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1. Peter Flach's PhD Thesis
conjectures. An inquiry concerning the logic of induction. Peter Flach. This thesis gives an account of my investigations into the logical foundations of inductive reasoning. I combine perspectives
http://www.cs.bris.ac.uk/~flach/Conjectures

Extractions: Bristol CS Index ML group Peter Flach ... Presentations This thesis gives an account of my investigations into the logical foundations of inductive reasoning. I combine perspectives from philosophy, logic, and artificial intelligence. P A Flach Peter.Flach@bristol.ac.uk . Last modified on Friday 20 November 1998 at 15:35. University of Bristol

2. F. Conjectures (Math 413, Number Theory)
A collection of easily stated conjectures which are still open. Each conjecture is stated along with a collection of references.
http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html

Extractions: F. Conjectures Number Theory, Math 413, Fall 1998 A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references. The Riemann Hypothesis Fermat Numbers Goldbach's Conjecture Catalan's Conjecture ... The Collatz Problem Def: Riemann's Zeta function, Z(s), is defined as the analytic extension of sum n infty n s Thm: Z( s )=prod i infty p i s , where p i is the i th prime. Conj: The only zeros of Z( s ) are at s s Thm: The Riemann Conjecture is equivalent to the conjecture that for some constant c x )-li( x c sqrt( x )ln( x where pi( x ) is the prime counting function. Def: n is perfect if it is equal to the sum of its divisors (except itself). Examples are 6=1+2+3, 28, 496, 8128, ... Def: The n th Mersenne Number, M n , is defined by M n n Thm: M n is prime implies that n n is perfect. (Euclid)

3. On Conjectures Of Graffiti
Graffiti is a computer program that makes conjectures in mathematics and chemistry. Links to the
http://cms.dt.uh.edu/faculty/delavinae/research/wowref.htm

4. Prime Conjectures And Open Question
Prime conjectures and Open Questions (Another of the Prime Pages resources). Below are just a few of the many conjectures concerning primes.
http://www.utm.edu/research/primes/notes/conjectures/

Extractions: Submit primes Below are just a few of the many conjectures concerning primes. Goldbach's Conjecture: Every even n Goldbach wrote a letter to Euler in 1742 suggesting that . Euler replied that this is equivalent to this is now know as Goldbach's conjecture. Schnizel showed that Goldbach's conjecture is equivalent to distinct primes It has been proven that every even integer is the sum of at most six primes [ ] (Goldbach's conjecture suggests two) and in 1966 Chen proved every sufficiently large even integers is the sum of a prime plus a number with no more than two prime factors (a P ). In 1993 Sinisalo verified Goldbach's conjecture for all integers less than 4 ]. More recently Jean-Marc Deshouillers, Yannick Saouter and Herman te Riele have verified this up to 10 with the help, of a Cray C90 and various workstations. In July 1998, Joerg Richstein completed a verification to 4

5. Conference On Stark's Conjectures
Johns Hopkins University, Baltimore, MD, USA; 59 August 2002. Online registration.
http://www.mathematics.jhu.edu/stark/

Extractions: Organizing Committee David Burns , King's College London, UK, david.burns@kcl.ac.uk Cristian Popescu , Johns Hopkins University, USA, cpopescu@math.jhu.edu Jonathan Sands , University of Vermont, USA, sands@math.uvm.edu David Solomon , King's College London, UK, solomon@mth.kcl.ac.uk Description of the conference In the last few years there has been a surge in research activity dedicated towards obtaining further explicit evidence for Stark's Conjecture, and in formulating and investigating natural variants, refinements or generalizations thereof. By bringing together the leading exponents of these different strands of research this conference aims to improve understanding of the links between them. In addition, the conference program will include a series of survey talks aimed at making accessible to as wide an audience as possible the main aspects of recent research into Stark's Conjecture. At this time, confirmed main speakers include.

