempt has been made to bring all the available literature into one volume. This book is a clear exposition of this important topic in control theory, which is not covered by any other text. Such an exposition finally enables the comparison and contrast of the theory and the applications, thus facilitating further development in this fascinating field.Table of Contents1. Ordinary Differential Equations 2. Integrodifferential Equations 3. Differential Equations with Delay 4. Difference Equations 5. Stochastic Differential Equations 6. Abstract Differential Equations 7. Impulsive Differential Equations Equations 3. Differential Equations with Delay 4. Difference Equations 5. Abstract Differential Equations 6. Impulsive Differential Equations 7. Stochastic Differential Equations

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Book SynopsisThis volume comprises selected papers presented at the Volterra Centennial Symposium and is dedicated to Volterra and the contribution of his work to the study of systems - an important concept in modern engineering. Vito Volterra began his study of integral equations at the end of the nineteenth century and this was a significant development in the theory of integral equations and nonlinear functional analysis. Volterra series are of interest and use in pure and applied mathematics and engineering.Table of Contents1. Retrospective of Vito Volterra and His Influence on Nonlinear Systems Theory 2. Volterra Integral Equations at Wisconsin 3. Stability and Asymptotic Behaviour of Solutions of Equations with Aftereffect 4. Generalized Halay Inequalities for Volterra Functional Differential Equations and Discretized Versions 5. Stochastic Convolutions with Kernels Arising in Volterra Equations 6. An Example of Lp-Regularity for Hyperbolic Integrodifferential Equations 7. The Present Status of UAS for Volterra and Delay Equations 8. Myopic Maps and Volterra Series Approximations 9. State Space Theory for Abstract Volterra Operators

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Book SynopsisThis book treats some basic topics in the spectral theory of dynamical systems. The treatment is at a general level, but two more advanced theorems, one by H. Helson and W. Parry and the other by B. Host, are presented. Moreover, Ornstein's family of mixing rank one automorphisms is described with construction and proof. Systems of imprimitivity and their relevance to ergodic theory are discussed, and Baire category theorems of ergodic theory, scattered in the literature, are derived in a unified way. Riesz products are considered and they are used to describe the spectral types and eigenvalues of rank one automorphisms.The major change in this edition is that a new chapter titled Calculus of Generalized Riesz Products has been added. This is based on some recent work of the author with El Houcein El Abdalaoui and supplements the material presented elsewhere in the book.

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Book SynopsisThe book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type.Trade ReviewFrom the reviews:“Hybrid systems are a recent concept in dynamical systems theory and have important and extensive applications. … The present book generalizes the concept of differential equations with piecewise constant argument by considering a more general type of equations and develops new methodological approaches to explore those challenging systems. … This book is well written and readable and will be extremely useful not only to expert readers but also to graduate and advanced undergraduate students.” (Meng Fan, Mathematical Reviews, January, 2013)Table of Contents1. Introduction.- 2. Linear and quasi-linear systems with piecewise constant argument.- 3. The reduction principle for systems with piecewise constant argument.- 4. The small parameter and differential equations with piecewise constant argument.- 5. Stability.- 6. The state-dependent piecewise constant argument.- 7. Almost periodic solutions.- 8. Stability of neural networks.- 9. The blood pressure distribution.- 10. Integrate-and-fire biological oscillators.

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Book SynopsisThe book is designed for undergraduate or beginning level graduate students, and students from interdisciplinary areas including engineers, and others who need to use partial differential equations, Fourier series, Fourier and Laplace transforms. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations.The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm-Liouville eigenvalue problems and series solutions.The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area.Table of ContentsIntroduction; First Order Partial Differential Equations; Solution to One Dimensional Wave Equations; Orthogonal Functions & Expansions, and Sturm-Liouville Theory; Method of Separation Variables for Solving PDE BVPs in Cartesian Coordinates; Various Fourier Series, Properties and Convergence; Series Solutions of PDEs; Fourier and Laplace Transforms; Numerical Solution Techniques; Appendices: ODE Review and Other Useful Information; Introduction to Maple;

