Title:
A Proof Theory for Description Logics by Alexandre Rademaker.
SpringerBriefs in Computer Science,
SpringerBriefs in Computer Science,
Author:
Rademaker, Alexandre. author.
SpringerLink (Online service)
General Notes:
Introduction -- Background -- Sequent Calculus for ALC -- Comparing SCalc with other ALC Deduction Systems -- Natural Deduction for ALC.- A Proof Theory for ALCQI -- Proofs and Explanations -- A Prototype Theorem Prover -- Conclusion.
Description Logics (DLs) is a family of formalisms used to represent knowledge of a domain. They are equipped with a formal logic-based semantics. Knowledge representation systems based on description logics provide various inference capabilities that deduce implicit knowledge from the explicitly represented knowledge. A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes.
Publisher:
Springer London : Imprint: Springer,
Publication Place:
London :
ISBN:
9781447140023
Subject:
Computer science.
Computer science.
Mathematical Logic and Formal Languages.
Mathematics of Computing.
Series:
SpringerBriefs in Computer Science,
SpringerBriefs in Computer Science,
Contents:
Introduction -- Background -- Sequent Calculus for ALC -- Comparing SCalc with other ALC Deduction Systems -- Natural Deduction for ALC.- A Proof Theory for ALCQI -- Proofs and Explanations -- A Prototype Theorem Prover -- Conclusion.
Physical Description:
X, 106 p. 16 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-1-4471-4002-3
Publication Date:
2012.
There are no items available
Title:
Proof Theory for Fuzzy Logics by George Metcalfe, Nicola Olivetti, Dov Gabbay.
Applied Logic Series,
Applied Logic Series,
Author:
Metcalfe, George.
Olivetti, Nicola.
Gabbay, Dov.
SpringerLink (Online service)
General Notes:
<P>1. Introduction -- 2. The Semantic Basis -- 3. Hilbert Systems -- 4. Gentzen Systems -- 5. Syntactic Eliminations -- 6. Fundamental Logics -- 7. Uniformity and Efficiency -- 8. First-Order Logics -- 9. Further Topics -- References -- Index.</P>.
<P>Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.</P>
Publisher:
Springer Netherlands,
Publication Place:
Dordrecht :
ISBN:
9781402094095
Subject:
Mathematics.
Logic.
Artificial intelligence.
Algebra.
Logic, Symbolic and mathematical.
Mathematics.
Mathematical Logic and Foundations.
Artificial Intelligence (incl. Robotics).
Logic.
Order, Lattices, Ordered Algebraic Structures.
Series:
Applied Logic Series, 36
Applied Logic Series, 36
Contents:
<P>1. Introduction -- 2. The Semantic Basis -- 3. Hilbert Systems -- 4. Gentzen Systems -- 5. Syntactic Eliminations -- 6. Fundamental Logics -- 7. Uniformity and Efficiency -- 8. First-Order Logics -- 9. Further Topics -- References -- Index.</P>.
Physical Description:
digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-4020-9409-5
Publication Date:
2009.
There are no items available
Title:
Proof Theory The First Step into Impredicativity / by Wolfram Pohlers.
Universitext
Universitext
Author:
Pohlers, Wolfram.
SpringerLink (Online service)
General Notes:
<P>1 Historical Background -- 2 Primitive Recursive Functions and Relations -- 3 Ordinals -- 4 Pure Logic -- 5 Truth Complexities for Pi 1-1-Sentences -- 6 Inductive Definitions -- 7 The Ordinal Analysis for Pean Arithmetic -- 8 Autonomous Ordinals and the Limits of Predicativity -- 9 Ordinal Analysis of the Theory for Inductive Definitions -- 10 Provably Recursive Functions of NT -- 11 Ordinal Analysis for Kripke Platek Set Theory with infinity -- 12 Predicativity Revisited -- 13 Non-Monotone Inductive Definitions -- 14 Epilogue.</P>.
<P>This book verifies with compelling evidence the author’s intent to "write a book on proof theory that needs no previous knowledge of proof theory". Avoiding the cryptic terminology of proof theory as far as possible, the book starts at an elementary level and displays the connections between infinitary proof theory and generalized recursion theory, especially the theory of inductive definitions. As a "warm up" Gentzen's classical analysis of pure number theory is presented in a more modern terminology, followed by an explanation and proof of the famous result of Feferman and Schütte on the limits of predicativity. The author also provides an introduction to ordinal arithmetic, introduces the Veblen hierarchy and employs these functions to design an ordinal notation system for the ordinals below Epsilon 0 and Gamma 0, while emphasizing the first step into impredicativity, that is, the first step beyond Gamma 0. This is first done by an analysis of the theory of non-iterated inductive definitions using Buchholz’s improvement of local predicativity, followed by Weiermann's observation that Buchholz’s method can also be used for predicative theories to characterize their provably recursive functions. A second example presents an ordinal analysis of the theory of $/Pi_2$ reflection, a subsystem of set theory that is proof-theoretically equivalent to Kripke-Platek set.</P> <P></P> <P>The book is pitched at undergraduate/graduate level, and thus addressed to students of mathematical logic interested in the basics of proof theory. It can be used for introductory as well as more advanced courses in proof theory. </P> <P></P> <P>An earlier version of this book was published in 1989 as volume 1407 of the "Lecture Notes in Mathematics" (ISBN 978-3-540-51842-6).</P>
Publisher:
Springer Berlin Heidelberg,
Publication Place:
Berlin, Heidelberg :
ISBN:
9783540693192
Subject:
Mathematics.
