101. 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

102. Open Problems open problems. open problems. The complexity of the correspondence problemdepends on the complexity of the scene. As described in the previous sections http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT11/node7.html

Next: Reconstruction of 3-D coordinates Up: Computer Vision IT412 Previous: Some existing matching algorithms Open problems The complexity of the correspondence problem depends on the complexity of the scene. As described in the previous sections, there are constraints and schemes that can help reduce the number of false matches, but many unsolved problems still exist in stereo matching. Some of these problems are: occlusion: given a feature m in the first image projected by a scene point M , the ``corresponding'' feature of m may not exist in the second image because from the second camera's viewpoint, M may be occluded. discontinuity: this is related to occlusion. Most matching algorithms use the continuity and/or relaxation as a global constraint to reduce false matches. This constraint works everywhere in the images except at depth discontinuities. regularity and repetitivity: repetitive patterns in the scene cause ambiguity in matching. Most existing matching algorithms are still not robust enough to handle this. Robyn Owens

103. 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. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. What is an $L$-function? Terminology and basic properties Functional equation Euler product ... Examples Dirichlet series associated with Maass forms Higher rank L-functions The Selberg class Dirichlet series Analytic Continuation Functional Equation ... Selberg Conjectures Analogues of zeta-functions Dynamical zeta-functions Spectral zeta functions Riemann Hypotheses Riemann Hypotheses for global L-functions The Riemann Hypothesis The Generalized Riemann Hypothesis The Extended Riemann Hypothesis ... The vertical distribution of zeros The Lindelof hypothesis and breaking convexity Perspectives on RH Analytic number theory Physics Probability Fractal geometry Equivalences to RH Primes The error term in the PNT More accurate estimates ... The Farey series Mikolas functions Amoroso's criterion Weil's positivity criterion Li's criterion Bombieri's refinement Complex function theory Speiser's criterion Logarithmic integrals An inequality for the logarithmic derivative of xi Function spaces ... Salem's criterion Other analytic estimates M. Riesz series

104. Open Problems In Topology open problems in Topology by Elliott Pearl (Feb 24, 2004) A new survey ofthe book open problems in Topology appeared in http://at.yorku.ca/cgi-bin/bbqa?forum=open_questions;task=show_msg;msg=0022

105. A Note On Open Problems In Infinite-dimensional Topology By Elliott Pearl open problems in topology, seventh status report, Topology Appl. 114 (2001), no . open problems in topology, 2004, To appear in Topology Appl. http://at.yorku.ca/i/a/a/z/03.htm

Topology Atlas Document # iaaz-03 A note on Open problems in infinite-dimensional topology Elliott Pearl pp. 139-140 in Problems from Topology Proceedings , Topology Atlas, 2003. AtlasImage for on-screen viewing PDF with hyperlinks (128.4 Kb) LaTeX source (9.6 Kb) DVI (6.3 Kb) PostScript (77.5 Kb) PDF (112.1 Kb) There is a well-known list of problems in infinite-dimensional topology with a long history. It appeared as an appendix to T.A. Chapman's 1975 volume, Lectures on Hilbert Cube Manifolds ], in the CBMS series of the American Mathematical Society. Ross Geoghegan edited a version of the problem list [ ] in Topology Proceedings as the result of a satellite meeting of infinite-dimensional topologists held at the 1979 Spring Topology Conference in Athens, OH. The problem list was updated and revised by James West [ ] in 1990 for the book Open problems in topology . The book [ ] is no longer available in print but the publisher has made it freely available online. For updates to this problem list, please find the series of status reports that have appeared in the journal Topology and its Applications ]. This long problem list will not be reproduced here.

