Home  Mathematical_Logic  Recursive Functions And Relations 
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1. JSTOR Recursive Number Theory (NorthHolland, Amsterdam) Recursive number theory is the study of the natural numbers in which only Recursive functions and relations may be defined. http://links.jstor.org/sici?sici=00255572(195812)2:42:342<326:RNT>2.0.CO;2Q 
2. Ohio Resource Center > Record > Trout Pond: Using Algebra And Discrete Mathemati use a variety of symbolic representations, including Recursive and parametric equations, for functions and relations;. Use mathematical models to represent http://www.ohiorc.org/record/1470.aspx  

3. Recursive Function (mathematics) Â Britannica Online Encyclopedia The theory of Recursive functions was developed by the 20thcentury truth that all Recursive or computable functions and relations are representable in http://www.britannica.com/eb/topic493975/article9062919  

4. Recursive Characterization Of Computable Realvalued Functions And Relations Recursive characterization of computable realvalued functions and relations. Source, Theoretical Computer Science archive http://portal.acm.org/citation.cfm?id=235897 
5. Springer Online Reference Works Suppose that are place primitive Recursive functions, and let be primitive Recursive relations such that for any set of argument values at most one of them http://eom.springer.de/P/p074610.htm  

6. PlanetMath: Recursive Function AMS MSC, 03D20 (Mathematical logic and foundations Computability and recursion theory Recursive functions and relations, subRecursive hierarchies) http://planetmath.org/encyclopedia/PrimitiveRecursion.html  

7. An Arguable Inconsistency In ZF We consequently note, in Metalemma 1, that we cannot introduce a finite number of arbitrary primitive Recursive functions and relations  as function http://alixcomsi.com/An_arguable_inconsistency_in_ZF.htm  

8. KENT CITY SCHOOLS MATH COMMITTEE INPUT Algebra Standard (Grades 912) Use a variety of symbolic algebra representations, including Recursive, explicit, polar, and parametric equations, for functions and relations. http://kent.k12.oh.us/boe/Alg_Precalculus_Adv_Precalc_Senior_Math.htm  

9. Languages And Machines 13.7 Turing Computability and MuRecursive functions 17.3 relations between Time and Space Complexity. 17.3 PSpace, NPSpace, and SavitchÂs Theorem http://www.cs.wright.edu/~tsudkamp/book.htm  

10. Reasoning With Recursive Rules Note again, that ;; functions and relations must be defined before they can be This is an important feature, since recursion is a very ;; natural and http://www.isi.edu/isd/LOOM/PowerLoom/documentation/examples/recursion.html  

11. Bibliographie Real Recursive functions and real extentions of Recursive functions. for understanding the relations between several analog computational models. http://www.loria.fr/~hainry/publi/Hainry.html  

12. Recursive Characterization Of Computable RealValued Functions And Relations Recursive Characterization of Computable RealValued functions and relations. Vasco Brattka. Journal Title Theoretical Computer Science. Date 1996 http://wotan.liu.edu/docis/show?doc=dbl/tcstcs/1996_162_1_45_RCOCRF.htm&query=si 
13. Theory Of Computing 2007/2008 (FUB MSc In Computer Science)  Lectures the basic definitions regarding functions, relations, and their properties showing computability of primitive Recursive functions; bounded operators http://www.inf.unibz.it/~calvanese/teaching/0708tc/lectures.html  

14. Book Languages And Machines, An Introduction To The Theory Of Computer Science ( relations, and functions 1.3 Equivalence relations 1.4 Countable and Chapter 13 MuRecursive functions 13.1 Primitive Recursive functions 13.2 Some http://www.lavoisier.fr/notice/gbQZOR333E2RB32O.html  

15. Grad Description Elements of set theory, functions and relations nondecimal numbers, Include Turing Machines, partial Recursive functions, Recursive and Recursively http://www.jsums.edu/~sst/cset/ComputerScience/computersciencegradcurriculum.ht 
16. Computability DCS301 Primitive Recursive functions and relations. Ackermann function. Read Chapters 6 and 7 of textbook. Look at Handout 3 and at Cohn, Algebra, Vol 1, Chapter 2 http://www.dcs.qmul.ac.uk/~bellin/coursepage.htm  

17. Overview Of Topics Operations on Sets of Objects; functions and relations; Domain and Range; Recursive functions; Composition of functions; Inverse functions; Bijection, http://www.4dsolutions.net/ocn/mainoutline.html  

18. BigOh For Recursive Functions: Recurrence Relations This web page gives an introduction to how recurrence relations can be used to help determine the bigOh running time of Recursive functions. http://www.cs.duke.edu/~ola/ap/recurrence.html  

