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Without the mathematics of division, humankind cannot function…  Marie Antoinette, Queen of France (infamously) said “If people have no bread, let them eat cake,” and while Ahmes ― the scribe of the Rhind Mathematical Papyrus ― dealt with loaves of bread, prosperous people in the twentieth century dealt with cake division, although bread is also uniformly available. You’ll be surprised, but there are at least four books and over 200 scientific (not gastronomical!) papers on cake division. Those authors were not overly concerned with obesity, one can guess, but whether distributing loaves, cakes, chores, or dividends, one needs to master division.  This book deals with a wide spectrum of division problems, and provides the historical background, giving a sense of how pervasive division is in our lives. In particular, the second part focuses on a problem that remained open until 1985, when Professor Robert John Aumann (Nobel laureate in Economics, 2005) and Professor Michael Maschler solved it using game-theoretic techniques. Simple alternative solutions are given, which are suitable for high schools and other educational institutions.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49748304232721,"sku":"NGR9783031404184","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51061865939217,"sku":"NIN9783031404184","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52585119187217,"sku":"NLS9783031404184","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3031404181.jpg?v=1751425377"},{"product_id":"finite-element-methods-for-structures-with-large-stochastic-variations-book-isaac-elishakoff-9780198526315","title":"Finite Element Methods for Structures with Large Stochastic Variations","description":"The finite element method (FEM) can be successfully applied to various field problems in solid mechanics, fluid mechanics and electrical engineering. FEM is a numerical method widely used in computer aided engineering, which allows for modelling and analysis of engineering and mathematical problems, e.g. safety testing. This reference text is the first to discuss finite element methods for structures with large stochastic variations. Stochastic variations are those that follow a random probability distribution or pattern and whose behaviour may be analysed statistically but not predicted precisely. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will find this a very useful reference. This book is the latest in the Oxford Texts in Applied and Engineering Mathematics series, which includes texts based on taught courses that explain the mathematical or computational techniques required for the resolution of fundamental applied problems, from the undergraduate through to the graduate level. Other books in the series include: Jordan and Smith: Nonlinear Ordinary Differential Equations: an introduction to dynamical systems; Sobey: Introduction to Interactive Boundary Layer Theory; Scott: Nonlinear Science: emergence and dynamics of coherent structures; Tayler: Mathematical Models in Applied Mechanics; Ram-Mohan: Finite Element and Boundary Element Applications in Quantum Mechanics.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50467302506769,"sku":"CIN0198526318VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51089262084369,"sku":"NIN9780198526315","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52342978707729,"sku":"NLS9780198526315","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0198526318.jpg?v=1751100989"},{"product_id":"multifaceted-uncertainty-quantification-book-isaac-elishakoff-9783111354217","title":"Multifaceted Uncertainty Quantification","description":"The book exposes three alternative and competing approaches to uncertainty analysis in engineering. It is composed of some essays on various sub-topics like random vibrations, probabilistic reliability, fuzzy-sets-based analysis, unknown-but-bounded variables, stochastic linearization, possible difficulties with stochastic analysis of structures.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51064171954449,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51064174412049,"sku":"NIN9783111354217","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3111354210.jpg?v=1751350497"},{"product_id":"nondeterministic-mechanics-book-isaac-elishakoff-9783709113059","title":"Nondeterministic Mechanics","description":"Table of contents: Stochastic methods in nonlinear structural dynamics.- Stochastic models of uncertainties in computational structural dynamics and structural acoustics.- The tale of stochastic linearization techniques: over half a century of progress.- Comprehensive modeling of uncertain systems using fuzzy set theory.- Bounding uncertainty in civil engineering: theoretical background and applications.- Combined methods in nondeterministic mechanics.  In this book the current state of the art of nondeterministic mechanics in its various forms is presented. The topics range from stochastic problems to fuzzy sets; from linear to nonlinear problems; from specific methodologies to combinations of various techniques; from theoretical considerations to practical applications. It is specially designed to illuminate the various aspects of the three methodologies (probabilistic or stochastic modelling, fuzzy sets based analysis, antioptimization of structures) to deal with various uncertainties  and deepen the discussion of their pros and cons.