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The Geography of Bosnia and Herzegovina: Between East and West (World Regional Geography Book Series)
by Haris Gekić Aida Bidžan-Gekić Nusret Drešković Ranko Mirić Péter ReményiThis monograph provides a comprehensive overview of fundamental scientific insights into the geographical features of a country which was and still is in the centre of the geopolitical battle of the large world powers and especially neighboring countries. The book presents the scientifically proven reserves of individual resources such as: mineral riches, land, forests, flora and fauna, water and climate features, to the extent needed, through statistical indicators and geographic maps. The authors point to features and specifics of the existing interdependence of economic and political development and impact of natural resources on spatial development which can be useful for potential investors, spatial planers, decision makers, politicians, geographers, students, large Bosnian diaspora and anyone interested in area of Bosnia and Herzegovina. This book fills the gap in geographical literature on Bosnia and Herzegovina in the English language. The monograph appeals to researchers and scholars of all levels in the fields of geography, geopolitics, history and related fields and everyone interested in this country between East and West.
Geography of South East Asia: தென்கிழக்கு ஆசியா
by G. Krishnamoorthyஇந்த தென்கிழக்கு ஆசிய புவியியல் புத்தகத்தில் தென்கிழக்கு ஆசியாவில் உள்ள மண்வளங்கள். கனிமங்கள், ஆறுகள், இயற்கை போன்றவற்றை பற்றி நாம் தெரிந்து கொள்வதற்கு நமக்கு பேரூதவியாக இருக்கிறது.
The Geography of the Third World: Progress and Prospect (Routledge Library Editions: Development)
by Michael PacioneFirst published in 1988, this reissue presents a comprehensive overview of contemporary developments and research into the geography of the Third World, at a time when economies and societies there were changing at a much more rapid rate than their counterparts in the developing world. It covers the topic both systematically and by region, showing how the unique background of each region affects developments there.
Geoinformatics and Modelling of Landslide Susceptibility and Risk: An RS & GIS-based Model Building Approach in the Eastern Himalaya (Environmental Science and Engineering)
by Sujit Mandal Subrata MondalThis book discusses various statistical models and their implications for developing landslide susceptibility and risk zonation maps. It also presents a range of statistical techniques, i.e. bivariate and multivariate statistical models and machine learning models, as well as multi-criteria evaluation, pseudo-quantitative and probabilistic approaches. As such, it provides methods and techniques for RS & GIS-based models in spatial distribution for all those engaged in the preparation and development of projects, research, training courses and postgraduate studies. Further, the book offers a valuable resource for students using RS & GIS techniques in their studies.
Geological and Geostatistical Aquifer Characterization of Wajid Sandstone, Saudi Arabia (Earth and Environmental Sciences Library)
by Osman Abdullatif Mohammad Makkawi Mohamed YassinThe book summarizes research work on the Wajid Sandstone, which provides integrated field and laboratory data to enable a detailed description of this unit including a facies analysis, porosity data, as well as permeability data to establish aquifer models. Detailed facies analysis at outcrop scale are supported by vertical and lateral sedimentological sections, facies and environmental analysis and supplemented by detailed laboratory petrographical and petrophysical data. The analysis and interpretation of the outcrop analog models include the reconstruction of the stratigraphic architecture at outcrop scale. Moreover, the results were described statistically, analyzed and eventually establish an outcrop-based aquifer model analogue. The book benefits undergraduate, graduate and researchers working on applied sedimentological studies, hydrogeology, statistical and geostatistical analysis and modeling.
Geomechanical Controls on Fracture Development in Chalk and Marl in the Danish North Sea: Understanding and Predicting Fracture Systems (Petroleum Engineering)
by Michael John Welch Mikael LüthjeThis book summarizes new discoveries on fracturing in chalk. Based on studies on the Danish North Sea, this book shows how observations from outcrop analogues, core and seismic data can be used to characterize the density, distribution and geometry of natural fractures in chalk and marl. Laboratory experiments on chalk samples reveal the controls on the geomechanical properties of chalk and thus on the growth of natural fractures. Finally, various modeling techniques are employed to investigate the mechanical deformation in the chalk structures of the Danish North Sea and to predict fracture distribution and geometry in the subsurface. An understanding of fracture density, distribution and geometry is essential for planning efficient fluid extraction or injection strategies and CO2 sequestration. This book provides the necessary knowledge.
