First Order Logic Raymond Smullyan

  first order logic raymond smullyan: First-order Logic Raymond M. Smullyan, 1995-01-01 Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in analytic or cut free methods. The focus in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations.
  first order logic raymond smullyan: A Beginner's Guide to Mathematical Logic Raymond M. Smullyan, 2014-07-23 Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. Dover (2014) original publication. See every Dover book in print at www.doverpublications.com
  first order logic raymond smullyan: Logical Labyrinths Raymond Smullyan, 2008-12-22 This book features a unique approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought. It serves as a bridge from the author's puzzle books to his technical writing in the fascinating field of mathematical logic. Using the logic of lying and truth-telling, the au
  first order logic raymond smullyan: The Gödelian Puzzle Book Raymond M. Smullyan, 2013-08-21 These logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. No background in formal logic necessary.
  first order logic raymond smullyan: Theory of Formal Systems Raymond M. Smullyan, 1961 This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.
  first order logic raymond smullyan: Raymond Smullyan on Self Reference Melvin Fitting, Brian Rayman, 2018-01-11 This book collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan’s work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor Smullyan operated, offering extensions and re-evaluations of his academic work on self-reference, applying self-referential logic to art and nature, and lastly, offering new puzzles designed to communicate otherwise esoteric concepts in mathematical logic, in the manner for which Professor Smullyan was so well known. This book is suitable for students, scholars and logicians who are interested in learning more about Raymond Smullyan's work and life.
  first order logic raymond smullyan: Alice in Puzzle-land Raymond M. Smullyan, Martin Gardner, Greer Fitting, 2011 Characters from Alice's Adventures in Wonderland and Through the Looking-Glass populate these 88 intriguing puzzles. Mathematician Raymond Smullyan re-creates the spirit of Lewis Carroll's writings in puzzles involving word play, logic and metalogic, and philosophical paradoxes. Challenges range from easy to difficult and include solutions, plus 60 charming illustrations. An ingenious book. — Boston Globe.
  first order logic raymond smullyan: The Lady Or the Tiger? Raymond M. Smullyan, 2009-01-01 Another scintillating collection of brilliant problems and paradoxes by the most entertaining logician and set theorist who ever lived. — Martin Gardner. Inspired by the classic tale of a prisoner's dilemma, these whimsically themed challenges involve paradoxes about probability, time, and change; metapuzzles; and self-referentiality. Nineteen chapters advance in difficulty from relatively simple to highly complex.
  first order logic raymond smullyan: To Mock a Mockingbird Raymond M. Smullyan, 2000 In this entertaining and challenging collection of logic puzzles, Raymond Smullyan -- author of Forever Undecided -- continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time. In the first part of the book, he transports us once again to that wonderful realm where knights, knaves, twin sisters, quadruplet brothers, gods, demons, and mortals either always tell the truth or always lie, and where truth-seekers are set a variety of fascinating problems. The section culminates in an enchanting and profound metapuzzle in which Inspector Craig of Scotland Yard gets involved in a search for the Fountain of Youth on the Island of Knights and Knaves. In the second part of To Mock a Mockingbird, we accompany the Inspector on a summer-long adventure into the field of combinatory logic (a branch of logic that plays an important role in computer science and artificial intelligence). His adventure, which includes enchanted forests, talking birds, bird sociologists, and a classic quest, provides for us along the way the pleasure of solving puzzles of increasing complexity until we reach the Master Forest and -- thanks to Godel's famous theorem -- the final revelation.
  first order logic raymond smullyan: Forever Undecided Raymond M. Smullyan, 2012-07-04 Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!
  first order logic raymond smullyan: Set Theory and the Continuum Problem Raymond M. Smullyan, Melvin Fitting, 2010 A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.
  first order logic raymond smullyan: What is the Name of this Book? Raymond M. Smullyan, 2011 A celebrated mathematician presents more than 200 increasingly complex problems that delve into Gödel's undecidability theorem and other examples of the deepest paradoxes of logic and set theory. Solutions.
  first order logic raymond smullyan: Introduction to Logic Alfred Tarski, 2013-07-04 This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.
  first order logic raymond smullyan: The Chess Mysteries of Sherlock Holmes Raymond M. Smullyan, 2012 Join Holmes and Watson as they examine interrupted games to deduce prior moves. A series of increasingly complex chess mysteries culminates in a double murder perpetrated by Professor Moriarty. The master sleuth instructs his companion (and us) in the intricacies of retrograde analysis; readers need only a knowledge of how the pieces move.
  first order logic raymond smullyan: Logic for Computer Science Jean H. Gallier, 2015-06-18 This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.
  first order logic raymond smullyan: Godel's Incompleteness Theorems Raymond M. Smullyan, 1992-08-20 Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently undecidable. His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
