Search results for "vectorization"
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Computational Formalisms In Euclidean Geometry, Vol. I: A Trigonometric, Vectorial And Complex Numbers Approach
This book explores three computational formalisms for solving geometric problems. Part I introduces a trigonometric-based formalism, enabling calculations of distances, angles, and areas using basic trigonometry. Part II focuses on complex numbers, representing points in the plane to manipulate geometric properties like collinearity and concurrency, making it particularly useful for planar problems and rotations. Part III covers vector formalism, applying linear algebra to both plane and solid geometry. Vectors are effective for solving problems related to perpendicularity, collinearity, and the calculation of distances, areas, and volumes.Each formalism has its strengths and limitations, with complex numbers excelling in the plane and vectors being more versatile in three-dimensional space. This book equips readers to choose the best approach for various geometric challenges. This book, designed for math majors, especially future educators, is also valuable for gifted high school students and educators seeking diverse proofs and teaching inspiration.
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Moduli Spaces and Vector Bundles
Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subject's leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.
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Volume of Vector Fields on Riemannian Manifolds
This book focuses on the study of the volume of vector fields on Riemannian manifolds. Providing a thorough overview of research on vector fields defining minimal submanifolds, and on the existence and characterization of volume minimizers, it includes proofs of the most significant results obtained since the subject’s introduction in 1986. Aiming to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results. The presentation is direct and deviates substantially from the usual approaches found in the literature, requiring a significant revision of definitions, statements, and proofs.A wide range of topics is covered, including: a discussion on the conditions for a vector field on a Riemannian manifold to determine a minimal submanifold within its tangent bundle with the Sasaki metric; numerous examples of minimal vector fields (including those of constant length on punctured spheres); a thorough analysis of Hopf vector fields on odd-dimensional spheres and their quotients; and a description of volume-minimizing vector fields of constant length on spherical space forms of dimension three.Each chapter concludes with an up-to-date survey which offers supplementary information and provides valuable insights into the material, enhancing the reader's understanding of the subject. Requiring a solid understanding of the fundamental concepts of Riemannian geometry, the book will be useful for researchers and PhD students with an interest in geometric analysis.
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Set Optimization and Applications - The State of the Art
This volume presents five surveys with extensivebibliographies and six original contributions on set optimization and its applicationsin mathematical finance and game theory. The topics range from moreconventional approaches that look for minimal/maximal elements with respect tovector orders or set relations, to the new complete-lattice approach thatcomprises a coherent solution concept for set optimization problems, along withexistence results, duality theorems, optimality conditions, variationalinequalities and theoretical foundations for algorithms. Modern approaches toscalarization methods can be found as well as a fundamental contribution to conditionalanalysis. The theory is tailor-made for financial applications, in particular riskevaluation and [super-]hedging for market models with transaction costs, but italso provides a refreshing new perspective on vector optimization. There is nocomparable volume on the market, making the book an invaluable resource forresearchers working in vector optimization and multi-criteria decision-making, mathematicalfinance and economics as well as [set-valued] variational analysis.
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Introduction to Parallel and Vector Solution of Linear Systems
Although the origins of parallel computing go back to the last century, it was only in the 1970s that parallel and vector computers became available to the scientific community. The first of these machines-the 64 processor llliac IV and the vector computers built by Texas Instruments, Control Data Corporation, and then CRA Y Research Corporation-had a somewhat limited impact. They were few in number and available mostly to workers in a few government laboratories. By now, however, the trickle has become a flood. There are over 200 large-scale vector computers now installed, not only in government laboratories but also in universities and in an increasing diversity of industries. Moreover, the National Science Foundation's Super computing Centers have made large vector computers widely available to the academic community. In addition, smaller, very cost-effective vector computers are being manufactured by a number of companies. Parallelism in computers has also progressed rapidly. The largest super computers now consist of several vector processors working in parallel. Although the number of processors in such machines is still relatively small (up to 8), it is expected that an increasing number of processors will be added in the near future (to a total of 16 or 32). Moreover, there are a myriad of research projects to build machines with hundreds, thousands, or even more processors. Indeed, several companies are now selling parallel machines, some with as many as hundreds, or even tens of thousands, of processors.
