{"title":"Takashi Suzuki","description":null,"products":[{"product_id":"romance-of-engines-book-takashi-suzuki-9781560919117","title":"The Romance of Engines","description":"This book examines the development of the engine from a historical perspective. Originally published in Japanese, The Romance of Engines' English translation offers readers insight into lessons learned throughout the engine's history. This book belongs on the bookshelves of all engine designers, engine enthusiasts, and automotive historians. Topics covered include: Newcomen's Steam Engine The Watt Steam Engine Internal Combustion Engine Nicolaus August Otto and His Engine Sadi Carnot and the Adiabatic Engine Radial Engines; Piston and Cylinder Problems Engine Life Problem of Cooling Engine Compartments Knocking; Energy Conservation Bugatti; Volkswagon Rolls Royce Packard Daimler-Benz DB601 Engine and more!","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50554648822033,"sku":"GOR005523916","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51036977627409,"sku":"NIN9781560919117","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ GOOD \/ SBYB","offer_id":51848304722193,"sku":"CIN1560919116G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52142910472465,"sku":"NLS9781560919117","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":53626083246353,"sku":"CIN1560919116VG","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1560919116.jpg?v=1751244997"},{"product_id":"chemotaxis-reaction-network-mathematics-for-self-organization-book-takashi-suzuki-9789813237735","title":"Chemotaxis, Reaction, Network: Mathematics For Self-organization","description":"This monograph is devoted to recent mathematical theories on the bottom up self-organization observed in closed and isolated thermo-dynamical systems. Its main features include:","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51067019067665,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51067021394193,"sku":"NIN9789813237735","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":51915551047953,"sku":"CIN9813237732VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52532467859729,"sku":"NLS9789813237735","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9813237732.jpg?v=1751287157"},{"product_id":"methods-of-geometry-in-the-theory-of-partial-differential-equations-principle-of-book-takashi-suzuki-9789811287893","title":"Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities","description":"Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena.In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years, several principles that ensure these successes are discovered very recently.This monograph focuses on one of them: cancellation of singularities derived from interactions of multiple species, which is described by the language of geometry, in particular, that of global analysis.Five objects of inquiry, scattered across different disciplines, are selected in this monograph: evolution of geometric quantities, models of multi-species in biology, interface vanishing of d - δ systems, the fundamental equation of electro-magnetic theory, and free boundaries arising in engineering.The relaxation of internal tensions in these systems, however, is described commonly by differential forms, and the reader will be convinced of further applications of this principle to other areas.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51067986379025,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51067987296529,"sku":"NIN9789811287893","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52615420870929,"sku":"NLS9789811287893","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9811287899.jpg?v=1751129640"},{"product_id":"mathematical-methods-for-cancer-evolution-book-takashi-suzuki-9789811036705","title":"Mathematical Methods for Cancer Evolution","description":"The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51068195012881,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51068195635473,"sku":"NIN9789811036705","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52404031979793,"sku":"NLS9789811036705","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9811036705.jpg?v=1750840113"},{"product_id":"applied-analysis-mathematical-methods-in-natural-science-2nd-edition-book-takashi-suzuki-9781848166523","title":"Applied Analysis: Mathematical Methods In Natural Science (2nd Edition)","description":"This book provides a general introduction to applied analysis; vector analysis with physical motivation, calculus of variation, Fourier analysis, eigenfunction expansion, distribution, and so forth, including a catalogue of mathematical theories, such as basic analysis, topological spaces, complex function theory, real analysis, and abstract analysis. This book also uses fundamental ideas of applied mathematics to discuss recent developments in nonlinear science, such as mathematical modeling of reinforced random motion of particles, semiconductor device equation in applied physics, and chemotaxis in biology. Several tools in linear PDE theory, such as fundamental solutions, Perron's method, layer potentials, and iteration scheme, are described, as well as systematic descriptions on the recent study of the blowup of the solution.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51136582189329,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51136584220945,"sku":"NIN9781848166523","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52663981277457,"sku":"NLS9781848166523","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1848166524.jpg?v=1750866207"},{"product_id":"semilinear-elliptic-equations-book-takashi-suzuki-9783110555356","title":"Semilinear Elliptic Equations","description":"This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51187738706193,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51187740934417,"sku":"NIN9783110555356","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52351297290513,"sku":"NLS9783110555356","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3110555352.jpg?v=1750902628"},{"product_id":"applied-analysis-mathematics-for-science-technology-engineering-third-edition-book-takashi-suzuki-9789811257353","title":"Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition)","description":"This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the integration of ODEs, inverse Strum Liouville problems, interface vanishing of the Maxwell system, method of gradient inequality, diffusion geometry, mathematical oncology. Several descriptions on the analysis of Smoluchowski-Poisson equation in two space dimension are corrected and extended, to ensure quantized blowup mechanism of this model, particularly, the residual vanishing both in blowup solution in finite time with possible collision of sub-collapses and blowup solutions in infinite time without it.