Logic, Symbolic and mathematical.
Mathematics.
Mathematical Logic and Foundations.
Series:
Universitext
Universitext
Contents:
<P>1 Historical Background -- 2 Primitive Recursive Functions and Relations -- 3 Ordinals -- 4 Pure Logic -- 5 Truth Complexities for Pi 1-1-Sentences -- 6 Inductive Definitions -- 7 The Ordinal Analysis for Pean Arithmetic -- 8 Autonomous Ordinals and the Limits of Predicativity -- 9 Ordinal Analysis of the Theory for Inductive Definitions -- 10 Provably Recursive Functions of NT -- 11 Ordinal Analysis for Kripke Platek Set Theory with infinity -- 12 Predicativity Revisited -- 13 Non-Monotone Inductive Definitions -- 14 Epilogue.</P>.
Physical Description:
digital.
Electronic Location:
http://dx.doi.org/10.1007/978-3-540-69319-2
Publication Date:
2009.
Title:
Proofs and algorithms : an introduction to logic and computability / Gilles Dowek.
Undergraduate topics in computer science,
Undergraduate Topics in Computer Science.
Author:
Dowek, Gilles.
General Notes:
Includes bibliographical references (p. 151) and index.
Part. 1. Proofs: -- 1. Predicate logic. --Inductive definitions -- Languages -- The languages of predicate logic -- Proofs -- Examples of theories -- Variations on the principle of the excluded middle -- 2. Models. -- The notion of a model -- The Soundness Theorem -- The Completeness Theorem -- Other applications of the notion of model -- Part 2. Algorithms: -- 3. Computable functions. -- Computability over lists and trees -- Eliminating recursion -- Programs -- 4. Computation as a sequence of small steps. -- Rewriting -- The Lambda-Calculus -- Turing Machines -- Part 3. Proofs and algorithms: -- 5. Church's Theorem. -- The notion of reduction -- Representing programs -- Church's Theorem -- Semi-decidabilty -- Gèodel's First Incompleteness Theorem -- 6. Automated theorem proving. -- Sequent Calculus -- Proof search in the sequent Calculus without cuts -- 7. Decidable theories -- 8. Constructivity -- 9. Epilogue.
Publisher:
Springer,
Publication Place:
London ; New York :
ISBN:
9780857291202
0857291203
Subject:
Logic, Symbolic and mathematical.
Algorithms.
Series:
Undergraduate topics in computer science,
Undergraduate Topics in Computer Science.
Contents:
Part. 1. Proofs: -- 1. Predicate logic. --Inductive definitions -- Languages -- The languages of predicate logic -- Proofs -- Examples of theories -- Variations on the principle of the excluded middle -- 2. Models. -- The notion of a model -- The Soundness Theorem -- The Completeness Theorem -- Other applications of the notion of model -- Part 2. Algorithms: -- 3. Computable functions. -- Computability over lists and trees -- Eliminating recursion -- Programs -- 4. Computation as a sequence of small steps. -- Rewriting -- The Lambda-Calculus -- Turing Machines -- Part 3. Proofs and algorithms: -- 5. Church's Theorem. -- The notion of reduction -- Representing programs -- Church's Theorem -- Semi-decidabilty -- Gèodel's First Incompleteness Theorem -- 6. Automated theorem proving. -- Sequent Calculus -- Proof search in the sequent Calculus without cuts -- 7. Decidable theories -- 8. Constructivity -- 9. Epilogue.
Physical Description:
xii, 155 p. : ill. ;
Publication Date:
c2011.
Title:
Proofs and Fundamentals A First Course in Abstract Mathematics / by Ethan D. Bloch.
Undergraduate Texts in Mathematics,
Undergraduate texts in mathematics,
Author:
Bloch, Ethan D.
SpringerLink (Online service)
General Notes:
Preface to the Second Edition -- Preface to the First Edition -- To the Student -- To the Instructor -- Part I. Proofs -- 1. Informal Logic -- 2. Strategies for Proofs -- Part II. Fundamentals -- 3. Sets -- 4. Functions -- 5. Relations -- 6. Finite and Infinite Sets -- Part III. Extras -- 7. Selected Topics -- 8. Explorations -- Appendix: Properties of Numbers -- Bibliography -- Index.
<p>This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis. </p><p>This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations. </p><p>A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. </p><p>Reviews of the first edition: </p><p><i>This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course.<br></i>—Zentralblatt Math</p><p><i>'Proofs and Fundamentals' has many strengths. One notable strength is its excellent organization... There are large exercise sets throughout the book... the exercises are well integrated with the text and vary appropriately from easy to hard... Perhaps the book’s greatest strength is the author’s zeal and skill for helping students write mathematics better.</i><br>—MAA Online</p>
Publisher:
Springer New York,
Publication Place:
New York, NY :
ISBN:
9781441971272
Subject:
Mathematics.
Algebra.
Combinatorics.
Logic, Symbolic and mathematical.
Mathematics.
Mathematical Logic and Foundations.
Algebra.
Combinatorics.
Series:
Undergraduate Texts in Mathematics,
Undergraduate texts in mathematics,
Contents:
Preface to the Second Edition -- Preface to the First Edition -- To the Student -- To the Instructor -- Part I. Proofs -- 1. Informal Logic -- 2. Strategies for Proofs -- Part II. Fundamentals -- 3. Sets -- 4. Functions -- 5. Relations -- 6. Finite and Infinite Sets -- Part III. Extras -- 7. Selected Topics -- 8. Explorations -- Appendix: Properties of Numbers -- Bibliography -- Index.
