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1. NSF 01-20 - Opportunities For The Mathematical Sciences - Model Theory And Tame The internal development of Model theory over the past thirty years (stability 12 A. Pillay and C. Steinhorn, Definable sets in ordered structures, http://www.nsf.gov/pubs/2002/nsf0120/nsf0120_25.htm

Table of Contents Preface Summary Article Individual Contributors Statistics as the information science Statistical issues for databases, the internet, and experimental data Mathematics in image processing, computer graphics, and computer vision Future challenges in analysis ... Complex stochastic models for perception and inference Model theory and tame mathematics Beyond flatland: the future of space and time Mathematics in molecular biology and medicine The year 2000 in geometry and topology Computations and numerical simulations ... List of Contributors with Affiliations Model Theory and Tame Mathematics A. Pillay There are a number of ways in which modern logic affects mathematics, science and technology. This is maybe most obvious in the theory and practice of computation where the first rigorous models of computation were provided by the "recursion-theorists." One expects this to continue and deepen, especially at the level of software specification and verification. However, I wish to discuss recent and possible future developments in model theory (a branch of mathematical logic) which have foundational imports of a rather different nature, in which general frameworks for understanding non-pathological behavior have been developed. Abraham Robinson, who developed nonstandard analysis as well as the theory of model-completeness, was a pioneer of this kind of work. Other early work in this direction was Tarski's decision procedure for elementary Euclidean geometry

2. Fmtbook The book is an introduction to finite Model theory that stresses computer science origins of the ordered structures; Complexity of FirstOrder Logic http://www.cs.toronto.edu/~libkin/fmt/

Elements of Finite Model Theory Leonid Libkin From the back cover: The book is an introduction to finite model theory that stresses computer science origins of the area. In addition to presenting the main techniques for analyzing logics over finite models, the book deals extensively with applications in databases, complexity theory, and formal languages, as well as other branches of computer techniques, complexity analysis of logics, including the basics of descriptive complexity, second-order logic and its fragments, connections with finite automata, fixed point logics, finite variable logics, zero-one laws, embedded finite models, and gives a brief tour of recently discovered applications of finite model theory. This book can be used both as an introduction to the subject, suitable for a one- or two-semester graduate course, or as reference for researchers who apply techniques from logic in computer science. Table of contents Introduction Preliminaries Ehrenfeucht-Fraisse Games Locality and Winning Games Ordered Structures Complexity of First-Order Logic Monadic Second-Order Logic and Automata Logics with Counting Turing Machines and Finite Models Fixed Point Logics and Complexity Classes Finite variable logics Zero-one laws Embedded Finite Models Other applications of finite model theory.

3. [Dbworld] Book Announcement: "Elements Of Finite Model Theory" ordered structures 6. Complexity of FirstOrder Logic 7. Embedded Finite Models 14. Other applications of finite Model theory. http://osdir.com/ml/db.dbworld/2004-07/msg00035.html

var addthis_pub = 'comforteagle'; db.dbworld Top All Lists Date Thread [Dbworld] Book announcement: "Elements of Finite Model Theory" Subject [Dbworld] Book announcement: "Elements of Finite Model Theory" List-id dbworld.cs.wisc.edu ELEMENTS OF FINITE MODEL THEORY by Leonid Libkin Springer Verlag, 2004, XIV, 315 p., Hardcover, ISBN 3-540-21202-7. (Series: Texts in Theoretical Computer Science.) http://www.cs.toronto.edu/~libkin/fmt http://www.springeronline.com/ http://lists.cs.wisc.edu/mailman/listinfo/dbworld More with this subject... Current Thread Previous by Date: [Dbworld] Deadline Approaching - CFP: SAG'04 Pilar Herrero Next by Date: [Dbworld] Call for Papers: GEOINFO 2004 - VI Brazilian Symposium on Geoinformatics André Bastos Previous by Thread: [Dbworld] Deadline Approaching - CFP: SAG'04 Pilar Herrero Next by Thread: [Dbworld] Call for Papers: GEOINFO 2004 - VI Brazilian Symposium on Geoinformatics André Bastos Indexes: Date Thread Top All Lists Recently Viewed: qnx.openqnx.dev...

4. Spotlight On Graduate Research A common technique in Model theory is to classify the definable sets for a given class of ordered structures, and turn out to have two nice properties http://www.math.umd.edu/research/spotlight/getcontent.cgi?previous_winners 2006-

5. Set Theory And Its Neighbours, Seventh Meeting Abstract Finite Model theory has strong connections with a number of topics (not necessarily ordered) finite structures that sits somewhere between a http://www.ucl.ac.uk/~ucahcjm/stn/stn9.html

Set theory and its neighbours , nineth meeting: The nineth one-day conference in the in the series Set theory and its neighbours , took place on Wednesday, 25th April 2001 at the London Mathematical Society building, De Morgan House, 57-58 Russell Square, London WC1. The speakers at the meeting were: Russell Barker (Oxford), Robinson-type relations and the relationship between the k-size and cardinality of finite structures In this talk I will introduce the notions of L^k, the restriction of first order logic to k-variables, the k-size of a model and, two conjectures proposed by Anuj Dawar. Then I shall define define a special kind of relation which I shall call a Robinson-type relation and prove some results about these relations. I shall go on to give a translation between these relations and the set of L^3 theories and then use the earlier results to disprove Dawar's second conjecture. (UEA), Combinatorial principles that follow from GCH-like cardinal arithmetic assumptions Abstract: We discuss various results showing that at certain cardinals diamond-like principles follow just from local GCH-like assumptions on cardinal arithmetic. Peter Koepke (Bonn)

6. Model Theory Working Seminar Archives, Department Of Mathematics & Statistics @ McMaster University, The Exchange Property in ordered structures some results and McMaster University, Resolving singularities for Model theory http://basef-dev.mcmaster.ca/talks/archives.php?end_date=10-09-01&seminar_id=10

7. Le Monde En Tique -- DROSTE : SEMANTICS OF PROGRAMMING LANGUAGES AND MODEL THEOR Many of the more difficult problems in the theory of computation require a combination of methods from Model theory, logic and ordered structures as well as http://www.lmet.fr/fiche.cgi?9782881249358

8. Synopsis Of Basic Theory And Techniques Of Order Analysis. Occasional Paper No. The probabilistic Model extends these principles within the framework of graph theory; it permits the generalization of ordered structures into their latent http://www.eric.ed.gov/ERICWebPortal/recordDetail?accno=ED105336

9. Model Theory And Real Exponentiation 1986 40 Definable sets in ordered structures (context) Pillay, Rabin - 1974 1 Introduction to the Model theory of fields (context) - Marker 1 Model http://nsdl.org/resource/2200/20061012021607558T

