345 results
Search Results
2. Application of the nonlinear methods in pneumocardiogram signals
- Author
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K. Gediz Akdeniz, Mahmut Akıllı, Tamer Zeren, Nazmi Yılmaz, Mustafa Ozbek, Department of Physics, Koç University, Istanbul, Turkey, Nonlinear Science Working Group, Istanbul, Turkey, Department of Physiology, Manisa Celal Bayar University Medical School, Manisa, Turkey, and Department of Biophysics, Manisa Celal Bayar University Medical School, Manisa, Turkey
- Subjects
0301 basic medicine ,Entropy ,Biophysics ,Complex system ,Lyapunov exponent ,01 natural sciences ,Electrocardiography ,03 medical and health sciences ,symbols.namesake ,0103 physical sciences ,Animals ,Molecular Biology ,Mathematics ,Original Paper ,Signal processing ,010304 chemical physics ,Entropy (statistical thermodynamics) ,Mathematical analysis ,Reproducibility of Results ,Wavelet transform ,Signal Processing, Computer-Assisted ,Cell Biology ,Atomic and Molecular Physics, and Optics ,Rats ,Nonlinear system ,030104 developmental biology ,Nonlinear Dynamics ,Aperiodic graph ,Calibration ,Boltzmann constant ,symbols - Abstract
In this work, the pneumocardiogram signals of nine rats were analysed by scale index, Boltzmann Gibbs entropy and maximum Lyapunov exponents. The scale index method, based on wavelet transform, was proposed for determining the degree of aperiodicity and chaos. It means that the scale index parameter is close to zero when the signal is periodic and has a value between zero and one when the signal is aperiodic. A new entropy calculation method by normalized inner scalogram was suggested very recently. In this work, we also used this method for the first time in an empirical data. We compared the both methods with maximum Lyapunov exponents and observed that using together the scale index and the entropy calculation method by normalized inner scalogram increases the reliability of the pneumocardiogram signal analysis. Thus, the analysis of the pneumocardiogram signals by those methods enables to compare periodical and/or nonlinear aspects for further understanding of dynamics of cardiorespiratory system. © 2020, Springer Nature B.V.
- Published
- 2020
3. Synergies in Analysis, Discrete Mathematics, Soft Computing and Modelling
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P. V. Subrahmanyam, V. Antony Vijesh, Balasubramaniam Jayaram, Prakash Veeraraghavan, P. V. Subrahmanyam, V. Antony Vijesh, Balasubramaniam Jayaram, and Prakash Veeraraghavan
- Subjects
- Mathematics—Data processing, Mathematical physics, Computer simulation, Mathematical analysis, Discrete mathematics
- Abstract
This book contains select papers on mathematical analysis and modeling, discrete mathematics, fuzzy sets, and soft computing. All the papers were presented at the international conference on FIM28-SCMSPS20 virtually held at Sri Sivasubramaniya Nadar (SSN) College of Engineering, Chennai, India, and Stella Maris College (Autonomous), Chennai, from November 23–27, 2020. The conference was jointly held with the support of the Forum for Interdisciplinary Mathematics. Both the invited articles and submitted papers were broadly grouped under three heads: Part 1 on analysis and modeling (six chapters), Part 2 on discrete mathematics and applications (six chapters), and Part 3 on fuzzy sets and soft computing (three chapters).
- Published
- 2023
4. Proceedings of the International Conference on Fractional Differentiation and Its Applications (ICFDA’21)
- Author
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Andrzej Dzielinski, Dominik Sierociuk, Piotr Ostalczyk, Andrzej Dzielinski, Dominik Sierociuk, and Piotr Ostalczyk
- Subjects
- Control engineering, Robotics, Automation, Dynamics, Nonlinear theories, System theory, Mathematical analysis
- Abstract
This book touches upon various aspects of a very interesting, and growing in popularity category of models of dynamical systems. These are the so-called fractional-order systems. Such models are not only relevant for many fields of science and technology, but may also find numerous applications in other disciplines applying the mathematical modelling tools. Thus, the book is intended for a very wide audience of professionals who want to expand their knowledge of systems modelling and its applications.The book includes the selections of papers presented at the International Conference on Fractional Calculus and its Applications organized by the Warsaw University of Technology and was held online on 6–8 September 2021.The International Conference on Fractional Calculus and its Applications (ICFDA) has an almost twenty years history. It started in Bordeaux (France) in 2004, followed by Porto (Portugal) 2006, Istanbul (Turkey) 2008, Badajoz (Spain) 2010, Nanjing (China) 2012, Catania (Italy) 2014, Novi Sad (Serbia) 2016, Amman (Jordan) 2018. Next ICFDA was planned in 2020 in Warsaw (Poland), but COVID-19 pandemic shifted it to 6–8 September 2021. Hence, the organizers were forced to change the form of the conference to the online one.In the volume twenty eight high-quality research papers presented during the ICFDA 2021 eleven Regular Sessions with an additional online Discussion Session are presented. The presented papers are scientifically inspiring, leading to new fruitful ideas. They cover a very broad range of many disciplines. Nowadays, and especially in such a subject as fractional calculus, it is very difficult to assign papers to specific scientific areas. So, many of the papers included have an interdisciplinary character.
- Published
- 2022
5. Harnack Inequalities and Nonlinear Operators : Proceedings of the INdAM Conference to Celebrate the 70th Birthday of Emmanuele DiBenedetto
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Vincenzo Vespri, Ugo Gianazza, Dario Daniele Monticelli, Fabio Punzo, Daniele Andreucci, Vincenzo Vespri, Ugo Gianazza, Dario Daniele Monticelli, Fabio Punzo, and Daniele Andreucci
- Subjects
- Mathematical analysis, Global analysis (Mathematics), Manifolds (Mathematics), Mathematical optimization, Calculus of variations, Potential theory (Mathematics)
- Abstract
The book contains two contributions about the work of Emmanuele DiBenedetto and a selection of original papers. The authors are some of the main experts in Harnack's inequalities and nonlinear operators. These papers are part of the contributions presented during the conference to celebrate the 70th birthday of Prof. Emmanuele DiBenedetto, which was held at “Il Palazzone” in Cortona from June 18th to 24th, 2017. The papers are focused on current research topics regarding the qualitative properties of solutions, connections with calculus of variations, Harnack inequality and regularity theory. Some papers are also related to various applications. Many of the authors have shared with Prof. DiBenedetto an intense scientific and personal collaboration, while many others have taken inspiration from and further developed his field of research. The topics of the conference are certainly of great interest for the international mathematical community.
- Published
- 2021
6. Ramanujan's Lost Notebook : Part V
- Author
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George E. Andrews, Bruce C. Berndt, George E. Andrews, and Bruce C. Berndt
- Subjects
- Mathematicians--India--Biography, Mathematical analysis, Number theory
- Abstract
In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated,'Ramanujan's lost notebook.'Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.This fifth and final installment of the authors'examination of Ramanujan's lost notebook focuses on the mock theta functions first introduced in Ramanujan's famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan's many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. Review from the second volume:'Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited.'- MathSciNetReview from the first volume:'Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete.'- Gazette of the Australian Mathematical Society
- Published
- 2018
7. Contributions in Mathematics and Engineering : In Honor of Constantin Carathéodory
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Panos M. Pardalos, Themistocles M. Rassias, Panos M. Pardalos, and Themistocles M. Rassias
- Subjects
- Mathematical analysis, Calculus of variations
- Abstract
The contributions in this volume aim to deepen understanding of some of the current research problems and theories in modern topics such as calculus of variations, optimization theory, complex analysis, real analysis, differential equations, and geometry. Applications to these areas of mathematics are presented within the broad spectrum of research in Engineering Science with particular emphasis on equilibrium problems, complexity in numerical optimization, dynamical systems, non-smooth optimization, complex network analysis, statistical models and data mining, and energy systems. Additional emphasis is given to interdisciplinary research, although subjects are treated in a unified and self-contained manner. The presentation of methods, theory and applications makes this tribute an invaluable reference for teachers, researchers, and other professionals interested in pure and applied research, philosophy of mathematics, and mathematics education. Some review papers published in this volume will be particularly useful for a broader audience of readers as well as for graduate students who search for the latest information. Constantin Carathéodory's wide-ranging influence in the international mathematical community was seen during the first Fields Medals awards at the International Congress of Mathematicians, Oslo, 1936. Two medals were awarded, one to Lars V. Ahlfors and one to Jesse Douglass. It was Carathéodory who presented both their works during the opening of the International Congress. This volume contains significant papers in Science and Engineering dedicated to the memory of Constantin Carathéodory and the spirit of his mathematical influence.
