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1. JSTOR Spherical Classes And The Lambda Algebra
Let pA = (k F be Singer s invarianttheoretic model of the dual of the lambda algebra with Hk(P^) - TorA4(F2, F2), where A denotes the mod 2 Steenrod<4447:SCATLA>2.0.CO;2-G

2. An {$M{\rm U}$}-analogue Of The Lambda Algebra
Errata Nobuo Shimada, Errata to ``An MUanalogue of the lambda algebra . Publ. Res. Inst. Math. Sci., Volume 23, Number 6 (1987), pp. 1015.
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    Nobuo Shimada Source: Publ. Res. Inst. Math. Sci. Volume 22, Number 6 (1986), 1191-1204.
    Related Items:
    Errata: Nobuo Shimada, Errata to ``An MU-analogue of the lambda algebra'. Publ. Res. Inst. Math. Sci., Volume 23, Number 6 (1987), pp. 1015. Mathematical Reviews (MathSciNet): Zentralblatt MATH: Primary Subjects: Secondary Subjects: Full-text: Access granted (open access) PDF File (1293 KB) Links and Identifiers Permanent link to this document: Mathematical Reviews number (MathSciNet): Zentralblatt Math identifier: back to Table of Contents
    [1] Adams, J. F., On the cobar construction, Colloque de Topologie Algebrique, Louvain, Paris (1956). Mathematical Reviews (MathSciNet): Zentralblatt MATH: [2] Adams, J. F., Lectures on generalized cohomology, Lecture Notes in Mathematics 99, Springer-Verlag, Berlin, 1969. Zentralblatt MATH: [3] Adams, J. F., Stable homotopy and generalised homology, Chicago Lectures in Mathematics, The Univ. of Chicago Press. 1974.

3. IngentaConnect On Singer's Invariant-theoretic Description Of The Lambda Algebra
The purpose of the paper is to give a mod p analogue for the Singer invarianttheoretic description of the lambda algebra. In other words, we give an
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4. An MU-analogue Of The Lambda Algebra
An MUanalogue of the lambda algebra. Source, Publications of the Research Institute for Mathematical Sciences archive Volume 22 , Issue 6 (December 1987)

5. CiNii - Some Acyclic Relations In The Lambda Algebra
Some acyclic relations in the lambda algebra We consider the relations $\omega \gamma=0 \in \Lambda$, and show that if $\omega \alpha=0$ then
Top Page Browse Publications Citation Index CiNii+Citation Index ... Japanese Journal Title
Hiroshima mathematical journal
Vol.34, No.2(20040700) pp. 147-160 Hiroshima University ISSN:00182079 Bibliography
Some acyclic relations in the lambda algebra
Hikida Mizuho
Hiroshima Prefectural University Abstract Read/Search Full Text External 1 Holdings NII Article ID (NAID) NII NACSIS-CAT ID (NCID) Text Lang ENG Databases NII-ELS Export Refer/BibIX Format BibTex Format Tab Separated Text (TSV) NII HOME ... NII-REO National Institute of Informatics

6. 6 New Papers This Time, From Baas-Dundas-Rognes (an Update
Richter/RichterLambda-EHP Title lambda algebra unstable composition products and the Lambda EHP sequence Author William Richter AMS Classification

7. Cookies Required
The author thanks Elmar Wagner for discussions on the general representation theory of C\lambda algebras, as well as Hanno Sahlmann for discussions on the
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    8. Abstracts Of John Palmieri's Papers
    We study the action of Sq0 on the Adams E2term using the lambda algebra. In particular, there is a Bockstein spectral sequence whose E1-term is the
    John Palmieri


    Abstracts of John Palmieri's papers
    Self-maps of modules over the Steenrod algebra, Journal of Pure and Applied Algebra For a finite module M over the Steenrod algebra A, we prove the existence of a non-nilpotent element in Ext A (M,M) ``parallel to the vanishing line.'' We use this result to give a proof of Margolis' construction to kill P s t -homology groups, at all primes. A nilpotence theorem for modules over the mod 2 Steenrod algebra, joint with Michael J. Hopkins, Topology We prove a conjecture of Adams: the mod 2 Steenrod algebra A satisfies the ``detection'' property; i.e., every non-nilpotent element of Ext A (Z/2, Z/2) can be detected by restricting to an exterior sub-Hopf algebra of A. Self maps of spectra, a theorem of J. Smith, and Margolis' killing construction, joint with Hal Sadofsky, Mathematische Zeitschrift We prove that certain spectra have self maps easily described in terms of Ext over the Steenrod algebra. We apply this to prove Jeff Smith's theorem that for each n, there is a finite spectrum admitting a v n -map. Other applications are Margolis' killing construction for spectra and a spectral sequence for computing the homotopy of some v

    9. Unstable Homotopy Groups Of Spheres
    This program can calculate the cohomology of the lambda algebra, LambdaData.m 10MB of data on bases for the lambda algebra that put the differential
    Unstable homotopy groups of spheres
    From the bottom of this page you can download Mathematica programs that know many results about the unstable homotopy groups of spheres up to the 19-stem. Most of the information is taken from Toda's book "Composition methods in homotopy groups of spheres"; a few additional facts are proved in an accompanying note or quoted from elsewhere. The program does not do any serious calculations for itself, it is merely a convenient way of organizing and accessing results obtained by traditional methods. One can also do some automated consistency checking to detect any errors. I have tried to use a fairly general framework so that other computations in unstable homotopy can be included later if people are interested.
    This program is not really finished, but I think it is already useful, and I have moved on to other things, so I have decided to release it. Here are some examples of things one can type, and the program's response: SpherePi[14,2]
    Z h e Z m Z n n n HomotopySet[Sphere[7],Sphere[4]]

    10. A PRIMER ON THE DICKSON INVARIANTS Clarence Wilkerson Purdue
    I want to sketch an application of the Dickson invariants to a description o* *f the DyerLashof algebra and the lambda algebra. This description arises in
    < 0, cn;n = 1, and cn;j= if j < n Pn f(X) = (-1)ncn;0f(X) i-1 Pi f(X) = Pp Pi-1 f(X); for i > n: A PRIMER ON THE DICKSON INVARIANTS 5 Given Propositions 2.1 and 2.2, one can quickly read off a recursion relatio* *n for the Steenrod algebra action. Corollary 2.3. i-1 k-pn-1 * * n a) Pk cn;i= Pk-p cn;i-1- (P cn;n-1)cn;i; ifk 6= or p b) Pj cn;i= ifi 6= j; < j < n Pj cn;j= (-1)j+1cn;0 if0 < j < n Pn cn;i= (-1)ncn;0cn;j j-1 Pj cn;i= Pp Pj-1 cn;ifor j > n: Corollary 2.4. k k n-1 a) Pp cn;i= ifp < 0. Proof of Proposition 2.2. TheiPi act as derivations, since they are primitive* * in Ap. Furthermore, Pi x2 = xp2. Hence X j Pj f(X) = f(X) (X - v)p -1 v2V in S(V )[X]. Thus f(X) divides Pj f(X) in S(V )GL(V )[X] also. By computation, using the derivation property, n-1X i j Pj f(X) = (-1)n-i(Pj cn;i)Xp + (-1)ncn;0Xp : i=0 For j < n, this has degree less than pn in X, and hence is zero. For j = n, Pn f(X) = (-1)ncn;0f(X): Comparing coefficients, we obtain Pj cn;i= fori 6= j; and j

