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BOKU, 2013,
Karolinum, 2013,
Kniha se zabývá konstrukcí a analýzou testů, se zvláštním zřetelem k potřebám testování znalostí na lékařských fakultách. Je míněna jako praktická pomůcka a návod pro pedagogy, kteří sami znalostní testy vytvářejí a využívají, nebo se k tomu chystají. Kniha se snaží být také uceleným vodítkem pro vedení fakult, které o koncepci testování rozhoduje na vyšší úrovni, například pro potřeby přijímacích testů nebo atestací.
Oxford University Press, 2013,
The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments. This allows enlightening reformulations of questions from matrix computations into the language of orthogonal polynomials, Gauss-Christoffel quadrature, continued fractions, and, more generally, of Vorobyev's method of moments. Using the concept of cyclic invariant subspaces, conditions are studied that allow the generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the important practical distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. The investigation includes effects of finite precision arithmetic and focuses on the method of conjugate gradients (CG) and generalised minimal residuals (GMRES) as major examples. There is an emphasis on the way algebraic computations must always be considered in the context of solving real-world problems, where the mathematical modelling, discretisation and computation cannot be separated from each other. The book also underlines the importance of the historical context and demonstrates that knowledge of early developments can play an important role in understanding and resolving very recent computational problems. Many extensive historical notes are included as an inherent part of the text as well as the formulation of some omitted issues and challenges which need to be addressed in future work. This book is applicable to a wide variety of graduate courses on Krylov subspace methods and related subjects, as well as benefiting those interested in the history of mathematics.
Karolinum, 2012,
Monografie dává ucelený přehled o současných technologiích aplikovaných v oblasti molekulární bioinformatiky a slouží k lepší orientaci ve statistických metodách v klinickém a bioinformatickém výzkumu nejen pro mladé a začínající vědce, ale i pro jednooborově zaměřené specialisty. Může pomoci vysokoškolským učitelům lékařských a přírodovědeckých fakult v pregraduálním, postgraduálním i celoživotním vzdělávání, výzkumným pracovníkům v biomedicínských oborech, lékařům a dalším zdravotnickým pracovníkům.
Matfyzpress, 2012,
Tato monografie je úvodem do základních metod používaných při maticových výpočtech. Vychází ze základních poznatků lineární algebry (kapitola 1), na druhé straně se dotýká funkcionální analýzy, resp. analýzy operátorů na konečně rozměrných prostorech. Jednotlivé kapitoly se týkají Schurovy věty (kap. 2), ortogonálních matic a QR rozkladů (kap. 3), Gaussovy eliminace a LU rozkladu (kap. 4), singulárního rozkladu (kap. 5), úloh nejmenších čtverců (kap. 6), částečného problému vlastních čísel, zejm. Lanczosova a Arnoldiho algoritmu (kap. 7), metody sdružených gradientů (kap. 8) a metod Krylovových podprostorů obecně (kap. 9).
Masarykova univerzita, 2012,
Kniha představuje statistické modely pro korelovaná data založené na zobecnění lineární regrese. Obsahuje řadu řešených příkladů (výpočty jsou prováděny v prostředí R). Těžištěm je popis a aplikace lineárního smíšeného modelu (jakožto speciálního případu regresního modelu s náhodnými koeficienty). Věnuje se ale také několika alternativním způsobům odhadu, zejména marginálně formulovaným modelům, GEE (generalized estimating equations) přístupu a Markovovsky formulovaným modelům.
College Publications, 2011,
Vague language and corresponding models of inference and information processing is an important and challenging topic as witnessed by a number of recent monographs and collections of essays devoted to the topic. This volume was published in 2011 by College Publications (London) as volume 36 of their book-series Studies in Logic. It collects fifteen papers, the majority of which originated with talks presented at the conference “Logical Models of Reasoning with Vague Information (LoMoReVI)”, September 14-17, 2009, in Čejkovice, that initiated a EUROCORES/LogICCC project with the same title. At least two features set the current volume apart from other texts: first, the interdisciplinary nature of the topic is nicely reflected by the wide range of interests of the authors, who include philosophers, linguists, logicians, as well as mathematicians and compute scientists. Secondly, all the papers are accompanied by comments written by other authors and a few outside experts. These comments and corresponding replies by the authors document the very lively ongoing debate on adequate models of vague language.