Physical Description:
XXIV, 360 p. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-4419-7127-2
Publication Date:
2011.
Title:
Proofs from THE BOOK by Martin Aigner, Günter M. Ziegler.
Author:
Aigner, Martin.
Ziegler, Günter M.
SpringerLink (Online service)
General Notes:
Preface -- Number Theory -- Geometry -- Analysis -- Combinatorics -- Graph Theory -- About the Illustrations -- Index.
<P>This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem". </P> <P> From the Reviews </P> <P>"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " <EM>Notices of the AMS, August 1999 </EM></P> <P>"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. Moreover, the exposition makes them transparent. ..." </P> <P><EM>LMS Newsletter, January 1999</EM></P>
Publisher:
Springer Berlin Heidelberg : Imprint: Springer,
Publication Place:
Berlin, Heidelberg :
ISBN:
9783642008566
Subject:
Mathematics.
Computer science.
Global analysis (Mathematics).
Combinatorics.
Geometry.
Number theory.
Mathematics.
Mathematics, general.
Number theory.
Geometry.
Combinatorics.
ANALYSIS.
Computer Science, general.
Edition:
Fourth Edition.
Contents:
Preface -- Number Theory -- Geometry -- Analysis -- Combinatorics -- Graph Theory -- About the Illustrations -- Index.
Physical Description:
VIII, 274 p. 250 illus. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-3-642-00856-6
Publication Date:
2010.
There are no items available
Title:
Proofs from THE BOOK by Martin Aigner, Günter M. Ziegler.
Author:
Aigner, Martin. author.
Ziegler, Günter M. author.
SpringerLink (Online service)
General Notes:
Number Theory: 1. Six proofs of the infinity of primes -- 2. Bertrand’s postulate -- 3. Binomial coefficients are (almost) never powers -- 4. Representing numbers as sums of two squares -- 5. The law of quadratic reciprocity -- 6. Every finite division ring is a field -- 7. The spectral theorem and Hadamard’s determinant problem -- 8. Some irrational numbers -- 9. Three times π2/6 -- Geometry: 10. Hilbert’s third problem: decomposing polyhedral -- 11. Lines in the plane and decompositions of graphs -- 12. The slope problem -- 13. Three applications of Euler’s formula -- 14. Cauchy’s rigidity theorem -- 15. The Borromean rings don’t exist -- 16. Touching simplices -- 17. Every large point set has an obtuse angle -- 18. Borsuk’s conjecture -- Analysis: 19. Sets, functions, and the continuum hypothesis -- 20. In praise of inequalities -- 21. The fundamental theorem of algebra -- 22. One square and an odd number of triangles -- 23. A theorem of Pólya on polynomials -- 24. On a lemma of Littlewood and Offord -- 25. Cotangent and the Herglotz trick -- 26. Buffon’s needle problem -- Combinatorics: 27. Pigeon-hole and double counting -- 28. Tiling rectangles -- 29. Three famous theorems on finite sets -- 30. Shuffling cards -- 31. Lattice paths and determinants -- 32. Cayley’s formula for the number of trees -- 33. Identities versus bijections -- 34. The finite Kakeya problem -- 35. Completing Latin squares -- Graph Theory: 36. The Dinitz problem -- 37. Permanents and the po wer of entropy -- 38. Five-coloring plane graphs -- 39. How to guard a museum -- 40. Turán’s graph theorem -- 41. Communicating without errors -- 42. The chromatic number of Kneser graphs -- 43. Of friends and politicians -- 44. Probability makes counting (sometimes) easy -- About the Illustrations -- Index.
This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant, and the remaining open questions so intriguing that every ma thematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.
Publisher:
Springer Berlin Heidelberg : Imprint: Springer,
Publication Place:
Berlin, Heidelberg :
ISBN:
9783662442050
Subject:
Mathematics.
Computer science.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Number theory.
Combinatorics.
Mathematics.
Mathematics, general.
Number theory.
Geometry.
Combinatorics.
ANALYSIS.
Computer Science, general.
Edition:
5th ed. 2014.
Contents:
Number Theory: 1. Six proofs of the infinity of primes -- 2. Bertrand’s postulate -- 3. Binomial coefficients are (almost) never powers -- 4. Representing numbers as sums of two squares -- 5. The law of quadratic reciprocity -- 6. Every finite division ring is a field -- 7. The spectral theorem and Hadamard’s determinant problem -- 8. Some irrational numbers -- 9. Three times π2/6 -- Geometry: 10. Hilbert’s third problem: decomposing polyhedral -- 11. Lines in the plane and decompositions of graphs -- 12. The slope problem -- 13. Three applications of Euler’s formula -- 14. Cauchy’s rigidity theorem -- 15. The Borromean rings don’t exist -- 16. Touching simplices -- 17. Every large point set has an obtuse angle -- 18. Borsuk’s conjecture -- Analysis: 19. Sets, functions, and the continuum hypothesis -- 20. In praise of inequalities -- 21. The fundamental theorem of algebra -- 22. One square and an odd number of triangles -- 23. A theorem of Pólya on polynomials -- 24. On a lemma of Littlewood and Offord -- 25. Cotangent and the Herglotz trick -- 26. Buffon’s needle problem -- Combinatorics: 27. Pigeon-hole and double counting -- 28. Tiling rectangles -- 29. Three famous theorems on finite sets -- 30. Shuffling cards -- 31. Lattice paths and determinants -- 32. Cayley’s formula for the number of trees -- 33. Identities versus bijections -- 34. The finite Kakeya problem -- 35. Completing Latin squares -- Graph Theory: 36. The Dinitz problem -- 37. Permanents and the po wer of entropy -- 38. Five-coloring plane graphs -- 39. How to guard a museum -- 40. Turán’s graph theorem -- 41. Communicating without errors -- 42. The chromatic number of Kneser graphs -- 43. Of friends and politicians -- 44. Probability makes counting (sometimes) easy -- About the Illustrations -- Index.