  first order logic raymond smullyan: Diagonalization and Self-reference Raymond M. Smullyan, 1994 The main purpose of this book is to present a unified treatment of fixed points as they occur in Godel's incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. The book provides a survey of introductory material and a summary of recent research. The firstchapters are of an introductory nature and consist mainly of exercises with solutions given to most of them.
  first order logic raymond smullyan: Satan, Cantor & Infinity Raymond M. Smullyan, 2009-01-01 Honorable knights, lying knaves, and other fanciful characters populate this unusual survey of the principles underlying the works of Georg Cantor. Created by a renowned mathematician, these engaging puzzles apply logical precepts to issues of infinity, probability, time, and change. They require a strong mathematics background and feature complete solutions.
  first order logic raymond smullyan: Mathematical Logic H.-D. Ebbinghaus, J. Flum, Wolfgang Thomas, 1996-11-15 This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
  first order logic raymond smullyan: This Book Needs No Title Raymond Smullyan, 1986-10-15 From Simon & Schuster, This Book Needs No Title is Raymond Smullyan's budget of living paradoxes—the author of What is the Name of This Book? Including eighty paradoxes, logical labyrinths, and intriguing enigmas progress from light fables and fancies to challenging Zen exercises and a novella and probe the timeless questions of philosophy and life.
  first order logic raymond smullyan: A Beginner's Guide to Mathematical Logic Raymond M. Smullyan, 2014-03-19 Combining stories of great writers and philosophers with quotations and riddles, this original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2014 edition.
  first order logic raymond smullyan: Modelling Puzzles in First Order Logic Adrian Groza, 2021-10-26 Keeping students involved and actively learning is challenging. Instructors in computer science are aware of the cognitive value of modelling puzzles and often use logical puzzles as an efficient pedagogical instrument to engage students and develop problem-solving skills. This unique book is a comprehensive resource that offers teachers and students fun activities to teach and learn logic. It provides new, complete, and running formalisation in Propositional and First Order Logic for over 130 logical puzzles, including Sudoku-like puzzles, zebra-like puzzles, island of truth, lady and tigers, grid puzzles, strange numbers, or self-reference puzzles. Solving puzzles with theorem provers can be an effective cognitive incentive to motivate students to learn logic. They will find a ready-to-use format which illustrates how to model each puzzle, provides running implementations, and explains each solution. This concise and easy-to-follow textbook is a much-needed support tool for students willing to explore beyond the introductory level of learning logic and lecturers looking for examples to heighten student engagement in their computer science courses.
  first order logic raymond smullyan: A First Course in Logic Mark Verus Lawson, 2018-12-07 A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists. There are three components to this course: propositional logic; Boolean algebras; and predicate/first-order, logic. Logic is the basis of proofs in mathematics — how do we know what we say is true? — and also of computer science — how do I know this program will do what I think it will? Surprisingly little mathematics is needed to learn and understand logic (this course doesn't involve any calculus). The real mathematical prerequisite is an ability to manipulate symbols: in other words, basic algebra. Anyone who can write programs should have this ability.
  first order logic raymond smullyan: First Course in Mathematical Logic Patrick Suppes, Shirley Hill, 2012-04-30 Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.
  first order logic raymond smullyan: Handbook of Tableau Methods M. D'Agostino, Dov M. Gabbay, Reiner Hähnle, J. Posegga, 2013-03-09 Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area.
  first order logic raymond smullyan: Mathematical Logic Stephen Cole Kleene, 2013-04-22 Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
  first order logic raymond smullyan: Introduction to Logic Harry J. Gensler, 2012-08-06 Introduction to Logic combines likely the broadest scope of any logic textbook available with clear, concise writing and interesting examples and arguments. Its key features, all retained in the Second Edition, include: • simpler ways to test arguments than those available in competing textbooks, including the star test for syllogisms • a wide scope of materials, making it suitable for introductory logic courses (as the primary text) or intermediate classes (as the primary or supplementary book) • engaging and easy-to-understand examples and arguments, drawn from everyday life as well as from the great philosophers • a suitability for self-study and for preparation for standardized tests, like the LSAT • a reasonable price (a third of the cost of many competitors) • exercises that correspond to the LogiCola program, which may be downloaded for free from the web. This Second Edition also: • arranges chapters in a more useful way for students, starting with the easiest material and then gradually increasing in difficulty • provides an even broader scope with new chapters on the history of logic, deviant logic, and the philosophy of logic • expands the section on informal fallacies • includes a more exhaustive index and a new appendix on suggested further readings • updates the LogiCola instructional program, which is now more visually attractive as well as easier to download, install, update, and use.
