81. Open Problems Research thrives on open problems. They On this page we have collecteda range of open problems that have not been stated before. These http://www.jmlg.org/open_problems.htm

Research thrives on open problems. They serve to challenge the researchers. On this page we have collected a range of open problems that have not been stated before. These problems carry a prize of $US100 payable by Journal of Machine Learning Gossip to the first person or group of persons who successfully solve them to the satisfaction of the editorial board. The decision of the board is final. Winners will be recorded in a hall of fame that will be constructed on the JMLG web site. Get a paper accepted at NIPS, COLT or ICML with the word "Marxist" in the title. Up to changes in mathematical notation, construct a paper accepted to NIPS, COLT or ICML which is wholly comprised of sentences taken from previous papers at the same conference. Provide a proof of construction. Get a paper accepted to NIPS, COLT or ICML which only refers to papers written by authors of the accepted paper. Get a paper accepted to NIPS, COLT or ICML which refers to no other papers (or maybe just one other paper ($25)). Get a paper accepted to NIPS with an average review score of less than 3 and explain how you did it. Proof of score needed.

82. Rational And Integral Points On Higher-dimensional Varieties Some of conjectures and open problems, compiled at AIM. http://aimath.org/WWN/qptsurface2/

Rational and integral points on higher dimensional varieties This web page highlights some of the conjectures and open problems concerning Rational and integral points on higher dimensional varieties. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Lecture Notes Colliot-Thelene 1: Rational points on surfaces with a pencil ... Colliot-Thelene 2: Rational points on surfaces with a pencil ... de Jong: Rationally Connected Varieties ... Miscellaneous Photos The individual participant contributions may have problems because converting complicated TeX into a web page is not an exact science. The dvi, ps, or pdf versions are your best bet.

83. Open Problems Virtual Library. Open Positions. open problems. Societies. Software. SMBDigest. Search.MTBIO ACTIVITIES. GALLERY. open problems. Entries total 4, Entries 1 - 4. Topic, http://www.mtbio.de/info.php3?aktID=Problems

84. Open Problems open problems. I offer here several open problems in areas of propositionallogic, bounded arithmetic, complexity theory and in related model theory. http://www.math.cas.cz/~krajicek/problemy.html

Open problems I offer here several open problems in areas of propositional logic, bounded arithmetic, complexity theory and in related model theory. They are by no means meant to represent all interesting open problems in the areas or even to sample them evenly. It is a collection of problems selected from those that were published in works that I (co-)authored, and that seem to me be interesting and possibly stimulating for further research. Their unifying theme (with few exceptions) are links to three interconnected main problems (just short of P/NP): lower bounds for EF, finite axiomatizability of bounded arithmetic, and provability of bounded (weak)PHP in bounded arithmetic. I have also included a couple of folklore problems (on F_d(MOD_p) and on conservativity in bounded arithmetic) to which papers that I (co-)authored contributed. I do not include problems already listed in P. Clote and J.Krajicek: "Open Problems", in: "Arithmetic, Proof Theory and Computational Complexity", eds. P. Clote and J. Krajicek, Oxford Press, (1993), pp.1-19. References point to papers with original formulation; further literature and background can be found in them.

85. Other Open Problems Other open problems. A number of very important questions have not been properlyaddressed or sufficiently discussed during the meeting due to a lack of time. http://caeinfo.in2p3.fr/theorie/trento_rap/node11.html

Next: About this document ... Up: Two weeks Trento Meeting Previous: Relevant observables Other open problems A number of very important questions have not been properly addressed or sufficiently discussed during the meeting due to a lack of time. In particular the experimental feasibility of equilibria and tools to control them have to be discussed. Transport properties of systems in connection with a phase transition have to be assessed. The origins of criticality in finite (open) systems have to be further explored. The quantum aspect of the question should be discussed. The clear success of the meeting has been due to the high quality presentations and enthousiastic and lively discussions of all the participants, but it also has been favoured by the excellent working and discussing conditions at the ECT . In particular the practical organization by Ines del Campo has been invaluable and the constant and kind disponibility of the whole ECT staff has allowed us, among other things, to profit for the whole period of the presence of a collegue with a reduced mobility. All the participants have also appreciated the abundance of working and discussing place, the informatic ressources and the pleasant environnement. M.D'Agostino (Bologna), Ph.Chomaz (GANIL), D.Gross (Berlin), F.Gulminelli (Caen), H.Haberland (Freiburg), co-organizers.