6. Some Open Problems
Open problems and conjectures concerning the determination of properties of families of graphs.
http://www.eecs.umich.edu/~qstout/constantques.html

Extractions: These problems and conjectures concern the determination of properties of families of graphs. For example, one property of a graph is its domination number. For a graph G , a set S of vertices is a dominating set if every vertex of G is in S or adjacent to a member of S . The domination number of G is the minimum size of a dominating set of G . Determining the domination number of a graph is an NP-complete problem, but can often be done for many graphs encountered in practice. One topic of some interest has been to determine the dominating numbers of grid graphs (meshes), which are just graphs of the form P(n) x P(m) , where P(n) is the path of n vertices. Marilynn Livingston and I showed that for any graph G , the domination number of the family G x P(n) has a closed formula (as a function of n ), which can be found computationally. This appears in M.L. Livingston and Q.F. Stout, ``Constant time computation of minimum dominating sets'', Congresses Numerantium (1994), pp. 116-128.

7. Equal Sums Of Like Powers
Unsolved Problems and conjectures. ( h = 1, 2, , n ); ( h = 1, 3, , 2n1 ); ( h = 2, 4, , 2n ). conjectures by Chen Shuwen (1997-2001)
http://member.netease.com/~chin/eslp/unsolve.htm

Extractions: Unsolved Problems and Conjectures The Prouhet-Tarry-Escott Problem Is it solvable in integers for any n How to find new solutions for n = 10 and How to find the general solution for n How to find a new solution of the type ( k =1, 2, 3, 4, 5, 6, 7, 8 ) How to find non-symmetric ideal solutions of ( k =1, 2, 3, 4, 5, 6, 7, 8 ) and ( k =1, 2, 3, 4, 5, 6, 7, 8, 9 ) How to find a solution chain of the type ( k = 1, 2, 3, 4 ) Some other open problems are present on Questions by Lander-Parkin-Selfrige (1967) a k + a k + ... + a m k = b k + b k + ... + b n k Is ( k m n ) always solvable when m n k Is it true that ( k m n ) is never solvable when m n k For which k m n such that m n k is ( k m n ) solvable ?

8. Conjectors / IEIS
conjectures That Go About Breaking Supercomputers. by; Brad Guth / IEIS (updated October 27, 2003) This is about the time where such capable conjectures bring every CRAY supercomputer to their

Extractions: by; Brad Guth / IEIS (updated: October 27, 2003) If you are still one of those cringing and fuming over my discovery, and that of my subsequent efforts at pushing this into mainstream, perhaps you're one of those doing everything you can think of to disqualify literally anything that happens to upset your personal "status quo" or skewed love of NASA, then this next challenging effort or at least the sequel will soon become even more so frightening and, I should think downright capable of even pissing off the Pope. Just maybe, we (mere Earthlings) were not the first on the scene and, ever since not even evolved into the brightest DNA/RNA about. (seems any God, or perhaps just that of a Saint, which could have provided salvation for those on Venus, is worth getting to know something about)

9. Institutt For Matematiske Fag
Summer School 2001 Homological conjectures for finite dimensional algebras August 12th 19th, Nordfjordeid, Norway.
http://www.math.ntnu.no/~oyvinso/Nordfjordeid/

10. The Prime Puzzles And Problems Connection
Problems Puzzles conjectures. 1. Goldbach s Conjecture. 6.- Quantity of primes in a given range Opperman, Brocard Schinzel conjectures?
http://www.primepuzzles.net/conjectures/

11. Conjecture 16.  N^n+1.
Problems Puzzles conjectures. Conjecture 16. n^n+1. Craig Johnston wrote at (23/12/99) I believe that there is no prime of the
http://www.primepuzzles.net/conjectures/conj_016.htm

Extractions: Conjectures Conjecture n^n+1. Craig Johnston wrote at (23/12/99): "I believe that there is no prime of the form (n^n)+1 for n > 4. The are two primes n=2,4 Note that all odd n are even. I have checked exhaustively to n=2500 I have been using PRIMEFORM for the problem. It then checks for probable primality and then tests with the P-1 method." Questions: 1. Can you provide us some published references about the primality or compositeness of this kind of numbers *An article in the Weisstein's Mathematics Encyclopedia. According to all these references the numbers S(n) = n^n+1 were studied by Sierspinski in 1958, who found that if S(n) is prime then S(n) must be equal to the Fermat We know that the Fermat numbers F(m) are prime for m = to 4 and nowadays is believed

A Workshop on the Moonshine conjectures and Vertex Algebras. ICMS, Edinburgh; 414 July 2004.
http://www.ma.hw.ac.uk/icms/meetings/2004/moonshine/

Extractions: The first part of the meeting will be expository, including such areas as Borcherds's proof of the Conway-Norton conjecture, Construction of the Monster, Vertex (operator) algebras, Modular Moonshine, BKM algebras and automorphic forms, FLM's constuction and proof of the McKay-Thompson conjecture. The second part of the meeting will consist of invited talks on current research.