    11. Vietnam, August, 2004
    Abstract There is an algebra endomorphism of the lambda algebra which sends lambda_n to lambda_{2n+1}. This map induces Sq^0 on the Adams E_2 term for the
    Conference and Summer School in Algebraic Topology
    in honor of Huynh Mui's 60th birthday
    Vietnam National University, Hanoi, August, 2004
    School: August 914
    Conference: August 1620
    Proceedings of this conference will be published. Here is some detail about this.
    Conference photograph
    Here is a jpg file of the conference photograph. It's a 9 megabyte file.
    Summer School Courses:
    John Hubbuck: Invariant theory and the Steenrod algebra
    Haynes Miller: The theory of p-compact groups
    Stewart Priddy: Stable splittings of classifying spaces of finite groups
    Confirmed Speakers at the Conference:
    Tilman Bauer, Muenster
    Carlos Broto, Barcelona
    Jesper Grodal, Chicago
    Le Minh Ha, Lille
    Hans-Werner Henn, Strasbourg
    Kenshi Ishiguro, Fukuoka
    Masaki Kameko, Toyama
    Nick Kuhn, Virginia John Martino, Western Michigan Mamoru Mimura, Okayama Pham Anh Minh, Hue Dietrich Notbohm, Leicester Tran Ngoc Nam, Hanoi Mara Neusel, Texas Tech John Palmieri, Seattle Geoffrey Powell, Paris XIII Peter Symonds, Manchester Michishige Tezuka, Ryukyu

    12. Trường Đại Học Khoa Học Tự Nhiên-Đ
    Vi t chung v i Nguy n Sum, On Singer invarianttheoretic description of the lambda algebra A mod p analogue, Jour. Pure and Appl. Algebra 99 (1995),

    13. Computing The Homology Of The Lambda Algebra Is Available From Bo
    Computing the Homology of the lambda algebra only $35.30, get the Computing the Homology of the lambda algebra book From!

    14. [plt-scheme] Build-vector Avoids Sharing Problem + Tensor Algebras
    And there s a differential, so we can take the homology Funny thing, the tensor algebra modulo these relations is called the lambda algebra .
    [plt-scheme] build-vector avoids sharing problem + tensor algebras
    Bill Richter
    Tue, 4 Feb 2003 19:22:54 -0600 Advanced Student's function `build-vector' solves a sharing problem that's puzzled me: How to define 2-d vector array where the "rows" aren't all shared? Below I get unwanted sharing with my first 2 tries (using R5RS functions), and only the 3rd (with build-vector) works: Welcome to DrScheme, version 203. Language: Pretty Big (includes MrEd and Advanced) custom. "#(0 0)" #3(#0=#3(6 53 zzz)) "(make-vector 3)" #3(#0=#3(6 53 zzz)) "build-vector" #3(#3(6 0) #3(0 53 0) #3(0 zzz)) >

    Moreover, the application and abstraction operations for this lambda algebra can actually be implemented in New Jersey SML, making essential use of

    16. 31
    The purpose of this paper is to give a mod panalogue of the Lomonaco invariant-theoretic description of the lambda algebra for p an odd prime.
    On an Invariant-Theoretic Description of the Lambda Algebra Nguyen Sum Abstract. The purpose of this paper is to give a mod p -analogue of the Lomonaco invariant-theoretic description of the lambda algebra for p an odd prime. More precisely, using modular invariants of the general linear group GL_n=GL(n and its Borel subgroup , we construct a differential algebra Q - which is isomorphic to the lamda algebra

    17. Vista Site - 1
    On an invarianttheoretic description of the lambda algebra The purpose of this paper is to give a mod-p analogue of the Lomonaco invariant-theoretic
    @import url(; @import url(; @import url(; Skip to content. Home Vietnam Journal of Mathematics Infoterra news letter ... Proceedings Local role Advanced Search Service Fulltext Database Library Services Email Electronic news ...
    Almost periodic solutions of evolution equations associated with C-semigroups; an approach via implicit difference equations
    The paper is concerned with the existence of almost periodic mild solutions to evolution equations of the form u(t) = Au(t) + f(t) (*), where A generates a C-semigroup and f is almost periodic. The author investigate the existence of almost periodic solutions of (*) by means of associated implicit difference equations which are well-studied in recent works on the subject. As results we obtain various sufficient conditions for the existence of almost periodic solutions to (*) which extend previous ones to a more general class of ill-posed equations involving C.semigroups. The paper is supported by a research grant of the Vietnam National University, Hanoi.
    Existence theorems for some generalized quasivariational inclusion problems
    In this paper we give sufficient conditions for the existence of solutions of Problem (P1) (resp. Problem (P2)) of finding a point (zo, xo) E B(zo, xo) x A(xo) such that F(zo,xo,x) E C(zo,xo,xo) (resp. F(zo,xo,xo) E C(zo,xo,x)) for all x E A(xo), where A, B, C, F are set-valued maps between locally convex Hausdorff spaces. Some known existence theorems are included as special cases of the main results of the paper.

    18. Publications Of RIMS: Author Index To Volumes 21-30
    SHIMADA, N. Errata to ``An MUanalogue of the lambda algebra . 23, 1015 (1987) SHIMAKAWA, K. Uniqueness of products in higher algebraic K-theory.
    Author Index to Volumes 21-30 (1985-1994)
    ABE, K. : On Lie algebras of vector fields on smooth orbifolds.
    ADELMAN, O. : On the Brownian curve and its circumscribing sphere.
    AEBI, R. : Ito's formula for non-smooth functions.
    AIDA, S. : Support theorem for diffusion processes on Hilbert spaces.
    ALBERTI, P.M. : On the simultaneous transformation of density operators by means of a completely positive, unity preserving linear map.
    ALBERTI, P.M. : Completely positive stochastic linear maps over AFD-factors and unitary mixing on generating U.H.F.-subalgebras.
    ALBERTI, P.M. : Completely positive linear maps in a concept of majorization on certain operator algebras. ALCANTARA-BODE, J. : On Grothendieck's problem of topologies. AMASAKI, M. AMASAKI, M. ANDO, Y. : On the higher Thom polynomials of Morin singularities. ANTOINE, J.P., KARWOWSKI, W. : Partial *-algebras of closed linear operators in Hilbert space. ANTOINE, J.-P., KARWOWSKI, W. : Addendum/Erratum to ``Partial *-algebras of closed linear operators in Hilbert space''. ANTOINE J.-P., INOUE, A., TRAPANI, C.