19. Recursive Function Theory The relation between Recursive functions and the description of flow control by flow charts is described in Reference 7. An ALGOL program can be described http://wwwformal.stanford.edu/jmc/basis1/node13.html  

20. Call Graphs Of Nestedly Recursive Functions  Wolfram Demonstration Project Nestedly Recursive functions nestedly call previous instances of themselves. Even very simple recursion relations can lead to a complex sequence of values http://demonstrations.wolfram.com/CallGraphsOfNestedlyRecursiveFunctions/  

21. The Set Of Primitive Recursive Functions Preliminaries; Sets of Compatible functions; Homogeneous relations; Primitive Recursiveness; The Set of Primitive Recursive functions; Examples http://mizar.org/JFM/Vol13/comput_1.html  

22. A PVS Formalization Of Well Founded Recursion Our theory applies to the definition of total Recursive relations the definition of total Recursive functions is a special case. http://uuu.enseirb.fr/~gloess/enseignement/spp/now/well_founded_recursion.html  

23. FOM: Concepts Of Recursion Theory This was not surprising; Church s Thesis shows that any result about Recursive functions or relations is in soie sense a result about computability. http://cs.nyu.edu/pipermail/fom/1998August/002024.html  

24. Finite Sets: Counting, Recursion, And Logic, Next Steps Iteration and Recursion; Sets defined by Propositions; The Art of Counting; relations and functions; Digraphs as relations; The Art of Searching http://www.mathwright.com/book_pgs/book651.html  

25. IngentaConnect Recursive Characterization Of Computable Realvalued Functions An Recursive functions we introduce a class of Recursive relations in metric spaces such that each relation is generated from a class of basic relations by a http://www.ingentaconnect.com/content/els/03043975/1996/00000162/00000001/art002  

26. Logic, 8 We define relations, functions and so on in the natural way RUP f1 . .. Recursion Theory Â compare this to SipserÂs Computation, Part II http://www.media.mit.edu/physics/pedagogy/babbage/texts/rt.html  

27. Recursive Functions A less trivial one we now introduce is defined by two relations. Immediately we run into the problems of such Recursive functions. http://www.geocities.com/CapeCanaveral/Lab/3550/meaning.htm  

28. SRF srf (Simple Recursive functions) interprets a very simple programming .. The file examples/relations in the source distribution has functions that match http://www.inlumineconsulting.com:8080/website/srf.html  

29. Vectorization Of Recursion Relations. Techniques for efficient vectorization of the simple Recursive relation (x sub j) = (a sub j)(x sub (j1)) + (d sub j) and the tridiagonal series of http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA 
30. Discrete Mathematics/Recursion  Wikibooks, Collection Of Opencontent Textbooks In mathematics, we can create Recursive functions, which depend on its previous values to create new ones. We often call these recurrence relations. http://en.wikibooks.org/wiki/Discrete_mathematics/Recursion  

31. Recurrence Relations/recursion & Induction Recurrence relations and Recursive definitions have a lot in common with induction the value of a function at a higher value is defined in terms of its http://mathcircle.berkeley.edu/BMC4/Handouts/induct/node9.html  

32. Phys. Rev. A 37 (1988): C. K. Lutrus And S. H. Suck Salk  Recursion Relations F Recursion relations for the overlap of a Morse continuum state with a Lanczos In their study, recursion relations for GreenÃ¢ÂÂs functions in the Lanczos http://link.aps.org/doi/10.1103/PhysRevA.37.3151  

33. Math 210 Topics include counting and combinations, laws of logic, methods of proof, set theory, cardinality, proof by induction, recursion, and relations/functions. http://www.cptc.ctc.edu/library/div4/math210sweerus4.htm  

34. Cook, Matthew M. (20050527) Networks Of Relations. Http://resolver.caltech.edu This thesis explores new ground regarding the composition of relations into this reachability question can be decided by primitive Recursive functions. http://etd.caltech.edu/etd/available/etd06032005140944/  

35. WellFoundedness And Recursion This is a proof of the recursion theorem for wellfounded Recursive definitions. It is modelled on Tobias Nipkow s proof for Isabelle HOL and uses relations http://www.rbjones.com/rbjpub/pp/x004.html  

36. Libra: Recursive Characterization Of Computable RealValued Functions And Relati Real Recursive functions and Real Extensions of Recursive functions(2004) (citation2). Olivier Bournez Emmanuel Hainry. Abstract Recently, functions over http://libra.msra.cn/papercited.aspx?id=759674 
37. Discrete Structures (DS) DS1. Functions, Relations, And Sets [core Explain with examples the basic terminology of functions, relations, and sets. Relate the ideas of mathematical induction to recursion and recursively http://www.sigcse.org/cc2001/DS.html  