86. Loop Quantum Gravity A general overview of ideas, results and open problems of loop quantum gravity. http://www.livingreviews.org/Articles/Volume1/1998-1rovelli/

87. Some Problems In Matroid Theory Some Problems in Matroid Theory. Compiled by Thomas Zaslavsky. Sources.Oxley s book has an entire chapter of open problems. (Some http://www.math.binghamton.edu/zaslav/Matroids/matroidprobs.html

Some Problems in Matroid Theory Compiled by Thomas Zaslavsky Sources Oxley's book has an entire chapter of open problems. (Some may have been solved by now.) Joseph P.S. Kung has written two articles called ``surveys'' that are replete with new results and open problems: ``Extremal matroid theory'', in: Neil Robertson and Paul Seymour, eds., Graph Structure Theory , pp. 21-61. Contemporary Mathematics, Vol. 147. American Mathematical Society, Providence, R.I., 1993. ``Critical problems'', in: Joseph E. Bonin, James G. Oxley, and Brigitte Servatius, eds., Matroid Theory , pp. 1-127. Contemporary Mathematics, Vol. 197. American Mathematical Society, Providence, R.I., 1996. Some Problems I've Found Interesting Bonin's Projective Bound Suppose a simple matroid G of rank r that does not split has no more than q r-1 points in each cocircuit. Conjecture r - 1)/(q - 1), which is the number of points in an r-1-dimensional projective geometry of order q if such exists. Furthermore, the upper bound is attained only by projective geometries. "Splitting" means that G is the union of two disjoint proper flats. This problem was proposed by Joe Bonin.

88. On A Generalization Of Perfect Numbers J. L. Pe introduces perfect numbers relative to an arithmetical function f. Under this scheme, the usual perfect numbers are just one among many species of fperfect numbers . Several open problems and examples of perfect number sets are given, as well as a few f-amicable pairs. http://www.geocities.com/windmill96/fperfect/fperfect.html

On a Generalization of Perfect Numbers A Problem Proposal ABSTRACT This paper presents a notion of perfect numbers relative to arithmetical functions: an arithmetical function f produces a set of f-perfect numbers. Two among the many examples considered are small “perturbations” of the normal definition; late in these two sequences, odd perfect numbers appear! (Could the situation be similar for the usual perfect numbers?) Also, this paper generalizes amicable pairs and sociable chains. Mysteries and open problems abound for those who like a challenge. There is also Mathematica code to start the reader on his own explorations. Download the paper (File: fperfect.pdf, about 178 Kb). Appeared in The Journal of Recreational Mathematics A ... web page version is also available, but is not very well formatted (since it was automatically generated by MS Word). Here is a paper on an especially intriguing sequence of generalized perfect numbers: Picture-Perfect Numbers and Other Digit-Reversal Diversions Number of Visits: J. L. Pe

89. ILC - LAperLA - Open Problems open problems About Type Recognition The problem of automatic recognition of thetext found when we are dealing with ancient documents is a part of the wide http://www.ilc.cnr.it/viewpage.php/sez=ricerca/id=76/vers=ing

90. The Valuation Theory Home Page - Open Problems open problems. Open Problem 1 Generalize Abhyankar s Going Up and ComingDown for local uniformization to arbitrary finite transcendence degree. http://math.usask.ca/fvk/Probl.html