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51294520344849,"sku":"NIN9789811257353","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52451250340113,"sku":"NLS9789811257353","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9811257353.jpg?v=1750936252"},{"product_id":"arthurian-and-other-studies-presented-to-shunichi-noguchi-book-tadao-kubouchi-9780859913805","title":"Arthurian and Other Studies presented to Shunichi Noguchi","description":"These essays for Shunichi Noguchi, by scholars from Britain, the USA and Japan, reflect his approach to English studies and his wide range of interests from Beowulf to Ulysses. The principal focus, however, is on medieval and renaissance studies: nine of the essays are on Arthurian themes, to which Professor Noguchi has devoted his academic life. There are also essays on Beowulf, Chaucer, the York miracle plays, and Shakespeare, as well as textual studies of Gower, Wulfstan, Wycliffe and Caxton. Contributors: SHUICHI AITA, SHINSUKE ANDO, DEREK BREWER, ANTONY DICKINSON, P.J.C. FIELD, KAZUO FUKUDA, EICHI HAYAKAWA, TADAHIRO IKEGAMI, MIKIKO ISHI, SOUJIWASAKI, GREGORY K. JEMBER, TOMOMI KATO, EDWARD DONALD KENEDY, TADAO KUBOUCHI, JOHN LAWLOR, KIYOKAZU MIZOBATA, GEORGE MOR, TSUYOSHI MUKAI, YUJI NAKAO, FUMIKO OKA, YUZUYO OKUMURA, ISAMU SAITO, SHIRO SHIBA, JAN SIMKO, JUN SUDO, TAKASHI SUZUKI, TOSHIYUKI TAKAMIYA, RAYMOND P. TRIP.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52336204316945,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52336204906769,"sku":"NLS9780859913805","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780859913805.jpg?v=1758162565"},{"product_id":"methods-of-mathematical-oncology-book-takashi-suzuki-9789811648687","title":"Methods of Mathematical Oncology","description":"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.\u003cbr\u003eMathematics 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.\u003cbr\u003eThe 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.\u003cbr\u003e\u003cbr\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52353468039441,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52353468760337,"sku":"NLS9789811648687","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789811648687.jpg?v=1758182944"},{"product_id":"mathematical-modeling-and-data-science-for-biology-and-medicine-book-takashi-suzuki-9783725846474","title":"Mathematical Modeling and Data Science for Biology and Medicine","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52477285466385,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52477287334161,"sku":"NLS9783725846474","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783725846474.jpg?v=1759845374"},{"product_id":"mean-field-theories-and-dual-variation-mathematical-structures-of-the-mesoscopic-book-takashi-suzuki-9789462391536","title":"Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model","description":"Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52489170092305,"sku":"NLS9789462391536","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789462391536.jpg?v=1759878277"},{"product_id":"methods-of-mathematical-oncology-book-takashi-suzuki-9789811648656","title":"Methods of Mathematical Oncology","description":"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.\u003cbr\u003eMathematics 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.\u003cbr\u003eThe 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.\u003cbr\u003e\u003cbr\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52532280033553,"sku":"NLS9789811648656","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789811648656.jpg?v=1760660197"},{"product_id":"applied-analysis-mathematics-for-science-technology-engineering-third-edition-book-takashi-suzuki-9789819820399","title":"Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition)","description":"This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the integration of ODEs, inverse Strum Liouville problems, interface vanishing of the Maxwell system, method of gradient inequality, diffusion geometry, mathematical oncology. Several descriptions on the analysis of Smoluchowski-Poisson equation in two space dimension are corrected and extended, to ensure quantized blowup mechanism of this model, particularly, the residual vanishing both in blowup solution in finite time with possible collision of sub-collapses and blowup solutions in infinite time without it.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52536833245457,"sku":"NLS9789819820399","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819820399.jpg?v=1760675872"},{"product_id":"free-energy-and-self-interacting-particles-book-takashi-suzuki-9780817643027","title":"Free Energy and Self-Interacting Particles","description":"This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this system of equations describes the motion of a mean ?eld of many particles, interacting under the gravitational inner force or the chemical reaction, and therefore this system is af?liated with a hierarchy of equations: Langevin, Fokker-Planck, Liouville-Gel'fand, and the gradient ?ow. All of the equations are subject to the second law of thermodynamics - the decrease of free energy. The mat- matical principle of this hierarchy, on the other hand, is referred to as the qu- tized blowup mechanism; the blowup solution of our system develops delta function singularities with the quantized mass.