Physical Description:
VIII, 308 p. 255 illus., 9 illus. in color. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-662-44205-0
Publication Date:
2014.
Title:
Proofs of the Cantor-Bernstein Theorem A Mathematical Excursion / by Arie Hinkis.
Science Networks. Historical Studies ;
Science Networks. Historical Studies ;
Author:
Hinkis, Arie. author.
SpringerLink (Online service)
General Notes:
Preface. - Part I: Cantor and Dedekind -- Cantor's CBT proof for sets of the power of (II) -- Generalizing Cantor's CBT proof -- CBT in Cantor's 1878 Beitrag -- The theory of inconsistent sets -- Comparability in Cantor's writings -- The scheme of complete disjunction -- Ruptures in the Cantor-Dedekind correspondence -- The inconsistency of Dedekind's infinite set -- Dedekind's proof of CBT -- Part II: The early proofs -- Schröder's Proof of CBT -- Bernstein, Borel and CBT -- Schoenflies' 1900 proof of CBT -- Zermelo's 1901 proof of CBT -- Bernstein's Division Theorem -- Part III: Under the logicist sky -- Russell's 1902 proof of CBT -- The role of CBT in Russell’s Paradox -- Jourdain's 1904 generalization of Grundlagen -- Harward 1905 on Jourdain 1904 -- Poincaré and CBT -- Peano's proof of CBT -- J. Kőnig's strings gestalt -- From kings to graphs -- Jourdain's improvements round -- Zermelo's 1908 proof of CBT -- Korselt's proof of CB -- Proofs of CBT in Principia Mathematica -- The origin of Hausdorff Paradox in BDT -- Part IV: At the Polish school -- Sierpiński's proofs of BDT -- Banach's proof of CBT -- Kuratowski's proof of BDT -- Early fixed-point CBT proofs: Whittaker; Tarski-Knaster -- CBT and BDT for order-types -- Sikorski's proof of CBT for Boolean algebras -- Tarski's proofs of BDT and the inequality-BDT -- Tarski's Fixed-Point Theorem and CBT -- Reichbach's proof of CBT -- Part V: Other ends and beginnings -- Hellmann's proof of CBT -- CBT and intuitionism -- CBT in category theory -- Conclusion -- Bibliography -- Index of names -- Index of subjects.
This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly anything but superficial, as the present book also offers new theoretical insights into the methodology of the development of mathematics (proof-processing), with implications for the historiography of mathematics.
Publisher:
Springer Basel : Imprint: Birkhäuser,
Publication Place:
Basel :
ISBN:
9783034802246
Subject:
Mathematics.
Algebra.
Logic, Symbolic and mathematical.
Mathematics.
History of Mathematical Sciences.
Mathematical Logic and Foundations.
Category Theory, Homological Algebra.
Series:
Science Networks. Historical Studies ; 45
Science Networks. Historical Studies ; 45
Contents:
Preface. - Part I: Cantor and Dedekind -- Cantor's CBT proof for sets of the power of (II) -- Generalizing Cantor's CBT proof -- CBT in Cantor's 1878 Beitrag -- The theory of inconsistent sets -- Comparability in Cantor's writings -- The scheme of complete disjunction -- Ruptures in the Cantor-Dedekind correspondence -- The inconsistency of Dedekind's infinite set -- Dedekind's proof of CBT -- Part II: The early proofs -- Schröder's Proof of CBT -- Bernstein, Borel and CBT -- Schoenflies' 1900 proof of CBT -- Zermelo's 1901 proof of CBT -- Bernstein's Division Theorem -- Part III: Under the logicist sky -- Russell's 1902 proof of CBT -- The role of CBT in Russell’s Paradox -- Jourdain's 1904 generalization of Grundlagen -- Harward 1905 on Jourdain 1904 -- Poincaré and CBT -- Peano's proof of CBT -- J. Kőnig's strings gestalt -- From kings to graphs -- Jourdain's improvements round -- Zermelo's 1908 proof of CBT -- Korselt's proof of CB -- Proofs of CBT in Principia Mathematica -- The origin of Hausdorff Paradox in BDT -- Part IV: At the Polish school -- Sierpiński's proofs of BDT -- Banach's proof of CBT -- Kuratowski's proof of BDT -- Early fixed-point CBT proofs: Whittaker; Tarski-Knaster -- CBT and BDT for order-types -- Sikorski's proof of CBT for Boolean algebras -- Tarski's proofs of BDT and the inequality-BDT -- Tarski's Fixed-Point Theorem and CBT -- Reichbach's proof of CBT -- Part V: Other ends and beginnings -- Hellmann's proof of CBT -- CBT and intuitionism -- CBT in category theory -- Conclusion -- Bibliography -- Index of names -- Index of subjects.
