61. History Of The Conjectures Previous Next Contents 1.iv. History of the conjectures. This renewed Sottile'sinterest in these conjectures and inspired the recent work. http://www.expmath.org/extra/9.2/sottile/SectI.4.html

1.iv. History of the conjectures Soon after Sottile obtained the results of his thesis [ ], Boris Shapiro and Michael Shapiro formulated a very general, but precise conjecture, which dealt with this phenomenon of reality in enumerative geometry for Grassmannians. ( Here are excerpts from letters giving more information.) Their conjecture was also concerned with the flag manifold. As stated, it is false - we describe a counterexample later. ]. While studying the pole placement problem numerically [ RS ], Rosenthal and Sottile decided to test some instances of the conjecture of Shapiro and Shapiro. Much to their surprise, the computations were all in agreement with the conjecture. ( Here is a description of that project.) RS HSS ]. Also, Sottile distributed two challenges to the systems solving community. One concerned ` hypersurface ' Schubert conditions (see Section 2 ), and the second concerned ` Pieri-type ' Schubert conditions (see Section 3 FRZ ] was in response to these challenges. They verified one instance of the conjecture involving the 462 4-planes meeting 12 3-panes in 7-space. This renewed Sottile's interest in these conjectures and inspired the recent work. To the best of our knowledge, this document and the paper [ ] mark the debut in print of the most general version of the conjecture of Shapiro and Shapiro.

62. CADiZ: Proving Conjectures Using Cadiz CADiZ Tutorial guides / Proving conjectures using cadiz. This documentwon't Obtaining conjectures to prove. The Z notation allows http://www-users.cs.york.ac.uk/~ian/cadiz/provingtut.html

Tutorial guides / Proving conjectures using cadiz This document won't teach you how to do proofs, but if you already have some idea on that, then it will tell you how to use cadiz to help find proofs. It assumes that you know the Z notation. You should already be familiar with interacting with cadiz, but a short review is given here. Contents of this page The terminology of proof Invoking proof steps Using the proof tree Recording and playing a proof ... General observations The terminology of proof A sequent consists of generic parameters, declarations, antecedent predicates, and consequent predicates. A sequent expresses the conjecture that the conjunction of the antecedents implies the disjunction of the consequents. In the following example, there is one generic parameter ( PERSON ), three declarations ( p and the two relations), three antecedent predicates, and one consequent predicate. Topic p knows CADiZ_interface, p knows Z p knows CADiZ_interface p can_do PROOF ? p can_do PROOF The syntax of a sequent permits a name to be associated with a sequent. The symbol separating the antecedents from the consequents ( ) is called the turnstile A sequent is proven (i.e. a conjecture is shown to be a

63. Kaplansky's Conjectures On Kaplansky's conjectures. Yorck Sommerhäuser. Abstract. We survey the knownresults on Kaplansky's ten conjectures on Hopf algebras. Introduction. http://www.mathematik.uni-muenchen.de/~sommerh/Publikationen/KaplConjwww/KaplCon

On Kaplansky's conjectures Extended version of a talk given at the conference `Interactions between Ring Theory and Representations of Algebras', Murcia, Spain, January 12-17, 1998 Preprint: Series "Graduiertenkolleg Mathematik im Bereich ihrer Wechselwirkung mit der Physik": gk-mp-9806/55 ( dvi, ps Book: F. v. Oystaeyen/M. Saorin (ed.): Interactions between Ring Theory and Representations of Algebras, Lect. Notes Pure Appl. Math., Vol. 210, Dekker, New York, 2000, 393-412 Abstract We survey the known results on Kaplansky's ten conjectures on Hopf algebras. Introduction In the autumn of 1973, I. Kaplansky gave a course on bialgebras in Chicago. For this course, he prepared some lecture notes that he originally intended to turn into a comprehensive account on the subject. In 1975, he changed his mind and published these lecture notes without larger additions. These lecture notes contain, besides a fairly comprehensive bibliography of the literature available at that time, two appendices. The first of these appendices is concerned with bialgebras of low dimension, whereas the second one contains a list of ten conjectures on Hopf algebras which are known today as Kaplansky's conjectures. Kaplansky's conjectures did not arise as the product of a long investigation in the field of Hopf algebras; also, Kaplansky did not make many contributions to the solution of his conjectures. He only intended to list a number of interesting problems at the end of his lecture notes - lecture notes that he himself called informal. Because of this, it happened that one conjecture in the list was already solved at the time of publication, another one is very simple. That the conjectures nevertheless gained considerable importance for the field is due to the fact that Kaplansky achieved to touch upon a number of questions of fundamental character.