    19. Computing The Homology Of The Lambda Algebra: Martin C. Tang
    Indigo Books Music is a Canadian bookseller committed to providing a stressfree approach to satisfying the booklover. Getting you the right book at the
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    Computing the Homology of the Lambda Algebra
    Author: Martin C. Tangora See more titles by Martin C. Tangora Our Price:
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    About this Book
    Format: Trade Paperback Published: January 12, 1985

    20. Research Seminars - MIMS
    There are other connections with power operations in Morava Etheory, as well as the classical Dyer-Lashof algebra and lambda algebra.
    You are here: MIMS events seminars MIMS SEMINAR SERIES algebra applied maths dynamical systems probability and statistics ... logic topology numerical analysis and scientific computing applied maths (informal) mathematical finance non-linear dynamics ... pure postgraduate seminars RELATED directions research areas SCHOOL OF MATHEMATICS staff list ... postgraduate area CONTACT DETAILS MIMS
    The University of Manchester
    School of Mathematics
    Oxford Road
    tel: +44 (0)161 306 3641
    fax: +44 (0)161 306 3669
    Topology Seminars 2007/08
    • 4 Feb
      Kostya Feldman (University of Cambridge)
      Time 4pm - Venue Frank Adams Room 2, Alan Turing Abstract (click to view) 11 Feb Mark Grant (University of Durham) Time 4pm - Venue Frank Adams Room 2, Alan Turing Abstract (click to view) 18 Feb Shoham Shamir (University of Sheffield) Time 4pm - Venue Frank Adams Room 2, Alan Turing Abstract (click to view) 25 Feb Time 4pm - Venue Frank Adams Room 2, Alan Turing Abstract (click to view) 3 Mar Time 4pm - Venue Frank Adams Room 2, Alan Turing Abstract (click to view) 10 Mar Models for the homotopy type of the Deligne-Mumford compactification of the moduli stack of curves Jeffrey Herschel Giansiracusa (University of Oxford) Time 4pm - Venue Frank Adams Room 2, Alan Turing

    21. Barendregt: Lambda Calculus
    A lambdaalgebra M is a combinatory-algebra if for all A and B in T(M) with In any lambda-algebra we have (confusing the terms with their
    The Omega Group TPS A higher-order theorem proving system This page was created and is maintained by Chad E Brown
    Barendregt, H. P. The Lambda Calculus: Its Syntax and Semantics. North Holland, Amsterdam (1984).
    Part I: TOWARDS THE THEORY Chapter 1: Introduction. Chapter 2: Conversion. Chapter 3: Reduction. Chapter 4: Theories. ... Chapter 5: Models. Part II: CONVERSION Chapter 6: Classical Lambda Calculus. Chapter 7: The Theory of Combinators. Chapter 8: Classical Lambda Calculus (Continued) Chapter 10: Bohm Trees. Part III: REDUCTION Chapter 11: Fundamental Theorems. Chapter 13: Reduction Strategies. Appendix A: Typed Lambda Calculus. Part I: TOWARDS THE THEORY Chapter 1: Introduction. Lambda calculus is a theory of functions as rules instead of graphs. The objects of study (type free lambda terms) can be used as both function and argument. Lambda calculus was originally invented to provide a general theory of functions which could be extended to provide a foundation for mathematics. Church's original system [1932/33] was inconsistent due to the Kleene-Rosser paradox [1935]. One response by Church [1941] was to study the subsystem given by the lambda-I calculus. [Another response was to study a system based on typed lambda calculus.] Curry proposed to extend pure combinatory logic by illative notions to give a foundation for mathematics. This program has not been completed. Another foundational approach related to lambda calculus is Feferman's [1975/80] systems for constructive mathematics based on partial application. These systems are related to Wagner [1969] and Strong's [1968] Uniformly Reflexive Structures. Also, there are relationships between typed lambda calculus, proof theory and category theory.

    22. Journal Of Lie Theory, Vol. 10, No. 2, Pp. 455-461, 2000
    We prove that any geodesic loop $L$ defines in the tangential space $T_eL$ a unique $\lambda $algebra, and that to any finite dimensional real $\lambda
    Journal of Lie Theory, Vol. 10, No. 2, pp. 455-461 (2000)
    Geodesic loops
    Ágota Figula
    Mathematisches Institut
    der Universität Erlangen-Nürnberg
    D-91054 Erlangen, Germany
    Abstract: Full text of the article: Previous Article Next Article Contents of this Number ELibM for the EMIS Electronic Edition

    23. 23 Suchergebnisse Für [clls]
    2 Parallelism constraints in underspecified semantics SciDok Parallelism constraints in underspecified semantics Relevanz 951 lambda-algebra 004 CLLS