- Published
- 2016
8. Seismic response for an isosceles triangle hill subjected to anti-plane shear waves
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Menghan Sun, Yong Yang, Zailin Yang, Yun-qiu Song, and Xinzhu Li
- Subjects
Shear waves ,Plane (geometry) ,Numerical analysis ,010102 general mathematics ,Coordinate system ,Mathematical analysis ,0211 other engineering and technologies ,02 engineering and technology ,Expression (computer science) ,Geotechnical Engineering and Engineering Geology ,01 natural sciences ,Isosceles triangle ,Earth and Planetary Sciences (miscellaneous) ,Boundary value problem ,0101 mathematics ,Wave function ,021101 geological & geomatics engineering ,Mathematics - Abstract
This paper presents an exact, analytical solution to the boundary value problem of the anti-plane (SH) waves scattering by an isosceles triangle hill on an elastic half-space by using the wavefunction expansion method. An appropriate region-matching technique is introduced to divide the half-space containing a triangle hill into two subregions. Then, the wavefield expression of each subregion is constructed in terms of an infinite series in two coordinate systems, respectively. Furthermore, a Graf’s addition formula is derived to unify the coordinate system and solve the unknown coefficients in the wave functions. Finally, numerical results are calculated to illustrate the effects on ground motion due to the existence of an isosceles triangle hill. This paper revises the existing analytical methods, and aims to provide a benchmark for numerical method verification and a reference for engineering practice.
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- 2022
9. New Trends in the Applications of Differential Equations in Sciences : NTADES 2023, Saints Constantine and Helena, Bulgaria, July 17–20
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Angela Slavova and Angela Slavova
- Subjects
- Differential equations, Mathematical physics, Mathematical analysis
- Abstract
This book convenes peer-reviewed, selected papers presented at the Tenth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Saints Constantine and Helena, Bulgaria, July 17–20, 2023. Contributions are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis.In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them to solve real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations.
- Published
- 2024
10. Path Integrals in Stochastic Engineering Dynamics
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Ioannis A. Kougioumtzoglou, Apostolos F. Psaros, Pol D. Spanos, Ioannis A. Kougioumtzoglou, Apostolos F. Psaros, and Pol D. Spanos
- Subjects
- Dynamics, Nonlinear theories, Engineering mathematics, Engineering—Data processing, Stochastic analysis, Mathematical analysis, Mathematical physics
- Abstract
This book organizes and explains, in a systematic and pedagogically effective manner, recent advances in path integral solution techniques with applications in stochastic engineering dynamics. It fills a gap in the literature by introducing to the engineering mechanics community, for the first time in the form of a book, the Wiener path integral as a potent uncertainty quantification tool. Since the path integral flourished within the realm of quantum mechanics and theoretical physics applications, most books on the topic have focused on the complex-valued Feynman integral with only few exceptions, which present path integrals from a stochastic processes perspective. Remarkably, there are only few papers, and no books, dedicated to path integral as a solution technique in stochastic engineering dynamics. Summarizing recently developed techniques, this volume is ideal for engineering analysts interested in further establishing path integrals as an alternative potent conceptual and computational vehicle in stochastic engineering dynamics.
- Published
- 2024
11. Hyperbolic Problems: Theory, Numerics, Applications. Volume II : HYP2022, Málaga, Spain, June 20-24, 2022
- Author
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Carlos Parés, Manuel J. Castro, Tomás Morales de Luna, María Luz Muñoz-Ruiz, Carlos Parés, Manuel J. Castro, Tomás Morales de Luna, and María Luz Muñoz-Ruiz
- Subjects
- Mathematical analysis, Mathematics—Data processing, Numerical analysis
- Abstract
The present volume contains a selection of papers from the XVIII International Conference on Hyperbolic Problems: Theory, Numerics, and Applications (HYP2022), which was held on June 20-24, 2022 in Málaga (Spain). The goal of this series of conferences is to bring together scientists with interests in the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models. The chapters in this volume correspond to selected contributions related to numerical aspects and applications.
- Published
- 2024
12. Accurate and locking-free analysis of beams, plates and shells using solid elements
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Miguel Cervera, Sungchul Kim, Michele Chiumenti, Savvas Saloustros, Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental, and Universitat Politècnica de Catalunya. RMEE - Grup de Resistència de Materials i Estructures en l'Enginyeria
- Subjects
Finite element method ,Beam structures ,Materials science ,Discretization ,Nearly incompressible ,Computational Mechanics ,Shell (structure) ,Concrete beams ,Ocean Engineering ,02 engineering and technology ,Plate structures ,Orthotropic material ,Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits [Àrees temàtiques de la UPC] ,Anisotropic materials ,Plaques (Enginyeria) ,01 natural sciences ,Displacement (vector) ,0203 mechanical engineering ,Làmines (Enginyeria) -- Models matemàtics ,Mixed finite elements ,0101 mathematics ,Applied Mathematics ,Mechanical Engineering ,Shell structures ,Isotropy ,Mathematical analysis ,Enginyeria civil::Materials i estructures::Materials i estructures de formigó [Àrees temàtiques de la UPC] ,Shells (Engineering)--Mathematical models ,010101 applied mathematics ,Computational Mathematics ,020303 mechanical engineering & transports ,Computational Theory and Mathematics ,Compressibility ,Plates (Engineering)--Mathematical models ,Bigues de formigó ,Beam (structure) - Abstract
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-020-01969-0. This paper investigates the capacity of solid finite elements with independent interpolations for displacements and strains to address shear, membrane and volumetric locking in the analysis of beam, plate and shell structures. The performance of the proposed strain/displacement formulation is compared to the standard one through a set of eleven benchmark problems. In addition to the relative performance of both finite element formulations, the paper studies the effect of discretization and material characteristics. The first refers to different solid element typologies (hexahedra, prisms) and shapes (regular, skewed, warped configurations). The second refers to isotropic, orthotropic and layered materials, and nearly incompressible states. For the analysis of nearly incompressible cases, the B-bar method is employed in both standard and strain/displacement formulations. Numerical results show the enhanced accuracy of the proposed strain/displacement formulation in predicting stresses and displacements, as well as producing locking-free discrete solutions, which converge asymptotically to the corresponding continuous problems. The authors gratefully acknowledge the financial support from the Ministry of Science, Innovation and Universities (MCIU) via: the ADaMANT project (Computational Framework for Additive Manufacturing of Titanium Alloy, Proyectos de I+D -Excelencia-, ref. num. DPI2017-85998-P); the SEVERUS project (Multilevel evaluation of seismic vulnerability and risk mitigation of masonry buildings in resilient historical urban centres, ref. num. RTI2018-099589-B-I00); and the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2018-000797-S). Sungchul Kim gratefully acknowledges the support received from the Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) and the European Social Fund (ESF) through the predoctoral FI grants (ref. num. 2019FI_B00727).
- Published
- 2021
13. Numerical methods for scattering problems in periodic waveguides
- Author
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Ruming Zhang
- Subjects
Scattering ,Applied Mathematics ,Numerical analysis ,Mathematical analysis ,Process (computing) ,Structure (category theory) ,Solver ,Methods of contour integration ,Computer Science::Other ,Computational Mathematics ,Wavenumber ,ddc:510 ,Mathematics ,Circle of a sphere - Abstract
In this paper, we propose new numerical methods for scattering problems in periodic waveguides. Based on [20], the “physically meaningful” solution, which is obtained via the Limiting Absorption Principle (LAP) and is called an LAP solution, is written as an integral of quasi-periodic solutions on a contour. The definition of the contour depends both on the wavenumber and the periodic structure. The contour integral is then written as the combination of finite propagation modes and a contour integral on a small circle. Numerical methods are developed and based on the two representations. Compared with other numerical methods, we do not need the LAP process during numerical approximations, thus a standard error estimation is easily carried out. Based on this method, we also develop a numerical solver for halfguide problems. The method is based on the result that any LAP solution of a halfguide problem can be extended to the LAP solution of a fullguide problem. At the end of this paper, we also give some numerical results to show the efficiency of our numerical methods.