64. Integermania - Theorems And Conjectures Integermania! Theorems and conjectures. Theorems and conjectures aboutIntegermania can be submitted to Steve Wilson for posting on this page. http://staff.jccc.net/swilson/integermania/theorems.htm

Steven J. Wilson Professor of Mathematics JCCC SHCM Division Math Integermania! - Theorems and Conjectures Theorems and conjectures about Integermania can be submitted to Steve Wilson for posting on this page. Warning: False conjectures could be bumped off this page by true conjectures! Definition 1: The exquisiteness of a solution to a Integermania problem is the highest level operation used in its construction, as given by the table of levels of exquisiteness , but the table is not repeated here. Definition 2: The exquisiteness of a set of numbers A at level L is the largest positive integer n L having the property that for every positive integer less than or equal to n L there exists a solution to the Integermania problem using set A with exquisiteness level less than or equal to L . Notationally, we can write: Exq A L n L , or Exq A n n n L Exquisiteness conjectures for each problem are available on each problem page. Theorem 1: In an Integermania problem with n values and k available binary operations, where each value is used exactly once, and values are combined by using only the available binary operations, there are at most positive integers which can be created. See

65. Wild Cryptographic Conjectures Bram's page These thoughts have been nagging me for a long time. Idon't believe current technologies (circa 2000) can come close http://bitconjurer.org/wild_cryptographic_conjectures.html

Bram's page These thoughts have been nagging me for a long time. I don't believe current technologies (circa 2000) can come close to determining the truth of either of them, but attacking them looks like a very fertile area of research. Conjecture - For any axiomatic system, there exists a function which runs in a practical amount of time which takes as inputs a statement in that axiomatic system and a fixed length string, such that given a proof of any statement in the axiomatic system it is possible in a practical amount of time to construct a string such that the function when given the statement and the string will return true, but it is computationally intractable to find a false statement and a string such that the function will return true. Conjecture - There is a method of encoding any program such that the encoded form of the program can be sent to an untrusted party and the untrusted party will be able to determine the outputs of the program when given any particular set of inputs but will be incapable of determining anything about the program's structure other than what can be deduced from the amount of time it took to compute the answer and the amount of memory it used. -Bram Cohen

66. The Evolution Of Consistent Conjectures Abstract In this paper we model the evolution of conjectures in an economyconsisting of a large number of firms which meet in duopolies. http://www.unites.uqam.ca/ideas/data/Papers/yoryorken01-16.html

This file is part of IDEAS , which uses RePEc data Papers Articles Software Books ... Help! The Evolution of Consistent Conjectures Author info Abstract Publisher info Related research ... Statistics Author Info Huw D Dixon and Ernesto Somma Additional information is available for the following registered author(s): HUW DAVID DIXON Abstract In this paper we model the evolution of conjectures in an economy consisting of a large number of firms which meet in duopolies. The duopoly game is modelled by the conjectural variation (CV) model. An evolutionary process leads to more profitable conjectures becoming more common (payoff monotone dynamics). Under payoff monotonic dynamics, convergence occurs to a small set of serially undominated strategies containing the consistent onjecture. This set can be made arbitrarily small by appropriate choice f the strategy set. If the game is dominance solvable, then the dynamics converges globally to the unique attractor. Publisher Info Paper provided by Department of Economics, University of York in its series Discussion Papers with number 01/16.