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10. First-order Model Theory (Stanford Encyclopedia Of Philosophy) 1. Firstorder languages and structures. Mathematical Model theory carries a heavy load of notation, and HTML is not the best container for it. http://plato.stanford.edu/entries/modeltheory-fo/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free First-order Model Theory First published Sat Nov 10, 2001; substantive revision Tue May 17, 2005 First-order model theory, also known as classical model theory, is a branch of mathematics that deals with the relationships between descriptions in first-order languages and the structures that satisfy these descriptions. From one point of view, this is a vibrant area of mathematical research that brings logical methods (in particular the theory of definition) to bear on deep problems of classical mathematics. From another point of view, first-order model theory is the paradigm for the rest of model theory ; it is the area in which many of the broader ideas of model theory were first worked out. 1. First-order languages and structures 2. Elementary maps 3. Five grand theorems 4. Three useful constructions ... Related Entries 1. First-order languages and structures A a ). Two exceptions are that variables are italic ( x y ) and that sequences of elements are written with lower case roman letters (a, b).

11. Model Theory - Wikipedia, The Free Encyclopedia This article focuses on finitary first order Model theory of infinite structures. The Model theoretic study of finite structures (for which see finite Model http://en.wikipedia.org/wiki/Model_theory

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Model theory From Wikipedia, the free encyclopedia Jump to: navigation search This article discusses model theory as a mathematical discipline and not the term mathematical model which is used informally in other parts of mathematics and science. In mathematics model theory is the study of (classes of) mathematical structures such as groups fields graphs or even models of set theory using tools from mathematical logic . Model theory has close ties to algebra and universal algebra This article focuses on finitary first order model theory of infinite structures. The model theoretic study of finite structures (for which see finite model theory ) diverges significantly from the study of infinite structures both in terms of the problems studied and the techniques used. Model theory in higher-order logics or infinitary logics is hampered by the fact that completeness does not in general hold for these logics. However, a great deal of study has also been done in such languages. Contents The role of model theory The areas of model theory Universal algebra Finite model theory ... Axiomatizability, elimination of quantifiers, and model-completeness

12. Model Theory -- From Wolfram MathWorld Mathematical structures obeying axioms in a system are called models of the system. The usual axioms of analysis are second order and are known to have http://mathworld.wolfram.com/ModelTheory.html

Search Site Algebra Applied Mathematics Calculus and Analysis ... Model Theory Model Theory Model theory is a general theory of interpretations of axiomatic set theory . It is the branch of logic studying mathematical structures by considering first-order sentences which are true of those structures and the sets which are definable in those structures by first-order formulas (Marker 1996). Mathematical structures obeying axioms in a system are called "models" of the system. The usual axioms of analysis are second order and are known to have the real numbers as their unique model. Weakening the axioms to include only the first-order ones leads to a new type of model in what is called nonstandard analysis SEE ALSO: Khovanski's Theorem Nonstandard Analysis Wilkie's Theorem [Pages Linking Here] REFERENCES: Doets, K. Basic Model Theory. New York: Cambridge University Press, 1996. Hodges, W. A Shorter Model Theory. New York: Cambridge University Press, 1997. Manzano, M. Model Theory. Oxford, England: Oxford University Press, 1999. Marker, D. "Model Theory and Exponentiation."

13. Descriptive Complexity Techniques and results of descriptive complexity theory are used in database theory and structures, first order logic (FO), first order queries. http://www.cs.nott.ac.uk/~nza/MGS/MGS00/

Descriptive Complexity Natasha Alechina School of Computer Science and IT University of Nottingham Descriptive complexity studies the relation between formal languages and computational resources (space and time) required to solve problems formulated in those languages. It turns out that many complexity classes, such as P and NP, have an independent logical characterisation (first order logic with inductive definitions and existential second order logic, respectively). Techniques and results of descriptive complexity theory are used in database theory and computer aided verification. The aim of the course is to introduce the basics of descriptive complexity theory and prove the theorem (due to Immerman and Vardi) that, on ordered structures, polynomial time queries are exactly those which can be formulated in first order logic plus the least fixed point operator. Below is the preliminary schedule of lectures: Lecture 1: Introduction and exercises. Structures, first order logic (FO), first order queries. Lecture 2: Compexity classes.

14. JSTOR Some Applications Of Model Theory In Set Theory. Theorem 2.23 lf T is a countable theory having a wellordered Model of power ,c Theorem 2.25 If ~A is an ordered structure having order type K where http://links.jstor.org/sici?sici=0022-4812(197409)39:3<597:SAOMTI>2.0.CO;2-1

15. MATHEMATICAL STRUCTURES RESEARCH Finite Model theory. SpringerVerlag 1995. Foldes, Stephan. Fundamental structures of Algebra and Discrete Mathematics. John Wiley, 1994; Gabbay, Dov (ed). http://www.mmsysgrp.com/mathstrc.htm

CATEGORY THEORY and MATHEMATICAL STRUCTURES Research topics include mathematical models and theories in the empirical sciences, models and theories in mathematics, category theory, and the use of mathematical structures in theoretical computer science. Research Bibliography Mathematical Theories and Models Scientific Theories and Models Category Theory Theoretical Computer Science ... WWW Research Sites Mathematical Theories and Models Agazzi and Darvas. Philosophy of Mathematics Today. Kluwer Academic Publishers, 1997 Anglin and Lambek. The Heritage of Thales. Springer-Verlag, 1995 Akin, Ethan. The General Topology of Dynamical Systems. American Mathematical Society, 1993 Barwise, Jon. (ed) Handbook of Mathematical Logic. North-Holland,1977 Barwise, Jon. "Axioms for Abstract Model Theory" ,Annals of Mathematical Logic 7(1974) 221-265. Bell, John and Machover,Moshe. A Course in Mathematical Logic. North-Holland, 1977 Bridge, Jane. Beginning Model Theory. Clarendon Press, 1977 Burgess, John and Rosen, Gifeon. A Subject with No Object Oxford Press, 1997

16. Finite Model Theory Schedule A. Introduction to finite models Firstorder logic, Second-order logic Monadic cardinality and probability Countable structures and first-order logic http://dimacs.rutgers.edu/SpecialYears/1995_1996/Summerschool/FM-schedule.html