- Published
- 2021
14. On hyperbolicity of the dynamic equations for plastic fluid-saturated solids
- Author
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V. A. Osinov
- Subjects
Well-posed problem ,Matrix (mathematics) ,ddc:690 ,Mechanical Engineering ,Mathematical analysis ,Zero (complex analysis) ,Boundary value problem ,Tensor ,Plasticity ,Buildings ,System of linear equations ,Eigenvalues and eigenvectors ,Mathematics - Abstract
The paper deals with the analysis of hyperbolicity of the dynamic equations for plastic solids, including one-phase solids and porous fluid-saturated solids with zero and nonzero permeability. Hyperbolicity defined as diagonalizability of the matrix of the system is necessary for the boundary value problems to be well posed. The difference between the system of equations for a plastic solid and the system for an elastic solid is that the former contains additional evolution equations for the dependent variables involved in the plasticity model. It is shown that the two systems agree with each other from the viewpoint of hyperbolicity: they are either both hyperbolic or both non-hyperbolic. Another issue addressed in the paper is the relation between hyperbolicity and the properties of the acoustic tensor (matrix). It remained unproved whether the condition for the eigenvalues of the acoustic matrix to be real and positive is not only necessary but also sufficient for hyperbolicity. It is proved in the paper that the equations are hyperbolic if and only if the eigenvalues of the acoustic matrix are real and positive with a complete set of eigenvectors. The analysis of the whole system of equations for a plastic solid can thus be reduced to the analysis of the acoustic matrix. The results are not restricted to a particular plasticity model but applicable to a wide class of models.
- Published
- 2021
- Full Text
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15. Evolving to Non-round Weingarten Spheres: Integer Linear Hopf Flows
- Author
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Brendan Guilfoyle and Wilhelm Klingenberg
- Subjects
Mathematics - Differential Geometry ,Partial differential equation ,Plane (geometry) ,Horizon ,Mathematical analysis ,Boundary (topology) ,Curvature ,Mathematics - Analysis of PDEs ,Differential Geometry (math.DG) ,Flow (mathematics) ,Principal curvature ,FOS: Mathematics ,Mathematics::Differential Geometry ,Linear combination ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
In the 1950's Hopf gave examples of non-round convex 2-spheres in Euclidean 3-space with rotational symmetry that satisfy a linear relationship between their principal curvatures. In this paper we investigate conditions under which evolving a smooth rotationally symmetric sphere by a linear combination of its radii of curvature yields a Hopf sphere. When the coefficients of the flow have certain integer values, the fate of an initial sphere is entirely determined by the local geometry of its isolated umbilic points. A surprising variety of behaviours is uncovered: convergence to round spheres and non-round Hopf spheres, as well as divergence to infinity. The critical quantity is the rate of vanishing of the astigmatism - the difference of the radii of curvature - at the isolated umbilic points. It is proven that the size of this quantity versus the coefficient in the flow function determines the fate of the evolution. The geometric setting for the equation is Radius of Curvature space, viewed as a pair of hyperbolic/AdS half-planes joined along their boundary, the umbilic horizon. A rotationally symmetric sphere determines a parameterized curve in this plane with end-points on the umbilic horizon. The slope of the curve at the umbilic horizon is linked by the Codazzi-Mainardi equations to the rate of vanishing of astigmatism, and for generic initial conditions can be used to determine the outcome of the flow. The slope can jump during the flow, and a number of examples are given: instant jumps of the initial slope, as well as umbilic circles that contract to points in finite time and 'pop' the slope. Finally, we present soliton-like solutions: curves that evolve under linear flows by mutual hyperbolic/AdS isometries (dilation and translation) of Radius of Curvature space. A forthcoming paper will apply these geometric ideas to non-linear curvature flows., 24 page latex, 1 figure. Proposition 5 uses binomial identities that were discussed on the MathOverflow threads at http://mathoverflow.net/questions/275214/is-there-a-simple-proof-of-the-following-identity-for-sum-k-m-1l-1km and http://mathoverflow.net/questions/278074/is-there-a-simple-proof-of-the-following-identity-part-2}
- Published
- 2021
16. New Trends in Geometric Analysis : Spanish Network of Geometric Analysis 2007-2021
- Author
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Antonio Alarcón, Vicente Palmer, César Rosales, Antonio Alarcón, Vicente Palmer, and César Rosales
- Subjects
- Geometry, Mathematical analysis
- Abstract
The aim of this book is to provide an overview of some of the progress made by the Spanish Network of Geometric Analysis (REAG, by its Spanish acronym) since its born in 2007. REAG was created with the objective of enabling the interchange of ideas and the knowledge transfer between several Spanish groups having Geometric Analysis as a common research line. This includes nine groups at Universidad Autónoma de Barcelona, Universidad Autónoma de Madrid, Universidad de Granada, Universidad Jaume I de Castellón, Universidad de Murcia, Universidad de Santiago de Compostela and Universidad de Valencia. The success of REAG has been substantiated with regular meetings and the publication of research papers obtained in collaboration between the members of different nodes.On the occasion of the 15th anniversary of REAG this book aims to collect some old and new contributions of this network to Geometric Analysis. The book consists of thirteen independent chapters, all of themauthored by current members of REAG. The topics under study cover geometric flows, constant mean curvature surfaces in Riemannian and sub-Riemannian spaces, integral geometry, potential theory and Riemannian geometry, among others. Some of these chapters have been written in collaboration between members of different nodes of the network, and show the fruitfulness of the common research atmosphere provided by REAG. The rest of the chapters survey a research line or present recent progresses within a group of those forming REAG.Surveying several research lines and offering new directions in the field, the volume is addressed to researchers (including postdocs and PhD students) in Geometric Analysis in the large.
- Published
- 2023
17. Analysis in Banach Spaces : Volume III: Harmonic Analysis and Spectral Theory
- Author
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Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis, Tuomas Hytönen, Jan van Neerven, Mark Veraar, and Lutz Weis
- Subjects
- Functional analysis, Fourier analysis, Harmonic analysis, Operator theory, Mathematical analysis
- Abstract
This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.
- Published
- 2023
18. New Trends in the Applications of Differential Equations in Sciences : NTADES 2022, Sozopol, Bulgaria, June 14–17
- Author
-
Angela Slavova and Angela Slavova
- Subjects
- Differential equations, Mathematical analysis, Mathematical physics, Mathematics
- Abstract
This book convenes peer-reviewed, selected papers presented at the Ninth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Sozopol, Bulgaria, June 17–20, 2022. The works are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis.In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them for solving real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations.The NTADES 2022 conference was organized in cooperation with the Society of Industrial and Applied Mathematics (SIAM), the major international organization for Industrial and Applied Mathematics and for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering, finance, and neuroscience.
- Published
- 2023
19. Excursions in Number Theory, Algebra, and Analysis
- Author
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Kenneth Ireland, Al Cuoco, Kenneth Ireland, and Al Cuoco
- Subjects
- Number theory, Algebra, Mathematical analysis
- Abstract
This textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate mathematics, the course focused on interrelationships and hands-on experience. Readers of this textbook will be taken on a modern rendering of Ireland's path of discovery, consisting of excursions into number theory, algebra, and analysis. Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on to study or teach mathematics. A pool of 200 ‘Dialing In'problems opens the book, providing fuel for active enquiry throughout a course. The following chapters develop theory to illuminate the observations and roadblocks encountered in the problems, situating them in the broader mathematical landscape. Topics cover polygons and modular arithmetic; the fundamental theorems of arithmetic and algebra; irrational, algebraic and transcendental numbers; and Fourier series and Gauss sums. A lively accompaniment of examples, exercises, historical anecdotes, and asides adds motivation and context to the theory. Return trips to the Dialing In problems are encouraged, offering opportunities to put theory into practice and make lasting connections along the way. Excursions in Number Theory, Algebra, and Analysis invites readers on a journey as important as the destination. Suitable for a senior capstone, professional development for practicing teachers, or independent reading, this textbook offers insights and skills valuable to math majors and high school teachers alike. A background in real analysis and abstract algebra is assumed, though the most important prerequisite is a willingness to put pen to paper and do some mathematics.