Physical Description:
XXIII, 429 p. 29 illus., 3 illus. in color. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-0348-0224-6
Publication Date:
2013.
Title:
Propaganda and Hogarth's Line of Beauty in the First World War by Georgina Williams.
Author:
Williams, Georgina. author.
SpringerLink (Online service)
General Notes:
Introduction -- 1. The Genealogy of the Line and the Role of Resemblances -- 2. The Poster as a Functional Object -- 3. The Static Representation of Movement in Art and War -- 4. Representing the Real in the Aesthetics of Conflict -- 5. Propaganda and the Wider Visual Ecology of the Era -- Conclusion. .
Propaganda and Hogarth’s ‘Line of Beauty’ in the First World War assesses the literal and metaphoric connotations of movement in William Hogarth’s eighteenth-century theory of a ‘line of beauty’, and subsequently employs it as a mechanism by which the visual propaganda of this era can be innovatively explored. Hogarth’s belief that this line epitomises not only movement, but movement at its most beautiful, creates conditions of possibility whereby the construct can be elevated from traditional analyses and consequently utilised to examine movement in artworks from both literal and metaphorical perspectives. Propagandist promotion of an alternate reality as a challenge to a current ‘real’ lends itself to these dual viewpoints; the early years of the twentieth century saw growth in the advertising of conflict via the pictorial poster, instigating intentionally or otherwise an aesthetic response from soldier-artists embroiled on the battlefields. The ‘line of beauty’ therefore serves as a productive mechanism by which this era of propaganda art can be appraised.
Publisher:
Palgrave Macmillan UK : Imprint: Palgrave Macmillan,
Publication Place:
London :
ISBN:
9781137571946
Subject:
History.
History, Modern.
Great Britain -- History.
Military history.
History.
History of Military.
Modern History.
History of Britain and Ireland.
Contents:
Introduction -- 1. The Genealogy of the Line and the Role of Resemblances -- 2. The Poster as a Functional Object -- 3. The Static Representation of Movement in Art and War -- 4. Representing the Real in the Aesthetics of Conflict -- 5. Propaganda and the Wider Visual Ecology of the Era -- Conclusion. .
Physical Description:
IX, 176 p. 11 illus., 6 illus. in color. online resource.
Electronic Location:
http://dx.doi.org/10.1057/978-1-137-57194-6
Publication Date:
2016.
Title:
Propagation and Extinction Studies of Laminar Lean Premixed Syngas/Air Flames by Yang Zhang.
Springer Theses, Recognizing Outstanding Ph.D. Research,
Springer Theses, Recognizing Outstanding Ph.D. Research,
Author:
Zhang, Yang. author.
SpringerLink (Online service)
General Notes:
Introduction -- Experimental Approach 35 -- Numerical Approach -- Laminar flame speed of lean premixed H2/CO/air flames 71 -- Extinction limit of lean premixed H2/CO/air flames -- Lower flammability limit of H2/CO mixtures -- Dilution effect on the propagation and extinction of lean premixed syngas/air flames 139 -- Conclusion and recommendation -- Nomenclature.
This thesis presents pioneering experimental and numerical studies on three aspects of the combustion characteristics of lean premixed syngas/air flames, namely the laminar flame speed, extinction limit and flammability limit. It illustrates a new extinction exponent concept, which enriches the combustion theory. Above all, the book provides the following: a) a series of carefully measured data and theoretical analyses to reveal the intrinsic mechanisms of the fuel composition effect on the propagation and extinction of lean syngas/air flames; b) a mixing model and correlation to predict the laminar flame speed of multi-component syngas fuels, intended for engineering computations; c) a new “extinction exponent” concept to describe the critical effects of chemical kinetics on the extinction of lean premixed syngas/air flames; and d) the effects and mechanism of the dilution of incombustible components on lean premixed syngas/air flames and the preferential importance among the thermal, chemical and diffusion effects.
Publisher:
Springer Singapore : Imprint: Springer,
Publication Place:
Singapore :
ISBN:
9789811046155
Subject:
Engineering.
Thermodynamics.
Heat engineering.
Heat transfer.
Mass transfer.
Fluid mechanics.
Engineering.
Engineering Fluid Dynamics.
Engineering Thermodynamics, Heat and Mass Transfer.
Thermodynamics.
Energy Efficiency.
Series:
Springer Theses, Recognizing Outstanding Ph.D. Research,
Springer Theses, Recognizing Outstanding Ph.D. Research,
Contents:
Introduction -- Experimental Approach 35 -- Numerical Approach -- Laminar flame speed of lean premixed H2/CO/air flames 71 -- Extinction limit of lean premixed H2/CO/air flames -- Lower flammability limit of H2/CO mixtures -- Dilution effect on the propagation and extinction of lean premixed syngas/air flames 139 -- Conclusion and recommendation -- Nomenclature.
Physical Description:
XVIII, 127 p. 50 illus., 40 illus. in color. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-981-10-4615-5
Publication Date:
2018.
Title:
Propagation Engineering in Radio Links Design by Abdollah Ghasemi, Ali Abedi, Farshid Ghasemi.
Author:
Ghasemi, Abdollah. author.
Abedi, Ali. author.
Ghasemi, Farshid. author.
SpringerLink (Online service)
General Notes:
Introduction to Radiowaves Propagation -- Antenna and Passive Reflectors -- Radiowave Propagation in Satelliet Communication -- Wireless Broadcasting -- Trans-horizon Radiowaves Propagation -- Propagation of Radar Waves -- Short Range Radio Communications -- Noise in Radiowave Propagation -- Improvement Techniques in Radiowave Reception.