    24. Ottawa Octoberfest 2005
    It is a classic result for the lambdacalculus that a lambda-algebra gives rise to a C-monoid and whence a cartesian closed category.
    Octoberfest 2005
    585 King Edward
    University of Ottawa
    Schedule and Abstracts
    Sunday talks are in Fauteux 351. Maps are on the Webpage.
    Oct. 22 Registration (Fee = $ 25) Rick Jardine (Plenary Speaker) Break Session A Jiri Rosicky Gabor Lukacs Claudio Hermida Susan Niefield Lunch (in Math Dept.) Session B Esfan Haghverdi Brian Redmond Sergey Slavnov Jeff Egger Break Session C Nicola Gambino Guy Beaulieu Dorette Pronk Sunday Oct. 23 Session D F. W. Lawvere J. Lambek M. Weber Break Session E Peter Freyd Robin Cockett Walter Tholen Lunch (in Math Dept.) Session F Jon Funk Larry Stout Abstracts
  • Guy Beaulieu: Adding Probabilistic Capabilities to Models of Nondeterminism. Abstract: I shall motivate and construct the Lawvere theory of mixed choice, which combines nondeterministic and probabilistic operators. Interestingly, the monad associated to the Lawvere theory of mixed choice is not the composition of the monads associated to the Lawvere theories of nondeterministic choice and probabilistic choice. However, we prove a factorization theorem which states its relation to the Eilenberg-Moore adjunctions capturing nondeterministic and probabilistic choice. Finally, we discuss the intricacies of adding probabilistic choice capabilities to a non-free model of nondeterministic choice.
    Robin Cockett: The partial lambda calculus (Joint work with Pieter Hofstra) It is a classic result for the lambda-calculus that a lambda-algebra gives rise to a C-monoid and whence a cartesian closed category. The purpose of the talk is to show how this result generalizes to the partial case. Taking the place of a cartesian closed category is a cartesian closed restriction category which is a formal category of partial maps with partial products and exponentials. The role of a lambda-algebra is taken by a partial combinatory algebra, sitting in an arbitrary restriction category, which must interpret the partial lambda calculus. We are now looking for models of these structures! A useful observation, in this regard, is that the D-infinity construction works almost verbatim (over DCPOs with partiality given by open inclusions) to produce extensional partial lambda-models.
  • 25. Stupid Question. | Lambda The Ultimate
    As far as it goes, lambdaalgebra is fine, but it does not go far enough. There are other relevant comments in the paper I ll mail a scanned version to
    @import "misc/drupal.css"; @import "themes/chameleon/ltu/style.css";
    Lambda the Ultimate
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    Stupid Question.
    I realize this may be a dumb question... having had some Abstract/Modern Algebra classes, I understand what an Algebra is, but I have never really understood what defines a "Calculus". What's the common thread between Lambda Calculus, Pi-Calculus, and traditional "Calculus"(and all the other calculi...) that merits them being called a calculus? I realize this may be an obvious thing, but my tendency is to assume that there is some formal definition of Calculus out there which is being used which I am just unaware of. Again, if I'm just being dumb, someone email me and put me out of my misery :) By Matt Estes LtU Forum previous forum topic next forum topic ... other blogs
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    26. Scientific Commons The Super-W$_{\infty}$($\lambda$) Algebra
    The superW$_{\infty}$($\lambda$) algebra (1990). Bergshoeff, EA,; Vasilev, MA,; De Wit, Bernard. Publication details
    ‹ìYmoÛ6þž_ÁA‘`±e'Àº¤¶ŠÖ Öbi$i»—%ÑSJÔHʎ7ì¿ï(J–üۍ›¶@õÁ–È»çŽäÝñŽì H=âù“‚ »3œ ~X¾¸Þë Iì:ÖÔ¾[ଳ?Íà.gø̱;ª…U¨óüÍdö§b”W0ÑgÚ?î…Z[äÍ4Ê@ÉBQžËLeÅP¬¥Pf@)@ i‘ Xg T‡Ú£

    27. Mathematics Bonn -- PhD Students Of Stefan Schwede
    We investigate the secondary structure in the lambdaalgebra, a preferred $ E_2$ -term for the Adams spectral sequence converging to the stable homotopy
    Uni Bonn Mathematics Faculty Schwede ... contact
    PhD Students of Stefan Schwede
    Andreas Heider
    Supervisor Stefan Schwede Research area Geometric structures in quantum physics Project Stable homotopy theory, structured ring spectra and topological modular forms
    Stable Model Categories and Recollements
    The main question in Morita theory is: when do two rings and have equivalent module categories? One can study this in different contexts, namely the classical case (Morita, 1950s), the derived case (Rickard, Keller, 1980s, 1990s), and the case of stable model categories (Schwede, Shipley, 2000s). In each case the answer is, roughly speaking: if and only if there is a `reasonable' small generator for the category of -modules whose endomorphism ring is isomorphic to A related question (and in a sense generalizing the latter) in the derived case is: when is the derived category of a differential graded algebra (DGA) `glued together' by the derived categories of two other DGAs. The notion making this precise is that of a recollement
    Martin Langer
    Supervisor Stefan Schwede Research area Moduli spaces of geometric structures and deformation theory Project Stable homotopy theory, structured ring spectra and topological modular forms

    28. Homology Of Lie Algebras With $\Lambda/q\Lambda$ Coefficients And Exact Sequence
    Using the long exact sequence of nonabelian derived functors, an eight term exact sequence of Lie algebra homology with $\lambda/q\lambda$ coefficients is
    Emzar Khmaladze Keywords: Lie algebra, nonabelian derived functor, exact sequence, homology group. 2000 MSC: 18G10, 18G50. Theory and Applications of Categories , Vol. 10, 2002, No. 4, pp 113-126.
    TAC Home

    29. Atlas: Boolean Algebra And Lambda Calculus By Antonino Salibra
    Boolean algebras for lambda calculus. 21th Annual IEEE Symposium on Logic in Computer Science (LICS 2006), IEEE Computer Society Press, 2006.
    August 5-9, 2007
    St Anne's College, University of Oxford
    Oxford, England Organizers
    Mai Gehrke and Hilary Priestley View Abstracts
    Conference Homepage
    Boolean algebra and lambda calculus
    Antonino Salibra
    University of Venice One of the milestones of modern algebra is the Stone representation theorem for Boolean algebras. In [1] Manzonetto and Salibra have shown that Comer's generalization of the Stone representation theorem holds also for combinatory algebras: any combinatory algebra is isomorphic to a weak Boolean product of directly indecomposable combinatory algebras. The proof of the representation theorem for combinatory algebras is based on the fact that every combinatory algebra has central elements, i.e., elements which define a direct decomposition of the algebra as the Cartesian product of two other combinatory algebras. Central elements in a combinatory algebra constitute a Boolean algebra, whose Boolean operations can be defined by suitable combinators. Then it is natural to investigate the semantics of lambda calculus given in terms of models, which are directly indecomposable as combinatory algebras (indecomposable semantics, for short). The indecomposable semantics includes all known models of lambda calculus (i.e., the continuous, stable and strongly stable semantics), and the term models of all semisensible lambda theories (theories which do not equate solvable and unsolvable terms). The class of indecomposible combinatory algebras is a universal class, so that it is closed under subalgebras and ultraproducts. This implies that, if the term model of a lambda theory T is decomposible in a non-trivial way, then every model of T can be also decomposible in a non-trivial way. It follows that the indecomposable semantics is incomplete because there exist lambda theories whose term models admit non-trivial central elements.