106. Open Problems In Group Theory We have collected here over 150 open problems in combinatorial group theory, andwe invite the mathematical community to submit more problems as well as http://zebra.sci.ccny.cuny.edu/web/nygtc/problems/oproblems.html

Open Problems in combinatorial and geometric group theory We have collected here over 150 open problems in combinatorial group theory, and we invite the mathematical community to submit more problems as well as comments, suggestions, and/or criticism. Please send us e-mail at daly@rio.sci.ccny.cuny.edu This collection of problems has been selected by G.Baumslag, A.Miasnikov and V.Shpilrain with the help of several members and friends of the New York Group Theory Cooperative. In particular, we are grateful to G.Bergman G.Conner W.Dicks R.Gilman ... I.Kapovich , V. Remeslennikov, V.Roman'kov E.Ventura and D.Wise for useful comments and discussions. Our policy Hall of Fame We have arranged the problems under the following headings: Outstanding Problems Free groups One-relator groups Finitely presented groups ... Algorithmic problems Periodic groups (under construction) Groups of matrices Hyperbolic and automatic groups Nilpotent groups Metabelian groups ... Group actions

107. Some Favourite Open Problems Some favourite open problems Disclaimer This page, under construction, will bean eclectic collection of problems, which share the feature that I tried http://www-ee.technion.ac.il/~zeitouni/openprob.html

Some favourite open problems: Problem number and authors PS Problem 1: S. Mallat and O. Zeitouni, "Optimality of the Karhunen-Loeve basis in nonlinear reconstruction" Problem 2: Conjecture: the (centered) Gaussian measure of the intersection of two convex, symmetric subsets of Euclidean space is greater or equal than the product of the measures of the two subsets. See for a review of the history of this problem and some partial results: Schechtman, G., Schlumprecht, Th., Zinn, J., On the Gaussian measure of the intersection. Ann. Probab. 26 (1998), 346357. MATH REVIEWS LINK. G. Harge A particular case of correlation inequality for the Gaussian measure. Ann. Probab. 27 (1999), 19391951. MATH REVIEWS LINK Problem(s) 3: RWRE questions, conjectures: 0-1 laws and other problems. See for details the review "Random walks in random environments", Proceedings ICM 2002, vol III, pp. 117127. For recent progress on related large deviations questions, see Varadhan's article MATH REVIEWS LINK.

108. 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 The page has been moved click Here

109. P Systems Web Page We collect here various open problems and research topics about P systems. This list of open problems is from the paper by Gheorghe Paun Further http://psystems.disco.unimib.it/problems.html

Some Open Problems We collect here various open problems and research topics about P systems. We indicate the author of the suggested problem and some related papers. When a problem is solved, we indicate the author and the paper where the solution appears. If you want to suggest a problem, send a mail to the webmaster. Open Problems List #3: January 2005 This list of open problems is from the paper by Gheorghe Paun "Further Twentysix Open Problems in Membrane Computing", written for the Third Brainstorming Meeting on Membrane Computing, Sevilla (Spain), feb. 2005. Click here to view this paper. Open Problems List #2: October 2002 This list of open problems is from the book by Gheorghe Paun "Membrane Computing. An Introduction". Click here to view this list. Open Problems List #1: October 2000 This list of open problems is from the article by Gheorghe Paun "Computing with Membranes (P Systems): Twenty Six Research Topics". Click here to view this list. If you have any comment, question or feedback, please contact the webmaster.

110. Open Problems INFORMATION / open problems INFORMATION Add Informations Conf./Workshops Journals Virtual Library Open Positions. open problems. Societies http://www.mtbio.de/info.php3?aktID=Problems

111. Phorum - STORK - Re: Open Problems In Cryptography To whom should comments on problems worth adding be directed? I think it wouldbe worth mentioning that a good, fast, Re open problems in Cryptography http://www.stork.eu.org/forum/read.php?f=1&i=12&t=7

112. Open Problems In The Spectral Analysis Of Evolutionary Dynamics Title, open problems in the Spectral Analysis of Evolutionary Dynamics. Author(s),Lee Altenberg. Files, pdf. Paper , 0506-025 http://www.santafe.edu/research/publications/wpabstract/200506025

Advanced Search Events Calendar Talks ... Contact Us Quick Links... Bulletin People Summer Schools Working Papers Visiting SFI Home Research Publications Working Papers > Abstract SFI Working Paper Abstract Title: Open Problems in the Spectral Analysis of Evolutionary Dynamics Author(s): Lee Altenberg Files: pdf Paper #: Abstract:

113. OUP: Variational Methods: Open Problems, Recent Progress, And Numerical Algorith Variational Methods open problems, Recent Progress, and Numerical Algorithms.John Neuberger. Price £52.25 (Paperback) 08218-3339-1 http://www.oup.co.uk/isbn/0-8218-3339-1

NEVER MISS AN OXFORD SALE (SIGN UP HERE) VIEW BASKET Quick Links About OUP Career Opportunities Contacts Need help? News oup.com Search the Catalogue Site Index American National Biography Booksellers' Information Service Children's Fiction and Poetry Children's Reference Dictionaries Dictionary of National Biography Digital Reference English Language Teaching Higher Education Textbooks Humanities International Education Unit Journals Law Medicine Music Online Products Oxford English Dictionary Reference Rights and Permissions Science School Books Social Sciences Very Short Introductions World's Classics Advanced Search UK and Europe Book Catalogue Help with online ordering How to order Postage Returns policy ... Table of contents Join the OED-BBC Wordhunt Visit www.oed.com for more details Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms John Neuberger Publication date: 7 October 2004 American Mathematical Society 285 pages, Series: Contemporary Mathematics Search for titles in the same series Ordering Individual customers order by phone, post, or fax

114. Open Problems open problems Lecture notes Links . Japanese. open problems. http://ega.math.hc.keio.ac.jp/vlabo/open/

Home Preprint Seminar schedule Open problems Lecture notes Links Japanese Open Problems

115. Hyperovals Open Problems We will provide a short list of the major open problems in the theory of hyperovalsin Open since 1955, it is considered to be a very difficult problem. http://www-math.cudenver.edu/~wcherowi/research/hyperoval/hyopen.htm

OPEN PROBLEMS We will provide a short list of the major open problems in the theory of hyperovals in Desarguesian planes. Classify the hyperovals in PG(2, 2 h This remains the chief problem in the area. Open since 1955, it is considered to be a very difficult problem. We believe that this might possibly be accomplished within the next ten years. The other problems listed here may be considered to be subproblems of this one. Classify the monomial hyperovals. This should be a much simpler problem given that these hyperovals have large automorphism groups, however this does not seem to have lead to an easy classification. Classify the hyperovals that are associated with flocks of cones (members of a herd). The monomial hyperovals associated with flocks of quadratic cones have been classified by Penttila and Storme. Penttila believes that all hyperovals associated with quadratic cones are now known. All known hyperovals, with the single exception of Penttila-O'Keefe, are associated with flocks of cones over translation ovals ( -cones).

116. Flocks Of Cones: Open Problems We will attempt to maintain a list of open problems in this area. The index below,indicates topic area and is linked to a fuller description of the problem http://www-math.cudenver.edu/~wcherowi/research/flopen.htm

Open Problems We will attempt to maintain a list of open problems in this area. The index below, indicates topic area and is linked to a fuller description of the problem. Whatever information is available is listed, including references and partial results (both positive and negative). Also included, is a list of researchers who have shown some interest in the problem. The information on these pages will only be up-to-date provided that individuals working in this area help to make it so. Suggestions, amendments and corrections should be sent to Bill Cherowitzo Index of Problems Adelaide Flocks (cyclic q-clan flocks) [Solved] Monomial Flocks of Type II (even characteristic) Oval (Conic) Blocking Sets

117. Final Remarks And Open Problems Final Remarks and open problems. Venkatesan and Rajagopalan VR92 showed thatthe distributional matrix representability problem is complete for DistNP by http://www.uncg.edu/mat/avg/avgnp/node34.html