- Published
- 2023
20. Homogenization of boundary value problems in plane domains with frequently alternating type of nonlinear boundary conditions: critical case
- Author
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Jesús Ildefonso Díaz Díaz, David Gómez-Castro, A. V. Podolskiy, and Tatiana A. Shaposhnikova
- Subjects
General Mathematics ,010102 general mathematics ,Mathematical analysis ,Poisson distribution ,Differential operator ,01 natural sciences ,Homogenization (chemistry) ,010101 applied mathematics ,symbols.namesake ,Nonlinear system ,In plane ,Bounded function ,symbols ,Critical radius ,Boundary value problem ,0101 mathematics ,Mathematics - Abstract
In the present paper we consider a boundary homogenization problem for the Poisson’s equation in a bounded domain and with a part of the boundary conditions of highly oscillating type (alternating between homogeneous Neumman condition and a nonlinear Robin type condition involving a small parameter). Our main goal in this paper is to investigate the asymptotic behavior as ε → 0 of the solution to such a problem in the case when the length of the boundary part, on which the Robin condition is specified, and the coefficient, contained in this condition, take so-called critical values. We show that in this case the character of the nonlinearity changes in the limit problem. The boundary homogenization problems were investigate for example in [1, 2, 4]. For the first time the effect of the nonlinearity character change via homogenization was noted for the first time in [5]. In that paper an effective model was constructed for the boundary value problem for the Poisson’s equation in the bounded domain that is perforated by the balls of critical radius, when the space dimension equals to 3. In the last decade a lot of works appeared, e.g., [6–10], in which this effect was studied for different geometries of perforated domains and for different differential operators. We note that in [6–10] only perforations by balls were considered. In papers [11, 12] the case of domains perforated by an arbitrary shape sets in the critical case was studied.
- Published
- 2020
21. Mathematical Analysis and Applications : MAA 2020, Jamshedpur, India, November 2–4
- Author
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Ouayl Chadli, Sourav Das, Ram N. Mohapatra, A. Swaminathan, Ouayl Chadli, Sourav Das, Ram N. Mohapatra, and A. Swaminathan
- Subjects
- Mathematical analysis, Approximation theory, Functions of complex variables
- Abstract
This 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.
- Published
- 2022
22. Mathematical Analysis in Interdisciplinary Research
- Author
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Ioannis N. Parasidis, Efthimios Providas, Themistocles M. Rassias, Ioannis N. Parasidis, Efthimios Providas, and Themistocles M. Rassias
- Subjects
- Mathematical analysis, Interdisciplinary research--Mathematics
- Abstract
This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.
- Published
- 2022
23. Weight-function identification for the preisach model of laminated steels using concentric hysteresis loops
- Author
-
Zeinali, Reza, Krop, Dave, Lomonova, Elena, Zamboni, Walter, Petrone, Giovanni, Electromechanics and Power Electronics, Power Electronics Lab, Cyber-Physical Systems Center Eindhoven, and Electromechanics Lab
- Subjects
Hysteresis ,Weight function ,Identification (information) ,Soft-magnetic material ,Mathematical analysis ,Hysteresis model ,Concentric ,Root-mean-square deviation ,Mathematics ,Analytic function ,Preisach model - Abstract
This paper proposes a new methodology to obtain the weight function of the Preisach model for non-oriented laminated steels using concentric hysteresis loops. In this methodology, first the experimental weight function is obtained from measured concentric hysteresis loops, and a mathematical technique is applied to remove the existing negative values. Based on the shape of the modified weight function, a new analytic function is proposed as a weight function for the Preisach model. The proposed analytic function is more advanced than the conventional probability functions proposed in literature, such that it is able to better mimic the actual shape of the weight function. The unknown parameters of the analytic weight function are identified by minimizing the error between the Preisach model and the modified measurements. Using the proposed analytic weight function, the minimum rms error is reduced to less than 0.5%, and a decent agreement is achieved between the model and the measurement.
- Published
- 2020
24. A High-Frequency Homogenization Approach Near the Dirac Points in Bubbly Honeycomb Crystals
- Author
-
Sanghyeon Yu, Erik Orvehed Hiltunen, and Habib Ammari
- Subjects
35R30, 35C20 ,Mechanical Engineering ,Mathematical analysis ,Complex system ,Metamaterial ,Physics::Optics ,Eigenfunction ,01 natural sciences ,Homogenization (chemistry) ,010101 applied mathematics ,Brillouin zone ,Crystal ,Mathematics (miscellaneous) ,Mathematics - Analysis of PDEs ,Normal mode ,0103 physical sciences ,FOS: Mathematics ,0101 mathematics ,010306 general physics ,Analysis ,Eigenvalues and eigenvectors ,Analysis of PDEs (math.AP) - Abstract
In (Ammari et al. in SIAM J Math Anal. arXiv:1811.03905), the existence of a Dirac dispersion cone in a bubbly honeycomb phononic crystal comprised of bubbles of arbitrary shape is shown. The aim of this paper is to prove that, near the Dirac points, the Bloch eigenfunctions is the sum of two eigenmodes. Each eigenmode can be decomposed into two components: one which is slowly varying and satisfies a homogenized equation, while the other is periodic across each elementary crystal cell and is highly oscillating. The slowly oscillating components of the eigenmodes satisfy a system of Dirac equations. Our results in this paper prove for the first time a near-zero effective refractive index near the Dirac points for the plane-wave envelopes of the Bloch eigenfunctions in a sub-wavelength metamaterial. They are illustrated by a variety of numerical examples. We also compare and contrast the behaviour of the Bloch eigenfunctions in the honeycomb crystal with that of their counterparts in a bubbly square crystal, near the corner of the Brillouin zone, where the maximum of the first Bloch eigenvalue is attained., Archive for Rational Mechanics and Analysis, 238, ISSN:0003-9527, ISSN:1432-0673
- Published
- 2020
25. Splash singularities for a general Oldroyd model with finite Weissenberg number
- Author
-
Elena Di Iorio, Stefano Spirito, Pierangelo Marcati, and Ministerio de Economía y Competitividad (España)
- Subjects
Splash ,Mechanical Engineering ,010102 general mathematics ,Mathematical analysis ,Existence theorem ,Boundary (topology) ,01 natural sciences ,010101 applied mathematics ,Physics::Fluid Dynamics ,Lagrangian and Eulerian specification of the flow field ,Mathematics (miscellaneous) ,Singularity ,Mathematics - Analysis of PDEs ,Finite strain theory ,FOS: Mathematics ,Weissenberg number ,Gravitational singularity ,0101 mathematics ,Analysis ,Mathematics ,Analysis of PDEs (math.AP) - Abstract
In this paper we study a 2D Oldroyd free-boundary model which describes the evolution of a viscoelastic fluid. We prove existence of splash singularities, namely points where the boundary remains smooth but self-intersects. This paper extends the previous results obtained for infinite Weissenberg number to the case of any finite Weissenberg number. The main difficulty of this paper is due to the non linear balance law of the elastic tensor which cannot be reduced, as in the case of infinite Weissenberg, to the transport equations for the deformation gradient. Our strategy in accurate local existence result depending on the Weissenberg number and the combination of Conformal and Lagrangian transformations. The existence of splash singularities is guarantee by a suitable choice of the initial data combined with stability estimates., Revised version. Accepted in Archive for Rational Mechanics and Analysis
- Published
- 2020
26. Recent Advances in Numerical Methods for Hyperbolic PDE Systems : NumHyp 2019
- Author
-
María Luz Muñoz-Ruiz, Carlos Parés, Giovanni Russo, María Luz Muñoz-Ruiz, Carlos Parés, and Giovanni Russo
- Subjects
- Numerical analysis, Mathematical analysis, Mathematics, Computer science—Mathematics, Mathematics—Data processing
- Abstract
The present volume contains selected papers issued from the sixth edition of the International Conference'Numerical methods for hyperbolic problems'that took place in 2019 in Málaga (Spain). NumHyp conferences, which began in 2009, focus on recent developments and new directions in the field of numerical methods for hyperbolic partial differential equations (PDEs) and their applications. The 11 chapters of the book cover several state-of-the-art numerical techniques and applications, including the design of numerical methods with good properties (well-balanced, asymptotic-preserving, high-order accurate, domain invariant preserving, uncertainty quantification, etc.), applications to models issued from different fields (Euler equations of gas dynamics, Navier-Stokes equations, multilayer shallow-water systems, ideal magnetohydrodynamics or fluid models to simulate multiphase flow, sediment transport, turbulent deflagrations, etc.), and the development of new nonlinear dispersive shallow-water models. The volume is addressed to PhD students and researchers in Applied Mathematics, Fluid Mechanics, or Engineering whose investigation focuses on or uses numerical methods for hyperbolic systems. It may also be a useful tool for practitioners who look for state-of-the-art methods for flow simulation.