    30. Semantics Course 2007
    CL is a syntactical lambdaalgebra. (For the definition of CL, see the previous exercises.)The proof of this fact is by induction on the proof of lambda
    Semantics course Fall 2007
    Herman Geuvers: home page
    • Selected chapter(s) from Hanne Riis Nielson and Flemming Nielson: Semantics with applications , 1999 (via internet: PDF My own Semantics Course Notes (via internet: PDF Notes on denotational semantics of lambda calculus. (Will be distributed later.)
    The first two pieces of material have an overlap, but that's only advantageous.
    Set up
    There are only few students, so the course consists of "self study" and one weekly get together Monday, 10.30 hr at my room HG 02.056.
    The course by week
  • September 14:
  • Study pages 85 94 of Nielson and Nielson Determine the denotational semantics of the program
    if x>y then x:=x-y else y:=y-1 Make Exercises 4.2, 4.3, 4.4, 4.5 and 4.7 September 24:
  • Study pages 95 103 until Example 4.32 of Nielson and Nielson Take special care of Example 4.20, Lemma 4.25, Lemma 4.30 and Example 4.31.
  • Make Exercises 4.12, 4.14, 4.19, 4.21, 4.22, 4.27, 4.28 Consider the flat domain of the booleans, containing tt, ff and a bottom element.
    Give all monotonic functions that sensibly represent the function "OR" on these booleans.
  • 31. Nabble - Lambda Prolog - CMS Winter 2007 Meeting: Computer Algebra Session
    CMS Winter 2007 Meeting Computer algebra Session. CALL for PARTICIPATION Algorithmic Challenges in
    Nabble.setVar("skin",null); = 'forum.TopicDump'; Nabble.addCssRule(document.styleSheets[0],'.nabble a:link','color:'+document.linkColor); Nabble.addCssRule(document.styleSheets[0],'.nabble a:visited','color:'+document.vlinkColor); Nabble Programming Languages Lambda Prolog Nabble.userHeader(14109);
    CMS Winter 2007 Meeting: Computer Algebra Session
    View: Threaded Chronologically All Messages Nabble.selectOption(Nabble.get("nabble.viewSelect"),Nabble.tview); New views Rating Filter: Alert me
    CMS Winter 2007 Meeting: Computer Algebra Session
    document.write(Nabble.ratingStars(3)); by document.write(''); document.write(''); document.write(Nabble.formatDateLong(new Date(1195920575000))); :: Rate this Message: Reply to Author View Threaded Show Only this Message
    C A L L for P A R T I C I P A T I O N
    Algorithmic Challenges in Polynomial and Linear Algebra
    CMS Winter Meeting, London Ontario
    December 8-10, 2007
    The Canadian Mathematical Society Winter 2007 Meeting will be held Dec 8-10
    in London, Ontario. This is a scientifically rich meeting with seven plenary

    32. Atlantis Press Paper Details: Algebra Gl(lambda) Inside The Algebra Of Different
    The Lie algebra gl() with C, introduced by B L Feigin, can be embedded into the Lie algebra of differential operators on the real line (see 7). index&id=691&que

    The usual connection made between the lambda calculus and algebra is to construct the integers using the lambda calculus and then construct algebraic (and
    ALGEBRA AND THE LAMBDA CALCULUS by Aubrey Jaffer ABSTRACT: An algebraic system which includes Church's lambda calculus and currying is presented. Closures, applications, and currying are implemented using variable elimination. The usual connection made between the lambda calculus and algebra is to construct the integers using the lambda calculus and then construct algebraic (and other formulas) by Godelizing them. The system described here reverses this connection by implementing the lambda calculus in an algebraic system. It is used in the JACAL symbolic mathematics system and gives JACAL the ability to represent functions as members of the algebraic system. All of the system's operations (including simplification) can then be applied to functions as easily as to expressions. ALGEBRAIC REPRESENTATION Given an underlying representation for multivariate polynomials we can represent an equation as a multivariate polynomial with the understanding that the polynomial is equal to zero. We can convert typical equations to this form by multiplying both sides by the denominators and then subtracting the left side from both sides. For instance: f/(c+d) = (a-b)/g; Yields: = (a - b) c + (a - b) d - f g How to represent expressions? The usual approach is to use a polynomial or a ratio of polynomials. Instead, we will introduce a special variable ""@, calling it the value variable. The value of a polynomial involving @ is that polynomial "solved" for @. For instance, the expression: -1 + x 1 + x is represented internally as: = -1 + x + (-1 - x) @ This allows us to represent irrational expressions as well: 5 = -1 - y - @ - @ Is the root of a fifth degree polynomial. For the rest of this paper the examples will not show @ if the values can be represented in usual mathematical notation without it (as JACAL does). SUBSTITUTION At this level of algebraic abstraction we do all operations using variable elimination. Variable elimination is the process of combining n polynomial equations so that m variables do not appear in the (n-m) resulting equations (where n > m). Common techniques used include resultants [1][2][4][5] and Groebner Bases [3][4][5]. eliminate([a+c^2=b,b+c^2=2],[c]); Yields: = 2 + a - 2 b Common symbolic transformations can be done by constructing auxiliary polynomial equations and eliminating variables between them and the original polynomial equations. The operation we are interested in for the next section is substitution. We can substitute an expression for a variable by constructing an auxiliary equation of the variable and then eliminating that variable. Suppose we want to substitute (a*x+b)^2 for g in g+1/g. We construct the equation g=(a*x+b)^2 and then: eliminate([g=(a*x+b)^2, g+1/g],[g]); 4 3 2 2 2 3 3 4 4 1 + b + 4 a b x + 6 a b x + 4 a b x + a x 2 2 2 b + 2 a b x + a x Eliminate deals only with polynomial equations so remember that g+1/g internally is: 2 = 1 + g - g @ and similarly for the result. FUNCTIONS A similar approach to the use of @ can be used for arguments as well. We will name these arguments @1, @2, and so on. Functions do not need to use all of their arguments. However, in this system, a function must use at least one of its arguments. With this constraint, the only difference between a function and an expression is the presence of @n variables. Our functions can return either equations or expressions; those containing @ are expressions and those without, equations. A function which ignores its first two arguments is lambda([x,y,z],1/z-z), which would be represented as 2 1 - @3 - @3 These functions can freely mix bound and free variables. The following expression, with free c and bound x and y, f : lambda([x,y],c*(y+x)/(y-x)); is simply: c @1 + c @2 - - @1 + @2 We can now apply this function. We don't have to always apply it to two arguments, we can apply it to just one also. This is called "currying" an argument. The application g : f(x); substitutes x for @1 from the polynomial equation for f. It also "bumps" @2 down to @1 (also by substitution). This results in a new function of one argument: c x + c @1 - x + @1 It this function is applied to one argument (which is a non-function) the result will be a non-function. For example g(a+b) yields: (- a - b) c - c x - - a - b + x This result is exactly the same as the result of applying f(x,a+b). ALPHA-CONVERSION The above method is sufficient when the arguments to functions are not themselves functions. But when applying functions to functions differences in the order of elimination produce different results. Consider applying @1-@2 to the arguments (@2, @1). The result should be @2-@1. But if we curry an argument we get @2-@2 -> applied to @1. This problem is similar to the inadvertent capture of free identifiers by macros in languages like C and Lisp. The solution to this problem is called alpha-conversion in the lambda calculus and Hygenic Macro Expansion in a paper of that title by E.E.Kohlbecker, D.P.Friedman, M.Fellinson, and B.Duba [6]. Since the names of bound identifiers are unimportant we will substitute new names for those lambda variables for which we will later substitute arguments. This eliminates possible conflicts between the variables bound in the current function and variables in its arguments (which are free relative to this function). In the above example substitute :@1 for @1 and :@2 for @2 in @1-@2 yielding :@1-:@2. Now substitute @2 for :@1 and @1 for :@2. This then yields the desired result @2-@1. Currying an argument would substitute @2 for :@1 and @1 for :@2 in :@1-:@2 to produce @2-@1. When this function is applied to the remaining argument, @1, the result is @2-@1 as before. LAMBDA A symmetrical situation to currying of arguments is binding a variable over a function. lambda([y],lambda([x],x-y)) should yield the same function as lambda([y,x],x-y). The trick here is to "bump up" any lambda variables in an expression when binding additional variables. To execute lambda([y],@1-y) we substitute @2 for @1 and then @1 for y. VECTORS AND MATRICES Vector and matrix valued functions can be represented by vectors and matrices some of whose entries are lambda expressions. Clearly a vector or matrix function applied to scalar arguments should return a vector or matrix with the same shape as the function. The case of a scalar function applied vector arguments can work if the multiplication used by the function is of a type compatible with the arguments. Inner product is commutative while matrix multiplication is not. Another possiblity here is to have a mechanism for allowing lambda expressions to reference elements vector and matrix arguments. The case of vector or matrix functions applied to vector or matrix arguments gets stickier. Allowing only elements of the arguements to be operated on is one solution; Another is to incorporate the structure of the arguments inside the structure of the function or vice versa. DIFFERENTIAL ALGEBRA These techniques can be extended to differential algebra as well. In differential algebra the derivative of a variable, written v', can act as an variable in polynomials. Derivatives of derivatives are also allowed and can be written v'' and so on. When applying a function, each distinct derivative of a lambda variable with a corresponding argument requires that an equation be generated and that derivative variable be eliminated. We equate the nth derivative variable with the nth total derivative of its corresponding argument. For instance to apply the function @1'/@2' to (x^3,x) we eliminate([@1'/@2',@1'=(x^3)',@2'=(x)'],[@1',@2']); 2 3 x As illustrated by this example, differential operators are now as easily expressed as functions. This worked well for the univariate case; what about multiple variables? (@1'/@2')((x+y)^2,x) yields 2 x x' + 2 x' y + (2 x + 2 y) y' x' We need to set y' to to get the expected answer 2 x + 2 y. But when we curry we need to have the differentials remain until all the lambda variables are consumed. (@1'/@2')((x+y)^2) gives 2 x x' + 2 x' y + (2 x + 2 y) y' @1' We don't want to set x' and y' to in the numerator because the result would be 0. We don't know which differential until @1' is substituted for. I think the solution here is to set to zero differentials occuring only in the numerator and only for those expressions containing no lambda variables or their derivatives. CONCLUSION I have shown how to implement functional abstraction (lambda), application and partial application (currying) in a system built on variable elimination from polynomials. BIBLIOGRAPHY [1] Bareiss, E.H.: Sylvester's identity and multistep integer-preserving Gaussian elimination. Mathematics of Computation 22, 565-578, 1968. [2] Uspensky, J.V.: Theory of Equations McGraw-Hill Book Co., Inc., 1948 [3] Thomas W. Dube: "The Structure of Polynomial Ideals and Groebner Bases", SIAM JOURNAL ON COMPUTING, (19,4) (August 1990) pp. 750-773. [4] Hoffmann, C. M.: Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers, Inc. San Mateo, California, 1989 [5] Geddes, K.O., Czapor, S.R., Labahn, G.: Algorithms for Computer Algebra. Kluwer Academic Publishers [6] Hygenic Macro Expansion E.E.Kohlbecker, D.P.Friedman, M.Fellinson, and B.Duba 1986 ACM Conference on Lisp and Functional Programming Pages 151-159