Geometric Algebra (Dover Books on Mathematics)
by Emil ArtinThis concise classic presents advanced undergraduates and graduate students in mathematics with an overview of geometric algebra. The text originated with lecture notes from a New York University course taught by Emil Artin, one of the preeminent mathematicians of the twentieth century. The Bulletin of the American Mathematical Society praised Geometric Algebra upon its initial publication, noting that "mathematicians will find on many pages ample evidence of the author's ability to penetrate a subject and to present material in a particularly elegant manner."Chapter 1 serves as reference, consisting of the proofs of certain isolated algebraic theorems. Subsequent chapters explore affine and projective geometry, symplectic and orthogonal geometry, the general linear group, and the structure of symplectic and orthogonal groups. The author offers suggestions for the use of this book, which concludes with a bibliography and index.
Geometric Algebra Applications Vol. II: Robot Modelling and Control
by Eduardo Bayro-CorrochanoThis book presents a unified mathematical treatment of diverse problems in the general domain of robotics and associated fields using Clifford or geometric alge- bra. By addressing a wide spectrum of problems in a common language, it offers both fresh insights and new solutions that are useful to scientists and engineers working in areas related with robotics. It introduces non-specialists to Clifford and geometric algebra, and provides ex- amples to help readers learn how to compute using geometric entities and geomet- ric formulations. It also includes an in-depth study of applications of Lie group theory, Lie algebra, spinors and versors and the algebra of incidence using the universal geometric algebra generated by reciprocal null cones. Featuring a detailed study of kinematics, differential kinematics and dynamics using geometric algebra, the book also develops Euler Lagrange and Hamiltoni- ans equations for dynamics using conformal geometric algebra, and the recursive Newton-Euler using screw theory in the motor algebra framework. Further, it comprehensively explores robot modeling and nonlinear controllers, and discusses several applications in computer vision, graphics, neurocomputing, quantum com- puting, robotics and control engineering using the geometric algebra framework. The book also includes over 200 exercises and tips for the development of future computer software packages for extensive calculations in geometric algebra, and a entire section focusing on how to write the subroutines in C++, Matlab and Maple to carry out efficient geometric computations in the geometric algebra framework. Lastly, it shows how program code can be optimized for real-time computations. An essential resource for applied physicists, computer scientists, AI researchers, roboticists and mechanical and electrical engineers, the book clarifies and demon- strates the importance of geometric computing for building autonomous systems to advance cognitive systems research.
Geometric Algebra for Physicists
by Anthony Lasenby Chris DoranGeometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra and is also suitable for researchers working in the fields of relativity and quantum theory.
A Geometric Algebra Invitation to Space-Time Physics, Robotics and Molecular Geometry (SpringerBriefs in Mathematics)
by Carlile Lavor Sebastià Xambó-Descamps Isiah ZaplanaThis book offers a gentle introduction to key elements of Geometric Algebra, along with their applications in Physics, Robotics and Molecular Geometry. Major applications covered are the physics of space-time, including Maxwell electromagnetism and the Dirac equation; robotics, including formulations for the forward and inverse kinematics and an overview of the singularity problem for serial robots; and molecular geometry, with 3D-protein structure calculations using NMR data. The book is primarily intended for graduate students and advanced undergraduates in related fields, but can also benefit professionals in search of a pedagogical presentation of these subjects.
Geometric Analysis: Cetraro, Italy 2018 (Lecture Notes in Mathematics #2263)
by Ailana Fraser André Neves Peter M. Topping Paul C. YangThis book covers recent advances in several important areas of geometric analysis including extremal eigenvalue problems, mini-max methods in minimal surfaces, CR geometry in dimension three, and the Ricci flow and Ricci limit spaces. An output of the CIME Summer School "Geometric Analysis" held in Cetraro in 2018, it offers a collection of lecture notes prepared by Ailana Fraser (UBC), André Neves (Chicago), Peter M. Topping (Warwick), and Paul C. Yang (Princeton). These notes will be a valuable asset for researchers and advanced graduate students in geometric analysis.