DIMACS Summer School on Applied Logic Tutorial on Finite Model Theory Tentative Schedule and Syllabus Daily Schedule and Timetable, Monday through Friday Track A: Expressive Power of Logics (Kolaitis) 10:30-11:00 Coffee Break Track B: Descriptive Complexity (Immerman) 12:30 - 2:30 Lunch Break Track C: Random Finite Models (Lynch) 4:00 - 4:30 Coffee Break 4:30- 5:30 "Office hours" and free discussion Monday, August 14 A. Introduction to finite models: First-order logic, Second-order logic Monadic existential second-order logic (monadic NP) Ehrenfeucht-Fraisse games for first-order and second-order logic B. Introduction to descriptive complexity: Complexity classes and complete problems FO is contained in LOGSPACE Fagin's theorem: "NP = Existential Second-Order Logic" C. Introduction to random models: Measures of size: cardinality and probability Countable structures and first-order logic: back-and-forth game Gaifman's 0-1 law Finite relational structures and first-order logic: 0-1 law of Fagin and Glebskii et al. Tuesday, August 15

17. Logicomp Finite Model Theory Preliminaries (2) Anthony Widjaja We now focus on a very important concept in finite Model theory `k`ary of a query in a logic (such as, first-order logic) on finite structures. http://logicomp.blogspot.com/2005/05/finite-model-theory-preliminaries-2.html

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?targetBlogID=12932458"); var BL_backlinkURL = "http://www.blogger.com/dyn-js/backlink_count.js";var BL_blogId = "12932458"; Logicomp Logic and Complexity Saturday, May 28, 2005 Finite Model Theory: Preliminaries (2) We now focus on a very important concept in finite model theory: `k`-ary queries. In fact, one goal of finite model theory is to establish a useful, if possible complete , criterion for determining expressibility (ie, definability) of a query in a logic (such as, first-order logic) on finite structures. For example, we may ask if the query connectivity for finite graphs, which asks whether a finite graph is connected, is expressible in first-order logic. The answer is 'no', though we won't prove this now. [Curious readers are referred to Libkin's Elements of Finite Model Theory or Fagin's excellent survey paper We shall start by recalling the notion of homomorphisms and isomorphisms between structures. Given two `sigma`-structures `fr A` and `fr B`, a homomorphism tuple-preserving functions (here, think of a tuple as an `r`-ary vector prepended by an `r`-ary relation symbol, eg, `R(1,2,3)`). Now

18. Intute: Science, Engineering And Technology - Search Results Sets, models and proofs. This is a set of lecture notes on basic axiomatic set theory, structures and languages for first order logic and proof trees, http://www.intute.ac.uk/sciences/cgi-bin/search.pl?term1=model theory&limit=0

19. Finite Model Theory/Logics And Structures - Wikibooks, Collection Of Open-conten Finite Model theory/Logics and structures The existential fragment (ESO) is secondorder logic without universal second-order quantifiers, http://en.wikibooks.org/wiki/Finite_Model_Theory/Logics_and_Structures

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikibooks"; Finite Model Theory/Logics and Structures From Wikibooks, the open-content textbooks collection Finite Model Theory Jump to: navigation search FMT studies logics on finite structures. An outline of the most important of these objects of study is given here. Contents Logics Fragments of FO Second Order Logic (SO) Fragments of Second Order Logic ... edit Logics The logics defined here and used thoughout the book are always relational, i.e. without function symbols, and finite, i.e. have a finite universe, without further notice. edit Fragments of FO The subsequent restrictions can analogously be found in other logics like SO. MFO ... ESO and USO ... FO n edit Second Order Logic (SO) Second-order logic extends first-order logic by adding variables and quantifiers that range over sets of individuals. For example, the second-order sentence says that for every set S of individuals and every individual x , either x is in S or it is not. I.e. the rulesareextended by: If X is a n-ary relation variable and t ... t

20. Dugald Macpherson's Homepage A firstorder structure is omega-categorical if it is countably infinite, goal is to develop a Model theory of supersimple measurable structures. http://www.maths.leeds.ac.uk/pure/staff/macpherson/macpherson.html

H. Dugald Macpherson Details E-mail address: Telephone: Department: Research Group: pmthdm@maths.leeds.ac.uk Pure Mathematics Mathematical Logic Research Interests I work in infinite permutation group theory and model-theoretic algebra. Some recent research interests are listed below. 1. Omega-categorical structures A first-order structure is omega-categorical if it is countably infinite, and isomorphic to any other countable structure which satisfies the same first-order sentences. Permutation groups are involved, via the Ryll-Nardzewski Theorem. This states that a countably infinite structure is omega-categorical if and only if its automorphism group has finitely many orbits on k-sets of every positive integer k. I have worked (and have continuing interest) on various topics involving omega-categoricity, such as: homogeneous relational structures; smoothly approximable structures; omega-categorical groups; the small index property, and other properties of the automorphism groups. In a recent paper with Simon Thomas, it is shown that a Polish group with a comeagre conjugacy class cannot be expressed non-trivially as a free product with amalgamation (many automorphism groups of omega-categorical structures satisfy the hypotheses). 2. Topics in permutation group theory

21. HeiDOK 03Cxx Model theory ( 0 Dok. ) 03C05 Equational classes, universal algebra ( 0 Dok. ) 03C07 Basic properties of firstorder languages and structures ( 0 http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03C&anzahl

22. OSU Algebraic Model Theory Seminar The OSU Algebraic Model theory Seminar. Jump to this week s talk. An old question about firstorder topological structures is If every set defined http://www.math.ohio-state.edu/~schoutens/seminar.html

The OSU Algebraic Model Theory Seminar Jump to this week's talk Schedule 2001/2002 Time Location Speaker Title and abstract Thursday, November 15, 2001 5:00 PM LIMA 322 Galvin Hall Chris Miller The Ohio State University A coherency result about expansions of the real line An old question about first-order topological structures is: If every set defined by a unary formula is a boolean combination of definable open sets, is the same true of every definable set (of any arity)? The question is open (as far as I know) even under the assumption that, in every elementarily equivalent structure, every set defined by a unary formula is a boolean combination of definable open sets. I will cast doubt on a positive answer (even under the stronger assumption) but show that a natural further strengthening of the hypotheses does yield a positive answer for expansions of the real line. Friday, November 30, 2001 2:30 PM COLUMBUS Ivo Herzog The Ohio State University The pure-injective envelope of a 1-dimensional domain It will be proved that the pure-injective envelope of such a domain (as a module over itself) carries a canonical ring structure compatible with that of the underlying domain.