- Published
- 2021
27. From Particle Systems to Partial Differential Equations : International Conference, Particle Systems and PDEs VI, VII and VIII, 2017-2019
- Author
-
Cédric Bernardin, François Golse, Patrícia Gonçalves, Valeria Ricci, Ana Jacinta Soares, Cédric Bernardin, François Golse, Patrícia Gonçalves, Valeria Ricci, and Ana Jacinta Soares
- Subjects
- Mathematical analysis, Mathematics, Probabilities
- Abstract
This book includes the joint proceedings of the International Conference on Particle Systems and PDEs VI, VII and VIII. Particle Systems and PDEs VI was held in Nice, France, in November/December 2017, Particle Systems and PDEs VII was held in Palermo, Italy, in November 2018, and Particle Systems and PDEs VIII was held in Lisbon, Portugal, in December 2019. Most of the papers are dealing with mathematical problems motivated by different applications in physics, engineering, economics, chemistry and biology. They illustrate methods and topics in the study of particle systems and PDEs and their relation. The book is recommended to probabilists, analysts and to those mathematicians in general, whose work focuses on topics in mathematical physics, stochastic processes and differential equations, as well as to those physicists who work in statistical mechanics and kinetic theory.
- Published
- 2021
28. Methods of Mathematical Oncology : Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020
- Author
-
Takashi Suzuki, Clair Poignard, Mark Chaplain, Vito Quaranta, Takashi Suzuki, Clair Poignard, Mark Chaplain, and Vito Quaranta
- Subjects
- Neural networks (Computer science), Mathematical models, Mathematical analysis
- Abstract
This 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.
- Published
- 2021
29. Emerging Problems in the Homogenization of Partial Differential Equations
- Author
-
Patrizia Donato, Manuel Luna-Laynez, Patrizia Donato, and Manuel Luna-Laynez
- Subjects
- Mathematics, Mathematical analysis, Neural networks (Computer science)
- Abstract
This book contains some of the results presented at the mini-symposium titled Emerging Problems in the Homogenization of Partial Differential Equations, held during the ICIAM2019 conference in Valencia in July 2019. The papers cover a large range of topics, problems with weak regularity data involving renormalized solutions, eigenvalue problems for complicated shapes of the domain, homogenization of partial differential problems with strongly alternating boundary conditions of Robin type with large parameters, multiscale analysis of the potential action along a neuron with a myelinated axon, and multi-scale model of magnetorheological suspensions. The volume is addressed to scientists who deal with complex systems that presents several elements (characteristics, constituents...) of very different scales, very heterogeneous, and search for homogenized models providing an effective (macroscopic) description of their behaviors.
- Published
- 2021
30. Asymptotic, Algebraic and Geometric Aspects of Integrable Systems : In Honor of Nalini Joshi On Her 60th Birthday, TSIMF, Sanya, China, April 9–13, 2018
- Author
-
Frank Nijhoff, Yang Shi, Da-jun Zhang, Frank Nijhoff, Yang Shi, and Da-jun Zhang
- Subjects
- Mathematical analysis, Geometry
- Abstract
This proceedings volume gathers together selected works from the 2018 “Asymptotic, Algebraic and Geometric Aspects of Integrable Systems” workshop that was held at TSIMF Yau Mathematical Sciences Center in Sanya, China, honoring Nalini Joshi on her 60th birthday. The papers cover recent advances in asymptotic, algebraic and geometric methods in the study of discrete integrable systems.The workshop brought together experts from fields such as asymptotic analysis, representation theory and geometry, creating a platform to exchange current methods, results and novel ideas.This volume's articles reflect these exchanges and can be of special interest to a diverse group of researchers and graduate students interested in learning about current results, new approaches and trends in mathematical physics, in particular those relevant to discrete integrable systems.
- Published
- 2020
31. Special Topics in Structural Dynamics & Experimental Techniques, Volume 5 : Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics 2020
- Author
-
David S. Epp and David S. Epp
- Subjects
- Statics, Mathematical analysis, Building materials, Civil engineering
- Abstract
Special Topics in Structural Dynamics & Experimental Techniques, Volume 5: Proceedings of the 38th MAC, A Conference and Exposition on Structural Dynamics, 2020, the fifth volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on:Analytical MethodsEmerging Technologies for Structural DynamicsEngineering ExtremesExperimental TechniquesFinite Element TechniquesGeneral Topics
- Published
- 2020
32. Mathematical Analysis and Applications in Modeling : ICMAAM 2018, Kolkata, India, January 9–12
- Author
-
Priti Kumar Roy, Xianbing Cao, Xue-Zhi Li, Pratulananda Das, Satya Deo, Priti Kumar Roy, Xianbing Cao, Xue-Zhi Li, Pratulananda Das, and Satya Deo
- Subjects
- Biomathematics, Mathematical models, Mathematical analysis
- Abstract
This book collects select papers presented at the “International Conference on Mathematical Analysis and Application in Modeling,” held at Jadavpur University, Kolkata, India, on 9–12 January 2018. It discusses new results in cutting-edge areas of several branches of mathematics and applications, including analysis, topology, dynamical systems (nonlinear, topological), mathematical modeling, optimization and mathematical biology. The conference has emerged as a powerful forum, bringing together leading academics, industry experts and researchers, and offering them a venue to discuss, interact and collaborate in order to stimulate the advancement of mathematics and its industrial applications.
- Published
- 2020
33. Differential Geometry, Algebra, and Analysis : ICDGAA 2016, New Delhi, India, November 15–17
- Author
-
Mohammad Hasan Shahid, Mohammad Ashraf, Falleh Al-Solamy, Yasunori Kimura, Gabriel Eduard Vilcu, Mohammad Hasan Shahid, Mohammad Ashraf, Falleh Al-Solamy, Yasunori Kimura, and Gabriel Eduard Vilcu
- Subjects
- Geometry, Differential, Algebra, Mathematical analysis, Manifolds (Mathematics)
- Abstract
This book is a collection of selected research papers, some of which were presented at the International Conference on Differential Geometry, Algebra and Analysis (ICDGAA 2016), held at the Department of Mathematics, Jamia Millia Islamia, New Delhi, from 15–17 November 2016. It covers a wide range of topics—geometry of submanifolds, geometry of statistical submanifolds, ring theory, module theory, optimization theory, and approximation theory—which exhibit new ideas and methodologies for current research in differential geometry, algebra and analysis. Providing new results with rigorous proofs, this book is, therefore, of much interest to readers who wish to learn new techniques in these areas of mathematics.
