21. Home Page For Constructive Approximation Open Problem Section Research problems section of the journal, edited by Peter Borwein, Albert Cohen, Ingrid Daubechies and Vilmos Totik. Includes problem statement (PostScript) and discussion. http://www.cecm.sfu.ca/personal/pborwein/CA_MOSAIC/CA_problems.html

Research Problems Section Edited by: Peter Borwein, Albert Cohen, Ingrid Daubechies and Vilmos Totik About the open problems section Problems available online Return to the Constructive Approximation Homepage The Brachistochrone Challenge "I, Johann Bernoulli, greet the most clever mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to earn the gratitude of the entire scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall then publicly declare him worthy of praise." Groningen, 1 January 1697 http://oldweb.cecm.sfu.ca/personal/pborwein/CA_MOSAIC/CA_problems.html Modified: 06/13/1995 by pborwein@cecm.sfu.ca (Peter Borwein).

22. Open Problems In Mathematical Physics open problems in Mathematical Physics Quick Access Soft phases in 2D O(N) models. Quantum Hall Conductance. Exponents dimensions http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

23. Open Problems Some questions compiled by Jon Perry. http://www.users.globalnet.co.uk/~perry/maths/openproblems/openproblems.htm

Open Problems [Home] [Other Maths] Open Problems This is a collection of my own open problems. These already have their own page: Triangular Transforms - see Triangular Transforms Lucas-Carmichaels - see Lucas-Carmichaels Prime Puzzles conjecture 33 Ramanujan's zeta(2) - see Two Ramanaujan conjectures These have no write-up as yet: Do we need all the integers to form all primes of the form 1mod4 as the sum of 2 squares? This can be stated as; for every x does there exists a y such that x +y is prime? Let A(n) be the set of integers less than n such that n+a_i is prime. Does A(n)=A(m) imply n=m? Goldbach Slim : Can every odd integer be represented as T(n)+p, with T(0)=0 allowed, and p optional? Playstation Numbers : Can every positive integer can be represented as some combination of 1, T(n), x and y (representing the circle, triangle, square and X)? Perfect Partition Problem : The conjecture states that the proper divisors of the perfect number 2^(p-1).(2^p-1)=T(2^p-1) always have a sumwise representation via the integers 1..T(2^p-1). e.g. the proper divisors of 28 are 1,2,4,7,14, and this can be written as 1,2,4,7,3+5+6.

24. Open Problems For Undergraduates A collection of open problems in Discrete Mathematics which are currently being researched by members of the DIMACS community. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

25. Graph Theory Open Problems Graph Theory open problems. Index of Problems http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

26. Open Problems In Discrete Mathematics From the SIAM DM activity group newsletter and other sources. http://www.siam.org/siags/siagdm/siagdmopen.htm

27. Some Open Problems 9) Problems on 2 dimensional partial orders open problems include several variants of scheduling problems (e.g. weighted completion time http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

28. Open Problems List open problems in Dynamical Systems open problems in holomorphic dynamics Two lists of problems are currently available online http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

29. Mesh Generation: Open Problems open problems. We proved (4/3/97) the existence of triangulations of any polygon or It is a famous open problem whether minimum length triangulation is http://www.ics.uci.edu/~eppstein/280g/open.html

ICS 280G, Spring 1997: Mesh Generation for Graphics and Scientific Computation Open Problems We proved ( ) the existence of triangulations of any polygon or straight line graph, and of convex quadrilateralizations of any orthogonal polygon. What about curved objects? Do spline-polygons have spline-triangulations? An example formed by connecting four quarter-ellipses shows Steiner points may be needed, even for quadratic splines, but maybe they only need to be added in the interior of the splinegon. On we went over dynamic programming techniques for optimal triangulation (e.g. minimum total edge length) of simple polygons, in O(n ) time or O(E ) if the visibility graph has E edges. So the slowest case is seemingly the most simple, when the polygon is convex. Can we find the minimum length triangulation of convex polygons in o(n ) time? Steve S. suggested Frances Yao's generalization of Knuth's speedup to optimal binary search tree construction (which has the same general dynamic programming form) but it doesn't seem to work. The same dynamic programming methods also work for optimal quadrilateralization, in time O(n

30. Open Problems Columns - Douglas B. West open problems Columns Douglas B. West http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