  first order logic raymond smullyan: The Blackwell Guide to Philosophical Logic Lou Goble, 2001-08-30 This volume presents a definitive introduction to twenty core areas of philosophical logic including classical logic, modal logic, alternative logics and close examinations of key logical concepts. The chapters, written especially for this volume by internationally distinguished logicians, philosophers, computer scientists and linguists, provide comprehensive studies of the concepts, motivations, methods, formal systems, major results and applications of their subject areas. The Blackwell Guide to Philosophical Logic engages both general readers and experienced logicians and provides a solid foundation for further study.
  first order logic raymond smullyan: Four Lives Jason Rosenhouse, Raymond M. Smullyan, 2014-02-20 This best of hardcover collection of works by Raymond Smullyan features logic puzzles, musings on mathematical logic and paradoxes, chess problems, and thoughts on the philosophy of religion, plus personal tributes to the author.
  first order logic raymond smullyan: Reflections: The Magic, Music And Mathematics Of Raymond Smullyan Raymond M Smullyan, 2015-04-23 This is an exciting if not rambling account of events of Raymond Smullyan's four lives — as a mathematical logician, musician, magician, and author — together with thoughts that come to his mind as he recalls them. This book includes topics from some of Smullyan's twenty-six books, as well as many of his favorite anecdotes and jokes. It also presents some generalizations of theorems of the great logicians Gödel and Tarski, and discusses logic in general, and how he won his wife with a logic trick! Smullyan also relates some of his teaching experiences, and expresses his views on mathematical education, and how our present textbooks are primarily responsible for its decline! About his life as a pianist, Smullyan relates a good deal about his experiences with the Piano Society — a wonderful organization to which he is a staunch contributor, and how he has had such delightful relations with many of its members. Last but not least, Smullyan recounts how he has known some lovely ladies over the years.
  first order logic raymond smullyan: Games for Your Mind Jason Rosenhouse, 2022-09-27 A lively and engaging look at logic puzzles and their role in mathematics, philosophy, and recreation Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself. In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt Gödel's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data. Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the Hardest Logic Puzzle Ever, metapuzzles, paradoxes, and the logic puzzles in detective stories.
  first order logic raymond smullyan: An Introduction to Mathematical Logic Richard E. Hodel, 2013-01-01 This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
  first order logic raymond smullyan: Logic, Logic, and Logic George Boolos, 1998 George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.
  first order logic raymond smullyan: First-Order Logic and Automated Theorem Proving Melvin Fitting, 2012-12-06 There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scien tists. Although there is a common core to all such books, they will be very different in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer science formal logic turns up in a number of areas, from pro gram verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theo rem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but, not incompleteness issues. The first item to be addressed is, What are we talking about and why are we interested in it? We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.
  first order logic raymond smullyan: An Introduction to Gödel's Theorems Peter Smith, 2007-07-26 Peter Smith examines Gödel's Theorems, how they were established and why they matter.
  first order logic raymond smullyan: An Introduction to Formal Logic Peter Smith, 2003-11-06 Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
  first order logic raymond smullyan: Let's Play Math Denise Gaskins, 2012-09-04
  first order logic raymond smullyan: Toposes, Triples and Theories M. Barr, C. Wells, 2013-06-09 As its title suggests, this book is an introduction to three ideas and the connections between them. Before describing the content of the book in detail, we describe each concept briefly. More extensive introductory descriptions of each concept are in the introductions and notes to Chapters 2, 3 and 4. A topos is a special kind of category defined by axioms saying roughly that certain constructions one can make with sets can be done in the category. In that sense, a topos is a generalized set theory. However, it originated with Grothendieck and Giraud as an abstraction of the of the category of sheaves of sets on a topological space. Later, properties Lawvere and Tierney introduced a more general id~a which they called elementary topos (because their axioms did not quantify over sets), and they and other mathematicians developed the idea that a theory in the sense of mathematical logic can be regarded as a topos, perhaps after a process of completion. The concept of triple originated (under the name standard construc in Godement's book on sheaf theory for the purpose of computing tions) sheaf cohomology. Then Peter Huber discovered that triples capture much of the information of adjoint pairs. Later Linton discovered that triples gave an equivalent approach to Lawverc's theory of equational theories (or rather the infinite generalizations of that theory). Finally, triples have turned out to be a very important tool for deriving various properties of toposes.
  first order logic raymond smullyan: First-order Logic, by Raymond M. Smullyan Raymond M. Smullyan, 1968
  first order logic raymond smullyan: Logic, Meaning and Computation C. Anthony Anderson, Michael Zelëny, 2012-12-06 This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.
对一个陌生的英文名字，如何快速确定哪个是姓哪个是名？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业、友善的社区 …