    34. AMCA: General Quantum Polynomials By V. A. Artamonov
    Denote by \lambda the associative kalgebra with a unit generated by elements X1 +/- 1, The algebra \lambda is a left and right Noetherian domain.
    Atlas Mathematical Conference Abstracts Conferences Abstracts Organizers ... About AMCA International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures
    May 21-24, 2002
    Vanderbilt University
    Nashville, TN, USA Organizers
    Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote View Abstracts
    Conference Homepage
    General quantum polynomials
    V. A. Artamonov
    Moscow State University
    General quantum polynomials
    Vyacheslav A. Artamonov
    Department of Algebra, Faculty of Mechanics and Mathematics Moscow State University, Moscow, 119899, RUSSIA
    Let k be a field with a fixed matrix Q=(q ij in ii =q ij q ji , ... , X r , X r+1 , ... , X n subject to defining relations X i X i =X i X i i X j =q ij X j X i quantum polynomials and the elements q ij are multiparameters A n Q A n Q general algebra of quantum polynomials that is all multiparameters q ij of the field k []. We show that all valuations on the division ring of fractions F are Abelian and all of them are classified by linear orders on Z n []. In some sense this is another classification of points of

    35. Lambda Calculus Tutor
    The algebra Helper software is the best tool to learn lambda calculus tutor. With it, you can learn at home, at your own pace and without needing a tutor.
    @import url("images/styles.css"); @import url("forum.css");
    l learn algebra variations l learn kid is flunking algebra what can i do kids algebra tutor kids learning tennis playing in carmel indiana ... ks3 algebra Author Message Mark Registered User Joined: 06 Feb 03 Posts: 6 Location: Dallas, US Posted: Fri Feb 06, 2003 6:23 pm ; Post subject: lambda calculus tutor Okay, so here's the deal. I'm just learning lambda calculus tutor and I need help. What's the best way to figure out this stuff? Back to top Profile PM WWW Author Message moderator Joined: 11 Jan 2003 Posts: 1264 Location: Salt Lake City, UT Posted: Fri Feb 06, 2003 6:50 pm ; Post subject: RE: lambda calculus tutor On the bright side, you have help besides fellow students and the teacher. The Algebra Helper software will literally help you work on your own algebra problems at your own pace. By the time you're done with your homework, you can show that teacher (and if you're nice - your classmates too) how it's done. It seems like algebra homework can take forever. It seems like all you do is sit there and stare at the equations hoping that it will just suddenly sink in. And yet…when you're done staring at the homework, you still probably have a ton of other homework to do. Who really needs help solving equations that aren't your own? Math labs and tutorials are great, but when you're done, you still have to do your own homework. Besides, how often do you really remember everything you go through in a tutorial?