31. Open Problems In Mathematical Physics This page leads to a collection of significant open problems gathered fromcolleagues during the academic year 1998/99. They are offered in the belief that http://www.math.princeton.edu/~aizenman/OpenProblems.iamp/

Open Problems in Mathematical Physics Quick Access: Soft phases in 2D O(N) models Quantum Hall Conductance dimensions ... IAMP This page leads to a collection of significant open problems gathered from colleagues during the academic year 1998/99. They are offered in the belief that good challenges stimulate our work, tempered by the dictum that preformulated questions should not discourage one from seeking new perspectives. All are invited to send pertinent comments, references to solutions, and contributions for this page to M. Aizenman (Editor): aizenman@princeton.edu List by Contributors By order of submission General Framework Quantum Field Theory Statistical Physics Quantum Many Body Systems Geometry and Physics Schroedinger Operators Disordered Systems Non-equilibrium Relativity and Gravitation Dynamical Systems Fluid Dynamics (Layout webmaster: aizenman@fas.harvard.edu

32. USATODAY.com - Coke CEO Takes Open Approach To Problems . Add USATODAY.com RSS feeds Coke CEO takes open approach to problems. By Theresa Howard, USA TODAY http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

33. Open Problems By Contributors open problems in Mathematical Physics. by order of submission. All are invitedto submit suitable contributions to aizenman@princeton.edu (Michael Aizenman http://www.math.princeton.edu/~aizenman/OpenProblems.iamp/OPlist.html

Open Problems in Mathematical Physics by order of submission All are invited to submit suitable contributions to: aizenman@princeton.edu (Michael Aizenman, O-P Editor). For further information see: O-P Front Page List by Contributors IAMP Soft phases in ... 2D O(N) models A. Patrascioiu and E. Seiler March 11, 1999. Quantum Hall Conductance J. Avron and R. Seiler March 11, 1999. Dimensions M. Aizenman Jan. 28, 1999. LRO for the Quantum Heisenberg Ferromagnet E.H. Lieb Jan. 27, 1999. Extended States M. Aizenman Dec. 15, 1998. Impossibility Theorems A. Lenard Nov. 10, 1998. Fermi Gas G. Gallavotti Nov. 6, 1998. Entropy Production G. Gallavotti Nov. 6, 1998. Separatrix Splitting G. Gallavotti Nov. 6, 1998. Navier-Stokes Ya. Sinai Oct. 5, 1998. Spin Glass C.M. Newman and D.L. Stein Sept. 18, 1998. Optimal Flux E.H. Lieb Sept. 15, 1998. Bose-Einstein Condensation E.H. Lieb Sept. 15, 1998. O-P Front Page List by Contributors IAMP (Layout webmaster: yair@macnn.com

34. L-functions And Random Matrix Theory Conjectures and open problems concerning Lfunctions, focussing on the areas in which there has been recent progress using results from Random Matrix Theory. Maintained at AIM. http://www.aimath.org/WWN/lrmt/

L-functions and Random Matrix Theory This web page highlights some of the conjectures and open problems concerning L-functions and Random Matrix Theory. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Distribution of zeros of L-functions The GUE hypothesis Correlations of zeros Neighbor spacing ... Statistics of the zeros of the derivative of xi Relationship between symplectic and odd orthogonal The Alternative Hypothesis p-adic L-functions Zeros and primes The distribution of primes ... Fractional moments Mollified mean values Mollifying a Family Long Mollifiers Moments of S(T) The integral of exp(i lambda S(t)) ... GOE and Graphs The individual 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.

35. Problems In Analysis Of Algorithms A list of open problems with updates and solutions. http://pauillac.inria.fr/algo/AofA/Problems/

PROBLEMS in ANALYSIS of ALGORITHMS PAGES Home Page Research Problems Bulletin board ... Resources Return to Analysis of Algorithms Home Page This page contains a list of interesting problems that we are aware of. You are encouraged to submit new ones by posting directly on the Bulletin Board . Typically 5 to 10 lines of TeX should be best for further editing. A digest of the main problems will be compiled here periodically by the Problem Editor Summer 97 Problem 1. Problem Solution ] By Conrado Martinez , 11-Jul-97. The depth of the j-th element in a random binary search tree of size n. Problem 2. Problem ] By Conrado Martinez , 11-Jul-97. Quicksort with median-of-three partitioning and halting on small subfiles. Problem 3. Problem Comments ] By Hsien-Kuei Hwang , 23-Jul-97. A limit distribution and zeros of a polynomial. Problem 4. Problem ] By Wojtek Szpankowski , 25-Jul-97. What is the distribution of node levels and height in digital search trees built on Bernoulli sources? Problem 5. Problem ] By Ed Coffman , 01-Aug-97. Analyse the waste in First-Fit bin-packing.