23. Cell Theory, Form, And Function: Fluid Mosaic Model Of Membrane Structure And Fu Fluid Mosaic Model of Membrane Structure and Function tend to move from a highenergy, ordered structure to a lower-energy, increasing randomness, http://www.infoplease.com/cig/biology/fluid-mosaic-model-membrane-structure-func

Site Map FAQ in All Infoplease Almanacs Biographies Dictionary Encyclopedia Spelling Checker Daily Almanac for Dec 24, 2007 Search White Pages Skip Navigation Home Almanacs ... Word of the Day Editor's Favorites Winter Holidays Winter Solstice Santa on Film New Year's Traditions ... 2008 Calendar Search: Infoplease Info search tips Search: Biographies Bio search tips Cell Theory, Form, and Function Fluid Mosaic Model of Membrane Structure and Function Cell Theory, Form, and Function Introduction Prokaryotes and Eukaryotes Viruses Fluid Mosaic Model of Membrane Structure and Function Cell Cycle: Interphase, Mitosis, Cytokinesis Membranes have many different functions within a typical cell, such as keeping unwanted viruses out, but probably the most valuable is the partitioning of the cell into functional and segregated compartments. Because of the incredible number and often conflicting biochemical reactions occurring in a cell at any one time, the cell must retain order via structural organization or risk chemical chaos. The internal membranes compartmentalize reactions to prevent interference. The cell membrane also separates life from the nonlife on its exterior. In so doing, an intact and healthy membrane is selectively permeable because it allows substances needed for cell prosperity to enter and attempts to prohibit the penetration of unwanted and unfriendly substances. Unfortunately the system is not always fool-proof. Sometimes unwanted substances pass through the membrane and may cause trouble within the cell.

24. MODNET Summer School 2007 Special Session in Model theory and Applications June 2122, 2007 A Definably Complete Structure is an expansion of an ordered field, such that every http://modnet07.cs.unicam.it/summerschool/perugia_en.aspx

Home Admin MODNET Events 2007 in Camerino Model Theory and Algebra Workshop ... Contacts UMI-DMV Joint Meeting - Perugia Special Session in Model Theory and Applications June 21-22, 2007 Organizers: A. Baudisch (HU Berlin), C. Toffalori (Camerino) Provisional Programme THURSDAY, JUNE 21 Chairman: C. Toffalori (Camerino) K. Tent (Bielefeld), Geometric constructions in Model Theory P. D'Aquino (Napoli 2), Quadratic forms in weak fragments of Arithmetic G. Terzo (Napoli 2-Lisboa), Exponential fields Coffee Break P. Rothmaler (CUNY), Cotorsion modules A. Fornasiero (Pisa), O-minimal spectrum and definability of types S. L'Innocente (Camerino), Theory of pseudofinite representations of sl(2, k) FRIDAY, JUNE 22 Chairman: A. Baudisch (HU Berlin) M. Hils (HU Berlin), From strongly minimal fusion to the construction of a bad field T. Servi (Pisa-Regensburg), Noetherian Varieties in Definably Complete Structures A. Berarducci (Pisa), Cohomology and o-minimal structures M. Ziegler (Freiburg)

25. Some Results In Dynamic Model Theory Firstorder structures over a fixed signature give rise to a family of the role played by Lindenbaum algebras in classical first-order Model theory. http://portal.acm.org/citation.cfm?id=1007974

26. Schloss Dagstuhl : Seminar Homepage These include for instance computable Model theory, the theory of automatic structures, graphs with decidable monadic secondorder theories, http://www.dagstuhl.de/de/programm/kalender/semhp/?semnr=2007441

27. OUP: UK General Catalogue Model theory is the branch of mathematical logic which concerns the relationship between mathematical structures and logic languages, and has become http://www.oup.com/uk/catalogue/?ci=9780198538516

28. Model Theory | Mathematical Institute - University Of Oxford The firstorder language for structures. The Compactness Theorem for first-order logic. (and much more) can also be found in W. Hodges, Model theory\/. http://www.maths.ox.ac.uk/courses/mfocs/model-theory

@import "/modules/aggregator/aggregator.css"; @import "/modules/node/node.css"; @import "/modules/system/defaults.css"; @import "/modules/system/system.css"; @import "/modules/user/user.css"; @import "/./sites/all/modules/calendar/calendar.css"; @import "/sites/all/modules/cck/content.css"; @import "/sites/all/modules/drutex/drutex.css"; @import "/sites/all/modules/event/event.css"; @import "/sites/all/modules/calendar/calendar.css"; @import "/sites/all/modules/date/date.css"; @import "/sites/all/modules/cck/fieldgroup.css"; @import "/sites/all/themes/maths/style.css"; Skip navigation Locator: Home » View Model Theory Main Home Prospective Students Current Students Teaching Staff ... About Us Departmental Members Login Username: Password: Model Theory HT View course material Number of lectures: 16 HT Lecturer(s): Boris Zilber Course Description Recommended Prerequisites This course presupposes basic knowledge of First Order Predicate Calculus up to and including the Soundness and Completeness Theorems. Also a familiarity with (at least the statement of) the Compactness Theorem would also be desirable. The course deepens student’s understanding of the notion of a mathematical structure and of the logical formalism that underlies every mathematical theory, taking B1 Logic as a starting point. Various examples emphasise the connection between logical notions and practical mathematics.

29. MegForce.com: Physics, Order Of The Forces, Fundamental Particle, Unifying Theor The Geatron Nuclear Model. The theory of the Order of the Forces with the Grand . fine structure, manybody problem, low-dimensional quantum structures, http://www.2xtreme.net/boris/physics.htm

Fundamental Particle Physics The Geatron Nuclear Model ISBN 0-9677172-0-5 A book which investigates the hypothesis that a single fundamental particle with four modes of existence could combine with like particles to form all of the known subatomic and atomic particles and the elementary forces. Author may have discovered a series of new rudimentary particles and 2 new forces. Nuclear Model Approaches Unification of the Fundamental Forces - Book NASA - Physics / Geophysics Abstracts Standard Model and QCD have LEAKS, Drawing Bound Nucleons have Masses Unique to each Element - APS Abstract ... Nuclear Particles This Document was last modified on: "The Order of the Forces" is a study in nuclear and fundamental particle physics through the Geatron Nuclear Model By Eugene B. Pamfiloff Notice: This Book Has SOLD OUT. Announcement: However, you still have the opportunity to learn about the Geatron Nuclear Model and The Order of the Forces, continue reading below: THE GEATRON NUCLEAR MODEL Announcement: The author has written a condensed description of the Geatron Nuclear Model that includes fascinating details of Fundamental and Elementary Particle Physics. This recent writing (web page publication) includes some useful information that was not included in the book (The Order of the Forces). This information would be of interest to anyone that wishes an understanding of the origins of the forces, energy, matter (mass) and their system of organization. It can be viewed here at the