Next: References Up: Average-Case Intractable NP Problems Previous: Distributional Matrix Transformation Final Remarks and Open Problems Venkatesan and Rajagopalan showed that the distributional matrix representability problem is complete for DistNP by reducing the distributional Post correspondence problem to it under a randomized reduction. They also attempted to show that the bounded version of Diophantine problem is average-case NP-complete. Their approach, however, depends on a number theoretic conjecture that remains unproven. The unbounded version of the Diophantine problem is essentially Hilbert's tenth problem, which was shown to be undecidable by Matijasevic based on the work of Davis, Putnam, and Robinson . (A simplified proof of this result can be found from ). The bounded version of the Diophantine problem has been studied by Adleman and Manders DISTRIBUTIONAL DIOPHANTINE PROBLEMS Instance . A positive integers , and an integer polynomial of degree with variables, where is a free term. Question . Do there exist non-negative integers such that for , and Distribution . First randomly choose polynomial and then randomly and independently choose with respect to the default random distributions. The polynomial

118. ALifeVIII: Open Problems In Artificial Life ALifeVIII open problems in Artificial Life alife ALife. http://www.alife.org/alife8/open-prob.html

Up: Alife VIII ALifeVIII: Open Problems in Artificial Life ALife VIII Proceedings ALife VIII Workshops Proceedings Call for Papers Topics ... Artificial Life Links affiliated conference Restricted area Organizer's Corner Collar Admin As published in Bedau et al. , Open problems in artificial life, Artificial Life How does life arise from the nonliving? Generate a molecular proto-organism in vitro Achieve the transition to life in an artificial chemistry in silico Determine whether fundamentally novel living organisms can exist Simulate a unicellular organism over its entire lifecycle Explain how rules and symbols are generated from physical dynamics in living systems What are the potentials and limits of living systems? Determine what is inevitable in the open-ended evolution of life Determine minimal conditions for evolutionary transitions from specific to generic response systems Create a formal framework for synthesizing dynamical hierarchies at all scales Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems Develop a theory of information processing, information flow and information generation for evolving systems

119. Workshop '3in1' Graphs Focus on solving some open problems in graph theory. Krynica, Poland; 1113 November 2004. http://galaxy.uci.agh.edu.pl/~3in1/

Faculty of Applied Mathematics AGH University of Science and Technology in Cracow 14th Workshop '3in1' Graphs 2005 Dobczyce, Poland November 10-12, 2005 When Where Who Why ... What about Dear Colleague, Faculty of Applied Mathematics AGH in Cracow cordially invites you to attend The 14th Workshop '3in1' Graphs 2005 to be held in Dobczce (Poland, ca 20 km from Cracow), November 10-12, 2005 (from Thursday noon till Saturday noon). The workshop will focus on solving some open problems in graph theory Approximate cost (bed and board + banquet + fee) ca 110 EUR. Additional accommodation (before or after the meeting) can be requested at the price 20 EUR (with breakfast). Single and double rooms only, with bathrooms, Proceedings of the Workshop will be published as a special volume of "Discussiones Mathematicae - Graph Theory" Weather conditions are unpredictable, from sun or rain to snow and frost, but the weather forecast for Dobczyce is available at this Web sites: Dreakmore Gazeta.pl e-mail: 3in1@uci.agh.edu.pl www: http://galaxy.uci.agh.edu.pl/~3in1

120. Chris Burdzy's Favorite Open Problems My favorite open problems. Krzysztof Burdzy. I offer a collection of open problems,mostly about Brownian motion. I tried to solve every problem on the list http://www.math.washington.edu/~burdzy/open.shtml

var sc_project=257326; var sc_invisible=1; My favorite open problems Krzysztof Burdzy I offer a collection of open problems, mostly about Brownian motion. I tried to solve every problem on the list but I failed to do so. Although I do not recall seeing these problems published anywhere, I do not insist on being their author-other probabilists might have proposed them independently. The rigorous statement of the problems is available in PDF 1. Probabilistic version of McMillan's Theorem in higher dimensions This problem is concerned with the direction of approach of the boundary for Brownian paths in mutidimensional domains. 2. Topology of planar Brownian trace Does the planar Brownian trace contain a (non-trivial) connected subset which does not interesect the boundary of any connected component of the complement of the trace? 3. Percolation dimension of planar Brownian trace What is the "shortest" (in the sense of the Hausdorff dimension) path within two-dimensional Brownian range? 4. Efficient couplings in acute triangles

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