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Knowledge Discovery with Support Vector Machines
An easy-to-follow introduction to support vector machines This book provides an in-depth, easy-to-follow introduction to support vector machines drawing only from minimal, carefully motivated technical and mathematical background material. It begins with a cohesive discussion of machine learning and goes on to cover: Knowledge discovery environments Describing data mathematically Linear decision surfaces and functions Perceptron learning Maximum margin classifiers Support vector machines Elements of statistical learning theory Multi-class classification Regression with support vector machines Novelty detection Complemented with hands-on exercises, algorithm descriptions, and data sets, Knowledge Discovery with Support Vector Machines is an invaluable textbook for advanced undergraduate and graduate courses. It is also an excellent tutorial on support vector machines for professionals who are pursuing research in machine learning and related areas.
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Calculus in Vector Spaces, Revised Expanded
Calculus in Vector Spaces addresses linear algebra from the basics to the spectral theorem and examines a range of topics in multivariable calculus. This second edition introduces, among other topics, the derivative as a linear transformation, presents linear algebra in a concrete context based on complementary ideas in calculus, and explains differential forms on Euclidean space, allowing for Green's theorem, Gauss's theorem, and Stokes's theorem to be understood in a natural setting. Mathematical analysts, algebraists, engineers, physicists, and students taking advanced calculus and linear algebra courses should find this book useful.
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Sendai Virus Vector
Sendai virus (SeV) is not just a mouse pathogen but is evolving into a cutting-edge component of biotechnology. SeV reverse genetics originating from a pure academic need to settle long-held questions in the biology and pathogenicity of nonsegmented negative strand RNA viruses (Mononegavirales) is about to bear the impressive fruit of multipurpose cytoplasmic (non-integrating) RNA vectors. This book brings together in one source the SeV biology revealed by conventional approaches and reverse genetics, the methods to construct the first-generation SeV vector and to generate safer versions, and the applications in medical settings that have left or are about to leave the laboratory bench. The applications, which already are diverse and have high medical impact, include use as vaccine vectors against AIDS and respiratory virus infections, creation of BioKnife to resect malignant tumors, induction of “footprint (transgene) free” pluripotent stem cells, and gene therapy for peripheral arterial disease. These achievements—which are just a few of many examples—were attainable only after rigorously incorporating the rich knowledge of SeV biology that has accumulated during the several decades since the discovery of the virus. Application of SeV vector is certain to expand greatly because of its extremely high performance in transgene expression and its remarkable target cell breadth.
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Vector Bundles on Complex Projective Spaces
These lecture notes are intended as an introduction to the methods of classi?cation of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = P . According to Serre (GAGA) the class- n cation of holomorphic vector bundles is equivalent to the classi?cation of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some fundamental results from these ?elds are summarized at the beginning. One of the authors gave a survey in the S´eminaire Bourbaki 1978 on the current state of the classi?cation of holomorphic vector bundles over P . This lecture then served as the basis for a course of lectures n in G¨ottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the - troductory nature of this book we have had to leave out some di?cult topics such as the restriction theorem of Barth. As compensation we have appended to each section a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of pa- graphs. Each section is preceded by a short description of its contents.
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800 Solved Problems Invector Mechanics for Engineers, Vol. I: Statics
This is a complete and expert source of problems with solutions in Vector mechanics for Engineers for 2nd-year college and university engineering students to cover all aspects of the basic course. This is the comprehensive solved-problem reference in the subject. It provides the student with all the problem solving drill ever needed, all in one book. There is no expository text. A course in engineering mechanics is required of all engineering students. Fifty per cent of the problems are SI.
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Topological Vector Spaces
This is a softcover reprint of the 1987 English translation of the second edition of Bourbaki's Espaces Vectoriels Topologiques. Much of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, reflecting decades of progress in the field.
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Support Vector Machines for Pattern Classification
A guide on the use of SVMs in pattern classification, including a rigorous performance comparison of classifiers and regressors. The book presents architectures for multiclass classification and function approximation problems, as well as evaluation criteria for classifiers and regressors. Features: Clarifies the characteristics of two-class SVMs; Discusses kernel methods for improving the generalization ability of neural networks and fuzzy systems; Contains ample illustrations and examples; Includes performance evaluation using publicly available data sets; Examines Mahalanobis kernels, empirical feature space, and the effect of model selection by cross-validation; Covers sparse SVMs, learning using privileged information, semi-supervised learning, multiple classifier systems, and multiple kernel learning; Explores incremental training based batch training and active-set training methods, and decomposition techniques for linear programming SVMs; Discusses variable selection for support vector regressors.