67. Problem Solving Island : About Conjectures About conjectures. A journal entry by Alex Hernandez.. A conjectureis informally, a guess, a hypothesis and a deduction. Of course http://www.math.grin.edu/~rebelsky/ProblemSolving/Essays/conjectures.html

About Conjectures [A journal entry by Alex Hernandez.] Conjuring conjectures is a very natural process (at least I think so) when ever you're dealing with problems because people tend to hate to be wrong or lose. So they want to find a way to be right and have other people think they are right and "know" that they are right, and that's what deduction is about. Front Door Problems Resolutions Essays ... Miscellaneous Warning! This site is under development. Source text last modified Tue May 5 10:08:34 1998. This page generated on Thu May 7 15:18:25 1998 by SiteWeaver. Contact our webmaster at rebelsky@math.grin.edu

68. Problem Solving Island : More Conjectures More conjectures. A Journal entry by Erica Chang.. Taking the exampleof A Fly in the Fries problem, several conjectures can be made. http://www.math.grin.edu/~rebelsky/ProblemSolving/Essays/moreconjectures.html

More Conjectures [A Journal entry by Erica Chang.] Front Door Problems Resolutions Essays ... Miscellaneous Warning! This site is under development. Source text last modified Thu May 7 16:01:59 1998. This page generated on Thu May 7 16:02:00 1998 by SiteWeaver. Contact our webmaster at rebelsky@math.grin.edu

69. Truncated Trickery Conjectures conjectures If there is a tiling in four dimensional space otherthan the hypercube, it has yet to be found. This is due to time http://www.theory.org/geotopo/tt/html/conjectures.html

70. Matter, Charge, And Conjectures Matter, Charge, and conjectures. One of the to choose. We're better offhaving more conjectures to choose from than having less. It's http://www.dragonscience.com/view/cnjctrs.html

Matter, Charge, and Conjectures One of the hot topics of discussion in the Monday meeting after last month's conference was the relative strengths of electricity and gravity. The electricians knew the electric force was 39 orders of magnitude stronger than gravity, and the graviticians knew the gravitational force was 40 orders of magnitude stronger than electricity. This misses the point. On the purely mathematical level, you can plug numbers into the equations to get any magnitude of force you want. The gravitational force between two 10 kg lead spheres placed 1 m apart is: F = GM^2/R^2 = 6.7x10^-11 times 10^2 divided by 1^2 = 6.7x10^-9 Newtons. To equal that force with electricity, the spheres would have to be charged to: 6.7x10^-9 = [1/(4 x pi x e-sub-naught)] times Q^2 divided by 1^2, or Q = sqrt (6.7x10^-9 divided by 9x10^9) = 8.6x10^-10 coulombs, or 860 micro-micro-coulombs. This could be achieved with a current of 1 microampere in less than a millisecond. The technology of nylon rods rubbed over cat fur can transfer enough static charge to overcome the gravitational attraction of lead spheres.

71. Novikov And Borel Conjectures Page @Goldfarb Novikov and Borel conjectures. And a telltale sign of the coming ubiquityof reallife applications of the two conjectures is www.borel.com. http://math.albany.edu:8000/~goldfarb/nbc.html

Novikov and Borel conjectures For other topics of interest to SUNY@Albany faculty, see this page The rigidity conjecture is about a class of manifolds which should never require surgery. They are the closed aspherical manifolds, that is, compact manifolds without boundary whose universal cover is contractible. Whether two such manifolds are homotopy equivalent can be detected already by comparing the fundamental groups. Topological Rigidity a.k.a. Borel Conjecture. If two closed aspherical manifolds are homotopy equivalent then they are, in fact, homeomorphic. Examples. There are many examples of aspherical manifolds such as closed nonpositively curved Riemannian manifolds, nilmanifolds and solvmanifolds, Davis' manifolds not covered by Euclidean spaces, asphericalizations of arbitrary closed manifolds a la Gromov. Many more important examples of aspherical manifolds come with boundary or with corners such as compactified arithmetic quotients of symmetric spaces, and there are relative rigidity conjectures for such manifolds. There are more refined versions of the Novikov and Borel conjectures stated in R. Kirby's List of Problems in Low-dimensional Topology, in Geometric Topology (W.H. Kazez, ed.), Studies in Adv. Math., Vol.2, Part 2, AMS (1997), pp. 355-358. This refers to the very last problem 5.29, one of several which are "high-dimensional". This 380 page list is available in PostScript from