38. ACL2 Version 2.3 Such wellfounded relations are used in the admissibility test for Recursive functions, in particular, to show that the recursion terminates. http://www.cs.utexas.edu/users/moore/acl2/v23/acl2doc56.html  

39. ScienceDirect  Physics Letters A : The Recursion Relations For The Ndimensiona Two recursion relations in terms of raising and lowering operators are derived for only the ÂprincipalÂ and ÂangularmomentumÂ quantum numbers through http://linkinghub.elsevier.com/retrieve/pii/S0375960104008321  

40. 22c:245 Advanced Artificial Intelligence The Y combinator for the definition of Recursive functions. Confluence of the reduction relation. equivalence of terms. Reduction strategies. http://www.cs.uiowa.edu/~tinelli/classes/185/Fall06/logs.shtml  

41. Recurrence Relations And Recursion  Maple Application Center  Maplesoft In this module, we ll examine recursion and solving recurrence relations in various forms and from symbolic, numeric, and geometric points of view. http://www.maplesoft.com/Applications/app_center_view.aspx?AID=853 
42. Recursion Definition of recursion, possibly with links to more information and implementations. Write a function to compute GCD based on the following relations http://www.nist.gov/dads/HTML/recursion.html  

43. Analytic Study Of Periodic Chaos. II Recursion Relations For The Power Spectr On the basis of the analytic formulas for the correlation functions of nonperiodic orbits, the recursion relations are obtained which fully characterize the http://adsabs.harvard.edu/abs/1985PThPh..73..349Y  

44. Recursion Relations In Component Form Recursion relations in Component Form. We will now present formulae for calculating , and . We do this by expanding ( gif ) and ( gif http://www.hpcoders.com.au/docs/thesis/node45.html  

45. Venanzio Capretta's Home Page For each language, we can define recursion and induction principles that work the use of wellfounded relations, implementation of operational semantics, http://www.cs.ru.nl/~venanzio/  

46. Question About Indicator Function Of Recursive And R.e. Sets  Object Mix relation and Recursive relation . In the first case, they say the characteristic function has to be effectively computable (ie. partial http://objectmix.com/theory/307390questionaboutindicatorfunctionrecursiver  

47. Front: [math.CA/0509058] Differential Recursion Relations For Laguerre Functions Title Differential Recursion relations for Laguerre functions on Symmetric we considered the family of generalized Laguerre functions on $\Omega$ that http://front.math.ucdavis.edu/0509.5058  

48. Recursion  Wikipedia, The Free Encyclopedia Some specific kinds of recurrence relation can be solved to obtain a nonRecursive definition. A classic example of recursion is the definition of the http://en.wikipedia.org/wiki/Recursion  

49. Tower Of Hanoi The above expression is known as a recurrence relation which, as you might have noticed, is but a Recursive function. TN is defined in terms of only one of http://www.cuttheknot.org/recurrence/hanoi.shtml  

50. Deep Blue At The University Of Michigan: QCD Recursion Relations From The Larges Moreover, the proof of the gluon recursion relations hinges on an identity in momentum space which we show to be nothing but the Fourier transform of the http://deepblue.lib.umich.edu/handle/2027.42/49174  

51. Tutorial: SQL Server Recursion  Parent Child Relations  VBForums Tutorial SQL Server recursion Parent child relations UtilityBank  Tutorials. http://www.vbforums.com/showthread.php?t=366078 
52. Citebase  Mirzakhani's Recursion Relations, Virasoro Constraints And The KdV Hi We present in this paper a differential version of Mirzakhani s recursion relation for the WeilPetersson volumes of the moduli spaces of bordered Riemann http://www.citebase.org/abstract?id=oai:arXiv.org:math/0601194 
53. TFL An Environment For Terminating Functional Programs Proving termination of a Recursively defined function divides into two tasks (1) finding a wellfounded relation R; (2) showing that the Recursive calls http://www.cl.cam.ac.uk/~ks121/tfl.html  

54. Shodor Interactivate: Recursion The Recursion uses JAVA technology. We are trying to determine whether you have this technology installed on your computer. This should only take a few http://www.shodor.org/interactivate/activities/Recursion/  

55. [hepth/0501052] Direct Proof Of TreeLevel Recursion Relation In YangMills The Recently, by using the known structure of oneloop scattering amplitudes for gluons in YangMills theory, a recursion relation for treelevel scattering http://arxiv.org/abs/hepth/0501052  

56. Recursion In ER Relationships Recursion is extremely powerful in modelling. A good example is its use in modelling a family tree. The simplest model stores data about one entity (Person) http://blogs.ittoolbox.com/eai/implementation/archives/recursioninerrelations  

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