Introduction to Singularities

Introduction to Singularities
Author: Shihoko Ishii
Publisher: Springer
Total Pages: 227
Release: 2014-11-19
Genre: Mathematics
ISBN: 443155081X

This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dim ensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied.

Theorem Proving in Higher Order Logics

Theorem Proving in Higher Order Logics
Author: Klaus Schneider
Publisher: Springer Science & Business Media
Total Pages: 408
Release: 2007-08-28
Genre: Computers
ISBN: 3540745904

This book contains the refereed proceedings of the 20th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2007, held in Kaiserslautern, Germany, September 2007. Among the topics of this volume are formal semantics of specification, modeling, and programming languages, specification and verification of hardware and software, formalization of mathematical theories, advances in theorem prover technology, as well as industrial application of theorem provers.

Isabelle/HOL

Isabelle/HOL
Author: Tobias Nipkow
Publisher: Springer
Total Pages: 220
Release: 2003-07-31
Genre: Mathematics
ISBN: 3540459499

This volume is a self-contained introduction to interactive proof in high- order logic (HOL), using the proof assistant Isabelle 2002. Compared with existing Isabelle documentation, it provides a direct route into higher-order logic, which most people prefer these days. It bypasses ?rst-order logic and minimizes discussion of meta-theory. It is written for potential users rather than for our colleagues in the research world. Another departure from previous documentation is that we describe Markus Wenzel’s proof script notation instead of ML tactic scripts. The l- ter make it easier to introduce new tactics on the ?y, but hardly anybody does that. Wenzel’s dedicated syntax is elegant, replacing for example eight simpli?cation tactics with a single method, namely simp, with associated - tions. The book has three parts. – The ?rst part, Elementary Techniques, shows how to model functional programs in higher-order logic. Early examples involve lists and the natural numbers. Most proofs are two steps long, consisting of induction on a chosen variable followed by the auto tactic. But even this elementary part covers such advanced topics as nested and mutual recursion. – The second part, Logic and Sets, presents a collection of lower-level tactics that you can use to apply rules selectively. It also describes I- belle/HOL’s treatment of sets, functions, and relations and explains how to de?ne sets inductively. One of the examples concerns the theory of model checking, and another is drawn from a classic textbook on formal languages.

Theorem Proving in Higher Order Logics

Theorem Proving in Higher Order Logics
Author: Stefan Berghofer
Publisher: Springer
Total Pages: 517
Release: 2009-08-20
Genre: Computers
ISBN: 3642033598

This book constitutes the refereed proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics, TPHOLs 200, held in Munich, Germany, in August 2009. The 26 revised full papers presented together with 1 proof pearl, 4 tool presentations, and 3 invited papers were carefully reviewed and selected from 55 submissions. The papers cover all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification such as formal semantics of specification, modeling, and programming languages, specification and verification of hardware and software, formalization of mathematical theories, advances in theorem prover technology, as well as industrial application of theorem provers.

Theorem Proving in Higher Order Logics

Theorem Proving in Higher Order Logics
Author: Richard J. Boulton
Publisher: Springer
Total Pages: 405
Release: 2003-06-30
Genre: Computers
ISBN: 3540447555

This volume constitutes the proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2001) held 3–6 September 2001 in Edinburgh, Scotland. TPHOLs covers all aspects of theorem proving in higher order logics, as well as related topics in theorem proving and veri?cation. TPHOLs 2001 was collocated with the 11th Advanced Research Working Conference on Correct Hardware Design and Veri?cation Methods (CHARME 2001). This was held 4–7 September 2001 in nearby Livingston, Scotland at the Institute for System Level Integration, and a joint half-day session of talks was arranged for the 5th September in Edinburgh. An excursion to Traquair House and a banquet in the Playfair Library of Old College, University of Edinburgh were also jointly organized. The proceedings of CHARME 2001 have been p- lished as volume 2144 of Springer-Verlag’s Lecture Notes in Computer Science series, with Tiziana Margaria and Tom Melham as editors. Each of the 47 papers submitted in the full research category was refereed by at least 3 reviewers who were selected by the Program Committee. Of these submissions, 23 were accepted for presentation at the conference and publication in this volume. In keeping with tradition, TPHOLs 2001 also o?ered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief preliminary talk and then discuss their work at a poster session. A supplementary proceedings containing associated papers for work in progress was published by the Division of Informatics at the University of Edinburgh.