30. MSC 2000 : CC = Order 03B10 Classical firstorder logic; 03B15 Higher-order logic and type theory; 03C07 Basic properties of first-order languages and structures; 03C64 Model http://portail.mathdoc.fr/cgi-bin/msc2000.py?L=fr&T=Q&C=msc2000&CC=Order

31. Springer Online Reference Works The proof theory of firstorder Horn clause logic has particularly simple of finite ordered structures which are recognizable in polynomial time. http://eom.springer.de/h/h120140.htm

Encyclopaedia of Mathematics H Article referred from Article refers to Horn clauses, theory of First-order Horn clause logic is a fragment of first-order logic (cf. also Mathematical logic Logical calculus ) which has remarkable properties otherwise not shared by first-order logic. It consists of formulas of the form where and are atomic formulas (and could also be or ). (Strict) propositional Horn clauses are propositional formulas of the form or, equivalently, where and are propositional variables or . In the strict case is excluded. A Horn theory is a set of Horn clauses. First-order clauses of this form were first introduced by J.C.C. McKinsey in in the context of decision problems. Their name, Horn clauses, alludes to a paper by A. Horn, who in was the first to point out some of their algebraic properties. Between and A.I. Mal'tsev studied systematically the algebraic properties of model classes of Horn theories and showed that Horn clause logic is the right framework for the study of quasi-varieties in universal algebra (cf. also

32. Model Theory « Mort Aux Triangles! It doesn’t really matter how many axioms from the theory of ordered fields we . This is because a Model homomorphism deals only with the structure of the http://nbornak.wordpress.com/category/model-theory/

@import url( http://s.wordpress.com/wp-content/themes/pub/connections/style.css?m=1198091327 ); Home Mort aux Triangles! Structures are the weapons of mathematicians. model theory Archived Posts from this Category September 25, 2007 Relationships are hard :( Posted by Nick Bornak under category theory model theory [2] Comments I stumbled across subobject classifiers and their relationship (pun not intended) to relations in Lawvere Theories, the UM The trick was to consider the relations in a theory not as an object in the theory subject to the commutative diagram for subobject classifers but instead to think of the relation as the entire commutative diagram. (I really should get around to replacing and This lets me consider all of the (definable, I think) relations with a fixed arity in a given theory as a category in its own right. Because each diagram is within the same theory, the arrows between and are all the identity arrow. If we think about the top face of the cube in the above diagram, if the arrow is monic then we can compose arrows in such a way as to collapse the cube into a subobject classifier diagram that says is a subobject of . In other words, the arrows of a category of relations are implications of the form

33. Seminar In Finite Model Theory Research seminar. in. Finite Model theory Igor Walukiewicz Monadic second order logic on treelike structures; David Janin and Igor Walukiewicz On the http://mtl.uta.fi/Opetus/seminaarit/AMTS/0304/

Research seminar in Finite model theory General information This research seminar in FMT is a joint seminar of the Department of Mathematics at the University of Helsinki and the Department of Mathematics, Statistics and Philosophy at the University of Tampere . The gatherings are held every second Friday at 12-14 so that in principle every second gathering is held in Helsinki and every second in Tampere - see the weekly schedule below. The possible changes in timetables and the titles are announced on this page before each gathering. The gatherings are open to everyone interested in the field or the current topic. The first gathering in the Autumn 2003 is held the 5th of September in Tampere at 12-14 in lecture room Pinni A 3112. The first garthering in the Spring 2004 is held the 23rd of January at 12-14 in Tampere in Pinni rh. B 4114 From 20th of Februaby on the gatherings in Tampere will be held at 13-15. Places: 20.2. in Pinni rh. B4122 and from there on again in rh. B 4114 The seminar has been active also in the Spring 2001 and during the academic years and . Unfortunately the previous webpages are available only in Finnish. Contents during the academic year 2003-2004 The theme of the seminar during the year 2003-04 is Fragments of Second Order Logic We will start by considering MSO, in particular its existential fragment, which has a nice game theoretic characterization. Later on, we will study some recent papers dealing with fragments of ESO, their connections to CSP and the question of tractability of these fragments.

34. Workshop On Modal Logic, Model Theory And (co)algebra Finally, I highlight difficulties in lifting first-order Model theory to but the outcome is a two sorted type of relational structures including what http://staff.science.uva.nl/~bcate/ml-workshop/

Amsterdam Workshop on Modal Logic, Model Theory and (Co)Algebras Friday February 25, 2005 On the occasion of the PhD defense of Balder ten Cate (on the 24th at noon in the Aula of the University of Amsterdam), a workshop will take place on February 25, 2005, on modal logic, model theory and (co)algebras. The provisional program is as follows ( abstracts below ). This program might still be changed. Yde Venema Automata and fixed point logics: a coalgebraic perspective Mai Gehrke Resource sensitive frames Michael Moortgat Grammatical invariants: enriching the Lambek vocabulary Maarten Marx XPath, the best known modal logic ever. And .... made in Amsterdam! Valentin Goranko Towards algorithmic correspondence and completeness in modal logic Lunch break Ian Hodkinson A canonical variety with no canonical axiomatization Jouko Vaananen Team logic Johan van Benthem Modal Logic and Fixed-Point Languages The lectures before the lunch break will take place in room and the lectures afer the lunch break will take place in room . Both rooms are in building I ("the diamond factory"), Nieuwe Achtergracht 170, in Amsterdam.

35. FOM: Midwest Model Theory Meeting SPEAKER Eric Rosen (UIC) TITLE Finite Model theory and the Model theory of finite structures ABSTRACT In this talk we will discuss some aspects of the http://cs.nyu.edu/pipermail/fom/1999-November/003475.html

FOM: Midwest Model Theory Meeting Harvey Friedman friedman at math.ohio-state.edu Mon Nov 8 09:14:45 EST 1999 Previous message: FOM: Formal Z and R/lengths of proofs Next message: FOM: Re: Midwest Model Theory Meeting Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: FOM: Formal Z and R/lengths of proofs Next message: FOM: Re: Midwest Model Theory Meeting Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

36. A Crèche Course In Model Theory A crèche course in Model theory. An introduction to Model theory and to the theory definability in firstorder structures. http://www.dm.unito.it/personalpages/zambella/papers/creche/

Quaderni Didattici del Dipartimento di Matematica, no.26, marzo 2004 An introduction to model theory and to the theory definability in first-order structures. Domenico Zambella Interactive version [pdf] (for computer monitors with a few internal hyperlinks). Printable version [pdf] or [ps] Printable version, two pages per sheet [pdf] or [ps]

37. 18.575 Model Theory Syllabus, Model theory is a branch of mathematical logic that considers properties of mathematical structures expressible in firstorder logic. http://www-math.mit.edu/~rosen/18.575/