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High Performance Computing on Vector Systems 2005
The book presents the state of the art in high performance computing and simulation on modern supercomputer architectures. It covers trends in hardware and software development in general and specifically the future of vector-based systems and heterogeneous architectures. The application contributions include computational fluid dynamics, physics, chemistry, astrophysics, and biology. Innovative application fields like multiphysics simulations and material science are presented.
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Topological Vector Spaces II
In the preface to Volume One I promised a second volume which would contain the theory of linear mappings and special classes of spaces im portant in analysis. It took me nearly twenty years to fulfill this promise, at least to some extent. To the six chapters of Volume One I added two new chapters, one on linear mappings and duality (Chapter Seven), the second on spaces of linear mappings (Chapter Eight). A glance at the Contents and the short introductions to the two new chapters will give a fair impression of the material included in this volume. I regret that I had to give up my intention to write a third chapter on nuclear spaces. It seemed impossible to include the recent deep results in this field without creating a great further delay. A substantial part of this book grew out of lectures I held at the Mathematics Department of the University of Maryland· during the academic years 1963-1964, 1967-1968, and 1971-1972. I would like to express my gratitude to my colleagues J. BRACE, S. GOLDBERG, J. HORVATH, and G. MALTESE for many stimulating and helpful discussions during these years. I am particularly indebted to H. JARCHOW (Ziirich) and D. KEIM (Frankfurt) for many suggestions and corrections. Both have read the whole manuscript. N. ADASCH (Frankfurt), V. EBERHARDT (Miinchen), H. MEISE (Diisseldorf), and R. HOLLSTEIN (Paderborn) helped with important observations.
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Lentiviral Vectors
This volume provides readers with an overview of lentiviral vector applications and includes detailed laboratory protocols relevant to neuroscience research. The chapters are organized into five sections: Section I provides an overview of lentiviral vector properties, including practical methods for vector preparation and delivery into the brains of rodents and non-human primates, as well as delivery into non-human primate embryos for transgenic animal production. Sections II to IV explore basic neuroscience covering anatomical, molecular and developmental, and behavioral and physiological neuroscience. Section V focuses on clinical neuroscience, offering protocols related to gene therapy for motor neuron and ocular diseases. Written in the highly successful Methods in Molecular Biology series format, each chapter includes an introduction to the topic, a list of required materials and reagents, step-by-step protocols that are easy to reproduce, and expert tips for troubleshooting and avoiding common pitfalls. Cutting-edge and thorough, Lentiviral Vectors: Application for Basic and Clinical Neuroscience is a valuable resource for any researcher looking to learn more about this important and advancing field.
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R 455.00
Vector Databases
The AI revolution is here, and at its core lies a game-changing technology that most developers haven't fully explored: vector databases. From powering semantic search to enabling large language models (LLMs) and generative AI, vector databases are reshaping how we build applications with unstructured data like text, images, and audio. But how do you go from curious to capable with this vital technology? That's where this book comes in.In this hands-on guide, author Nitin Borwankar takes you through the "why, what, and how" of vector databases, starting with the basic theory behind vector embeddings and progressing to building applications with real-world tools. You'll learn about Word2vec, how to convert open source SQL databases like SQLite3 and PostgreSQL into vector databases, and integrate them into retrieval-augmented generation (RAG) applications. Whether you're a Python developer, data engineer, or ML practitioner, this book gives you the foundation to leverage vector databases confidently in your AI projects.Understand the connection between vector databases, embeddings, and LLMsLearn practical approaches for transforming SQL databases into vector databasesBuild RAG applications for both personal and enterprise useApply vector databases to solve real-world AI challengesLearn how to use vector databases with LLMs to build applications
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Bio-Carrier Vectors
This detailed book explores techniques used in research efforts to adopt and combine the best capabilities from natural and artificial vector systems to assemble improved delivery technologies aimed for specific applications. The collection discusses vectors other than the traditional viral and non-viral systems and explores ideas for blending the best features of bacteria, nanoparticles, peptides, and hybrid systems for the delivery of biomaterials into cells, as well as a chapter on the application of shotgun proteomics and mass spectrometry as a tool to analyze the proteomic profile changes in cells that result from these interventions. Written in the highly successful Methods in Molecular Biology format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and practical, Bio-Carrier Vectors: Methods and Protocols serves as an ideal guide for researchers working toward harnessing the power of multiple vectors in gene and drug delivery.