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52136412184849,"sku":"NLS9783709113059","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783709113059.jpg?v=1757553922"},{"product_id":"fair-share-book-isaac-elishakoff-9783031404214","title":"Fair Share","description":"Kofi Annan, former Secretary General of the United Nations, argued that “We need to create a world that is equitable, that is stable and a world where we bear in mind the needs of others, and not only what we need immediately. We are all in the same boat.”American businessman, John Landgraf stated: “I hope that most of us believe that we actually would all benefit from living in a more equitable society. If that's not happening, we're squandering human potential.” For the world to be fair, one needs to know how to divide. Without the mathematics of division, humankind cannot function…  Marie Antoinette, Queen of France (infamously) said “If people have no bread, let them eat cake,” and while Ahmes ― the scribe of the Rhind Mathematical Papyrus ― dealt with loaves of bread, prosperous people in the twentieth century dealt with cake division, although bread is also uniformly available. You’ll be surprised, but there are at least four books and over 200 scientific (not gastronomical!) papers on cake division. Those authors were not overly concerned with obesity, one can guess, but whether distributing loaves, cakes, chores, or dividends, one needs to master division.  This book deals with a wide spectrum of division problems, and provides the historical background, giving a sense of how pervasive division is in our lives. In particular, the second part focuses on a problem that remained open until 1985, when Professor Robert John Aumann (Nobel laureate in Economics, 2005) and Professor Michael Maschler solved it using game-theoretic techniques. Simple alternative solutions are given, which are suitable for high schools and other educational institutions.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":52153153126673,"sku":"NGR9783031404214","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031404214.jpg?v=1757619084"},{"product_id":"non-classical-problems-in-the-theory-of-elastic-stability-book-isaac-elishakoff-9780521020107","title":"Non-Classical Problems in the Theory of Elastic Stability","description":"When a structure is put under an increasing compressive load, it becomes unstable and buckling occurs. Buckling is a particularly significant concern in designing shell structures such as aircraft, automobiles, ships, or bridges. This book discusses stability analysis and buckling problems and offers practical tools for dealing with uncertainties that exist in real systems. The techniques are based on two complementary theories which are developed in the text. First, the probabilistic theory of stability is presented, with particular emphasis on reliability. Both theoretical and computational issues are discussed.  Secondly, the authors present the alternative to probability based on the notion of 'anti-optimization', a theory that is valid when the necessary information for probabilistic analysis is absent, that is, when only scant data are available. Design engineers, researchers, and graduate students in aerospace, mechanical, marine, and civil engineering who are concerned with issues of structural integrity will find this book a useful reference source.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52332633456913,"sku":"NLS9780521020107","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52735504711953,"sku":"NIN9780521020107","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521020107.jpg?v=1758152247"},{"product_id":"nondeterministic-mechanics-book-isaac-elishakoff-9783709116708","title":"Nondeterministic Mechanics","description":"Table of contents: Stochastic methods in nonlinear structural dynamics.- Stochastic models of uncertainties in computational structural dynamics and structural acoustics.- The tale of stochastic linearization techniques: over half a century of progress.- Comprehensive modeling of uncertain systems using fuzzy set theory.- Bounding uncertainty in civil engineering: theoretical background and applications.- Combined methods in nondeterministic mechanics.  In this book the current state of the art of nondeterministic mechanics in its various forms is presented. The topics range from stochastic problems to fuzzy sets; from linear to nonlinear problems; from specific methodologies to combinations of various techniques; from theoretical considerations to practical applications. It is specially designed to illuminate the various aspects of the three methodologies (probabilistic or stochastic modelling, fuzzy sets based analysis, antioptimization of structures) to deal with various uncertainties  and deepen the discussion of their pros and cons.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52407378837777,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52407379558673,"sku":"NLS9783709116708","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783709116708.jpg?v=1758772076"},{"product_id":"philosophies-of-structural-safety-and-reliability-book-isaac-elishakoff-9781032209302","title":"Philosophies of Structural Safety and Reliability","description":"Uncertainty is certain to be found in structural engineering, making it crucial to structure design. This book covers three competing philosophies behind structural safety and reliability: probabilistic analysis, fuzzy-sets based treatments, and the convex approach.