Software Composition

Software Composition
Author: Cesare Pautasso
Publisher: Springer Science & Business Media
Total Pages: 272
Release: 2008-03-17
Genre: Computers
ISBN: 3540787887

The goal of the International Symposia on Software Composition is to advance the state of the research in component-based software development. We focus on the challenges related to component development, reuse, veri?cation and, of course,composition.Softwarecompositionisbecomingmoreandmoreimportant as innovation in software engineering shifts from the development of individual components to their reuse and recombination in novel ways. To this end, for the 2008 edition, researchers were solicited to contribute on topics related to component adaptation techniques, composition languages, calculi and type systems, as well as emerging composition techniques such as aspect-oriented programming, service-oriented architectures, and mashups. In line with previous editions of SC, contributions were sought focusing on both theory and practice, with a particular interest in e?orts relating them. This LNCS volume contains the proceedings of the 7th International S- posium on Software Composition, which was held on March 29–30, 2008, as a satellite event of the European Joint Conferences on Theory and Practice of Software (ETAPS), in Budapest, Hungary. We received 90 initial submissions from all over the world, out of which 70 were considered for evaluation by a Program Committee consisting of 30 - ternational experts. Among these submissions, we selected 13 long papers and 6 short papers to be included in the proceedings and presented at the conf- ence. Each paper went through a thoroughrevisionprocess and was reviewedby three to ?ve reviewers. This ensured the necessary quality for publishing these proceedings in time for the event, a ?rst in the history of the symposium.

Parity games, separations, and the modal μ-calculus

Parity games, separations, and the modal μ-calculus
Author: Dittmann, Christoph
Publisher: Universitätsverlag der TU Berlin
Total Pages: 295
Release: 2017-03-08
Genre: Computers
ISBN: 3798328870

The topics of this thesis are the modal μ-calculus and parity games. The modal μ-calculus is a common logic for model-checking in computer science. The model-checking problem of the modal μ-calculus is polynomial time equivalent to solving parity games, a 2-player game on labeled directed graphs. We present the first FPT algorithms (fixed-parameter tractable) for the model-checking problem of the modal μ-calculus on restricted classes of graphs, specifically on classes of bounded Kelly-width or bounded DAG-width. In this process we also prove a general decomposition theorem for the modal μ-calculus and define a useful notion of type for this logic. Then, assuming a class of parity games has a polynomial time algorithm solving it, we consider the problem of extending this algorithm to larger classes of parity games. In particular, we show that joining games, pasting games, or adding single vertices preserves polynomial-time solvability. It follows that parity games can be solved in polynomial time if their underlying undirected graph is a tournament, a complete bipartite graph, or a block graph. In the last chapter we present the first non-trivial formal proof about parity games. We explain a formal proof of positional determinacy of parity games in the proof assistant Isabelle/HOL. Die Themen dieser Dissertation sind der modale μ-Kalkül und Paritätsspiele. Der modale μ-Kalkül ist eine häufig eingesetzte Logik im Bereich des Model-Checkings in der Informatik. Das Model-Checking-Problem des modalen μ-Kalküls ist polynomialzeitäquivalent zum Lösen von Paritätsspielen, einem 2-Spielerspiel auf beschrifteten, gerichteten Graphen. Wir präsentieren die ersten FPT-Algorithmen (fixed-parameter tractable) für das Model-Checking-Problem des modalen μ-Kalküls auf Klassen von Graphen mit beschränkter Kelly-Weite oder beschränkter DAG-Weite. Für diesen Zweck beweisen wir einen allgemeineren Zerlegungssatz für den modalen μ-Kalkül und stellen eine nützliche Definition von Typen für diese Logik vor. Angenommen, eine Klasse von Paritätsspielen hat einen Polynomialzeit-Lösungs-Algorithmus, betrachten wir danach das Problem, diese Klassen zu erweitern auf eine Weise, sodass Polynomialzeit-Lösbarkeit erhalten bleibt. Wir zeigen, dass dies beim Join von Paritätsspielen, beim Pasting und beim Hinzufügen einzelner Knoten der Fall ist. Wir folgern daraus, dass das Lösen von Paritätsspielen in Polynomialzeit möglich ist, falls der unterliegende ungerichtete Graph ein Tournament, ein vollständiger bipartiter Graph oder ein Blockgraph ist. Im letzten Kapitel präsentieren wir den ersten nicht-trivialen formalen Beweis über Paritätsspiele. Wir stellen einen formalen Beweis für die positionale Determiniertheit von Paritätsspielen im Beweis-Assistenten Isabelle/HOL vor.