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52589903380753,"sku":"NLS9780817643027","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":53626133709073,"sku":"NGR9780817643027","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780817643027.jpg?v=1761061023"},{"product_id":"fundamentals-of-general-equilibrium-analysis-book-takashi-suzuki-9789811219610","title":"Fundamentals Of General Equilibrium Analysis","description":"The aim of this book is to incorporate Marshallian ideas such as external increasing returns and monopolistic competitions into the general equilibrium framework of Walrasian tradition. New chapters and sections have been added to this revised and expanded edition of General Equilibrium Analysis of Production and Increasing Returns (World Scientific, 2009).The new material includes a presentation of equilibrium existence and core equivalence theorems for an infinite horizon economy with a measure space of consumers. These results are currently the focus of extensive studies by mathematical theorists, and are obtained by an application of an advanced mathematical concept called saturated (super-atomless) measure space.The second major change is the inclusion of a simple toy model of a liberal society which implements the difference principle proposed by J Rawls as a principle of distributive justice. This new section opens up a possibility to connect theoretical economics and political philosophy.Thirdly, the author presents the marginal cost pricing equilibrium and discusses welfare properties of the external increasing returns, which also belong to Marshall\/ Pigou tradition of the Cambridge school.Finally, a new mathematical appendix treats basics of singular homology theory. Although the fixed point theorem is originally a theorem of algebraic topology, most economic students know its proof only in the context of the differentiable manifold theory presented by J Milnor. Considering the significance of the fixed point theorem and its playing a key role in general equilibrium theory, the purpose of this new appendix is to provide readers with the idea of a proof of Brower's fixed point theorem from the \"right place\".This volume will be helpful for graduate students and researchers of mathematical economics, game theory, and microeconomics.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52668364390673,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52668365275409,"sku":"NLS9789811219610","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789811219610.jpg?v=1762284832"},{"product_id":"general-equilibrium-analysis-of-production-and-increasing-returns-book-takashi-suzuki-9789812833310","title":"General Equilibrium Analysis Of Production And Increasing Returns","description":"The scope of the general equilibrium (GE) theory has so far been limited to the Walrasian tradition. Indeed, the theories of competitive equilibria and the core are nothing but the modern mathematical analysis of the economic ideas due to Walras, Edgeworth and Pareto. Consequently, recent books in this field are inclined to be heavily technical and mathematical.On the other hand, the modern GE theory has not completed the study of increasing returns and monopolistic competition, which belong to the alternative important stream of economic thought, namely the Marshallian tradition. This book aims to fill this gap, by proving the existence of a competitive equilibrium with increasing returns coming from externalities in a dynamic economy and a monopolistically competitive equilibrium with the technologies exhibiting increasing returns coming from a large set-up cost. Also intended as a basic graduate textbook on GE theory, it contains all the basic results and mathematical techniques in this field, such as measure theory, manifold theory and Banach space theory.A unique feature of the book compared to classical monographs on GE is its emphasis on the historical nature of the subject, and not only the mathematical nature. Students are expected to learn that those mathematically formidable techniques are indeed necessary for tackling many economic problems which have been significant not only in the mathematical or technical context, but also in the historical and traditional context.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52674066284817,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52674066874641,"sku":"NLS9789812833310","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789812833310.jpg?v=1762298661"},{"product_id":"liouvilles-theory-in-linear-and-nonlinear-partial-differential-equations-book-takashi-suzuki-9789819519743","title":"Liouville’s Theory in Linear and Nonlinear Partial Differential Equations","description":"A variety of theorems named the Liouville property play fundamental roles in modern theory of mathematical analysis. Understanding each of them individually is not so difficult nowadays. What are they pointing toward in their totality, however? This monograph asserts that self-organization may be an answer, searching recent studies on linear and nonlinear partial differential equations. Critical breakthroughs have emerged in accordance with the widely spread classical ideas of J. Liouville in various forms, that is, the spectral, elliptic, surface, and transport theories, in turn. A fusion of them is seen in recently developing research fields--mathematical oncology, non-equilibrium statistical mechanics, dynamical theory, and shape optimization--which taken together may be called the potential for self-organization.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52820863189265,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52820863975697,"sku":"NLS9789819519743","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819519743.jpg?v=1764330738"},{"product_id":"mean-field-theories-and-dual-variation-a-mathematical-profile-emerged-in-the-non-book-takashi-suzuki-9789078677147","title":"Mean Field Theories And Dual Variation: A Mathematical Profile Emerged In The Nonlinear Hierarchy","description":"A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of duality according to the PDE weak solutions and hierarchy for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":53213717070097,"sku":"NLS9789078677147","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789078677147.jpg?v=1772756813"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-takashi-suzuki.oembed","provider":"World of Books ","version":"1.0","type":"link"}