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Continuous Functions of Vector Variables
This is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. The author covers boundedness, extreme values, and uniform continuity of functions, along with connections between continuity and topological concepts such as connectedness and compactness. The order of topics mimics the order of development in elementary calculus, with analogies and generalizations from such familiar ideas as the Pythagorean theorem.
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Quadratic Forms in Infinite Dimensional Vector Spaces
For about a decade I have made an effort to study quadratic forms in infinite dimensional vector spaces over arbitrary division rings. Here we present in a systematic fashion half of the results found du ring this period, to wit, the results on denumerably infinite spaces (" ~O- forms") . Certain among the resul ts included here had of course been published at the time when they were found, others appear for the first time (the case, for example, in Chapters IX, X, XII where I in clude results contained in the Ph.D.theses by my students w. Allenspach, L. Brand, U. Schneider, M. Studer). If one wants to give an introduction to the geometric algebra of infinite dimensional quadratic spaces, a discussion of ~ -dimensional 0 spaces ideally serves the purpose. First, these spaces show a large nurober of phenomena typical of infinite dimensional spaces. Second, most proofs can be done by recursion which resembles the familiar pro cedure by induction in the finite dimensional Situation. Third, the student acquires a good feeling for the linear algebra in infinite di mensions because it is impossible to camouflage problems by topological expedients (in dimension ~O it is easy to see, in a given case, wheth er topological language is appropriate or not) .
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Vector Bundles on Curves - New Directions
The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. It deals with: 1. The relation between conformal blocks and generalised theta functions (Lectures by S. Kumar) 2. Drinfeld Shtukas (Lectures by G. Laumon) 3. Drinfeld modules and Elliptic Sheaves (Lectures by U. Stuhler) The latter topics are useful in connection with Langlands programme for function fields. The contents of the book would give a comprehensive introduction of these topics to graduate students and researchers.
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Lectures on Vector Bundles
This work consists of two courses on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The construction and elementary properties of the moduli spaces of stable bundles are also discussed. In particular, Hilbert-Grothendieck schemes of vector bundles are constructed, and Mumford's geometric invariant theory is succinctly treated. The second part centres on the structure of the moduli space of semi-stable sheaves on the projective plane. Existence conditions for sheaves of given rank and Chern Class and construction ideas are sketched in the general context of projective algebraic surfaces. Professor Le Potier has provided a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.
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Vector 287
Vector is the critical journal of the British Science Fiction Association, publishing articles and features on genre fiction across the world, with some focus on UK science fiction. Vector publishes two to three issues per year. Vector magazine was founded in 1958. Its contributors have included such authors and critics as Brian Aldiss, Gregory Benford, Christopher Fowler, Mary Gentle, Damon Knight, Michael Moorcock, Brian Stableford, and of course many more. In addition to writers and scholars, various artists have generously permitted their work to be used as cover art for the magazine.
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Introduction to Support Vector Machines and Other Kernel-based Learning Methods
This is the first comprehensive introduction to Support Vector Machines (SVMs), a generation learning system based on recent advances in statistical learning theory. SVMs deliver state-of-the-art performance in real-world applications such as text categorisation, hand-written character recognition, image classification, biosequences analysis, etc., and are now established as one of the standard tools for machine learning and data mining. Students will find the book both stimulating and accessible, while practitioners will be guided smoothly through the material required for a good grasp of the theory and its applications. The concepts are introduced gradually in accessible and self-contained stages, while the presentation is rigorous and thorough. Pointers to relevant literature and web sites containing software ensure that it forms an ideal starting point for further study. Equally, the book and its associated web site will guide practitioners to updated literature, new applications, and on-line software.
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