72. Pratt's Conjectures PrevNextIndexThread Pratt's conjectures. To types@theory.LCS.MIT.EDU;Subject Pratt's conjectures; From thatte%cs@ucsd.edu (Satish Thatte); http://www.cis.upenn.edu/~bcpierce/types/archives/1988/msg00178.html

[Prev] [Next] [Index] [Thread] Pratt's conjectures To types@theory.LCS.MIT.EDU Subject : Pratt's conjectures From thatte%cs@ucsd.edu (Satish Thatte) Date : Tue, 22 Nov 88 18:08:54 EST Sender meyer@theory.LCS.MIT.EDU Prev: Re: Wand on final algebra semantics Next: More on Pratt's conjectures Index(es): Main Thread

73. More On Pratt's Conjectures More on Pratt's conjectures. To types@theory.LCS.MIT.EDU; Subject Moreon Pratt's conjectures; From thatte%cs@ucsd.edu (Satish Thatte); http://www.cis.upenn.edu/~bcpierce/types/archives/1988/msg00179.html

[Prev] [Next] [Index] [Thread] More on Pratt's conjectures To types@theory.LCS.MIT.EDU Subject : More on Pratt's conjectures From thatte%cs@ucsd.edu (Satish Thatte) Date : Tue, 22 Nov 88 15:30:33 PST Prev: Pratt's conjectures Next: final algebras Index(es): Main Thread

74. Resolution Of Conjectures On The Sustainability Of Natural Resolution of conjectures on the Sustainability of Natural Monopoly. TitleResolution of conjectures on the Sustainability of Natural Monopoly. http://www.rje.org/abstracts/abstracts/1984/Spring_1984_._pp._135_141.html

Resolution of Conjectures on the Sustainability of Natural Monopoly Volume: Volume 15, No. 1 Issue: Spring 1984 Pages: pp. 135-141 Authors: Thijs ten Raa Title: Resolution of Conjectures on the Sustainability of Natural Monopoly Abstract: Sharkey has conjectured that for a natural monopoly: (1) the core price vector of some output vector (which renders any partial supply of the output unprofitable) lies on the demand curve; and (2) such a price vector is sustainable, meaning that supply by an entrant would be unprofitable, even at lower prices. This article demonstrates that (1) is true even under quite general conditions that allow for interdependent demand, (2) is true provided that demand is independent, but (2) can be invalidated by demand interdependence. JEL Classification Microeconomics Theory of Firm and Industry under Imperfectly Competitive Market Structures (0226) Market Structure: Industrial Organization and Corporate Strategy (6110) Search Abstracts Order Back Issues Order Individual Articles RAND Journal of Economics WWW Page ... RJE@rand.org

75. Graded Associative Algebras And Grothendieck Standard Conjectures Graded associative algebras and Grothendieck Standard conjectures.This paper is concerned with Grothendieck's standard conjectures http://math1.uibk.ac.at/mathematik/jordan/archive/gr-conjectures/

Graded associative algebras and Grothendieck Standard Conjectures This paper is concerned with Grothendieck's standard conjectures on algebraic cycles, introduced independently by Grothendieck and Bombieri to explain the Weil conjectures on the zeta-function of algebraic varieties. We prove that the semisimplicity of the algebra of algebraic correspondences A(X) of a projective irreducible smooth variety X implies the standard conjecture of Lefschetz type for X. It was proved by U. Jannsen that the algebra A(X) is semisimple when the numerical and homological equivalences of algebraic cycles on X are the same. Thus, with Jannsen's theorem our result asserts that the standard conjecture of Lefschetz type follows from Grothendieck's conjecture about the equality of the numerical and homological equivalences. This was known before only in the presence of the standard conjecture of Hodge type. (This paper has appeared in Invent. Math. 128 (1997), 201206) O. N. Smirnov