13. Conjectures
conjectures from latin, conjectus, literally, to throw together, from com+jacere to throwmore at; interpretation of events; conclusions by guesswork. conjectures journal of reflections on spirit
http://conjectures.blogspot.com/

Extractions: Conjectures: from latin, conjectus, literally, to throw together, from com+jacere to throw-more at; interpretation of events; conclusions by guesswork. Conjectures: journal of reflections on spirit and society. ''At the bottom of the heart of every human being, from earliest infancy until the tomb, there is something that goes on indomitably expecting, in the teeth of all experience of crimes committed, suffered and witnessed, that good and not evil will be done.'' Simone Weil The Covenant Network commissioned and published the booklet in hopes that, as Gene Bay writes in his Foreword, readers will "meet some of those whose gifts for ministry are not being used by our church. . . , will recognize their faith, feel the pain of their rejection, understand their passion for ministry, and realize the authenticity of their calls." Dr. Bay, pastor of the Bryn Mawr [PA] Presbyterian Church and Co-Moderator of the Covenant Network, continues, "You will, I believe, begin to question our denominations present policies."

14. Thèse G. Chenevier
th¨se, Ga«tan Chenevier, Paris 7, 2003.
http://www.dma.ens.fr/~chenevie/articles/abstract.html

Extractions: J. Bellaïche This work is a contribution to the study of p-adic deformations of automorphic forms. In the first part, we construct p-adic families of finite slope eigenforms for unitary groups G/Q such that G(R) is the compact unitary group and G(Qp)=GLn(Qp). As a consequence, we obtain p-adic refined deformations of the Galois representations studied by Clozel, Kottwitz and Harris-Taylor. In a second part, we show that the Jaquet-Langlands correspondence between usual and quaternionic modular forms extends to a rigid-analytic isomorphism between some eigencurves. In the last part, in collaboration with J.Bellaïche , we apply the results of the first chapter to some non tempered endoscopic forms for U(3) studied by Rogawski, in order to construct extensions between some Galois characters which are predicted by Bloch-Kato conjectures.

15. Conjectures In Geometry
conjectures in Geometry. An educational web site created for high school geometry students Basic concepts, conjectures, and theorems found in typical geometry texts are introduced
http://www.geom.umn.edu/~dwiggins/mainpage.html

Extractions: Jodi Crane, Linda Stevens, and Dave Wiggins This site constitutes our final project for Math 5337-Computational Methods in Elementary Geometry , taken at the University of Minnesota's Geometry Center during Winter of 1996. This course could be entitled "Technology in the Geometry Classroom" as one of its more important objectives is to provide students (presumably math educators) with a wide variety of activities (demonstrations and assignments) utilizing computer software that could be incorporated into a high school geometry classroom. This page has been designed to provide an interactive technological resource for students studying elementary high school geometry. Basic concepts, conjectures, and theorems found in typical geometry texts are introduced, explained, and investigated. Follow-up activities are provided to further demonstrate meanings and applications of concepts. The objective is to ensure that students develop a firm understanding of both the content and applications of each main idea given below in the list of conjectures. Working towards this objective, we have included:

16. FRANCO MORETTI - MORE CONJECTURES
Replying to critics of his conjectures on World Literature (NLR 1), Franco Moretti considers the objections to a worldsystems theory of the relations
http://www.newleftreview.net/NLR25402.shtml

Extractions: Conjectures on World Literature New Left Review , Emily Apter and Jale Parla elsewhere. My thanks to all of them; and as I obviously cannot respond to every point in detail, I will focus here on the three main areas of disagreement among us: the (questionable) paradigmatic status of the novel; the relationship between core and periphery, and its consequences for literary form; and the nature of comparative analysis. I thousand lingua franca entire everywhere is both very implausible and extraordinarily boring. But before indulging in speculations at a more abstract level, we must learn to share the significant facts of literary history across our specialized niches. Without collective work, world literature will always remain a mirage. II Yes, forms can move in several directions. But do that movement from the periphery to the centre is less rare, but still quite unusual, while that from the centre to the periphery is by far the most frequent.

