الصفحة 2
الصفحة 2
High Order Difference Methods for Time Dependent PDE
Many books have been written on ?nite difference methods (FDM), but there are good reasons to write still another one. The main reason is that even if higher order methods have been known for a long time, the analysis of stability, accuracy and effectiveness is missing to a large extent. For example, the de?nition of the formal high order accuracy is based on the assumption that the true solution is smooth, or expressed differently, that the grid is ?ne enough such that all variations in the solution are well resolved. In many applications, this assumption is not ful?lled, and then it is interesting to know if a high order method is still effective. Another problem that needs thorough analysis is the construction of boundary conditions such that both accuracy and stability is upheld. And ?nally, there has been quite a strongdevelopmentduringthe last years, inparticularwhenit comesto verygeneral and stable difference operators for application on initial–boundary value problems.
Hands-on question answering systems with BERT : Applications in neural networks and natural language processing
Begins with an overview of the technology landscape behind BERT. It takes you through the basics of NLP, including natural language understanding with tokenization, stemming, and lemmatization, and bag of words. Next, you’ll look at neural networks for NLP starting with its variants such as recurrent neural networks, encoders and decoders, bi-directional encoders and decoders, and transformer models. Along the way, you’ll cover word embedding and their types along with the basics of BERT. After this solid foundation, you’ll be ready to take a deep dive into BERT algorithms such as masked language models and next sentence prediction. You’ll see different BERT variations followed by a hands-on example of a question answering system. You will: Examine the fundamentals of word embeddings / Apply neural networks and BERT for various NLP tasks / Develop a question-answering system from scratch / Train question-answering systems for your own data
Handbook on Decision Support Systems 2 : Variations
As the most comprehensive reference work dealing with decision support systems (DSS), this book is essential for the library of every DSS practitioner, researcher, and educator. Written by an international array of DSS luminaries, its more than 70 chapters approach decision support systems from a wide variety of perspectives ranging from classic foundations to cutting-edge thought, informative to provocative, theoretical to practical, historical to futuristic, human to technological, and operational to strategic. The chapters are conveniently organized into 10 major sections: foundations of decision support systems, DSS fundamentals, multiparticipant DSSs, intelligent DSSs, effects of decision support, time & space issues, scopes of decision support, developing & managing decision support systems, cases &applications, and decision support horizons. Novices and experts alike will refer to the authoritative and stimulating content again and again for years to come.
Gravity, Geoid and Space Missions ; GGSM 2004. IAG International Symposium. Porto, Portugal. August 30 - September 3, 2004
GGSM2004 aimed to bring together scientists from different areas in the geosciences, working with gravity and geoid related problems, both from the theoretical and practical points of view. Topics of interest included the integration of heterogeneous data and contributions from satellite and airborne techniques to the study of the spatial and temporal variations of the gravity field. In addition to the special focus on the CHAMP, GRACE, and GOCE satellite missions, attention was also directed toward projects addressing topographic and ice field mapping using SAR, LIDAR, and laser altimetry, as well as missions and studies related to planetary geodesy.
Geometric mechanics on riemannian manifolds : Applications to partial differential equations
This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger's, Einstein's and Newton's equations. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases (e.g., the case of quartic oscillators) these methods do not work. New geometric methods are introduced in the work that have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods. And, conservation laws of the Euler–Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible. It includes : Lagrangian formalism on Riemannian manifolds; energy momentum tensor and conservation laws; Hamiltonian formalism; Hamilton–Jacobi theory; harmonic functions, maps, and geodesics; fundamental solutions for heat operators with potential; and a variational approach to mechanical curves.
Geodetic Deformation Monitoring : From Geophysical to Engineering Roles ; IAG Symposium Jaén, Spain, March 7-19,2005
Geodesy is the science dealing with the determination of the position of points in space, the shape and gravity field of the Earth and with their time variations. A consequence is that geodesists feel as a permanent subject of research, the detection, analysis and interpretation of spatial deformation as well as gravity field variation. This book collects 36 selected papers from the International Symposium on Geodetic Deformation Monitoring held in Jaén (Spain) from 17th to 19th March 2005. The main topics covered in the symposium were: mathematical and statistical models for crustal deformation analysis, deformation monitoring from GPS and InSAR data: analysis and geophysical interpretation, geodetic monitoring of movements in civil engineering, integration of spatial and terrestrial techniques in deformation studies, geodynamical applications of gravimetric observations and present-day geodetic instrumentation for deformation monitoring. This volume is a good overview of theoretical matters, models and results.