The Valuation Theory Home Page Open Problems Open Problem 1: Generalize Abhyankar's "Going Up" and "Coming Down" for local uniformization to arbitrary finite transcendence degree. Possible applications: To local uniformization and resolution of singularities, in particular, in positive characteristic. Posted by F.-V. Kuhlmann on February 4, 1999 A valued field (K,v) is called spherically complete if every nest of balls has a non-empty intersection. This holds if and only if every Pseudo-Cauchy sequence in K has a pseudo limit in K. By the work of Kaplansky, this in turn holds if and only if the field is maximally valued, i.e., has no proper immediate extensions. Take a polynomial f with coefficients in K. The following is known: 1) If f is a polynomial in one variable, then the image f(K) is spherically complete, just as a set with the ultrametric induced by the valuation v. If f is an additive polynomial in several variables, then under a certain additional condition, f(K) is again spherically complete. Open Problem 2: Prove or disprove that f(K) is spherically complete for all additive polynomials in several variables.

91. Open Problems open problems Here is the list of problems generated during the panel discussionheld after the Saturday night banquet of the Midwest Geometry Conference. http://www.math.wustl.edu/MGC2003/prob.htm

Midwest Geometry Conference 2003 General Information Organization Open Problems Invited Speakers Local Information Participants Open Problems Here is the list of problems generated during the panel discussion held after the Saturday night banquet of the Midwest Geometry Conference. The panel comprised the invited speakers of the conference. Many conference participants contributed to the discussion. Problems (PS) Washington University in St. Louis Math Department Campux Box 1146 St. Louis, MO 63130

92. Science Search > Open Problems s of...... Home. Current location Math Research open problems, 1. UnsolvedMathematics Problems Compiled by Steven Finch. http://www.science-search.org/index/Math/Research/Open_Problems/

Search for: Current Category Everything What's new Top Searches Statistics Science News ... Home Current location: Math Research > Open Problems Unsolved Mathematics Problems Compiled by Steven Finch. Descriptions of some unsolved problems and numerous links to other collections. http://www.mathsoft.com/asolve/ detailed information Rating: [7.00] Votes: [1963] Millennium Prize Problems Millennium Prize Problems http://www.claymath.org/prize_problems/ detailed information Rating: [6.00] Votes: [2043] Mathematical Problems In various subjects, compiled by Torsten Sillke. http://www.mathematik.uni-bielefeld.de/~sillke/problems.html detailed information Rating: [5.00] Votes: [1629] Most Wanted List Elementary unsolved problems in mathematics, listed at the MathPages archive. http://mathpages.com/home/mwlist.htm detailed information Rating: [5.00] Votes: [879] Some Unsolved Problems with Elementary Formulation Satements of some famous problems compiled by Frank Wikstrom, Umeå University. http://abel.math.umu.se/~frankw/unsolved.html

93. Open Problems Cambridge CQC open problems open problems. Navigation, http://qubit.damtp.cam.ac.uk/open_problems/index.php

Cambridge CQC Open Problems > Open Problems Navigation Home Home Page Site Map Educational FAQ Part III Lectures Tutorials Video Lectures The CQC People Our Research How to Find Us Sponsors ... CMI Further Information Forthcoming Events Jobs QC Groups QC History Links Quant-ph arXiv PRL Other Links Search WWW CQC Website Currently Visiting Kwek Leong Chuan 21 May 04 - 11 Jul 04 Pawel Horodecki 02 Jun 04 - 08 Jun 04 Forthcoming Talks 09 Jun 04 CQC Seminar 10 Jun 04 - Blackboard Seminar, Graeme Mitchison 17 Jun 04 - Blackboard Seminar, Suguru Furuta About this Site This website is for the Centre for Quantum Computation, based in Cambridge, UK. It is kept up to date with relevant local information, as well as some information of interest to the general quantum information community. On this page we collect problems in Quantum Information Theory we or our contributors find worthy of attention. Click on the title to find the statement of the problem and some information on known partial results. This information will be updated whenever significant progress is brought to our attention. To make this page interesting we obviously need input from the community, so please