Last name 和 First name 到底哪个是名哪个是姓？ - 知乎
Last name 和 First name 到底哪个是名哪个是姓？ 上学的时候老师说因为英语文化中名在前，姓在后，所以Last name是姓，first name是名，假设一个中国人叫孙悟空，那么他的first nam…

GM、VP、FVP、CIO都是什么职位？ - 知乎
FVP(First Vice President)第一副总裁 . AVP(Assistant Vice President)副总裁助理 . CEO(Chief Executive Officer)首席执行官，类似总经理、总裁，是企业的法人代表。 COO(Chief Operations …

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在使用cursor导入deepseek的API时报错如下所示，是本人操作有所不对吗？

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a.First （ = First of all）I must finish this work.（含义即，先完成这项工作再说，因为这是必须的，重要的，至于其它，再说吧） b.First come，first served .先来，先招待（最重要） c.Friendship …

贝塞尔函数及其性质 - 知乎
为第一类贝塞尔函数 (Bessel functions of the first kind)， 为第二类贝塞尔函数 (Bessel functions of the second kind)，有的也记为 。 第一类贝塞尔函数积分表达式. 对于整数阶n， 该公式也 …

有大神公布一下Nature Communications从投出去到Online的审稿 …
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业、友善的社区 …

EndNote如何设置参考文献英文作者姓全称，名缩写？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业、友善的社区 …

论文作者后标注了共同一作（数字1）但没有解释标注还算共一 …
Aug 26, 2022 · 是在不同作者姓名的右上角标了数字1吗？ 共同作者可不是这么标的。 标注共同一作的方法并不是有的作者以为的上下并列，而是在共同第一作者的右上角标注相同的符号，比如“*、# …

发表sci共同第一作者(排名第二)有用吗？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业、友善的社区 …

对一个陌生的英文名字，如何快速确定哪个是姓哪个是名？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业、友善的社区氛围、独特的产品机制以及结构化和易获得的优质内 …

Last name 和 First name 到底哪个是名哪个是姓？ - 知乎
Last name 和 First name 到底哪个是名哪个是姓？ 上学的时候老师说因为英语文化中名在前，姓在后，所以Last name是姓，first name是名，假设一个中国人叫孙悟空，那么他的first nam…

GM、VP、FVP、CIO都是什么职位？ - 知乎
FVP(First Vice President)第一副总裁 . AVP(Assistant Vice President)副总裁助理 . CEO(Chief Executive Officer)首席执行官，类似总经理、总裁，是企业的法人代表。 COO(Chief Operations Officer)首席运营官，类似常务总经 …

在使用cursor导入deepseek的API时报错如下所示，该怎么办？ - 知乎
在使用cursor导入deepseek的API时报错如下所示，是本人操作有所不对吗？

first 和 firstly 的用法区别是什么？ - 知乎
a.First （ = First of all）I must finish this work.（含义即，先完成这项工作再说，因为这是必须的，重要的，至于其它，再说吧） b.First come，first served .先来，先招待（最重要） c.Friendship first， competition second.友 …