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52448092619025,"sku":"NLS9781032209302","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53656527700241,"sku":"NIN9781032209302","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781032209302.jpg?v=1759271450"},{"product_id":"whys-and-hows-in-uncertainty-modelling-book-isaac-elishakoff-9783709125038","title":"Whys and Hows in Uncertainty Modelling","description":"This book presents, as a single package, three semingly contradictory and often competitive approaches to deal with ever present uncertainty in science and engineering. The book describes, as a unique view, probabilistic, fuzzy sets based and antioptimization based approaches, in order to remedy the present tower ob Babel situation, in which researchers in competing fields do not communicate. Integrative approach will attract scientists and engineers alike and provide a strong impetus towards integrative, hybrid approaches.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52454680199441,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52454680690961,"sku":"NLS9783709125038","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783709125038.jpg?v=1759371901"},{"product_id":"mechanical-vibration-where-do-we-stand-book-isaac-elishakoff-9783211998946","title":"Mechanical Vibration: Where Do We Stand?","description":"''There is always a delightful sense of movement, vibration and life\"\". Theodore Robinson (1852-1896) \"\/ have never solved a major mechanical or interpretive problem at the keyboard. I have always solved it in my mind\". Jorge Bolet (1914-1990) The idea of this book stems from the realization that scientists, not unlike laymen, should occasionally interrupt their regular work and reflect on the past, to see both the accomplishments and the drawbacks, so as to be able to plan for future research in the \"proper\" perspective. But an inquisitive reader may ask: Can one really document in any field, let alone mechanical vibrations (whose very name signifies change), ''where do we stand\"? Did not a Greek philosopher famously claim that one cannot enter a river twice? Another, on an even more sophisticated note, added that actually it is impossible to enter a river even once! For in the process of entering, both entrant and river change. Likewise, one can argue that it is nearly impossible to answer the question posed in the title of this volume. But experience shows, despite the sage observations of the philosophers, that one does enter a river, lake, sea, or ocean. Likewise, scientists do stop (if not for a minute, for a conference) to reflect on the past, and if not in its detail, then at least in big strokes on various topics presented by the participants; questions by the listeners often change the research direction of the presenter.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52455581122833,"sku":"NLS9783211998946","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52932495311121,"sku":"NIN9783211998946","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783211998946.jpg?v=1759374723"},{"product_id":"safety-factors-and-reliability-friends-or-foes-book-isaac-elishakoff-9789048165001","title":"Safety Factors and Reliability: Friends or Foes?","description":"Have you ever wondered where the safety factors come from? Why  is it that deterministic analysis has reached a very sophisticated  level, but in the end empirical factors are still needed? Is there a  way to select them, rather than assigning them arbitrarily as is often  done?    This book clearly shows that safety factors are closely related with  the reliability of structures, giving yet another demonstration of  Albert Einstein's maxim that \"It is incomprehensible that Nature is  comprehensible\". The book shows that the safety factors are much more  comprehensible if they are seen in a probabilistic context. Several  definitions of the safety factors are given, analytical results on  insightful numbers are presented, nonprobabilistic safety factors are  shown, as well as their estimates derived by the inequalities of  Bienayme, Markov, Chebushev and Camp-Meidell. A special chapter is  devoted to important contributions by Japanese experts.    This volume will help to critically re-think the issue of safety  factors, which can create a false feeling of security. The  deterministic paradigm can be enhanced by incorporating probabilistic  concepts wisely where they are needed without treating all variables  as probabilistic ones. The book shows that there is a need of their  integration rather than separation.    This book is intended for engineers, graduate students, lecturers and  researchers.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52475878965521,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52475879981329,"sku":"NLS9789048165001","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789048165001.jpg?v=1759843203"},{"product_id":"safety-factors-and-reliability-friends-or-foes-book-isaac-elishakoff-9781402017797","title":"Safety Factors and Reliability: Friends or Foes?","description":"Have you ever wondered where the safety factors come from? Why  is it that deterministic analysis has reached a very sophisticated  level, but in the end empirical factors are still needed? Is there a  way to select them, rather than assigning them arbitrarily as is often  done?    This book clearly shows that safety factors are closely related with  the reliability of structures, giving yet another demonstration of  Albert Einstein's maxim that \"It is incomprehensible that Nature is  comprehensible\". The book shows that the safety factors are much more  comprehensible if they are seen in a probabilistic context. Several  definitions of the safety factors are given, analytical results on  insightful numbers are presented, nonprobabilistic safety factors are  shown, as well as their estimates derived by the inequalities of  Bienayme, Markov, Chebushev and Camp-Meidell. A special chapter is  devoted to important contributions by Japanese experts.    