Geometric Analysis of Quasilinear Inequalities on Complete Manifolds: Maximum and Compact Support Principles and Detours on Manifolds (Frontiers in Mathematics)
by Bruno Bianchini Luciano Mari Patrizia Pucci Marco RigoliThis book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Geometric Analysis of the Bergman Kernel and Metric
by Steven G. KrantzThis text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.
Geometric Analysis on Real Analytic Manifolds (Lecture Notes in Mathematics #2333)
by Andrew D. LewisThis monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings.Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.
Geometric and Cohomological Group Theory (London Mathematical Society Lecture Note Series #444)
by Ian J. Leary Peter H. Kropholler Conchita Martínez-Pérez BRITA E.A. NUCINKISThis volume provides state-of-the-art accounts of exciting recent developments in the rapidly-expanding fields of geometric and cohomological group theory. The research articles and surveys collected here demonstrate connections to such diverse areas as geometric and low-dimensional topology, analysis, homological algebra and logic. Topics include various constructions of Thompson-like groups, Wise's theory of special cube complexes, groups with exotic homological properties, the Farrell-Jones assembly conjectures and new applications of Garside structures. Its mixture of surveys and research makes this book an excellent entry point for young researchers as well as a useful reference work for experts in the field. This is the proceedings of the 100th meeting of the London Mathematical Society series of Durham Symposia.
Geometric and Ergodic Aspects of Group Actions (Infosys Science Foundation Series)
by S. G. Dani Anish GhoshThis book gathers papers on recent advances in the ergodic theory of group actions on homogeneous spaces and on geometrically finite hyperbolic manifolds presented at the workshop “Geometric and Ergodic Aspects of Group Actions,” organized by the Tata Institute of Fundamental Research, Mumbai, India, in 2018. Written by eminent scientists, and providing clear, detailed accounts of various topics at the interface of ergodic theory, the theory of homogeneous dynamics, and the geometry of hyperbolic surfaces, the book is a valuable resource for researchers and advanced graduate students in mathematics.
Geometric and Harmonic Analysis on Homogeneous Spaces: TJC 2017, Mahdia, Tunisia, December 17–21 (Springer Proceedings in Mathematics & Statistics #290)
by Ali Baklouti Takaaki NomuraThis book presents a number of important contributions focusing on harmonic analysis and representation theory of Lie groups. All were originally presented at the 5th Tunisian–Japanese conference “Geometric and Harmonic Analysis on Homogeneous Spaces and Applications”, which was held at Mahdia in Tunisia from 17 to 21 December 2017 and was dedicated to the memory of the brilliant Tunisian mathematician Majdi Ben Halima. The peer-reviewed contributions selected for publication have been modified and are, without exception, of a standard equivalent to that in leading mathematical periodicals. Highlighting the close links between group representation theory and harmonic analysis on homogeneous spaces and numerous mathematical areas, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics, the book is intended for researchers and students working in the area of commutative and non-commutative harmonic analysis as well as group representations.
Geometric and Harmonic Analysis on Homogeneous Spaces and Applications: TJC 2015, Monastir, Tunisia, December 18-23 (Springer Proceedings in Mathematics & Statistics #207)
by Ali Baklouti Takaaki NomuraThis book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications. It also includes the most recent developments on other areas of mathematics including algebra and geometry.Lie group representation theory and harmonic analysis on Lie groups and on their homogeneous spaces form a significant and important area of mathematical research. These areas are interrelated with various other mathematical fields such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics. Keeping up with the fast development of this exciting area of research, Ali Baklouti (University of Sfax) and Takaaki Nomura (Kyushu University) launched a series of seminars on the topic, the first of which took place on November 2009 in Kerkennah Islands, the second in Sousse on December 2011, and the third in Hammamet on December 2013. The last seminar, which took place December 18th to 23rd 2015 in Monastir, Tunisia, has promoted further research in all the fields where the main focus was in the area of Analysis, algebra and geometry and on topics of joint collaboration of many teams in several corners. Many experts from both countries have been involved.