18.575: Model Theory (Spring 2007) Meetings MW 3:00-4:30, 2-142 Instructor Eric Rosen Office Email rosen (at) math (dot) mit (dot) edu Office Hours Wed. 2-3, Thur. 11-12, and by appointment Syllabus The course will be designed to provide the necessary model-theoretic background to understand significant recent applications to, e.g., diophantine geometry and motivic integration, in the work of Hrushovski, Kazhdan, Scanlon, Cluckers, Denef, and Loeser. Text Model Theory: An Introduction , by David Marker (Springer GTM). The introduction is available here . More information, including the table of contents, can be found on amazon Recommended reading Some other good introductions to the subject include Model Theory and A Shorter Model Theory , both by Wilfrid Hodges, and A Course in Model Theory by Bruno Poizat. These will be put on reserve in the library. An elegant description of the subject, also by Hodges, can be found here Lecture schedule: (tentative) My aim for the semester is to prove Morley's famous categoricity theorem, which was really the starting point for contemporary model theory. Much of the material covered in chapters 2, 4, and 5 gets used in the proof of this theorem. The ideas, tools, and techniques developed in these chapters are also fundamental to all further developments in the subject. Along the way, we will also examine connections with other areas of mathematics, especially algebra. In particular, chapter 3 contains an extended discussion of the model theory of algebraically closed fields, with glimpses at basic ideas in algebraic geometry.

38. Model Theory, Feb 2002, Birmingham Max Dickmann (Paris). Model theory and quadratic forms For this purpose small profinite structures may be useful. They appear naturally for example as http://web.mat.bham.ac.uk/R.W.Kaye/models2002/models2002.html

Model theory, Feb 2002, Birmingham This conference follows a regional meeting of the London Mathematical Society and takes place from Thursday Feb 28th 2002 to Saturday March 2nd 2002. The following is a DRAFT programme. Please note that some details may change. However, the end of the meeting will be at 4.30 on the Saturday, to give plenty of time for people to travel home, or for further discussion in the pub, as is traditional. Thursday Friday Saturday Zilber Wagner Simonetta Wood ... Baudisch Break Break Break Casanovas Dickmann Point Lunch Lunch Lunch Wilkie Kuhlmann Steinhorn Lascar ... Scanlon Tea Tea Tea Schoutens Chatzidakis Talks on the Thursday and Friday will be in Lecture room B (first floor, Watson Building) whereas talks on the Saturday will be in Lecture room A (ground floor) This meeting is supported by the London Mathematical Society . A limited amount of money may be available for travel or other expenses for participants. Please enquire if you are interested in attending. Invited speakers, titles, and short abstracts Andreas Baudisch (Humboldt University, Berlin)

39. Cornell Math - Thesis Abstracts (Logic) Characterizations for Computable structures. Abstract A major theme in computable Model theory is the study of necessary and sufficient conditions for the http://www.math.cornell.edu/Research/Abstracts/logic.html

Ph.D. Recipients and their Thesis Abstracts Logic Algebra Analysis Combinatorics Differential Equations / Dynamical Systems ... Topology Reba Schuller , August 2003 Advisor: Anil Nerode A Theory of Multitask Learning for Learning from Disparate Data Sources Abstract: Many endeavors require the integration of data from multiple data sources. One major obstacle to such undertakings is the fact that different sources may vary considerably in the way they choose to represent their data, even if their data collections are otherwise perfectly compatible. In practice, this problem is usually solved by a manual construction of translations between these data representations, although there have been some recent attempts at supplementing this with automated algorithms based on machine learning methods. This work addresses the problem of making classification predictions based on data from multiple sources, without constructing explicit translations between them. We view this problem as a special case of the problem of multitask learning: Both intuition and much empirical work indicate that learning can be improved by attacking multiple related tasks simultaneously; however, thus far, no theoretical work has been able to support this claim, and no concrete definition has been proposed for what it means for two learning tasks to be "related."

40. INI Programme MAA Pure Model theory studies abstract properties of first order theories, and derives structure theorems for their Models. Applied Model theory on the other http://www.newton.cam.ac.uk/programmes/MAA/index.html

@import url("/css/prog-non_n4.css"); Institute Home Page Programmes Web-Seminars Programme Home Seminars Full list Workshops Participants Long Stay Short Stay Additional Links Contacts Mailing List Final Scientific Report (145KB.pdf) Isaac Newton Institute for Mathematical Sciences Model Theory and Applications to Algebra and Analysis 17 Jan - 15 Jul 2005 Organisers Professor Z Chatzidakis ( CNRS ), Professor HD Macpherson ( Leeds ), Professor A Pillay ( Illinois ), Professor A Wilkie ( Oxford Programme theme Model theory is a branch of mathematical logic dealing with abstract structures (models), historically with connections to other areas of mathematics. In the past decade, model theory has reached a new maturity, allowing for a strengthening of these connections and striking applications to diophantine geometry, analytic geometry and Lie theory, as well as strong interactions with group theory, representation theory of finite-dimensional algebras, and the study of the p-adics. The main objective of the semester will be to consolidate these advances by providing the required interdisciplinary collaborations. Model theory is traditionally divided into two parts pure and applied. Pure model theory studies abstract properties of first order theories, and derives structure theorems for their models. Applied model theory on the other hand studies concrete algebraic structures from a model-theoretic point of view, and uses results from pure model theory to get a better understanding of the structures in question, of the lattice of definable sets, and of various functorialities and uniformities of definition. By its very nature, applied model theory has strong connections to other branches of mathematics, and its results often have non-model-theoretic implications. A substantial knowledge of algebra, and nowadays of algebraic and analytic geometry, is required.

41. Atlas: Model Theory Versus Topology By Brian Davey In it, we investigate firstorder axiomatic descriptions of naturally The interplay between the Model theory and the topology is somewhat mysterious. http://atlas-conferences.com/c/a/s/r/03.htm

Atlas home Conferences Abstracts about Atlas 2006 New Zealand Mathematics Colloquium December 4-6, 2006 Dept of Mathematics, University of Waikato Hamilton, New Zealand. Organizers Stephen Joe (Convener and Secretary), Tim Stokes (Treasurer), Ian Hawthorn (Mathematics Education Day), Rua Murray (Dynamical Systems Day), Sean Oughton (Programme Director), Ernie Kalnins (Excursion Director) View Abstracts Conference Homepage Model theory versus topology by Brian Davey Dept of Mathematical and Statistical Sciences, La Trobe University, Australia Coauthors: David Clark, Marcel Jackson and Jane Pitkethly This talk is based on a paper coauthored with David Clark, Marcel Jackson and Jane Pitkethly. In it, we investigate first-order axiomatic descriptions of naturally occurring classes of Boolean topological structures. We illustrate the range of possible axiomatizations of these classes with applications to Boolean topological lattices, graphs, ordered structures, unary algebras and semigroups. . For example, it is known that the class of all k-colorable graphs is axiomatized by special first-order sentences called universal Horn sentences. In contrast, the class of continuously k-colourable Boolean topological graphs cannot be axiomatized by any set of first-order sentences. The interplay between the model theory and the topology is somewhat mysterious. Sometimes the two are more or less independent, sometimes adding a Boolean topology destroys an axiomatization (as in the case of k-colourable graphs mentioned above), and sometimes adding a Boolean topology will convert a class that is not axiomatizable into one that is.