17. Paul B. Van Wamelen
Louisiana State University. Genus 2 curves, class number formulae, Jacobi sums, Stark's conjectures, computational projects.
http://www.math.lsu.edu:80/~wamelen/

Extractions: Graduate: University of California, San Diego My main research interest is Number Theory. My thesis and some subsequent work dealt with genus 2 curves. I've done some work on class number formulas, Jacobi sums, and recently, some computational work on Stark's conjectures. Currently I'm working on various computational projects. The Stark's conjecture paper has not been published yet, but for now a question: Can you see a pattern (any pattern!) in this picture ? If you can let me know and we might be famous... The following are data sets that I have computed. Some of this did not fit in the various articles and are only published here.

18. Conjectures In Geometry
conjectures in Geometry. Twenty conjectures in Geometry Vertical Angle Conjecture Nonadjacent angles formed by two intersecting lines.
http://www.geom.uiuc.edu/~dwiggins/mainpage.html

Extractions: Jodi Crane, Linda Stevens, and Dave Wiggins This site constitutes our final project for Math 5337-Computational Methods in Elementary Geometry , taken at the University of Minnesota's Geometry Center during Winter of 1996. This course could be entitled "Technology in the Geometry Classroom" as one of its more important objectives is to provide students (presumably math educators) with a wide variety of activities (demonstrations and assignments) utilizing computer software that could be incorporated into a high school geometry classroom. This page has been designed to provide an interactive technological resource for students studying elementary high school geometry. Basic concepts, conjectures, and theorems found in typical geometry texts are introduced, explained, and investigated. Follow-up activities are provided to further demonstrate meanings and applications of concepts. The objective is to ensure that students develop a firm understanding of both the content and applications of each main idea given below in the list of conjectures. Working towards this objective, we have included:

19. Villegas, Fernando Rodriguez
University of Texas at Austin. Special values of Lseries (in particular, those related to the conjectures of Birch/Swinnerton-Dyer and Bloch/Beilinson), the arithmetic of elliptic curves and modular forms.
http://www.ma.utexas.edu/users/villegas/

Extractions: E-mail: villegas@math.utexas.edu dvi, ps, pdf. I am interested in special values of L-series (in particular, those related to the conjectures of Birch-Swinnerton-Dyer and Bloch-Beilinson), the arithmetic of elliptic curves and modular forms. I am part of the Number Theory group here at UT Austin. You can find more details in my research page. The upcoming Arizona Winter School will take place in Austin on March 13 - 17, 2004. Last updated Jan 20, 2004

20. Conjectures In Geometry: Parallelogram Conjectures
Parallelogram conjectures. Explanation A parallelogram is a quadrilateral with two pairs of parallel sides. The precise statement of the conjectures are
http://www.geom.uiuc.edu/~dwiggins/conj22.html

Extractions: A parallelogram is a quadrilateral with two pairs of parallel sides. If we extend the sides of the parallelogram in both directions, we now have two parallel lines cut by two parallel transversals. The parallel line conjectures will help us to understand that the opposite angles in a parallelogram are equal in measure. When two parallel lines are cut by a transversal corresponding angles are equal in measure. Also, the vertical angles are equal in measure. Now we need to extend our knowledge to two parallel lines cut by two parallel transversals. We have new pairs of corresponding angles What can be said about the adjacent angles of a parallelogram. Again the parallel line conjectures and linear pairs conjecture can help us. The measures of the adjacent angles of a parallelogram add up to be 180 degrees, or they are supplementary. Conjecture ( Parallelogram Conjecture I Opposite angles in a parallelogram are congruent. Conjecture ( Parallelogram Conjecture II Adjacent angles in a parallelogram are supplementary.

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