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Book SynopsisWritten in a straightforward and easily accessible style, this volume is suitable as a textbook for advanced undergraduate or first-year graduate students in mathematics, physical sciences, and engineering. The aim is to provide students with a strong background in the theories of Ordinary Differential Equations, Dynamical Systems and Boundary Value Problems, including regular and singular perturbations. It is also a valuable resource for researchers.This volume presents an abundance of examples in physical and biological sciences, and engineering to illustrate the applications of the theorems in the text. Readers are introduced to some important theorems in Nonlinear Analysis, for example, Brouwer fixed point theorem and fundamental theorem of algebras. A chapter on Monotone Dynamical Systems takes care of the new developments in Ordinary Differential Equations and Dynamical Systems.In this third edition, an introduction to Hamiltonian Systems is included to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics.

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Book SynopsisThis monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.

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Book SynopsisThis book explains the notion of Brakke’s mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory. The focus of study is a time-parameterized family of k-dimensional surfaces in the n-dimensional Euclidean space (1 ≤ k < n). The family is the mean curvature flow if the velocity of motion of surfaces is given by the mean curvature at each point and time. It is one of the simplest and most important geometric evolution problems with a strong connection to minimal surface theory. In fact, equilibrium of mean curvature flow corresponds precisely to minimal surface. Brakke’s mean curvature flow was first introduced in 1978 as a mathematical model describing the motion of grain boundaries in an annealing pure metal. The grain boundaries move by the mean curvature flow while retaining singularities such as triple junction points. By using a notion of generalized surface called a varifold from geometric measure theory which allows the presence of singularities, Brakke successfully gave it a definition and presented its existence and regularity theories. Recently, the author provided a complete proof of Brakke’s existence and regularity theorems, which form the content of the latter half of the book. The regularity theorem is also a natural generalization of Allard’s regularity theorem, which is a fundamental regularity result for minimal surfaces and for surfaces with bounded mean curvature. By carefully presenting a minimal amount of mathematical tools, often only with intuitive explanation, this book serves as a good starting point for the study of this fascinating object as well as a comprehensive introduction to other important notions from geometric measure theory.

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Book SynopsisThis book aims to establish a foundation for fractional derivatives and fractional differential equations. The theory of fractional derivatives enables considering any positive order of differentiation. The history of research in this field is very long, with its origins dating back to Leibniz. Since then, many great mathematicians, such as Abel, have made contributions that cover not only theoretical aspects but also physical applications of fractional calculus. The fractional partial differential equations govern phenomena depending both on spatial and time variables and require more subtle treatments. Moreover, fractional partial differential equations are highly demanded model equations for solving real-world problems such as the anomalous diffusion in heterogeneous media. The studies of fractional partial differential equations have continued to expand explosively. However we observe that available mathematical theory for fractional partial differential equations is not still complete. In particular, operator-theoretical approaches are indispensable for some generalized categories of solutions such as weak solutions, but feasible operator-theoretic foundations for wide applications are not available in monographs.To make this monograph more readable, we are restricting it to a few fundamental types of time-fractional partial differential equations, forgoing many other important and exciting topics such as stability for nonlinear problems. However, we believe that this book works well as an introduction to mathematical research in such vast fields.Trade Review“The book is written nicely and useful as an introductory book on time fractional derivatives in abstract spaces.” (Syed Abbas, zbMATH 1485.34002, 2022)Table of Contents

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Book SynopsisThis book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.Trade Review“The author provides extensive references for each chapter … . It offers a breadth of ideas and approaches that could be fertile ground for further research.” (Bill Satzer, MAA Reviews, December 12, 2021)Table of ContentsPart I Qualitative and Quantitative Features of Delay Differential Equations: 1. Delay Differential Equations.- 2. Numerical Solutions of Delay Differential Equations.- 3. Stability Concepts of Numerical Solutions of Delay Differential Equations.- 4. Parameter Estimation with Delay Differential Equations.- Part II Applications of Delay Differential Equations: 5. Delay Differential Equations with Infectious Diseases.- 6. Delay Differential Equations with Cell Growth Dynamics.- 7. Delay Differential Equations with Tumour-Immure Interactions and External Treatments.- 8. Delay Differential Equations with Ecological Systems.- 9. Fractional-Order Delay Differential Equations with Applications.- 10. Sensitivity Analysis.