94. Digraphs, Theory, Algorithms, Applications A comprehensive source of results, notions and open problems on directed graphs, with 12 chapters, 754 pages, 186 figures and 705 exercises. The book is aimed at undergraduate and graduate students, mathematicians, computer scientists and operational researchers. Site has preface, contents, chapter 1 and other extracts (PS) with errata, updates and ordering information. http://www.imada.sdu.dk/Research/Digraphs/

IMADA Research activities Digraphs: Theory, Algorithms and Applications Springer-Verlag, London Springer Monographs in Mathematics ISBN 1-85233-268-9 October 2000 754 pages; 186 figures; 705 exercises Second printing has been released from Springer in April 2001. Softcover version is available as of May 2002 at 29.50 British Pounds. The ISBN number is 1852336110. Welcome to the web page for the book Digraphs: Theory, Algorithms and Applications, by and Gregory Gutin. This page contains some useful information about the book. The page will be updated frequently. Should you have questions, please contact one of the authors by email jbj@imada.sdu.dk gutin@cs.rhul.ac.uk You may also consult Springer's catalogue page for the book at Springer's book catalogue Selected parts of the book (postscript). Preface List of Contents Subject index Chapter 1 ... Pages 658-659 Mathematics Subjects Classifications: 05C20, 05C38, 05C40, 05C45, 05C70, 05C85, 05C90, 05C99, 68R10, 68Q25, 68W05, 68W40 90B06, 90B70, 90C35, 94C15 How to order Springer's book catalogue Amazon.co.uk

95. Open Problems In Strongly Correlated Electron Systems|KLUWER Academic Publishers Books » open problems in Strongly Correlated Electron Systems. OpenProblems in Strongly Correlated Electron Systems. Add to cart. http://www.wkap.nl/prod/b/0-7923-6896-7

Title Authors Affiliation ISBN ISSN advanced search search tips Books Open Problems in Strongly Correlated Electron Systems Open Problems in Strongly Correlated Electron Systems Add to cart edited by Sarben Sarkar Faculty of Physics, King's College London, UK Book Series: NATO SCIENCE SERIES: II: Mathematics, Physics and Chemistry Volume 15 It has become increasingly evident that strong correlations between electrons are an essential, unifying factor in a range of phenomena encountered in solid state physics, such as high temperature superconductivity, colossal magnetoresistance, the quantum Hall effect, heavy fermion metals and Coulomb blockade in single-electron transistors. A new emergent paradigm - non-Fermi liquid behaviour - is in a number of systems coming to replace the Fermi liquid paradigm. Despite major achievements, the study of strongly correlated systems is still in its infancy. Anomalous electron properties have been studied in some generic models of correlated electrons, such as the Hubbard and t-J models, Anderson and Kondo impurity models, and their lattice equivalents. Powerful numerical methods for studying many-body models, including the approximate techniques of many-body theory and exact results in low and high dimensional systems, are providing new insights, all of which are providing convincing evidence for the breakdown of the Fermi liquid concept. This book focuses on several major, open questions in the theory of anomalous metals with correlated electrons, complementing theoretical advances with the latest experimental results on related materials, all presented by leaders in the field. The main emphasis is on the physics of cuprates and high temperature superconductors, charge- and spin-ordering and fluctuations, manganites and colossal magnetoresistance, low-dimensional systems and transport, Mott-Hubbard transition and infinite dimensional systems, and the quantum Hall effect.

96. The Riemann Hypothesis Some of the conjectures and open problems concerning RH, compiled by the AIM. http://aimath.org/WWN/rh/

The Riemann Hypothesis This web page highlights some of the conjectures and open problems concerning The Riemann Hypothesis. Click on the subject to see a short article on that topic. If you would like to print a hard copy of the entire web page, you can download a dvi postscript or pdf version. What is an $L$-function? Terminology and basic properties Functional equation Euler product ... Anecdotes about the Riemann Hypothesis

97. NSenet - Navier-Stokes Equations On Net open problems. Open problem proposed by GP Galdi (Pittsburgh University,USA, April 2000) postscript version. This open problem concerns http://wwwlma.univ-bpclermont.fr/NSenet/openproblems/