Game Theory : A Multi-Leveled Approach
This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book concludes with a problem section. Hints, answers and solutions are included.
From Nano to Space : Applied Mathematics Inspired by Roland Bulirsch
Graduate students and postgraduates in Mathematics, Engineering and the Natural Sciences want to understand Applied Mathematics for the solution of everyday problems. Scholars of Roland Bulirsch working at universities, at research institutions and in industry combine research and review papers in this anthology. Their work is summed up under the title "From Nano to Space – Applied Mathematics Inspired by Roland Bulirsch". More than 20 contributions are divided into scales: nano, micro, macro, space and real life. The contributions survey current research and present case studies very interesting and informative for both graduate students and postgraduates. The contributions show how modern Applied Mathematics influences our everyday lives. Several contributions include complex graphics and illustrations, many of them in color.
Fractures du genou = Knee fractures
Provides a comprehensive yet practical overview of the management of knee fractures and their complications. The editorial team comprises specialists from France, Switzerland, Belgium, the United States, and Ireland, many of whom are members of the AO group. Imaging strategies, assessment, classification, and anatomical variations are reviewed for each anatomical location. All therapeutic approaches are discussed without exception: conventional implants, intramedullary nailing, minimally invasive techniques, including the role of external fixation, and newer technologies such as the LISS. These approaches are subjected to critical analysis to identify the best options based on the indications and individual circumstances. The patellar apparatus is addressed in its functional unity. Postoperative management, influenced by functional prognosis, is also covered, as is the management of malunion, stiffness, and other complications. Finally, very specific problems are discussed, such as pediatric injuries, patellectomies, periprosthetic fractures, often complex projectile injuries, the role of immediate arthroplasty and massive grafts, but also associated injuries which sometimes have a heavy impact on the final prognosis.
Farewell to the Internal Clock : A contribution in the field of chronobiology
Nearly everything making up what we call the “environment” of a plant has an infuence on the way it grows. Sunlight, te- perature, moisture contents of soil and atmosphere and vib- tions are all obvious examples of environmental components, and transient variations in their amount or intensity lead the plant to manifest more or less immediate responses. Small changes in carbon dioxide level in the atmosphere can even have effects, but these take a longer time to be registered – at least those that are visible, albeit at the microscopic level. Plants meet the challenges of the environment by means of acclimation. In this respect, plants are notable for the pl- ticity of their development. However, where morphological or physiological plasticity is no longer an option, the responses would be by means of adaptations as a result of genetic - lection or genetic “assimilation” (Waddington 1957).
European Variations as a Key to Cooperation
This book offers a novel view on the benefits of a lasting variation between the member states in the EU. In order to bring together thirty very different European states and their citizens, the EU will have to offer more scope for variation. Unlike the existing differentiation by means of opt-outs and deviations, variation is not a concession intended to resolve impasses in negotiations; it is, rather, a different structuring principle. It takes differences in needs and in democratically supported convictions seriously
Entropy Methods for the Boltzmann Equation : Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level. During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.
Ennio De Giorgi : Selected Papers
The book contains a selection of 43 scientific papers by the great mathematician Ennio De Giorgi (1928-1996), which display the broad range of his achievements and his entire intellectual career as a problem solver and as a proponent of deep and ambitious mathematical theories. All papers are written in English and 17 of them appear also in their original Italian version in order to give an impression of De Giorgi’s original style. The editors also provide a short biography of Ennio De Giorgi and a detailed account of his scientific achievements, ranging from his seminal paper on the solution of Hilbert’s 19th problem to the theory of perimeter and minimal surfaces, the theory of G-convergence and the foundations of mathematics.
