81. The Valuation Theory Home Page A forum for all mathematicians who work in or use valuation theory. Directory of people, meetings, preprints, bibliography, open problems and news. http://math.usask.ca/fvk/Valth.html

Welcome, dear reader, to The Valuation Theory Home Page This home page is intended to be a forum for all mathematicians who work in valuation theory or apply valuation theoretical results in their own field of research. The home page offers: postscript- or dvi-files of recent papers, books and theses in valuation theory information about conferences and special events, names and email addresses of mathematicians working in or with valuation theory, and, if possible, links to their home pages a comprehensive bibliography as Bibtex-, dvi- and postscript file, which presently contains 770 entries, a page for open problems and, hopefully, their solutions, interesting NEWS in connection with valuation theory, some useful links a page for historical information and related questions, a page for errors, pitfalls and the nicest proofs in valuation theory (to come). If you have suggestions, questions, ideas, news, or if you want your name and address on the above mentioned list, or if you have a recent paper in or applying valuation theory, then write to valth@math.usask.ca

82. Open Problems Previous Error analysis. open problems. There are a variety of naturalquestions left unanswered by the work described. Below, we http://www.usenix.org/publications/library/proceedings/ec98/full_papers/harkavy/

Next: References Up: Electronic Auctions with Private Previous: Error analysis Open Problems There are a variety of natural questions left unanswered by the work described. Below, we list a few natural directions for further work in this area. Work is under way on variations on the protocol which will address tie-breaking issues, reduce communication costs, and Tie-breaking The protocol described does not provide efficient tie-breaking without some loss of privacy. Communication Costs While we believe the communication costs are sufficiently small to make this protocol practical in many situations, low-value auctions are likely to play an increasingly important role in electronic commerce. Efficiency improvements that enable auctions with private bids in these low-value situations could be very useful. Hierarchical Auctions In some situations, it might be advantageous to hold sub-auctions which partially determine the outcome of the auction. For example, each country might hold a sub-auction, with the leading candidates from each country participating in a final auction. In order to preserve privacy, the winners of the sub-auctions and their bids must not be revealed. Double Auctions and Auction Markets A double auction is a more general form of auction where there are multiple sellers and multiple buyers. All parties tender bids and a market clearing price is determined from those bids. A market clearing price is the equilibrium price at which the supply and demand (in units of the good) are equal. An auction market is a generalization of a double auction to continuous time. New bids are added and removed over time, causing the market clearing price to fluctuate. The stock market is a well known example of an auction market. Double auctions and auction markets are powerful market mechanisms, and privacy protecting protocols for these mechanism would be desirable. However, to be useful, such protocols must be highly efficient, particularly in the case of auction markets.

83. The Steiner Tree Page Overview, researchers, open problems and bibliography. http://ganley.org/steiner/

ganley.org The Steiner Tree Page Maintained by Joe Ganley NOTE : As regular readers have doubtless noticed, I'm not doing much to keep this updated any more, nor am I particularly good about responding to emails. So, I've created a Steiner tree mailing list, through which the Steiner tree community can easily communicate with one another. To subscribe: Subscribe to steinertree Powered by groups.yahoo.com Welcome to the Steiner Tree Page. I'll be adding to this later; for example, I plan to add a table giving the complexity of the problem for restricted classes of inputs, and to expand the introduction a bit to describe other variants on the problem. Another thing I plan to add eventually is code for various Steiner tree problems, starting with my own implementation of Dreyfus-Wagner and my exact rectilinear Steiner tree algorithms. Please email me if you have ideas for other information that would be useful here. Introduction : problem definition, variants, etc. What's New? : recent changes and late-breaking results. Bibliography : in HTML (with links to online papers) or in BibTeX People : information on Steiner tree researchers.

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. Geombinatorics: Making Math Fun Again A journal of open problems in combinatorical and discrete geometry and related areas. Includes tables of contents. http://www.uccs.edu/~asoifer/geombinatorics.html

GEOMBINATORICS ISSN 1065-7371 A journal of OPEN PROBLEMS of combinatorial and discrete geometry and related areas. "This quarterly journal, started by Alexander Soifer at the University of Colorado at Colorado Springs , specializes in geometry and combinatorics , but what really distinguishes it from the field is attitude!" Paul Kainen EDITORS CONTENTS 1991 - PRESENT AUTHORS INDEX 1991 - PRESENT ERDÖS ISSUE ... ORDER FORM "Dear Alex, Finally got around to reading the October Geombinatorics , which contains more than the usual supply of gems the bits by Vizing and Alon were worth more than a year's subscription, if it's not too crass to put a money value on great mathematics, and why should it be, art is sold for money all the time ..." Peter D. Johnson, Dec. 18, 1995 Subscriptions are only $24/year for individuals, with a slight extra charge for shipping. Articles are written in an informal style so they are more accessible to undergraduate and gifted high school students, than is common in other mathematical journals. The list of editors is distingished , and Geombinatorics is now reviewed both by MATHEMATICAL REVIEWS and ZENTRALBLATT FÜR MATHEMATIK . The Table of Contents for Vol. VIII, Issue 1 (July 1998) will give an idea of specialization.