76. A SET OF CONJECTURES ON SMARANDACHE SEQUENCE A SET OF conjectures ON SMARANDACHE SEQUENCES*. Sylvester Smith. Departmentof Mathematics, Yuma Community College. ABSTRACT. Searching http://www.gallup.unm.edu/~smarandache/sylsmith.htm

A SET OF CONJECTURES ON SMARANDACHE SEQUENCES* Sylvester Smith Department of Mathematics, Yuma Community College ABSTRACT Searching through the Archives of the Arizona State University, I found interesting sequences of numbers and problems related to them. I display some of them, and the readers are welcome to contribute with solutions or ideas. Key words: Smarandache P-digital subsequences, Smarandache P-partial subsequences, Smarandache type partition, Smarandache S-sequences, Smarandache uniform sequences, Smarandache operation sequences. n The new sequence obtained is called: Smarandache P-digital subsequences. For example: (a) Smarandache square-digital subsequence: i.e. from 0, 1, 4, 9, 16, 25, 36, ..., n , ... we choose only the terms whose digits are all perfect squares (therefore only 0, 1, 4, and 9). Disregarding the square numbers of the form 2k zeros where N is also a perfect square, how many other numbers belong to this sequence? (b) Smarandache cube-digital subsequence: i.e. from 0, 1, 8, 27, 64, 125, 216, . . . , n , . . . we choose only the terms whose digits are all perfect cubes

77. Citations: Explicit Expanders And The Ramanujan Conjectures - Lubotzky, Phillips A. Lubotzky, R. Phillips, P. Sarnak, Explicit Expanders and the Ramanujanconjectures , Proc. Explicit Expanders and the Ramanujan conjectures. http://citeseer.nj.nec.com/context/125129/0

26 citations found. Retrieving documents... A. Lubotzky, R. Philips, and P. Sarnak. Explicit expanders and the Ramanujan conjecture . In Proceedings of the 18th Annual ACM Symposium on Theory of Computing, pages 240-246, 1986. Home/Search Document Not in Database Summary Related Articles Check This paper is cited in the following contexts: First 50 documents Hyper-Encryption against Space-Bounded Adversaries from On-Line.. - Lu (Correct) ....bit of a codeword is a parity of a small number of input bits. Here we give another code with a better parameter. 4.1 An On Line List Decodable Code We will use some type of graphs called expander graphs which have their second largest eigenvalue bounded away from their largest one. Lemma There exists an explicit family of expander graphs (G n ) n2N with the following property. There is a constant d and a constant d such that for every n 2 N, G n is a d regular graph of n vertices with the second largest eigenvalue . Expander graphs enjoys some pseudo random properties, and .... A. Lubotzky, R. Philips, and P. Sarnak.

78. Ask Jeeves: Search Results For "Conjectures" Popular Web Sites for conjectures . Search Results 1 10 Ranked by Popularity,Next . 1. Some Open Problems Open problems and conjectures http://webster.directhit.com/webster/search.aspx?qry=Conjectures

79. Notes On Serre's Conjectures Lectures on Serre's conjectures. Kenneth A. Ribet. Ken Ribet delivered a seriesof lectures on Serre's conjectures at Park City in the Summer of 1999. http://modular.fas.harvard.edu/papers/serre/

Lectures on Serre's conjectures Kenneth A. Ribet William A. Stein Ken Ribet delivered a series of lectures on Serre's Conjectures at Park City in the Summer of 1999. Karl Rubin took a picture of Ken delivering the lectures. The notes are below. This is the final version. It appeared in Arithmetic Algebraic Geometry ribet-stein.ps ribet-stein.pdf ribet-stein.dvi ... ribet-stein.tgz (Latex files, etc.) PCMI version http://shimura.math.berkeley.edu/~was/Tables/Notes/PCMI/index.html Last modified: April 3, 2000 Lecture Notes Database

80. Conjectures On Original Composition (1759) - Edward Young - Kalliope Kalliope Digtere Edward Young Værker conjectures on OriginalComposition (1759). conjectures on Original Composition (1759) http://www.kalliope.org/vaerktoc.pl?fhandle=young&vhandle=1759

Page 4     61-80 of 94    Back | 1  | 2  | 3  | 4  | 5  | Next 20