Introduction to Public Law and Human Rights – REVISION GUIDE

Introduction to Public Law and Human Rights – REVISION GUIDE
Author: Özgür Heval Çınar
Publisher: Transnational Press London
Total Pages: 177
Release: 2021-10-15
Genre: Law
ISBN: 1801350671

Public Law and Human Rights is a core module in the legal education of the United Kingdom (UK). Throughout the world it is known as common law. While common law consists of case-law and statutes, it has reached its present state by incorporating elements of international law, prerogative power and other legal and non-legal sources such as conventions and customs. This book closely examines the public law (constitution and administrative law) and human rights system of the UK (England and Wales in particular). The reason for the emergence of this book is that other publications do not explain such a complex issue in plain language, which makes it very difficult for those taking an interest, in particular A-level as well as LLB/LLM law students. This book does not repeat material that is available in many textbooks that are in print. Rather, it endeavours to present every topic in plain language and concludes every chapter with a fictitious, explanatory sample case. This book will also assist students to prepare for examinations. It comes with a test that summarizes all the subjects contained in the book, which is appropriate to the first stage SQE (Solicitors Qualifying Examination) examination. This concise text brings clearly into focus the key elements of public law and human rights. The Q&A approach, examples and exercises provide an excellent way for students to both gain knowledge and apply that knowledge to this complex area of law. – Dr Ryan Hill, Deputy Head of School, Anglia Ruskin University, Law School, UK This resource presents the core framework of Public Law and human rights within the United Kingdom, and also the key current debates surrounding this subject, in clear and accessible language. The technique of using fictional cases to work through practical issues is an excellent way for students to gain insight into the real world application of theoretical principles. Not only does this book help prepare learners for assessments, it also provides support in developing critical legal thinking which will be of great value in their professional lives. – Javier Garcia Oliva, Professor of Law, The University of Manchester, UK CONTENTS: Abbreviations About the author Foreword PART A. Constitutional Law CHAPTER I. Introduction: The Nature and Sources of the Constitution CHAPTER II. Fundamental Constitutional Principles CHAPTER III. Houses of Parliament and the Legislative Process PART B. Human Rights CHAPTER IV. Human Rights in the UK: Human Rights Act 1998 and European Convention on Human Rights CHAPTER V. Fundamental Freedoms in the Human Rights Act/European Convention on Human Rights PART C. Administrative Law CHAPTER VI. The Principles of Judicial Review and Preliminary Requirements CHAPTER VII. Judicial Review Grounds I: Illegality and Unreasonableness/Irrationality CHAPTER VIII. Judicial Review Grounds II: Procedural Impropriety CHAPTER IX. Administrative Justice: Inquiries, Ombudsman and Tribunals SUMMARY: Sample Test Questions PART A – Constitutional Law PART B – Human Rights PART C – Administrative Law ANSWERS

Rigorous State-Based Methods

Rigorous State-Based Methods
Author: Silvia Bonfanti
Publisher: Springer Nature
Total Pages: 405
Release: 2024
Genre: Application software
ISBN: 3031637909

This book constitutes the refereed proceedings of the 10th International Conference on Rigorous State-Based Methods, ABZ 2024, held in Bergamo, Italy, during June 25-28, 2024. The 29 papers included in this volume were carefully reviewed and selected from 47 submissions. They were organized in topical sections as follows: research papers; short research papers; case study; doctoral symposium.