    36. Algebras And Representation Theory - Blog » 2006 » December
    in the center of $\bar \lambda = \lambda/r$ if is isomorphic to a generalized path algebra with weak relations. Representations of the generalized path

    37. Aufgabe 1 (define-struct Pair (fst Snd)) (define Zip (lambda (l1
    (pairfst p) arg) (pair-snd p) (lookup (rest fun) arg))))))) (define kata (lambda (t algebra env) (cond ((var? t) (lookup env (var-name t))) ((null? t)
    ;; Aufgabe 1 (define-struct pair (fst snd)) (define zip (lambda (l1 l2) (cond ((empty? l1) empty) ((cons? l1) (cond ((empty? l2) empty) ((cons? l2) (cons (make-pair (first l1) (first l2)) (zip (rest l1) (rest l2))))))))) ;; Aufgabe 3 ;; (a) (define number*- < (lambda (a b) (cond ((equal? a '-infty) (not (equal? a '-infty))) ((number? a) (or (equal? b '+infty) ( < a b) a b))) ;; (b) (define-struct branch (left elem right)) (define number*-min-3 (lambda (a b c) (number*-min a (number*-min b c)))) (define btree-min (lambda (t) (cond ((empty? t) '+infty) ((branch? t) (number*-min-3 (btree-min (branch-left t)) (branch-elem t) (btree-min (branch-right t))))))) ;; Aufgabe 4 ;; (a) ;; Implementierung von Mengen als unsortierte Listen ;; (mit Wiederholungen) (define set-union (lambda (s1 s2) (cond ((empty? s1) s2) ((cons? s1) (set-insert (first s1) (set-union (rest s1) s2)))))) ;; (b) ;; Implementierung von Mengen als aufsteigend sortierte Listen ;; (ohne Wiederholungen) (define set-elem? (lambda (x s) (cond ((empty? s) #f) (( < x (first s)) #f) ((= x (first s)) #t) ((> x (first s)) (set-elem? x (rest s)))))) (define set-insert (lambda (x s) (cond ((empty? s) (list x)) ((

    38. Lie Algebra Question Text - Physics Forums Library
    We can use these maps to construct two vector fields X_L^\rho and X_L^\lambda for each vector L in the Lie algebra X_L^\rho _g=Lg X_L^\lambda _g=gL
    Physics Help and Math Help - Physics Forums Mathematics PDA View Full Version : Lie algebra question Fredrik I'm reading about gauge theory and the text goes through some stuff about Lie groups and algebras rather quickly. I tried to prove one of the things they state without proof and got stuck.
    We can use either right or left multiplication to map the Lie algebra onto the tangent space at any other point g:
    Let's simplify the notation a bit:
    Either of these two vector fields can be used to define a Lie bracket on the Lie Algebra:
    (I assume that anyone who can help me with this already knows the definition of the commutator of two vector fields, which is used on the right).
    The claim I haven't been able to prove is that these two definitions of the Lie bracket are equivalent, i.e. that it doesn't matter if we define it using right or left multiplication. So my question is, can someone help me prove that?
    A few observations:
    What am I missing? I have a feeling it's something simple. quidamschwarz Hi Fredrik

    39. Mode Lisp; -*- ;;;; Algebra System For CPS ;;; Copyright (c) 1986
    The function SETUPalgebra-PROBLEM sets up the algebra problem space. . exp) (not (listp exp))) nil) (t (setq xts (remove-if (lambda (e) (no-unknown? e

    40. Preparing An Abstract
    \begin{theorem} Let $\lambda$ be an artin algebra and $M$ an indecomposable module in $\mod\lambda$. Then $\End_\lambda(M)$ is a local ring. \end{theorem}
    Preparing an abstract
    Go back to ICRA Home Page
    How to prepare an abstract?
    The format of the abstract
    GO TO TOP We ask all of you who want to submit an abstract for the conference to prepare it using LaTeX2e (LaTeX) and in the following format:
    Predefined commands
    GO TO TOP We plan to compile the abstracts in one LaTeX document, so we need to have some standards when it comes to defining user defined commands. We supply a list below of commands that most probably will cover most of your needs, but if you do not find the command that you need on this list, put your definitions after and before
    Theorems and other stuff
    GO TO TOP To typeset a theorem use the following format: If you want to put an attribute to the theorem, you do the following This will come out like Theorem 1 (Auslander) if for example this is the first result mentioned in the abstract. To typeset a corollary, conjecture, lemma, proposition or definition, just substitute theorem with the wanted word, namely, write exactly corollary, conjecture, lemma, proposition or definition instead of theorem. Theorems, corollaries, lemmas, propositions and definitions will be numbered with the same counter, while conjectures will be numbered by their own counter.

    41. Modules Over Iwasawa Algebras, By J. Coates, P. Schneider, R. Sujatha
    We recall that the Iwasawa algebra $\lambda(G)$ is defined to be the completed group ring of $G$ over the ring of $p$adic integers.
    Modules over Iwasawa algebras, by J. Coates, P. Schneider, R. Sujatha

    J. Coates, P. Schneider, R. Sujatha

    42. R: Basic Linear Algebra Utilities And Other Computations Supporting The Krig Fun
    Default is NA, i.e. use the value in out\$lambda . The engines are the code modules that handle the basic linear algebra needed to computed the
    R Documentation
    Basic linear algebra utilities and other computations supporting the Krig function.
    These are internal functions to Krig that compute the basic matrix decompositions or solve the linear systems needed to evaluate the Krig/Tps estimate. Others listed below do some simple housekeeping and formatting. Typically they are called from within Krig but can also be used directly if passed a Krig object list.
    Krig.engine.default(out, verbose = FALSE) Krig.engine.knots(out, verbose = FALSE) Krig.engine.fixed( out, verbose=FALSE, lambda=NA) Krig.coef(out, lambda = out$lambda, y = NULL, yM = NULL, verbose = FALSE) Krig.check.xY(x, Y,Z, weights, na.rm, verbose = FALSE) Krig.cor.Y(obj, verbose = FALSE) Krig.transform.xY(obj, knots, verbose = FALSE) Krig.make.W( out, verbose=FALSE) Krig.make.Wi ( out, verbose=FALSE)
    out A complete or partial Krig object. If partial it must have all the information accumulated to this calling point within the Krig function. obj Same as out verbose If TRUE prints out intermediate results for debugging.