86. Open Problems - SpiritWiki Home open problems. SpiritWiki RecentChanges Preferences Openproblems. List stuff operator syntax (ie +a % ',' or http://spirit.sourceforge.net/wiki/index.php?page=Open problems

87. The Formal Approach To Meaning Short survey of semantics of natural language by Barbara Abbott, at University of Michigan. Focusses upon Montague semantics, and tries to give a feel for the main open problems in the field. http://www.msu.edu/user/abbottb/formal.htm

The formal approach to meaning: Formal semantics and its recent developments [This paper is in Journal of Foreign Languages (Shanghai), 119:1 (January 1999), 2-20.] Barbara Abbott Michigan State University June 1998 abbottb@pilot.msu.edu Like Spanish moss on a live oak tree, the scientific study of meaning in language has expanded in the last 100 years, and continues to expand steadily. In this essay I want to chart some central themes in that expansion, including their histories and their important figures. Our attention will be directed toward what is called 'formal semantics', which is the adaptation to natural language of analytical techniques from logic.[ The first, background, section of the paper will survey the changing attitudes of linguists toward semantics into the last third of the century. The second and third sections will examine current formal approaches to meaning. In the final section I will summarize some of the common assumptions of the approaches examined in the middle sections of the paper, sketch a few alternatives, and make some daring predictions. 'Meaning' is a broad term that can encompass any aspect of the potential for cognitive or emotive impact of speech on interlocutors. However in linguistic semantics these days the cognitive aspects are the center of focus. On the other hand the traditional distinction between semantics, as the study of the relation between linguistic expressions and what they are used to talk about (people and things, events and situations, etc.) and pragmatics, as the study of anything involving the use of language, has become less certain and is in fact lost in several different current approaches.

88. Open Problems open problems Page. Graphs and Applications. List of open problems. Hereis a list of the different problems that have been communicated to us. http://www.labri.fr/Recherche/CombAlgo/graphes/open_problem/

Open Problems Page Graphs and Applications This page gathers several open problems that have been presented in our weekly Seminar . For each problem, a short presentation is given. If any of those problems finds an answer in the future, all the necessary informations (results, references, etc.) will be given in this page. List of Open Problems Here is a list of the different problems that have been communicated to us. Clicking on the title of a problem will download the PostScript file containing a short presentation of the problem. k-dominating set of diameter at most 2k in planar graphs (communicated by Cyril Gavoille Complexity of an algorithm of recognition of Cayley graphs (communicated by Cyril Gavoille On the number of simple, undirected connected graphs (communicated by Cyril Gavoille Recognizing permutation graphs (communicated by Christophe Paul Hamiltonian decomposition of Knödel graphs (communicated by Guillaume Fertin All these problems are gathered here All these problems are gathered in this PostScript file Links There are other interesting Open Problems Web pages. Here are two of them.

89. Cogprints - Two Open Problems And A Conjecture In Mathematical Logic Two open problems and a Conjecture in Mathematical Logic. Nambiar, Kannan(2002) Two open problems and a Conjecture in Mathematical Logic. http://cogprints.ecs.soton.ac.uk/archive/00002044/

Cogprints Home About Browse Search ... Help Two Open Problems and a Conjecture in Mathematical Logic Nambiar, Kannan (2002) Two Open Problems and a Conjecture in Mathematical Logic. Full text available as: PDF - Requires Adobe Acrobat Reader or other PDF viewer. Abstract Keywords: Continuum hypothesis; Incompleteness theorems; Derivation rules. Subjects: Computer Science Language Philosophy Logic ID Code: Deposited By: Nambiar, Kannan Deposited On: 22 January 2002 Alternative Locations: http://www.rci.rutgers.edu/~kannan/science/open_problem_screen.pdf Cogprints Editor: cogprints@ecs.soton.ac.uk Cogprints Technical Administrator: cogprints-admin@ecs.soton.ac.uk