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Book SynopsisThis book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday.The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.Table of ContentsPoint Spread Function Engineering for 3D Imaging of Space Debris using a Continuous Exact $\ell_0$ Penalty (CEL0) Based Algorithm\.- An Adjoint State Method for a Schr\"odinger Inverse Problem.- On A New Diffeomorphic Multi-modality Image Registration Model and Its Convergent Gauss-Newton Solver.- Fast Algorithms for Surface Reconstruction from Point Cloud.- A Total Variation Regularization Method for Inverse Source Problem with Uniform Noise.- AUTOMATIC PARAMETER SELECTION BASED ON RESIDUAL WHITENESS FOR CONVEX NON-CONVEX VARIATIONAL RESTORATION.- Total Variation Gamma Correction Method for Tone Mapped HDR Images.- On the Optimal Proximal Parameter of an ADMM-like Splitting Method for Separable Convex Programming.- A new initialization method for neural networks with weight sharing.- The Shortest path amid 3-D polyhedral obstacles.- Multigrid Methods for Image Registration Model based on Optimal Mass Transport.

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Book SynopsisThis book collects select papers presented at the International Conference on Applications of Basic Sciences, held at Tiruchirappalli, Tamil Nadu, India, from 19-21 November 2019. The book discusses topics on singular perturbation problems, differential equations, numerical analysis, fuzzy logics, fuzzy differential equations, and mathematical physics, and their interdisciplinary applications in all areas of basic sciences: mathematics, physics, chemistry, and biology. It will be useful to researchers and scientists in all disciplines of basic sciences. This book will be very useful to know the different scientific approaches for a single physical system.Table of Contents1. Virtual Element Method for Singularly Perturbed Reaction-Diffusion Problems on Polygonal Domains: J.L. Gracia and D. Irisarri.- 2. Global Uniform Convergence for Weakly Coupled System of Singularly Perturbed Convection Diffusion Problems: S. Chandra Sekhara Rao, Varsha Srivastava, and Abhay Kumar Chaturvedi.- 3. A Parameter Uniform Fitted Mesh Method for a Weakly Coupled System of Three Partially Singularly Perturbed Convection-Diffusion Equations: Valarmathi Sigamani, Saravana Sankar Kalaiselvan, John J H Miller.- 4. Numerical Method for a Boundary Value Problem for a Linear System of Partially Singularly Perturbed Parabolic Delay Differential Equations of Reaction-Diffusion Type: Parthiban Saminathan and Franklin Victor.- 5. A First-Order Convergent Parameter Uniform Numerical Method for a Singularly Perturbed Second-Order Delay-Differential Equation of Reaction-Diffusion Type with a Discontinuous Source Term: Manikandan Mariappan, John J H Miller, Valarmathi Sigamani.- 6. Fitted Numerical Method with Linear Interpolation for Third-Order Singularly Perturbed Delay Problems: R. Mahendran and V. Subburayan.- 7. A Parameter Uniform Essentially First-Order Convergence of a Fitted Mesh Method for a Class of Parabolic Singularly Perturbed Robin Problem for a System of Reaction-Diffusion Equations: R. Ishwariya, Valarmathi Sigamani, John J H Miller.- 8. Finite Difference Method and Analysis for First-Order Hyperbolic Delay Differential Equations: S. Karthick and V. Subburayan.- 9. Fitted Mesh Methods for a Class of Weakly Coupled System of Singularly Perturbed Convection-Diffusion Equations: Saravana Sankar Kalaiselvan, Valarmathi Sigamani, John J H Miller.- 10. Numerical Analysis of a Finite Difference Method for a Linear System of Singularly Perturbed Parabolic Delay Differential Reaction-Diffusion Equations with Discontinuous Source Terms: Parthiban Saminathan and Franklin Victor.