This volume will help to critically re-think the issue of safety  factors, which can create a false feeling of security. The  deterministic paradigm can be enhanced by incorporating probabilistic  concepts wisely where they are needed without treating all variables  as probabilistic ones. The book shows that there is a need of their  integration rather than separation.    This book is intended for engineers, graduate students, lecturers and  researchers.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52480217350417,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52480218333457,"sku":"NLS9781402017797","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781402017797.jpg?v=1759849891"},{"product_id":"mechanical-vibration-where-do-we-stand-book-isaac-elishakoff-9783211685860","title":"Mechanical Vibration: Where Do We Stand?","description":"But experience shows, despite the sage observations of the philosophers, that one does enter a river, lake, sea, or ocean.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52481083605265,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52481084883217,"sku":"NLS9783211685860","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783211685860.jpg?v=1759851203"},{"product_id":"eigenvalues-of-inhomogeneous-structures-book-isaac-elishakoff-9780849328923","title":"Eigenvalues of Inhomogeneous Structures","description":"The engineering community generally accepts that there exists only a small set of closed-form solutions for simple cases of bars, beams, columns, and plates. Despite the advances in powerful computing and advanced numerical techniques, closed-form solutions remain important for engineering; these include uses for preliminary design, for evaluation of the accuracy of approximate and numerical solutions, and for evaluating the role played by various geometric and loading parameters.  Eigenvalues of Inhomogeneous Structures: Unusual Closed-Form Solutions offers the first new treatment of closed-form solutions since the works of Leonhard Euler over two centuries ago. It presents simple solutions for vibrating bars, beams, and plates, as well as solutions that can be used to verify finite element solutions. The closed solutions in this book not only have applications that allow for the design of tailored structures, but also transcend mechanical engineering to generalize into other fields of engineering. Also included are polynomial solutions, non-polynomial solutions, and discussions on axial variability of stiffness that offer the possibility of incorporating axial grading into functionally graded materials.  This single-package treatment of inhomogeneous structures presents the tools for optimization in many applications. Mechanical, aerospace, civil, and marine engineers will find this to be the most comprehensive book on the subject. In addition, senior undergraduate and graduate students and professors will find this to be a good supplement to other structural design texts, as it can be easily incorporated into the classroom.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52487022903569,"sku":"NLS9780849328923","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53035363631377,"sku":"NIN9780849328923","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780849328923.jpg?v=1759860136"},{"product_id":"refined-dynamical-theories-of-beams-plates-and-shells-and-their-applications-book-isaac-elishakoff-9783540175735","title":"Refined Dynamical Theories of Beams, Plates and Shells and Their Applications","description":"As is known, classical theories of vibration of the most fre- quently encountered structural elements (e. g., beams, plates and shells) disregard the effects of the shear deformation and rotary inertia. Refined theories, with these effects taken into account, have been pioneered by Bresse, Lord Rayleigh, Timoshenko, Eric Reissner, Mindlin and others. These refined theories have been fruitfully applied in recent decades in both theoretical and prac- tical solid mechanics problems. The European Mechanics Committee approved holding EURO illCH Colloquium 219 on Refined Dynamical Theories of Beams, Plates and Shells and Their Applications for reviewing the recent devel- opments, providing guidelines for future investigations and presenting a forum for current work of younger researchers. The Colloquium was held during September 23 - 26, 1986, at the Uni- versitat-Gesamthochschule Kassel, in the city of Kassel, Federal Republic of Germany. 45 Representatives of academia and industry, from nine European countries, as well as from Israel, USA and India participated in this Colloquium. IV 36 lectures were presented during the five sessions: Session A: Theory of Vibrations of Plates and Shells Session B: Various Approaches for Dynamical Problems of Beams Session C: Random Vibrations and Dynamic Stability Session D: Vibrations of Composite Structures Session E: Special Dynamical Problems of Beams, Plates and Shells The papers in this volums were divided into two parts: papers of invited keynote lectures and those of the invited contributed lectures.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52617606365457,"sku":"NLS9783540175735","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540175735.jpg?v=1761530805"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-isaac-elishakoff.oembed","provider":"World of Books ","version":"1.0","type":"link"}