42. Algorithmics Research Group The structure of locally finite varieties with polynomially many Models, manuscript Sheaaves in universal algebra and Model theory, Part II, http://tcs.uj.edu.pl/Idziak

Theoretical Computer Science Faculty of Mathematics and Computer Science Jagiellonian University Algorithmics Research Group guest TCS - home algorithmics cs foundations news ... links events: computer science on trail (pl) UZI - January 12, 2008(pl) CLA 2007 past events seminars: Algorithmic Aspects of Combinatorics Cryptography Theoretical Computer Science achievements: faculty, phd students students faculty: Iwona Cieà ›lik Tomasz Gorazd Jarosà ‚aw Grytczuk Zbigniew Hajto Pawel M. Idziak Marcin Kozik Grzegorz Matecki Maciej à šlusarek secretary: Monika Gillert phd students: Bartà ‚omiej Bosek Przemysà ‚aw Broniek Maciej Chociej Lech Duraj ... Maciej à »enczykowski msc students: Arkadiusz Pawlik Jacek Samolià „ski Bartosz Walczak graduates: phd thesis msc thesis login: password: Pawel M. Idziak professor phone: fax: email: office: ul. Gronostajowa 3, 30-387 Krakow room: office hours: Wednesday 14:30 - 16:00 research interests algorithms computational complexity cryptography algebra logic finite model theory selected publications Paweà ‚ M. Idziak, Petar Marković, Ralph McKenzie, Matthew A. Valeriote and Ross Willard, Tractability and learnabilty arising from algebras with few subpowers

43. Pure Model Theory, UEA, July 2005. Classically, Model theory studies elementary classes using full first order logic. I will discuss two alternatives to this setting which have been studied http://www.mth.uea.ac.uk/~h120/PureModAbs.html

Further information: Home Registration, accommodation and funding ... About Norwich Supported by: EPSRC Newton Institute, Cambridge London Mathematical Society Workshop on Pure Model Theory University of East Anglia, Norwich, 4-8 July 2005. Satellite meeting of the Newton Institute Programme Model Theory and Applications to Algebra and Analysis Programme A programme of the meeting is available as a .pdf file here Abstracts of Talks Tutorials Itay Ben-Yaacov (Madison), Model theory in positive and continuous logics Ludomir Newelski (Wroclaw) Multiplicity; Small profinite structures; type-generated equivalence relations Bruno Poizat (Lyon), AMALGAMES/Amalgams Plenary Talks John Baldwin (Chicago), Perspectives on expansions Elisabeth Bouscaren (Paris) Byunghan Kim (MIT), Generalized type-amalgamation and n-simplicity I Chris Laskowski (Maryland), Interpreting groups in strictly stable theories Kobi Peterzil (Haifa), Pillay's group conjecture and its solution Mike Prest (Manchester), Functorial methods in model theory Boris Zilber (Oxford) Martin Ziegler (Freiburg) Other Talks Hans Adler (Freiburg)

44. Descriptive Complexity Extending this theorem, our research has related firstorder . Descriptive Complexity is part of Finite Model theory, a branch of Logic and Computer http://www.cs.umass.edu/~immerman/descriptive_complexity.html

Descriptive Complexity Computational complexity was originally defined in terms of the natural entities of time and space, and the term complexity was used to denote the time or space used in the computation. Rather than checking whether an input satisfies a property S, a more natural question might be, what is the complexity of expressing the property S? These two issues checking and expressing are closely related. It is startling how closely tied they are when the latter refers to expressing the property in first-order logic of finite and ordered structures. In 1974 Fagin gave a characterization of nondeterministic polynomial time as the set of properties expressible in second-order existential logic. Extending this theorem, our research has related first-order expressibility to computational complexity. Some of the results arising from this approach include characterizing polynomial time as the set of properties expressible in first-order logic plus a least fixed-point operator, and showing that parallel time on a Parallel Random Access Machine is linearly related to first-order inductive depth. This research has settled a major, long standing question in complexity theory by proving the following result: For all s(n) greater than or equal to log n, nondeterministic space s(n) is closed under complementation. See Neil Immerman's Recent Publications , for available on-line publications on descriptive complexity, and, Descriptive Complexity Survey for the slides of a recent survey talk on descriptive complexity.

45. Session DC - Turbulence Theory III. DC.001 Statistics of Helicity Flux in Shell Models of Turbulence . DC.011 Selfsimilarity of the second-order structure function http://flux.aps.org/meetings/YR01/DFD01/abs/S340.html

Previous session Next session Session DC - Turbulence Theory III. ORAL session, Sunday afternoon, November 18 Marriott Hall 1, Marriott Hotel and Marina San Diego [DC.001] Statistics of Helicity Flux in Shell Models of Turbulence Qiaoning Chen, Shiyi Chen (The Johns Hopkins University, Dept. of Mechanical Engineering), Gregory L. Eyink (University of Arizona, Depts. of Mathematics and Physics), Darryl D. Holm (Los Alamos National Laboratory, T-7) [DC.002] Helicity in Three-dimensional Forced Turbulence Shiyi Chen, Qiaoning Chen (Department of Mechanical Engineering, The Johns Hopkins University), Gregory Eyink (Department of Mathematics, University of Arizona), Darryl Holm (Theoretical Division, Los Alamos National Laboratory) Direct numerical simulation of three-D isotropic turbulence is carried out for studying helical turbulence. The intermittency exponents of helicity flux for 3D forced Navier-Stokes turbulence are presented and compared with those for energy flux. The statistical correlation between the helicity flux and the energy flux and spatial structures of these two quantities are studied. [DC.003]

46. Metalogic :: Satisfaction Of A Theory By A Structure: Finite And Infinite Models Britannica online encyclopedia article on metalogic, Satisfaction of a theory by a structure finite and infinite models A realization of a language (for http://www.britannica.com/eb/article-65880/metalogic

var britAdCategory = "other"; Already a member? LOGIN Encyclopædia Britannica - the Online Encyclopedia Home Blog Advocacy Board ... Free Trial Britannica Online Content Related to this Topic This Article's Table of Contents Expand all Collapse all Introduction Nature, origins, and influences of metalogic Syntax and semantics The axiomatic method Logic and metalogic Semiotic ... Influences in other directions Nature of a formal system and of its formal language Example of a formal system Formation rules Axioms and rules of inference Truth definition of the given language ... The undecidability theorem and reduction classes Model theory Background and typical problems changeTocNode('toc65879','img65879'); Satisfaction of a theory by a structure: finite and infinite models Elementary logic Nonelementary logic and future developments Characterizations of the first-order logic ... Print this Table of Contents Linked Articles Bernhard Bolzano Tarski transfinite numbers Shopping Revised, updated, and still unrivaled. 2008 Britannica Ultimate DVD/CD-ROM The world's premier software reference source.