90. Open Problems In Continuum Theory open problems in Continuum Theory. FastCounter by bCentral. 8, 1983, 361394.open problems in topology, Edited by Jan van Mill and George M. Reed. http://web.umr.edu/~wjcharat/problems/

Open Problems in Continuum Theory FastCounter by bCentral Last Modified: Thursday, 13-Mar-2003 17:55:50 CST Edited by Janusz R. Prajs Technical editor Wlodzimierz J. Charatonik In the first half of the twentieth century, when foundations of general topology had been established, many famous topologists were particularly interested in properties of compact connected metric spaces, called continua . What later emerged as continuum theory Janusz R. Prajs Department of Mathematics Idaho State University Pocatello, ID 83209 mailto:prajjanu@isu.edu or Wlodzimierz J. Charatonik Department of Mathematics and Statistics University of Missouri-Rolla Rolla, MO 65401 mailto:wjcharat@umr.edu News on the List March 13, 2003 Problem 11 was added January 20, 2003 Problems 7, 15, and 16, all on homogeneous continua, were added. August 18, 2002 Problem 28 and an essay by J. J. Charatonik about this problem were added. June 27, 2002. Problems 13 and 14 appeared on the list. They are related to the study of spaces such as the space of autohomeomorphisms of the Menger continua M n,k

91. RFW: Open Problems Back to Reinhard F. Werner's home page Some open problems. A list of open problemsin Quantum Information Theory, which is planned for this server. http://www.imaph.tu-bs.de/home/werner/problems.html

Back to Reinhard F. Werner's home page Some Open Problems At conferences I like to ask people "If a Fairy offers you the key idea for proving a Theorem of your choice, what would you pick?". It is the information you don't usually find in published papers. The following sites collect such material. A well structured list of Mathematical Physics Problems maintained by Michael Aizenman for the IAMP . Send your stuff there! A list maintained by Stephen Finch at MathSoft with many(!) links to similar pages. A list of open problems in Quantum Information Theory , which is planned for this server. We are already open for submissions. So if any of these ring a bell, or you know of partial results LET ME KNOW! . If any problem gets solved, I will also place a link to the solution. tr exp (A+itB) [Nov. 1996] A conjecture of Bessis, Moussa, and Villani ( J.Math.Phys. positive measure. This would entail a number of interesting inequalities not just for quantum partition functions, but also for their dervatives (a badly needed tool). Despite a lot of work, some by prominent mathematical physicists, only some simple cases have been decided. So far all results, including fairly extensive numerical experiments, are in agreement with the conjecture. I have been collecting material on this problem with Mark Fannes (along with our own work). Uniqueness of q-relations [Nov. 1996]

92. 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

var PUpage="76001088"; var PUprop="geocities"; 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.doc, about 61 Kb). To appear 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

93. Chris Burdzy's Favorite Open Problems My favorite open problems. Krzysztof Burdzy. I offer a collectionof open problems, mostly about Brownian motion. I tried to http://www.math.washington.edu/~burdzy/open.shtml

KRZYSZTOF BURDZY HOME TEACHING RESEARCH AND OTHER PROFESSIONAL ACTIVITIES PHILOSOPHY ... BROWNIAN MOTION SIMULATIONS (JAVA) 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 and postscript 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

94. KLUWER Academic Publishers | Open Problems In Strongly Correlated Electron Syste 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 Proceedings of the NATO Advanced Research Workshop, Bled, Slovenia, 26-30 April 2000 edited by Janez Bonca University of Ljubljana, Jozef Stefan Institute, Slovenia University of Ljubljana, Jozef Stefan Institute, Slovenia University of Ljubljana, Jozef Stefan Institute, Slovenia 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.

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

96. I've Got Open Problems With Pine 4.05 I've got open problems with Pine 4.05. To Pine Discussion Forum pineinfo@u.washington.edu ;Subject I've got open problems with Pine 4.05; http://www.washington.edu/pine/pine-info/1998.11/msg00005.html

Search Directories Reference Tools UW Home ... Computing and Networking This is one of many messages in the archives of the public, unmoderated Pine-Info mailing list . The mailing list and archive are provided as a public service by the University of Washington, which assumes no responsibility for the contents or accuracy of the messages therein. The subject of this mailing list is the email and newsreading program Pine . Do not send messages on unrelated matters to the list. Before sending a question to the mailing list, check whether it was already asked by using the archives' searchable index. Date Prev Date Next Thread Prev ... Thread Index I've got open problems with Pine 4.05 To Subject : I've got open problems with Pine 4.05 From Date : Wed, 4 Nov 1998 23:04:24 +1100 (EST) Sender : PINE-INFO-owner@u.washington.edu http://www.washington.edu/pine/pine-info/ Follow-Ups I also have open problems with Pine 4.05 From: [Index] [Thread] Pine Information Center homepage Comments?