- Published
- 2020
34. Mathematical Modelling, Applied Analysis and Computation : ICMMAAC 2018, Jaipur, India, July 6-8
- Author
-
Jagdev Singh, Devendra Kumar, Hemen Dutta, Dumitru Baleanu, Sunil Dutt Purohit, Jagdev Singh, Devendra Kumar, Hemen Dutta, Dumitru Baleanu, and Sunil Dutt Purohit
- Subjects
- Mathematical models, Mathematics—Data processing, Numerical analysis, Mathematical analysis, Differential equations, Special functions
- Abstract
This book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and alsonew efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics.
- Published
- 2019
35. On the relationship between the stochastic Galerkin method and the pseudo-spectral collocation method for linear differential algebraic equations
- Author
-
Paolo Manfredi, D. De Zutter, and Dries Vande Ginste
- Subjects
GENERALIZED POLYNOMIAL CHAOS ,Orthogonal polynomials ,General Mathematics ,0211 other engineering and technologies ,MathematicsofComputing_NUMERICALANALYSIS ,Polynomial chaos ,02 engineering and technology ,Stochastic collocation method ,01 natural sciences ,Linear differential algebraic equations ,Collocation method ,Stochastic simulation ,Stochastic Galerkin method ,Orthogonal collocation ,0101 mathematics ,UNCERTAINTY QUANTIFICATION ,Mathematics ,021103 operations research ,Collocation ,Matrix factorization ,Mathematical analysis ,General Engineering ,010101 applied mathematics ,Stochastic partial differential equation ,Stochastic optimization ,IBCN ,Differential algebraic equation - Abstract
Polynomial chaos-based methods have been extensively applied in electrical and other engineering problems for the stochastic simulation of systems with uncertain parameters. Most of the implementations are based on either the intrusive stochastic Galerkin method or on non-intrusive collocation approaches, of which a very common example is the pseudo-spectral method based on Gaussian quadrature rules. This paper shows that, for the important class of linear differential algebraic equations, the latter can be cast as an approximate factorization of the stochastic Galerkin approach, thus generalizing recent discussions in literature in this regard. Consistently with this literature, we show that the factorization turns out to be exact for first-order random inputs, and hence the two methods coincide under this assumption. Further, the presented results also generalize recent work in the field of electrical circuit simulation, in which a similar decomposition was derived ad hoc, via error minimization, for the case of Hermite chaos. We demonstrate that the factorization stems from the general properties of orthogonal polynomials and the error introduced by the approximation—or in other terms, the error of the stochastic collocation method in comparison with the stochastic Galerkin method—is carefully quantified and assessed. An illustrative example concerning the stochastic analysis of an RLC circuit is used to illustrate the main findings of this paper. In addition, a more complex and real-life example allows emphasizing the generality of the achieved results.
- Published
- 2018
36. A closed-form formula for the RBF-based approximation of the Laplace-Beltrami operator
- Author
-
Miguel Moscoso, Pedro González-Rodríguez, Diego Álvarez, and Ministerio de Economía y Competitividad (España)
- Subjects
Surface (mathematics) ,Matemáticas ,Cardiology ,010103 numerical & computational mathematics ,Curvature ,01 natural sciences ,Theoretical Computer Science ,Radial basis functions ,Operator (computer programming) ,Radial basis function ,0101 mathematics ,Biología y Biomedicina ,Mathematics ,Second derivative ,Numerical Analysis ,Applied Mathematics ,Mathematical analysis ,General Engineering ,Surface Laplacian ,010101 applied mathematics ,Computational Mathematics ,Computational Theory and Mathematics ,Laplace–Beltrami operator ,Closed-form expression ,Surface PDE ,Normal ,Software - Abstract
In this paper we present a method that uses radial basis functions to approximatethe Laplace&-Beltrami operator that allows to solve numerically diffusion (and reaction&-diffusion) equations on smooth, closed surfaces embedded in R3. The novelty of the methodis in a closed-form formula for the Laplace&-Beltrami operator derived in the paper, whichinvolve the normal vector and the curvature at a set of points on the surface of interest.An advantage of the proposed method is that it does not rely on the explicit knowledgeof the surface, which can be simply defined by a set of scattered nodes. In that case, thesurface is represented by a level set function from which we can compute the needed normalvectors and the curvature. The formula for the Laplace&-Beltrami operator is exact for radialbasis functions and it also depends on the first and second derivatives of these functionsat the scattered nodes that define the surface. We analyze the converge of the method andwe present numerical simulations that show its performance. We include an application thatarises in cardiology. This work has been supported by Spanish MICINN Grant FIS2016-77892-R. We thank the anonymous reviewer for his or her careful reading of our manuscript and his or her many insightful comments and suggestions.
- Published
- 2018
37. Canard Explosion Near Non-Liénard Type Slow–Fast Hopf Point
- Author
-
Renato Huzak
- Subjects
Singular perturbation ,Mathematics::Dynamical Systems ,Partial differential equation ,010102 general mathematics ,Mathematical analysis ,Codimension ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,Continuation ,Ordinary differential equation ,family blow-up ,normal forms ,singular perturbation theory ,slow–fast Hopf point ,Limit (mathematics) ,0101 mathematics ,Analysis ,Saddle ,Mathematics - Abstract
In this paper we study birth of canards near a smooth slow–fast Hopf point of non-Lienard center type which plays an important role in slow–fast codimension 3 saddle and elliptic bifurcations. We show that the number of limit cycles created in the birth of canards in such a slow–fast non-Lienard case is finite. Our paper is also a natural continuation of Dumortier and Roussarie (Discrete Contin Dyn Syst Ser S 2(4):723–781, 2009) where slow–fast Hopf points of Lienard type have been studied. We use geometric singular perturbation theory and the family blow-up.
- Published
- 2018
38. Variational Problems Involving a Caputo-Type Fractional Derivative
- Author
-
Ricardo Almeida
- Subjects
Caputo-type fractional derivative ,Control and Optimization ,Generalization ,Mathematics::Classical Analysis and ODEs ,Mathematics::Optimization and Control ,Holonomic constraints ,Variational problems ,Systems and Control (eess.SY) ,Management Science and Operations Research ,Type (model theory) ,01 natural sciences ,Generalizations of the derivative ,FOS: Mathematics ,FOS: Electrical engineering, electronic engineering, information engineering ,Applied mathematics ,0101 mathematics ,Mathematics - Optimization and Control ,Mathematics ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Fractional calculus ,Order (ring theory) ,Function (mathematics) ,010101 applied mathematics ,Optimization and Control (math.OC) ,Computer Science - Systems and Control ,Calculus of variations - Abstract
The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo--Hadamard fractional derivatives, that are dependent on a real parameter ro. Sufficient and necessary conditions of the first and second order are presented. The cases of integral and holonomic constraints are also considered., Comment: This is a preprint of a paper whose final and definite form will be published in Journal of Optimization Theory and Applications
- Published
- 2017
39. Cross-Diffusion Systems for Image Processing: II. The Nonlinear Case
- Author
-
Adérito Araújo, Sílvia Barbeiro, Angel Durán, and Eduardo Cuesta
- Subjects
Statistics and Probability ,Lyapunov function ,010103 numerical & computational mathematics ,02 engineering and technology ,Positive-definite matrix ,01 natural sciences ,symbols.namesake ,Matrix (mathematics) ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Filtering problem ,Neumann boundary condition ,0101 mathematics ,Mathematics ,Partial differential equation ,Mathematical model ,94A08, 94A12, 68U10, 35K55, 35K61 ,Applied Mathematics ,Mathematical analysis ,Condensed Matter Physics ,Nonlinear system ,Modeling and Simulation ,symbols ,020201 artificial intelligence & image processing ,Geometry and Topology ,Computer Vision and Pattern Recognition ,Analysis of PDEs (math.AP) - Abstract
In this paper we study the application of $$2\times 2$$2×2 nonlinear cross-diffusion systems as mathematical models of image filtering. These are systems of two nonlinear, coupled partial differential equations of parabolic type. The nonlinearity and cross-diffusion character are provided by a nondiagonal matrix of diffusion coefficients that depends on the variables of the system. We prove the well-posedness of an initial-boundary-value problem with Neumann boundary conditions and uniformly positive definite cross-diffusion matrix. Under additional hypotheses on the coefficients, the models are shown to satisfy the scale-space properties of shift, contrast, average grey and translational invariances. The existence of Lyapunov functions and the asymptotic behaviour of the solutions are also studied. According to the choice of the cross-diffusion matrix (on the basis of the results on filtering with linear cross-diffusion, discussed by the authors in a companion paper and the use of edge stopping functions ) the performance of the models is compared by computational means in a filtering problem. The numerical results reveal differences in the evolution of the filtering as well as in the quality of edge detection given by one of the components of the system, in terms of the cross-diffusion matrix.