47. Institutions Many logical systems have been shown to be institutions, including first order logic (with first order structures as models), many sorted equational logic http://www-cse.ucsd.edu/~goguen/projs/inst.html

Institutions 1. Motivation The enormous and still growing diversity of logics used in computer science presents a formidable challenge. One approach to bringing some order to this chaos is to formalize the notion of "a logic" and then systematically study general properties of logics using this formalization, including the representation, implementation, and translation of logics. This is the purpose of the theory of institutions , as developed and applied in a literature that now has hundreds of papers. The original application of institutions defined powerful mechanisms for structuring theories over any logical system; this was applied in the module systems of languages in the OBJ family , including BOBJ, CafeOBJ, Maude, CASL, and OBJ3, each of which has a different logic, under the name "parameterized programming," and it was later extended to module systems for programming languages. The module systems of Ada, C++, Lotos, and ML were all influenced by these ideas, which are most nearly fully implemented in the so-called signatures, structures, and functors of SML. Institutions have also been applied to the semantics of databases and ontologies, e.g. for the semantic web. Here the main contribution of institutions is to formalize the notion of translation from one logic to another in such as way as to preserve truth, and to provide a number of basic results about such translations, such as when they preserve the modular structure of an ontology; see

48. Molecular Orbital Theory Although the Lewis structure and molecular orbital models of oxygen yield the same bond order, there is an important difference between these models. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch8/mo.html

Molecular Orbital Theory Valence Bond Model vs. Molecular Orbital Theory Forming Molecular Orbitals Why Some Molecules Do Not Exist Molecular Orbitals of the Second Energy Level ... Bond Order Valence Bond Model vs. Molecular Orbital Theory Because arguments based on atomic orbitals focus on the bonds formed between valence electrons on an atom, they are often said to involve a valence-bond theory. The valence-bond model can't adequately explain the fact that some molecules contains two equivalent bonds with a bond order between that of a single bond and a double bond. The best it can do is suggest that these molecules are mixtures, or hybrids, of the two Lewis structures that can be written for these molecules. This problem, and many others, can be overcome by using a more sophisticated model of bonding based on molecular orbitals . Molecular orbital theory is more powerful than valence-bond theory because the orbitals reflect the geometry of the molecule to which they are applied. But this power carries a significant cost in terms of the ease with which the model can be visualized. Forming Molecular Orbitals Molecular orbitals are obtained by combining the atomic orbitals on the atoms in the molecule. Consider the H

49. Keith Price Bibliography Texture Models, Analysis Techniques Analyzing Natural Images A Computational theory of Texture Vision, MIT AI Memo334, June 1975. BibRef 7506 Higher-order structure in natural scenes, http://www.visionbib.com/bibliography/twod317.html

7.9.1 Texture Models, Analysis Techniques Chapter Contents (Back) Texture Models Schreiber, W.F. The Measurement of Third Order Probability Distributions of Television Signals IT(2) , No. 3, September 1956, pp. 94-106. BibRef Stultz, K.F. Zweig, H.J. Roles of Sharpness and Graininess in Photographic Quality and Definition JOSA(52) , 1962, pp. 45-50. BibRef Rosenfeld, A. On Models for the Perception of Visual Texture MPSVF BibRef Hawkins, J.K. Textural Properties for Pattern Recognition BibRef Read, J.S. , and Jayaramamurthy, S.N. Automatic Generation of Texture Feature Detectors TC(21) , No. 7, July 1972, pp. 803-812. BibRef McCormick, B.H. , and Jayaramamurthy, S.N. A Decision Theory Method for the Analysis of Texture CIS(4) , 1975, pp. 1-38. BibRef And: CIS(3) , 1974, pp. 329-343. BibRef Marr, D.[David] Early Processing of Visual Information Royal(B-275) , 1976, pp. 483-524. BibRef And: On the Purpose of Low-level Vision MIT AI Memo -324, December 1974. Postscript Version . (Another reference gave different page numbers: 97-137.) The early paper that is always referenced, but is seldom seen. See also Vision: A Computational Investigation into the Human Representation and Processing of Visual Information BibRef Marr, D.

50. Molecular Models And Calculations In Microscopic Theory Of Order-Disorder Struct Molecular Models and Calculations in Microscopic theory of OrderDisorder Structural Phase Transitions Application to KH2PO4 and Related Compounds http://pubs.acs.org/cgi-bin/abstract.cgi/jpchax/1996/100/i15/abs/jp9527970.html

[Journal Home Page] [Search the Journals] [Table of Contents] [PDF version of this article] ... [Purchase Article] J. Phys. Chem. Molecular Models and Calculations in Microscopic Theory of Order-Disorder Structural Phase Transitions: Application to KH PO and Related Compounds Alexandr A. Levin* and Sergey P. Dolin NS Kurnakov Institute of General and Inorganic Chemistry, Leninskii pr. 31, 117907 Moscow, Russia Received: September 20, 1995 In Final Form: January 15, 1996 Abstract: Applications of quantum chemistry approaches are considered to elucidate the mechanisms of structural phase transitions in H-bonded molecular crystals. The KH PO (KDP) family and squaric acid (H O-H O on the basis of the vibronic theory of ligand substitution effects in molecules and complexes. Proton positions within H-bonds are described using the pseudospin formalism. For the energy of crystal this approach results in the Ising model, where the Ising and Slater parameters are expressed in terms of the MO structure of molecular units of crystal. Quantum-chemical calculations are used to determine the MO structure of these units with dependence on the proton positions within the H-bonds. The values of the Slater parameters derived are in reasonable agreement with the experimental data, and the compositional trends for T c behavior observed for the KDP-type compounds are explained. Applications of the direct quantum-chemical modeling to study of properties of H-bonded crystal are briefly described.