Propagation Engineering in Radio Link Design covers the basic principles of radiowaves propagation in a practical manner. This fundamental understanding enables the readers to design radio links efficiently. This book elaborates on new achievements as well as recently developed propagation models. This is in addition to a comprehensive overview of fundamentals of propagation in various scenarios. It examines theoretical calculations, approaches and applied procedures needed for radio links design. The authors study and analysis of the main propagation phenomena and its mechanisms based on the recommendations of International Telecommunications Union, (ITU). The book has been organized in 9 chapters and examines the role of antennas and passive reflectors in radio services, propagation mechanisms related to radar, satellite, short distance, broadcasting and trans-horizon radio links, with two chapters devoted to radio noise and main parameters of radio link design. The book presents some 278 illustrations, 50 tables, 110 solved examples, 200 questions and 170 problems.
Publisher:
Springer New York : Imprint: Springer,
Publication Place:
New York, NY :
ISBN:
9781461453147
Subject:
Engineering.
Computer network architectures.
Telecommunication.
Engineering.
Communications Engineering, Networks.
Signal, Image and Speech Processing.
Computer Systems Organization and Communication Networks.
Contents:
Introduction to Radiowaves Propagation -- Antenna and Passive Reflectors -- Radiowave Propagation in Satelliet Communication -- Wireless Broadcasting -- Trans-horizon Radiowaves Propagation -- Propagation of Radar Waves -- Short Range Radio Communications -- Noise in Radiowave Propagation -- Improvement Techniques in Radiowave Reception.
Physical Description:
XVIII, 549 p. 274 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-1-4614-5314-7
Publication Date:
2013.
Title:
Propagation Engineering in Wireless Communications by Abdollah Ghasemi, Ali Abedi, Farshid Ghasemi.
Author:
Ghasemi, Abdollah. author.
Abedi, Ali. author.
Ghasemi, Farshid. author.
SpringerLink (Online service)
General Notes:
Ch. 1 Introduction to Radiowaves -- Ch. 2 Basic Principles in Radiowave Propagation -- Ch. 3 Radiowave Propagation in Troposphere -- Ch. 4 Radiowave Propagation in Ionosphere -- Ch. 5 Propagation in 3 KHz to 30 MHz Band -- Ch. 6 Terrestrial Mobile Radio Propagation -- Ch. 7 Line of Sight Propagation -- Ch. 8 Selected Topics in Radiowave Propagation.
Wireless communications has seen explosive growth in recent decades, in a realm that is both broad and rapidly expanding to include satellite services, navigational aids, remote sensing, telemetering, audio and video broadcasting, high-speed data communications, mobile radio systems and much more. Propagation Engineering in Wireless Communications deals with the basic principles of radiowaves propagation for frequency bands used in radio-communications, offering descriptions of new achievements and newly developed propagation models. The book bridges the gap between theoretical calculations and approaches, and applied procedures needed for advanced radio links design. The primary objective of this two-volume set is to demonstrate the fundamentals, and to introduce propagation phenomena and mechanisms that engineers are likely to encounter in the design and evaluation of radio links of a given type and operating frequency. Volume one covers basic principles, along with tropospheric and ionospheric propagation, MF/HF ionospheric links and mobile and fixed line of sight tropospheric radio communications complete with special topics related to radiowaves propagation in guided media and FSO links. The second volume examines propagation mechanisms related to radar, satellite, short distance, broadcasting and trans-horizon radio links, with two chapters devoted to radio noise and main parameters of radio link design. Each chapter offers an introduction, definitions, basic formulas and expressions, applied relations, calculation procedures, tables, figures, examples, summary, questions and problems related to the chapter topic. Most of the principles discussed here are based on the recommendations of the International Telecommunications Union (ITU). The book presents some 140 illustrations, 20 tables, 80 solved examples, 180 questions and 140 problems, along with acronyms and appendices.
Publisher:
Springer New York : Imprint: Springer,
Publication Place:
New York, NY :
ISBN:
9781461410775
Subject:
Engineering.
Computer network architectures.
Microwaves.
Telecommunication.
Engineering.
Communications Engineering, Networks.
Computer Systems Organization and Communication Networks.
Microwaves, RF and Optical Engineering.
Edition:
1.
Contents:
Ch. 1 Introduction to Radiowaves -- Ch. 2 Basic Principles in Radiowave Propagation -- Ch. 3 Radiowave Propagation in Troposphere -- Ch. 4 Radiowave Propagation in Ionosphere -- Ch. 5 Propagation in 3 KHz to 30 MHz Band -- Ch. 6 Terrestrial Mobile Radio Propagation -- Ch. 7 Line of Sight Propagation -- Ch. 8 Selected Topics in Radiowave Propagation.
Physical Description:
XVII, 434p. 176 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-1-4614-1077-5
Publication Date:
2012.
Title:
Propagation Engineering in Wireless Communications by Abdollah Ghasemi, Ali Abedi, Farshid Ghasemi.
Author:
Ghasemi, Abdollah. author.
Abedi, Ali. author.
Ghasemi, Farshid. author.
SpringerLink (Online service)
General Notes:
Introduction to Radiowaves -- Basic Principles in Radiowave Propagation -- Radiowave Propagation in Troposphere -- Radiowave Propagation in Ionosphere -- Propagation in 3KHz to 30MHz Band -- Terrestrial Mobile Radio Propagation -- Line of Sight Propagation -- Propagation in Guided Media -- Selected Topics in Radiowave Propagation -- Appendix -- Acronyms -- References -- Index.