- Published
- 2017
40. Generalized Hammerstein Equations and Applications
- Author
-
John R. Graef, Lingju Kong, and Feliz Minhós
- Subjects
Applied Mathematics ,Hammerstein integral equation ,010102 general mathematics ,Mathematical analysis ,Order (ring theory) ,Function (mathematics) ,Krasnosel’skiĭ–Guo theorem ,01 natural sciences ,Integral equation ,Prime (order theory) ,010101 applied mathematics ,Combinatorics ,Nonlinear system ,Mathematics (miscellaneous) ,Discontinuous kernels ,Partial derivative ,Boundary value problem ,0101 mathematics ,Mathematics ,Variable (mathematics) - Abstract
In this paper the authors study the Hammerstein generalized integral equation $$\begin{aligned} u(t)=\int _{0}^{1}k(t,s)\text { }g(s)\text { }f(s,u(s),u^{\prime }(s),\dots ,u^{(m)}(s))\,ds, \end{aligned}$$ where $$k:[0,1]^{2}\rightarrow {\mathbb {R}}$$ are kernel functions, $$m\ge 1$$ , $$g:[0,1] \rightarrow [0,\infty )$$ , and $$f:[0,1]\times {\mathbb {R}}^{m+1} \rightarrow [0,\infty )$$ is a $$L^{\infty }-$$ Caratheodory function. The existence of solutions of integral equations has been studied in concrete and abstract cases, by different methods and techniques. However, in the existing literature, the nonlinearity depends only on the unknown function. This paper is one of a very few to consider equations having discontinuous nonlinearities that depend on the derivatives of the unknown function and having discontinuous kernels functions that have discontinuities in the partial derivatives with respect to their first variable. Our approach is based on the Krasnosel’skiĭ–Guo compression/expansion theorem on cones and it can be applied to boundary value problems of arbitrary order $$n>m$$ . The last two sections of the paper contain an application to a third order nonlinear boundary value problem and a concrete example.
- Published
- 2017
41. Topological and Statistical Methods for Complex Data : Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces
- Author
-
Janine Bennett, Fabien Vivodtzev, Valerio Pascucci, Janine Bennett, Fabien Vivodtzev, and Valerio Pascucci
- Subjects
- Topology, Mathematical analysis, Visualization
- Abstract
This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data.The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends.Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.
- Published
- 2015
42. On the existence of proper Nearly Kenmotsu manifolds
- Author
-
Piotr Dacko, I. Küpeli Erken, Cengizhan Murathan, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Erken, İrem Küpeli, Dacko, Piotr, Murathan, Cengizhan, ABE-8167-2020, and ABH-3658-2020
- Subjects
Mathematics - Differential Geometry ,Pure mathematics ,General Mathematics ,Kähler manifold ,01 natural sciences ,Warped Product ,Kaehler Manifold ,Sasakian Space Form ,Almost contact metric manifold ,0103 physical sciences ,FOS: Mathematics ,0101 mathematics ,Real line ,Mathematics::Symplectic Geometry ,Mathematics, applied ,Mathematics ,Mathematics::Complex Variables ,010102 general mathematics ,Mathematical analysis ,Mathematics::Geometric Topology ,Manifold ,Kenmotsu manifold ,Differential Geometry (math.DG) ,Nearly Kenmotsu manifold ,Product (mathematics) ,010307 mathematical physics ,Mathematics::Differential Geometry ,53C25, 53C55, 53D15 - Abstract
This is an expository paper, which provides a first approach to nearly Kenmotsu manifolds. The purpose of this paper is to focus on nearly Kenmotsu manifolds and get some new results from it. We prove that for a nearly Kenmotsu manifold is locally isometric to warped product of real line and nearly K\"ahler manifold. Finally, we prove that there exist no nearly Kenmotsu hypersurface of nearly K\"ahler manifold. It is shown that a normal nearly Kenmotsu manifold is Kenmotsu manifold.
- Published
- 2016
43. Generalized convolution quadrature based on Runge-Kutta methods
- Author
-
María López-Fernández, Stefan A. Sauter, University of Zurich, and Lopez-Fernandez, Maria
- Subjects
Overlap–add method ,Discretization ,65R20 ,010103 numerical & computational mathematics ,65L06 ,Convolution power ,01 natural sciences ,65M15 ,65M38 ,applied mathematics ,computational mathematics ,Mathematics::Numerical Analysis ,510 Mathematics ,2604 Applied Mathematics ,0101 mathematics ,Convolution theorem ,Mathematics ,Physics::Computational Physics ,Summation by parts ,Mathematical analysis ,Computer Science::Numerical Analysis ,Circular convolution ,Quadrature (mathematics) ,010101 applied mathematics ,10123 Institute of Mathematics ,Runge–Kutta methods ,2605 Computational Mathematics - Abstract
In this paper, we develop the Runge-Kutta generalized convolution quadrature with variable time stepping for the numerical solution of convolution equations for time and space-time problems and present the corresponding stability and convergence analysis. For this purpose, some new theoretical tools such as tensorial divided differences, summation by parts with Runge-Kutta differences and a calculus for Runge-Kutta discretizations of generalized convolution operators such as an associativity property will be developed in this paper. Numerical examples will illustrate the stable and efficient behavior of the resulting discretization.
- Published
- 2016
44. Non-smooth Atomic Decompositions for Generalized Orlicz-Morrey Spaces of the Third Kind
- Author
-
Sabir G. Hasanov, Yoshihiro Sawano, Vagif S. Guliyev, Takahiro Noi, and Kırşehir Ahi Evran Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
- Subjects
Mathematics::Functional Analysis ,Partial differential equation ,Maximal operators ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Mathematics::Classical Analysis and ODEs ,Predual ,Orlicz-Morrey spaces ,Non smooth ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,Atomic decomposition ,Operator (computer programming) ,Maximal operator ,Decomposition method (constraint satisfaction) ,0101 mathematics ,Mathematics - Abstract
WOS: 000382700200006 We deal with the generalized Orlicz-Morrey space of the third kind and consider the decomposition method. Also we characterize its predual space. Some maximal estimates for generalized Orlicz-Morrey spaces of the third kind are also obtained by using the weighted Hardy operators. As an application, we consider the Olsen inequality, which is a bilinear estimate on the fractional integral operator. As an appendix, we consider a general form of the vector-valued boundedness of the Hardy-Littlewood maximal operator, where in the definition of depends on as well. This paper contains a remedy for the mistake in the proof of the Olsen inequality of the 2014 paper by the second author (Iida et al. in Z. Anal. Anwend. 33(2):149-170, 2014). Science Development Foundation under the President of the Republic of AzerbaijanScience Development Foundation (SDF) - Azerbaijan [EIF-2013-9(15)-46/10/1]; Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS) The research of V. Guliyev was partially supported by the grant of Science Development Foundation under the President of the Republic of Azerbaijan, Grant EIF-2013-9(15)-46/10/1 and by the grant of Presidium Azerbaijan National Academy of Science 2015. This paper is written during the stay of Y. Sawano in Ahi Evran University. Y. Sawano is thankful to Ahi Evran University for this support of the stay there. Y. Sawano is thankful to Professor Jie Xiao for his pointing out that (7.18) is correct under some restricted conditions. The authors are thankful to Professor Mitsuo Izuki at Okayama University for his careful reading of the manuscript.