    43. ( )
    The aim of the paper is to prove that given a positively graded locally finite $K$algebra $\lambda = \sum_{i \geq 0} \lambda_i$ and a finite grading

    44. From Kramsay@aol.commangled (Keith Ramsay) Subject Re Graded
    For example let M be a module over the commutative ring K. Then T(M) and lambda(M), the tensor algebra and exterior algebra respectively, are graded
    From: kramsay@aol.commangled (Keith Ramsay) Subject: Re: graded algebra Date: 22 Nov 1999 04:23:52 GMT Newsgroups: sci.math In article , Julius Ross Subject: Re: graded algebra Date: Mon, 22 Nov 1999 08:32:47 GMT Newsgroups: sci.math In article , Julius Ross

    45. Baztech Informacja O Publikacji
    Streszczenie angielskie lambda abstraction algebras are designed to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras

    46. C*-algebras Associated With Presentations Of Subshifts II. Ideal Structure And L
    As a result, the class of the C*algebras associated with $\lambda$ -graph systems under condition (II) is closed under quotients by its ideals.
    J. Aust. Math. Soc.
    -algebras associated with presentations of subshifts II. Ideal structure and lambda-graph subsystems
    Kengo Matsumoto
    Department of Mathematical Sciences
    Yokohama City University
    Seto 22-2, Kanazawa-ku
    Yokohama 236-0027

    Abstract A -graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In Doc. Math. C* -algebra associated with a -graph system from a graph theoretic view-point. If a -graph system comes from a finite labeled graph, the algebra becomes a Cuntz-Krieger algebra. In this paper, we prove that there is a bijective correspondence between the lattice of all saturated hereditary subsets of and the lattice of all ideals of the algebra , under a certain condition on called (II). As a result, the class of the C* -algebras associated with -graph systems under condition (II) is closed under quotients by its ideals.
    Download the article in PDF format
    (size 169 Kb) Australian Mathematical Publishing Association Inc.

    47. Fundamenta Informaticae, Volume 30, Abstracts
    lambda abstraction algebras are designed to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras algebraize the
    Abstracts of Fundamenta Informaticae Volume 33.
    Number 1
    L. CZAJA
    Minimal-Maximal Time Cause-Effect Structures pages 1-16

    It is shown that minimal-time singly-valued (counterparts of 1-safe Petri nets) cause-effect (c-e) structures are of the same expressive power as no-time singly-valued c-e structures, while maximal-time multi-valued c-e structures are of essentially greater expressive power than no-time multi-valued c-e structures.
    L. CZAJA
    Cause-Effect Structures - Structural and Semantic Properties Revisited pages 17-42

    On Scott Consequence Systems pages 43-70

    The notion of Scott consequence system (briefly, S-system) was introduced by D. Vakarelov in [32] in an analogy to a similar notion given by D. Scott in [26]. In part one of the paper we study the category SSyst
    In part two of the paper we prove that the separation theorem for S-systems is equivalent in ZF to some other separation principles, including the separation theorem for filters and ideals in Boolean algebras and separation theorem for convex sets in convexity spaces.

    48. Nonlinear Deformations Of Su(2) And Su(1,1) Generalizing Witten's Algebra
    For lambda =2, such algebras are equivalent to Witten s (1990) first deformation of su(2) or su(1,1). For any lambda , the spectrum of J0 is exponential
    @import url(; User guide Site map Athens login IOP login: Password:
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    Nonlinear deformations of su(2) and su(1,1) generalizing Witten's algebra
    C Delbecq et al J. Phys. A: Math. Gen. L127-L134 doi:10.1088/0305-4470/26/4/001 PDF (303 KB) References Articles citing this article
    C Delbecq
    and C Quesne
    Physique Nucl. Theorique et Physique Math., Univ. Libre de Bruxelles, Belgium Abstract. Nonlinear deformations of su(2) and su(1,1) involving two deforming functions f(J ) and g(J ) are considered. For g(J )=1, they reduce to some algebras first studied by Polychronakos (1990) and Rocek (1991). Spatial emphasis is laid on the case where g(J ) is a linear function of J . It is shown that for any lambda =2,3,. . ., there exist ( lambda -1)-parameter algebras that are deformations of su(2) or su(1,1) respectively, and for which f(J ) is a polynomial of degree lambda . For lambda =2, such algebras are equivalent to Witten's (1990) first deformation of su(2) or su(1,1). For any lambda , the spectrum of J is exponential instead of linear as in the case where g(J Print publication: Issue 4 (21 February 1993)
    PDF (303 KB)
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    49. FLoC 2006 - LICS
    Boolean algebras for lambda calculus In this paper we show that the Stone representation theorem for Boolean algebras can be generalized to combinatory
    LICS 2006 Twenty First Annual IEEE Symposium on Logic in Computer Science
    Seattle, August 12 - 15, 2006 FLoC Home About FLoC MEETINGS CAV ICLP IJCAR LICS ... Workshops (by conf.) PROGRAM Room Assignments FLoC at a glance Social Events Invited Talks ... Workshop Proceedings FACILITIES Conference Hotel Event Space Internet Access SEATTLE Travel to/in Seattle Dining Guide Sightseeing in Seattle ORGANIZATION Steering Committee Program Committee Organizing Committee Sponsors MISCELLANEOUS Related Events Site Design OUT-OF-DATE Registration Visa Information Student Travel Support
    LICS on Monday, August 14th
    Chair: Patrice Godefroid
    Location: Metropolitan A
    Orna Kupferman (Hebrew University, Israel)
    Avoiding Determinization [ppt]
    Automata on infinite objects are extensively used in system specification, verification, and synthesis. While some applications of the automata-theoretic approach have been well accepted by the industry, some have not yet been reduced to practice. Applications that involve determinization of automata on infinite words have been doomed to belong to the second category. This has to do with the intricacy of Safra's optimal determinization construction, the fact that the state space that results from determinization is awfully complex and is not amenable to optimizations and a symbolic implementation, and the fact that determinization requires the introduction of acceptance conditions that are more complex than the Buchi acceptance condition. Examples of applications that involve determinization and belong to the unfortunate second category include model checking of omega-regular properties, decidability of branching temporal logics, and synthesis and control of open systems.

    50. Peter Selinger Papers
    Equivalently, the open and closed term algebras of the untyped lambda calculus cannot be nontrivially partially ordered. Our second result is a syntactical
    This is a list of Peter Selinger 's papers, along with abstracts and hyperlinks. See also:
    A linear-non-linear model for a computational call-by-value lambda calculus
    Proceedings of the Eleventh International Conference on Foundations of Software Science and Computation Structures (FOSSACS 2008), Budapest

    51. Citebase - On Spaces Of Connected Graphs II: Relations In The Algebra Lambda
    Université Paris VII preprint, July 1995 (revised 1997). G/A, 7 Pierre Vogel, The universal Lie algebra, Université Paris VII preprint, June 1999.

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