Open problems Presentation Introduction Press review Information Correspondents ... Mailing list and FAQ People Links Bibliography Books Accepted Papers Preprints Actualities Conferences Announcements Journals Documentation Lecture Notes Open Problems Comments on books Simulation Packages PhD PhD thesis summaries PhD/Postdoctoral Positions Open Positions All persons are kindly invited to send an e-mail to NSemaster@math.univ-bpclermont.fr in order to send open problems on Navier Stokes equations and related topics. Open problem proposed by G.P. Galdi (Pittsburgh University, USA, April 2000) postscript version This open problem concerns existence of Leray's (symmetric) solutions for the twodimensional steady, exterior domain for arbitrary Reynolds number. Open problem proposed by the Clay Mathematical Institute Clay Mathematical Institute offers $1,000,000 prize for a solution to any one of seven mathematical problems. One of them concerns 3D Navier-Stokes existence and smoothness, see Navier-Stokes for the description by Charles Fefferman. nsemaster@math.univ-bpclermont.fr

98. Interval Computations: Open Problems open problems. http://www.cs.utep.edu/interval-comp/openprob.html

Open Problems "Grand challenge" interval problems (by A. Neumaier) Guaranteeing Bounds on Uncertainty in Metrology Back to the main menu of the Interval Computations website

99. Open Problems In Knot Theory A List of Approachable open problems in Knot Theory. (.ps and .pdffiles also available) Suggested by Colin Adams during the Knot http://www.williams.edu/Mathematics/cadams/knotproblems.html

A List of Approachable Open Problems in Knot Theory .ps and .pdf files also available) Suggested by Colin Adams during the Knot Theory Workshop at Wake Forest University during June 24-28, 2002. Problems. What knots with high symmetries have projections that demonstrate this symmetry? (eg. the Figure-8 knot) Find specific families of knots satisfying the property c(K_1#K_2) = c(K_1)+c(K_2), where c=c(K) is the crossing number and # means knot composition. (eg. This is known for alternating knots.) What about torus knots? [In a 2003 preprint, Yuanan Diao demonstrated that this does hold for compositions of torus knots, as well. This was also independently proved by Herman Gruber. His paper is available at arxiv.org under math.GT/0303273.] When is a knot equivalent to its inverse? (The inverse has the same projection but with an opposite orientation). (eg. the trefoil and its inverse) Hass and Lagrias proved that if you have an n-crossing projection of the trivial knot, you can turn it into a trivial projection by using no more than 2^(1,000,000,000n) Reidemeister moves. Find a better upper bound. Find a pair of non-tricolorable knots whose composition istricolorable or show that this is not possible. (To show it's false, it's enough to show that an open knot is tricolorable if and only if its closure is tricolorable.)

100. The Geomblog: Open Problems (continued...) Friday, March 12, 2004. open problems (continued ). Karen asks I wonder whetherthe ability to pick out interesting problems is innate or can be taught. http://geomblog.blogspot.com/2004/03/open-problems-continued.html

The Geomblog Ruminations on computational geometry, algorithms, theoretical computer science and life Friday, March 12, 2004 Open problems (continued...) Karen asks: I wonder whether the ability to pick out interesting problems is innate or can be taught. What do you think? I really am not sure. A professor I used to know said that taste in problems is something that can't be taught. I am not sure I agree with that completely though. I think that in grad school it is possible to train people to ask why a question should be considered interest. In fact one might argue that asking the right questions is the core of good research. Every field has the foundational issues that drive them. In theoretical computer science, and computational geometry, one of the key issues is often: What is the key process underlying the structure of a problem, and how can this be used to solve it ? A paper that can answer this question will more often than not be deemed interesting. So it is important to understand what the raison d'etre of your chosen field is. This is usually never stated explicitly, but there is usually a tacit broad consensus on what it is, and this is where an advisor, and good training, can help a lot.

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