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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 textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes in details the research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also includes latest findings, such as variable order derivative, distributed order derivative and its applications. Different from other textbooks in this subject, the book avoids lengthy mathematical demonstrations, and presents the theories in close connection to the applications in an easily readable manner. This textbook is intended for students, researchers and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.Table of ContentsPreface Chapter 1 Introduction 1.1 History of fractional calculus 1.2 Geometric and physical interpretation of fractional derivative equation 1.3 Application in science and engineering Chapter 2 Mathematical foundation of fractional calculus 2.1 Definition of fractional calculus 2.2 Properties of fractional calculus 2.3 Fourier and Laplace transform of the fractional calculus 2.4 Analytical solution of fractional-order equations 2.5 Questions and discussions Chapter 3 Fractal and fractional calculus 3.1 Fractal introduction and application 3.2 The relationship between fractional calculus and fractal Chapter 4 Fractional diffusion model 4.1 The fractional derivative anomalous diffusion equation 4.2 Statistical model of the acceleration distribution of turbulence particle 4.3 Lévy stable distributions 4.4 Stretched Gaussian distribution 4.5 Tsallis distribution 4.6 Ito formula 4.7 Random walk model Chapter 5 Typical applications of fractional differential equations 5.1 Power-law phenomena and non-gradient constitutive relation 5.2 Fractional Langevin equation 5.3 The complex damped vibration 5.4 Viscoelastic and rheological models 5.5 The power law frequency dependent acoustic dissipation 5.6 The fractional variational principle of mechanics 5.7 Fractional Schrödinger equation 5.8 Other application fields 5.9 Some applications of fractional calculus in biomechanics 5.10 Some applications of fractional calculus in the modeling of drug release process Chapter 6 Numerical methods for fractional differential equations 6.1 Time fractional differential equations 6.2 Space fractional differential equations 6.3 Open issues of numerical methods for FDEs Chapter 7 Current development and perspectives of fractional calculus 7.1 Summary and Discussion 7.2 Perspectives Appendix I Special Functions Appendix II Related electronic resources of fractional dynamics

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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.

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Book SynopsisThis monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.Table of ContentsFourier Multiplier, Function Spaces; Navier-Stokes Equation; Strichartz Estimates for Linear Dispersive Equations; Local and Global Wellposedness for Nonlinear Dispersive Equations; The Low Regularity Theory for the Nonlinear Dispersive Equations; Frequency-Uniform Decomposition Method; Conservations, Morawetz' Inequalities of NLS; Boltzmann Equation without Angular Cutoff.

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Book SynopsisGlobally integrable quantum systems and their perturbations.- On two-dimensional Dirac operators with $delta$-shell interactions supported on unbounded curves with straight ends.- Attractor Subspace and Decoherence-Free Algebra of Quantum Dynamics.- Algebraic localization of generalized Wannier bases implies Roe triviality in any dimension.- Hearing the boundary conditions of the one-dimensional Dirac operator Bosonized Momentum Distribution of a Fermi Gas via Friedrichs Diagrams.- Self-adjointness and Domain of Generalized Spin–Boson Models with Mild Ultraviolet Divergences.- Random Linear Systems with Quadratic Constraints: from Random Matrix Theory to replicas and back.- New analytical and geometrical aspects on Trudinger-Moser type inequality in 2D.- Resolvent limits of exterior boundary value problems and singular perturbation of Laplace operator in 3D.- The Search for NLS Ground States on a hybrid domain: motivations, methods, and results.- From microscopic to macroscopic: the large number dynamics of agents and cells, possibly interacting with a chemical background.- Open problems and perspectives on solving Friedrichs systems by Krylov approximation.- Singularity: a Seventh Memo.

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Book SynopsisChapter 1 Initial Trace of Positive Solutions of Some Diffusion Equations with Absorption.- Chapter 2 Graph Gradient Glows: from Discrete to Continuum.

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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.

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Book Synopsis

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