Employment Deconcentration in European Metropolitan Areas : Market Forces versus Planning Regulations
Spatial deconcentration of economic activities, particularly the growth of suburban office, retail and entertainment concentrations, has become a prime concern in European metropolitan areas. This book provides a cross-national comparative perspective on employment deconcentration within selected metropolitan areas in Europe. Whereas most debate over urban sprawl and deconcentration is oriented towards the North American context, this book aims at a better understanding of this phenomenon in the European context, emphasizing the location of economic activities rather than residential patterns. It provides insights on whether different governance attributes produce particular forms of deconcentration versus the influence of market attributes and local specificities, also commenting on quality of life impacts and possible governance and policy implications of the deconcentration process. Introduction of a comparative framework is followed by eight case study chapters, three representing northern Europe, three the southern European-Mediterranean region and two post-communist central Europe. Most chapters examine two metropolitan areas, usually a large one and a smaller one. The comparison reveals considerable variations in the magnitude, form, and process of employment deconcentration, only partly in line with expected influences of governance systems. Evidence does not fully confirm an anticipated distinction between Northern and Mediterranean Europe; the Czech Republic and Israel seem to diverge most from prevailing European trends.
Direct Methods in the Calculus of Variations
Studies vectorial problems in the calculus of variations and quasiconvex analysis. It is a new edition of the earlier book published in 1989 and has been updated with some new material and examples added. This monograph will appeal to researchers and graduate students in mathematics and engineering.
Differential Equations, Chaos and Variational Problems
Differential equations are a fast evolving branch of mathematics and one of the mathematical tools most used by scientists and engineers. This book gathers a collection of original articles and state-of-the-art contributions, written by highly distinguished researchers working in differential equations, delay-differential equations, differential inclusions, variational problems, Young measures, control theory, dynamical systems, chaotic systems and their relations with physical systems. The forefront of research in these areas is represented in this volume.
Deliberative public engagement with science : An empirical investigation
This compact open access reference delves beyond popular concepts of educated consumers and an informed public by examining the science behind deliberative engagement. Using data from four longitudinal studies, the authors assess public engagement methods in deliberative discussions of ethical, legal, and social issues concerning innovations in nanotechnology. Coverage includes the theoretical origins of the studies, forms of engagement and variations used, and in-depth details on cognitive, affective, and social components that go into the critical thinking process and forming of opinions. Not only are the findings intriguing in and of themselves, but researchers from varied fields will also find them useful in pursuing their own projects.
Deformation and Gravity Change : Indicators of Isostasy, Tectonics, Volcanism, and Climate Change
During the last decades, measurements of various geodynamic processes have gained ever increasing importance. Temporal variations of the deformation and gravity fields monitored by geodetic measuring techniques reflect isostatic, tectonic or volcanic processes in the earth’s interior.Recordings of hydrologic or oceanographic phenomena allow conclusions on surface processes. This volume reflects the major developments during recent years in these areas of research.Most of the papers in this book were presented at the workshop on"Deformation and Gravity Change: Indicators of Isostasy, Tectonics, Volcanism and Climate Change", which took place at the Casa de los Volcanes on Lanzarote,Spain, 2005.
Data Assimilation : The Ensemble Kalman Filter
Data Assimilation comprehensively covers data assimilation and inverse methods, including both traditional state estimation and parameter estimation. This text and reference focuses on various popular data assimilation methods, such as weak and strong constraint variational methods and ensemble filters and smoothers. It is demonstrated how the different methods can be derived from a common theoretical basis, as well as how they differ and/or are related to each other, and which properties characterize them, using several examples.It presents the mathematical framework and derivations in a way which is common for any discipline where dynamics is merged with measurements. The mathematics level is modest, although it requires knowledge of basic spatial statistics, Bayesian statistics, and calculus of variations. Readers will also appreciate the introduction to the mathematical methods used and detailed derivations, which should be easy to follow, are given throughout the book. The codes used in several of the data assimilation experiments are available on a web page.The focus on ensemble methods, such as the ensemble Kalman filter and smoother, also makes it a solid reference to the derivation, implementation and application of such techniques. Much new material, in particular related to the formulation and solution of combined parameter and state estimation problems and the general properties of the ensemble algorithms, is available here for the first time.
Convex Functional Analysis
This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.