This book covers the basic principles for understanding radio wave propagation for common frequency bands used in radio-communications. This includes achievements and developments in propagation models for wireless communication. This book is intended to bridge the gap between the theoretical calculations and approaches to the applied procedures needed for radio links design in a proper manner. The authors emphasize propagation engineering by giving fundamental information and explain the use of basic principles together with technical achievements. This new edition includes additional information on radio wave propagation in guided media and technical issues for fiber optics cable networks with several examples and problems. This book also includes a solution manual - with 90 solved examples distributed throughout the chapters - and 158 problems including practical values and assumptions.
Publisher:
Springer International Publishing : Imprint: Springer,
Publication Place:
Cham :
ISBN:
9783319327839
Subject:
Engineering.
Computer organization.
Microwaves.
Optical engineering.
Electrical engineering.
Engineering.
Communications Engineering, Networks.
Computer Systems Organization and Communication Networks.
Microwaves, RF and Optical Engineering.
Edition:
2nd ed. 2016.
Contents:
Introduction to Radiowaves -- Basic Principles in Radiowave Propagation -- Radiowave Propagation in Troposphere -- Radiowave Propagation in Ionosphere -- Propagation in 3KHz to 30MHz Band -- Terrestrial Mobile Radio Propagation -- Line of Sight Propagation -- Propagation in Guided Media -- Selected Topics in Radiowave Propagation -- Appendix -- Acronyms -- References -- Index.
Physical Description:
XVII, 458 p. 193 illus., 5 illus. in color. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-319-32783-9
Publication Date:
2016.
Title:
Propagation of SLF/ELF Electromagnetic Waves by Weiyan Pan, Kai Li.
Advanced Topics in Science and Technology in China,
Advanced Topics in Science and Technology in China,
Author:
Pan, Weiyan. author.
Li, Kai. author.
SpringerLink (Online service)
General Notes:
Historical and Technical Overview of SLF/ELF Electromagnetic Wave Propagation -- Excitation and Propagation of SLF/ELF Electromagnetic Waves in the Earth-Ionosphere Waveguide/Cavity -- Spherical Harmonic Series Solution for SLF/ELF Field in Earth-Ionosphere Waveguide/Cavity -- SLF/ELF Field in Air and Ionosphere Generated by Earthquake Radiation Source -- Propagation of SLF/ELF Waves in Anisotropic Ionosphere -- ELF Wave Propagation along Sea-Rock Boundary and Marine Controlled-Source Electromagnetics Method -- Radiation and Propagation of SLF/ELF Electromagnetic Waves of Space Borne Transmitter -- Atmospheric Noises in SLF/ELF Ranges.
This book deals with the SLF/ELF wave propagation, an important branch of electromagnetic theory. The SLF/ELF wave propagation theory is well applied in earthquake electromagnetic radiation, submarine communication, thunderstorm detection, and geophysical prospecting and diagnostics. The propagation of SLF/ELF electromagnetic waves is introduced in various media like the earth-ionospheric waveguide, ionospheric plasma, sea water, earth, and the boundary between two different media or the stratified media. Applications in the earthquake electromagnetic radiation and the submarine communications are also addressed. This book is intended for scientists and engineers in the fields of radio propagation and EM theory and applications. Prof. Pan is a professor at China Research Institute of Radiowave Propagation in Qingdao (China). Dr. Li is a professor at Zhejiang University in Hangzhou (China).
Publisher:
Springer Berlin Heidelberg : Imprint: Springer,
Publication Place:
Berlin, Heidelberg :
ISBN:
9783642390500
Subject:
Engineering.
Geophysics.
Algebra.
Field theory (Physics).
Optics.
Electrodynamics.
Microwaves.
Optical engineering.
Engineering.
Microwaves, RF and Optical Engineering.
Geophysics/Geodesy.
Optics and Electrodynamics.
Field Theory and Polynomials.
Series:
Advanced Topics in Science and Technology in China,
Advanced Topics in Science and Technology in China,
Contents:
Historical and Technical Overview of SLF/ELF Electromagnetic Wave Propagation -- Excitation and Propagation of SLF/ELF Electromagnetic Waves in the Earth-Ionosphere Waveguide/Cavity -- Spherical Harmonic Series Solution for SLF/ELF Field in Earth-Ionosphere Waveguide/Cavity -- SLF/ELF Field in Air and Ionosphere Generated by Earthquake Radiation Source -- Propagation of SLF/ELF Waves in Anisotropic Ionosphere -- ELF Wave Propagation along Sea-Rock Boundary and Marine Controlled-Source Electromagnetics Method -- Radiation and Propagation of SLF/ELF Electromagnetic Waves of Space Borne Transmitter -- Atmospheric Noises in SLF/ELF Ranges.
Physical Description:
X, 265 p. 132 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-642-39050-0
Publication Date:
2014.
Title:
Propagation Phenomena in Real World Networks edited by Dariusz Król, Damien Fay, Bogdan Gabryś.
Intelligent Systems Reference Library,
Intelligent Systems Reference Library,
Author:
Król, Dariusz. editor.
Fay, Damien. editor.
Gabryś, Bogdan. editor.