College Publications, 2011,
Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers. This two-volume handbook was published in 2011 by College Publications (London) in their book-series Mathematical Logic and Foundations (a subseries of Studies in Logic). It provides an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, that may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. Despite being located in the realm of pure mathematical logic, this handbook will also be useful for readers interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness. The second volume is devoted to Łukasiewicz logic and MV-algebras, Gödel-Dummett logic and its variants, fuzzy logics in expanded propositional languages, studies of functional representations for fuzzy logics and their free algebras, computational complexity of propositional logics, and arithmetical complexity of first-order logics.
College Publications, 2011,
Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers. This two-volume handbook was published in 2011 by College Publications (London) in their book-series Mathematical Logic and Foundations (a subseries of Studies in Logic). It provides an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, that may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. Despite being located in the realm of pure mathematical logic, this handbook will also be useful for readers interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness. The first volume contains a gentle introduction to MFL, followed by a presentation of an abstract algebraic framework for MFL, chapters on proof theory and algebraic semantics of fuzzy logics, and, finally, an algebraic study of Hájek’s logic BL.
Wiley, 2011,
This book provides the orthopedic, biomechanical, and mathematical basis for the simulation of surgical techniques in orthopedics. It focuses on the numerical modeling of total human joint replacements and simulation of their functions, along with the rigorous biomechanics of human joints and other skeletal parts. The book includes: An introduction to the anatomy and biomechanics of the human skeleton, biomaterials, and problems of alloarthroplasty; Constructions of mathematical model problems of the biomechanics of the human skeleton and its parts; Replacement parts of the human skeleton and corresponding mathematical model problems; Detailed mathematical analyses of mathematical models based on functional analysis and finite element methods; Biomechanical analyses of particular parts of the human skeleton, joints, and corresponding replacements; A discussion of the problems of data processing from nuclear magnetic resonance imaging and computer tomography. The theories presented are applied to specific problems of orthopedics. Numerical results are presented and discussed from both biomechanical and orthopedic points of view and treatment methods are also briefly addressed. Emphasis is placed on the variational approach to the investigated model problems while preserving the orthopedic nature of the investigated problems. The book also presents a study of algorithmic procedures based on these simulation models. This is a highly useful tool for designers, researchers, and manufacturers of joint implants who require the results of suggested experiments to improve existing shapes or to design new shapes. It also benefits graduate students in orthopedics, biomechanics, and applied mathematics.
Cambridge University Press, 2011,
Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and geometry can help in visualizing the behaviour of the problem. In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful. The author has discovered a method that in many (symmetric) cases helps to split huge systems into smaller parts. Many readers will welcome this book, from undergraduates to specialists in mathematics, as well as non-specialists who only use mathematics occasionally, and anyone who enjoys geometric theorems. It acquaints the reader with basic matrix theory, graph theory and elementary Euclidean geometry so that they too can appreciate the underlying connections between these various areas of mathematics and computer science.
FCC Public, 2011,
Process Control is a basic essence in this digital age that helps to keep industries competitive. This book is a detailed guide through the fundamentals of understanding, designing, and practicing control systems. Although an introductory nature of the text, it covers the major elements of process control applicable for students studying automatic control courses, as well as for professionals looking for proven guidance usable in day-to-day operations. Unique features of the text include succinctly comprehensive presentation, complete teaching environment, sensitive selection of methods and techniques, piece of the newest original research, introduction of concepts which are untypical in current process control books, introduction to the modern concepts versus classical concepts and serious effort to emphasize readable language with using acceptable mathematics.
Karolinum, 2010,
Čtvrtý díl edice Biomedicínská informatika je věnován různým typům dat a znalostí, s nimiž se můžeme v biomedicínské oblasti setkat, a to v širokém tematickém záběru od zpracování signálů a obrazů v medicíně přes databázové a informační systémy až po telemedicínské aplikace či modelování biologických systémů. Publikace je určena nejen studentům a učitelům na vysokých školách, ale i výzkumným pracovníkům v biomedicíně, lékařům a dalším zdravotnickým pracovníkům.