97. The Practice Of Logical Frameworks - Pfenning (ResearchIndex) Comprehensive survey article by Frank Pfenning (1996) discussing the history of work on logical frameworks and their current open problems. http://citeseer.nj.nec.com/pfenning96practice.html

The Practice of Logical Frameworks (1996) (Make Corrections) (18 citations) Frank Pfenning Proceedings of the Colloquium on Trees in Algebra and Programming Home/Search Context Related View or download: cmu.edu/project/fox/mosa caap96.ps.gz cmu.edu/~fp/public/elfp caap96.ps.gz ... cmu.edu/~fp/papers/caap96.ps.gz Cached: PS.gz PS PDF DjVu ... Help From: cmu.edu/project/fox/mo homepage (more) From: cmu.edu/afs/cs/misc/mo Pfenning Homepages: F.Pfenning HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) Abstract: Introduction Deductive systems, given via axioms and rules of inference, are a common conceptual tool in mathematical logic and computer science. They are used to specify many varieties of logics and logical theories as well as aspects of programming languages such as type systems or operational semantics. A logical framework is a meta-language for the specification of deductive systems. Research on logical frameworks is still in its infancy. Nonetheless, different frameworks have been... (Update) Context of citations to this paper: More 1 Refinement Terms We would be interested to see how this calculus might be usefully combined with work on logical frameworks [ ] The use of logical variables there is an example of underdeterminism.

98. EuroWorkshop - CONJECTURES, RECENT RESULTS AND OPEN PROBLEMS RELATED TO THE MACD Cambridge, UK. EuroWorkshop. CONJECTURES, RECENT RESULTS AND open problemsRELATED TO THE MACDONALD POLYNOMIALS. 8 –12 January 2001 http://www.newton.cam.ac.uk/programs/SFM/sfmw01.html

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK EuroWorkshop CONJECTURES, RECENT RESULTS AND OPEN PROBLEMS RELATED TO THE MACDONALD POLYNOMIALS 8 –12 January 2001 Programme Participants Organisers: Professor P Hanlon, Professor IG Macdonald and Professor AO Morris. The overall programme: In the 1980s, IG Macdonald formulated a series of conjectures which predicted the constant terms of expressions that involve an important new class of symmetric functions called the Macdonald polynomials Since their introduction, these conjectures and polynomials have been a central topic of study in Algebraic Combinatorics. Of particular note has been the variety of approaches used in efforts to solve the conjectures or to find an algebraic or geometric interpretation for the Macdonald polynomials themselves. Different approaches involve double affine Hecke algebras, homology of nilpotent Lie algebras, generalized traces of Lie algebra representations and diagonal actions of the symmetric group on polynomial rings in two sets of variables. In this programme we will attempt to unify these different approaches to the Macdonald polynomials and some of the outstanding conjectures that have resulted from this work.

99. 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@dcs.rhbnc.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

100. Daswani, Neil; Garcia-Molina, Hector; Yang, Beverly: Open Problems In Data-shari open problems in Datasharing Peer-to-peer Systems, ICDT 2003 In a Peer-To-Peer(P2P) system, autonomous computers pool their resources (eg, files, storage http://dbpubs.stanford.edu/pub/2003-1

Pagewise preview Category Value Available via http://dbpubs.stanford.edu/pub/2003-1 Submitted on 23rd of October 2002 Author Daswani, Neil; Garcia-Molina, Hector; Yang, Beverly Title Open Problems in Data-sharing Peer-to-peer Systems Date of publication January 2003 Published in ICDT 2003 Citation Daswani, Neil; Garcia-Molina, Hector; Yang, Beverly. Open Problems in Data-sharing Peer-to-peer Systems, ICDT 2003 Number of pages Language English Project Peers Type Conference or Journal Paper Subject group Miscellaneous Abstract In a Peer-To-Peer (P2P) system, autonomous computers pool their resources (e.g., files, storage, compute cycles) in order to inexpensively handle tasks that would normally require large costly servers. The scale of these systems, their "open nature," and the lack of centralized control pose difficult performance and security challenges. Much research has recently focused on tackling some of these challenges; in this paper, we propose future directions for research in P2P systems, and highlight problems that have not yet been studied in great depth. We focus on two particular aspects of P2P systems search and security and suggest several open and important research problems for the community to address. Keywords Peer-to-peer, search, security

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