- Published
- 2016
45. Finite and infinitesimal flexibility of semidiscrete surfaces
- Author
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Oleg Karpenkov
- Subjects
Surface (mathematics) ,Flexibility (engineering) ,Mathematics - Differential Geometry ,Degree (graph theory) ,General Mathematics ,Infinitesimal ,Mathematical analysis ,Functional Analysis (math.FA) ,Mathematics::Numerical Analysis ,Mathematics - Functional Analysis ,52C25 ,Differential Geometry (math.DG) ,System of differential equations ,FOS: Mathematics ,QA ,Mathematics - Abstract
In this paper we study infinitesimal and finite flexibility for generic semidiscrete surfaces. We prove that generic 2-ribbon semidiscrete surfaces have one degree of infinitesimal and finite flexibility. In particular we write down a system of differential equations describing isometric deformations in the case of existence. Further we find a necessary condition of 3-ribbon infinitesimal flexibility. For an arbitrary $n\ge 3$ we prove that every generic $n$-ribbon surface has at most one degree of finite/infinitesimal flexibility. Finally, we discuss the relation between general semidiscrete surface flexibility and 3-ribbon subsurface flexibility. We conclude this paper with one surprising property of isometric deformations of developable semidiscrete surfaces.
- Published
- 2015
46. Multivariate copulas with given values at two arbitrary points
- Author
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Damjana Kokol Bukovšek, Erich Peter Klement, Susanne Saminger-Platz, Nik Stopar, and Matjaž Omladič
- Subjects
Statistics and Probability ,quasi-copula ,matematične metode ,mathematics ,multivariate distribution ,matematika ,matematična analiza ,mathematical methods ,copula ,Statistics, Probability and Uncertainty ,bounds ,udc:51 ,mathematical analysis - Abstract
Copulas are functions that link an n-dimensional distribution function with its one-dimensional margins. In this contribution we show how n-variate copulas with given values at two arbitrary points can be constructed. Thereby, we also answer a so far open question whether lower and upper bounds for n-variate copulas with given value at a single arbitrary point are achieved. We also introduce and discuss the concept of an $$\mathbf{F}$$ F -copula which is needed for proving our results.
- Published
- 2023
47. A remark on the computation of the gravitational potential of masses with linearly varying density
- Author
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Maria Grazia D'Urso
- Subjects
Physics ,Computation ,Mathematical analysis ,Null (mathematics) ,Surface integral ,Divergence theorem ,Linear density variation ,Gravitational potential ,Volume integral ,Classical mechanics ,Gravitational singularity ,Density contrast ,Singularities ,Polyhedron ,Settore ICAR/06 - Topografia e Cartografia - Abstract
The potential of a polyhedral body with linearly varying density has been given two different expressions in Holstein (Geophysics 68:157–167, 2003) and Hamayun et al. (J Geodesy 83:1163–1170, 2009) although in both papers the derivation is started from the same surface integral obtained by transforming the original volume integral via the Gauss theorem. Conversely, we prove that a suitable modification of the approach exploited by Hamayun et al. (J Geodesy 83:1163–1170, 2009) yields the formula derived by Holstein (Geophysics 68:157–167, 2003). Furthermore, an additional expression of the surface integral, which is also proved in this paper, allows us to derive a variant of the linear part of the potential, i.e. the integral multiplying the gradient of the density contrast, which filters the null contribution of faces containing the observation point. The new formula is specialized to the case of a prism.
- Published
- 2015
48. Analysis of an Augmented HDG Method for a Class of Quasi-Newtonian Stokes Flows
- Author
-
Filánder A. Sequeira and Gabriel N. Gatica
- Subjects
GALERKIN METHOD ,Numerical Analysis ,GALERKIN DISCONTINUO HIBRIDABLE (HDG) ,Applied Mathematics ,Mathematical analysis ,Linear system ,General Engineering ,Mixed finite element method ,Finite element method ,Theoretical Computer Science ,Computational Mathematics ,Nonlinear system ,Computational Theory and Mathematics ,Rate of convergence ,Discontinuous Galerkin method ,MIXED FINITE ELEMENT METHOD ,Nonlinear functional analysis ,Reduction (mathematics) ,Software ,Mathematics - Abstract
In this paper we introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for numerically solving a class of nonlinear Stokes models arising in quasi-Newtonian fluids. Similarly as in previous papers dealing with the application of mixed finite element methods to these nonlinear models, we use the incompressibility condition to eliminate the pressure, and set the velocity gradient as an auxiliary unknown. In addition, we enrich the HDG formulation with two suitable augmented equations, which allows us to apply known results from nonlinear functional analysis, namely a nonlinear version of Babuka-Brezzi theory and the classical Banach fixed-point theorem, to prove that the discrete scheme is well-posed and derive the corresponding a priori error estimates. Then we discuss some general aspects concerning the computational implementation of the method, which show a significant reduction of the size of the linear systems involved in the Newton iterations. Finally, we provide several numerical results illustrating the good performance of the proposed scheme and confirming the optimal order of convergence provided by the HDG approximation. En este artículo presentamos y analizamos un método de Galerkin discontinuo hibridable (HDG) para resolver numéricamente una clase de modelos de Stokes no lineales que surgen en fluidos cuasi-newtonianos. De manera similar, como en artículos anteriores que tratan sobre la aplicación de métodos mixtos de elementos finitos a estos modelos no lineales, usamos la condición de incompresibilidad para eliminar la presión y establecemos el gradiente de velocidad como una incógnita auxiliar. Además, enriquecemos la formulación HDG con dos ecuaciones aumentadas adecuadas, lo que nos permite aplicar los resultados conocidos del análisis funcional no lineal, a saber, una versión no lineal de la teoría de Babuka-Brezzi y el teorema clásico del punto fijo de Banach, para demostrar que el esquema discreto está bien planteada y derivar las correspondientes estimaciones de error a priori. Luego discutimos algunos aspectos generales relacionados con la implementación computacional del método, que muestran una reducción significativa del tamaño de los sistemas lineales involucrados en las iteraciones de Newton. Finalmente, proporcionamos varios resultados numéricos que ilustran el buen desempeño del esquema propuesto y confirman el orden óptimo de convergencia proporcionado por la aproximación HDG. Universidad Nacional, Costa Rica Escuela de Matemática
- Published
- 2015
49. A dichotomy in area-preserving reversible maps
- Author
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Mário Bessa and Alexandre A. P. Rodrigues
- Subjects
Pure mathematics ,Conjecture ,Closed manifold ,Dense set ,Closing Lemma ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Perturbation (astronomy) ,01 natural sciences ,Reversing symmetry ,Elliptic point ,0103 physical sciences ,Discrete Mathematics and Combinatorics ,Periodic orbits ,Area-preserving map ,010307 mathematical physics ,0101 mathematics ,Mathematics - Abstract
In this paper we study R-reversible area-preserving maps f : M → M on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that R ◦ f = f−1 ◦ R where R: M → M is an isometric involution. We obtain a C1-residual subset where any map inside it is Anosov or else has a dense set of elliptic periodic orbits, thus establishing the stability conjecture in this setting. Along the paper we derive the C1-Closing Lemma for reversible maps and other perturbation toolboxes. info:eu-repo/semantics/publishedVersion
- Published
- 2015
50. Acceleration of shape optimization analysis using model order reduction by Karhunen-Loève expansion
- Author
-
Hideyuki Azegami and Shuichi Tango
- Subjects
Karhunen–Loève theorem ,Model order reduction ,Acceleration ,Applied Mathematics ,Mathematical analysis ,General Engineering ,Shape optimization ,Mathematics - Abstract
This paper presents a method to reduce the computational time required to solve shape optimization problems. A volume minimization problem under the mean compliance constraint is chosen as an example of the shape optimization problem. To solve this problem, an iterative algorithm based on the H^1 gradient method is considered as a conventional approach. In this study, we attempt to use a method of model order reduction for solving the linear elasticity problem based on the idea by Karhunen-Loève expansion (KLE). We consider the displacements obtained by the conventional method to be sampling data of a random variable; the orthonormal bases of KLE are defined as eigenfunctions of the eigenvalue problem obtained as the optimality condition of the variance maximization problem for the random variable. The feasibility of the proposed method is illustrated by testing the numerical scheme to a linear elastic body of the connecting rod type.
- Published
- 2022
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