SpringerLink (Online service)
General Notes:
Epidemic Models: their Spread, Analysis and Invasions in Scale-Free Networks -- Information Propagation in a Social Network: The Case of a Fish Schooling Algorithm -- Models for Trust Inference in Social Networks.-Assessing the role of network effects in propagation phenomena in real world networks -- Resource Constrained Randomized Coverage Strategies for Unstructured Networks -- Petri Net-Based Modelling and Simulation of Transport Network Segments -- Bio-inspired Routing Strategies for Wireless Sensor Networks -- Analysis of Peer-to-Peer Botnet Attacks and Defenses -- Generating Robust and Efficient Networks Under Targeted Attacks -- Cancer - a Story on Fault Propagation in Gene-Cellular Networks -- Propagation Models and Analysis for Mobile Phone Data Analytics -- Information Propagation in Social Networks during Crises: A structural Framework -- Simulations of Financial Contagion in Interbank Networks: Some Methodological Issues -- Maximizing Social Influence in Real-World Networks - the State of the Art and Current Challenges.
“Propagation, which looks at spreading in complex networks, can be seen from many viewpoints; it is undesirable, or desirable, controllable, the mechanisms generating that propagation can be the topic of interest, but in the end all depends on the setting. This book covers leading research on a wide spectrum of propagation phenomenon and the techniques currently used in its modelling, prediction, analysis and control. Fourteen papers range over topics including epidemic models, models for trust inference, coverage strategies for networks, vehicle flow propagation, bio-inspired routing algorithms, P2P botnet attacks and defences, fault propagation in gene-cellular networks, malware propagation for mobile networks, information propagation in crisis situations, financial contagion in interbank networks, and finally how to maximize the spread of influence in social networks. The compendium will be of interest to researchers, those working in social networking, communications and finance and is aimed at providing a base point for further studies on current research. Above all, by bringing together research from such diverse fields, the book seeks to cross-pollinate ideas, and give the reader a glimpse of the breath of current research.”.
Publisher:
Springer International Publishing : Imprint: Springer,
Publication Place:
Cham :
ISBN:
9783319159164
Subject:
Engineering.
Artificial intelligence.
Computational intelligence.
Engineering.
Computational intelligence.
Artificial Intelligence (incl. Robotics).
Series:
Intelligent Systems Reference Library, 85
Intelligent Systems Reference Library, 85
Contents:
Epidemic Models: their Spread, Analysis and Invasions in Scale-Free Networks -- Information Propagation in a Social Network: The Case of a Fish Schooling Algorithm -- Models for Trust Inference in Social Networks.-Assessing the role of network effects in propagation phenomena in real world networks -- Resource Constrained Randomized Coverage Strategies for Unstructured Networks -- Petri Net-Based Modelling and Simulation of Transport Network Segments -- Bio-inspired Routing Strategies for Wireless Sensor Networks -- Analysis of Peer-to-Peer Botnet Attacks and Defenses -- Generating Robust and Efficient Networks Under Targeted Attacks -- Cancer - a Story on Fault Propagation in Gene-Cellular Networks -- Propagation Models and Analysis for Mobile Phone Data Analytics -- Information Propagation in Social Networks during Crises: A structural Framework -- Simulations of Financial Contagion in Interbank Networks: Some Methodological Issues -- Maximizing Social Influence in Real-World Networks - the State of the Art and Current Challenges.
Physical Description:
XVIII, 364 p. 97 illus., 32 illus. in color. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-319-15916-4
Publication Date:
2015.
Title:
Propagazione delle onde elettromagnetiche edited by Dario Graffi.
C.I.M.E. Summer Schools ;
C.I.M.E. Summer Schools ;
Author:
Graffi, Dario. editor.
SpringerLink (Online service)
General Notes:
Lectures: G. Toraldo di Francia: Lezioni sulla teoria della diffrazione elettromagnetica -- C.J. Bouwkamp: Développement en série de multipôles du champ électromagnétique rayonné par des sources données -- Seminars: G. Eckart: Sur le fading des ondes ultracourtes et son analyse -- G. Agostinelli: Sulla teoria delle guide d´onda -- D. Graffi: Guide d´onda con dielettrico eterogeneo.
Lectures: G. Toraldo di Francia: Lezioni sulla teoria della diffrazione elettromagnetica.- C.J. Bouwkamp: Theorie des multipoles, de l'antenne et de la diffraction des ondes.- Seminars: G. Eckart: Sur le fading des ondes ultracourtes et son analyse.- G. Agostinelli: Sulla teoria delle guide d´onda.- D. Graffi: Guide d´onda con dielettrico eterogeneo.
Publisher:
Springer Berlin Heidelberg,
Publication Place:
Berlin, Heidelberg :
ISBN:
9783642109171
Subject:
Mathematics.
Differential equations, Partial.
Microwaves.
Mathematics.
Partial differential equations.
Microwaves, RF and Optical Engineering.
Series:
C.I.M.E. Summer Schools ; 10
C.I.M.E. Summer Schools ; 10
Contents:
Lectures: G. Toraldo di Francia: Lezioni sulla teoria della diffrazione elettromagnetica -- C.J. Bouwkamp: Développement en série de multipôles du champ électromagnétique rayonné par des sources données -- Seminars: G. Eckart: Sur le fading des ondes ultracourtes et son analyse -- G. Agostinelli: Sulla teoria delle guide d´onda -- D. Graffi: Guide d´onda con dielettrico eterogeneo.
Physical Description:
231pagg. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-642-10917-1
Publication Date:
2012.
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