Geometric and Numerical Optimal Control: Application to Swimming at Low Reynolds Number and Magnetic Resonance Imaging (SpringerBriefs in Mathematics)
by Bernard Bonnard Monique Chyba Jérémy RouotThis book introduces readers to techniques of geometric optimal control as well as the exposure and applicability of adapted numerical schemes. It is based on two real-world applications, which have been the subject of two current academic research programs and motivated by industrial use – the design of micro-swimmers and the contrast problem in medical resonance imaging. The recently developed numerical software has been applied to the cases studies presented here. The book is intended for use at the graduate and Ph.D. level to introduce students from applied mathematics and control engineering to geometric and computational techniques in optimal control.
Geometric and Topological Aspects of the Representation Theory of Finite Groups: Pims Summer School And Workshop, July 27-august 5 2016 (Springer Proceedings in Mathematics & Statistics #242)
by Jon F. Carlson Srikanth B. Iyengar Julia PevtsovaThese proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.
Geometric and Topological Inference (Cambridge Texts in Applied Mathematics #57)
by Jean-Daniel Boissonnat Frédéric Chazal Mariette YvinecGeometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of topological data analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this self-contained book covers key aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.
Geometric and Topological Mesh Feature Extraction for 3D Shape Analysis
by Jean-Luc Mari Franck Hétroy-Wheeler Gérard SubsolThree-dimensional surface meshes are the most common discrete representation of the exterior of a virtual shape. Extracting relevant geometric or topological features from them can simplify the way objects are looked at, help with their recognition, and facilitate description and categorization according to specific criteria. This book adopts the point of view of discrete mathematics, the aim of which is to propose discrete counterparts to concepts mathematically defined in continuous terms. It explains how standard geometric and topological notions of surfaces can be calculated and computed on a 3D surface mesh, as well as their use for shape analysis. Several applications are also detailed, demonstrating that each of them requires specific adjustments to fit with generic approaches. The book is intended not only for students, researchers and engineers in computer science and shape analysis, but also numerical geologists, anthropologists, biologists and other scientists looking for practical solutions to their shape analysis, understanding or recognition problems.
A Geometric Approach to the Unification of Symbolic Structures and Neural Networks (Studies in Computational Intelligence #910)
by Tiansi DongThe unification of symbolist and connectionist models is a major trend in AI. The key is to keep the symbolic semantics unchanged. Unfortunately, present embedding approaches cannot. The approach in this book makes the unification possible. It is indeed a new and promising approach in AI. -Bo Zhang, Director of AI Institute, TsinghuaIt is indeed wonderful to see the reviving of the important theme Nural Symbolic Model. Given the popularity and prevalence of deep learning, symbolic processing is often neglected or downplayed. This book confronts this old issue head on, with a historical look, incorporating recent advances and new perspectives, thus leading to promising new methods and approaches. -Ron Sun (RPI), on Governing Board of Cognitive Science SocietyBoth for language and humor, approaches like those described in this book are the way to snickerdoodle wombats. -Christian F. Hempelmann (Texas A&M-Commerce) on Executive Board of International Society for Humor Studies
Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2020-2022 (Lecture Notes in Mathematics #2327)
by Ronen Eldan Bo’az Klartag Alexander Litvak Emanuel MilmanThis book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.
Geometric Aspects of Functional Analysis
by Bo'Az Klartag Shahar Mendelson Vitali D. MilmanThis collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the general trends of Asymptotic Geometric Analysis, understood in a broad sense, and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convex bodies, inequalities involving volumes of such bodies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensional spaces and characterization of classical constructions in Geometry and Analysis (like the Legendre and Fourier transforms, derivation and others). All the papers here are original research papers.