36. Open Problems In Group Theory Part of the Magnus project. Contains over 150 problems in group theory, both well known and relatively new. http://zebra.sci.ccny.cuny.edu/web/nygtc/problems/

Open Problems in combinatorial and geometric group theory This page has been accessed times since 10/16/97. 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) Groujps of matrices Hyperbolic and automatic groups Nilpotent groups Metabelian groups ... Group actions

37. The RTA List Of Open Problems Since October 1997 the list of open problems is maintained as a web service. Note that problems marked as solved may still leave open the question of http://www.lsv.ens-cachan.fr/rtaloop/

The RTA list of open problems The RTA list of open problems summarizes open problems in the field of the International Conference on Rewriting Techniques and Applications (RTA). For the RTA 2002 conference, the topics of RTA were given as Applications: case studies; rule-based programming; symbolic and algebraic computation; theorem proving; functional and logic programming; proof checking. Foundations: matching and unification; completion techniques; strategies; constraint solving; explicit substitutions. Frameworks: string, term, and graph rewriting; lambda-calculus and higher-order rewriting; conditional rewriting; proof nets; constrained rewriting and deduction; categorical and infinitary rewriting. Implementation: compilation techniques; parallel execution; rewriting tools. Semantics: equational logic; rewriting logic. The RTA list of open problems was created in 1991 by Nachum Dershowitz Jean-Pierre Jouannaud and Jan Willem Klop on occasion of the RTA'91 conference. Updated lists have since been published at RTA'93, RTA'95 and RTA'98. Since October 1997 the list of open problems is maintained as a web service. This effort is, at the moment, led by

38. Ideas, Concepts, And Definitions In a community of mathematicians, an open problem is a question that no one open problems are not a source of frustration, they are a source of delight. http://www.c3.lanl.gov/mega-math/gloss/math/openpr.html

Open Problems In a community of mathematicians, an open problem is a question that no one has found the answer to. Open problems are not a source of frustration, they are a source of delight. Open problems are the lifeblood of mathematics. For you, as an individual mathematician, your own open problems are the questions you raise that you cannot answer. Anyone who does mathematics for very long soon discovers that open problems are abundant, and even more of them are generated as mathematicians think about something and ask themselves questions in an effort to understand it. One of a mathematician's hardest choices is deciding which open problems to give focused attention to and try to solve. When you raise a question for yoursef, and you cannot answer it, it becomes an open problem for you. It is a good idea to share this problem with other mathematicians friends, classmates, teachers, etc. to see if they know of a solution or have ideas about solving it. Share your open problems with MegaMath! Don't abandon your open problems just because they remain unsolved for a long time. Set them aside and think about them gently . A solution might surprise you and arrive when you least expect it. You might even dream it!

39. Process Algebra: Open Problems And Future Directions A web page with a list of open problems and future directions in process algebrathat were discussed during the workshop is now available in draft form. http://www.cs.auc.dk/~luca/BICI/pa2003.html

Process Algebra: Open Problems and Future Directions July 21-25, 2003 University of Bologna Residential Center Bertinoro Forlì ), Italy What the Meeting is About Seminar Schedule Output of the Workshop Location ... Local Weather Forecast What the Meeting is About Process algebra (also known under the names `process calculi' or `process theory') is a successful method for reasoning about concurrent systems that originates from original insights of key figures like Bergstra, Hoare, Klop and Milner. The foundations of process algebra have been studied thoroughly over the last twenty years, and are still leading to large numbers of interesting results and fruitful ideas. In recent years, powerful tool sets for the analysis of concurrent systems, such as Caesar/Aldebaran, muCRL, Concurrency Factory, FDR, FC2Tools and Concurrency Workbench Edinburgh, have been developed on the basis of process algebra. A wide range of advanced protocols and distributed algorithms have been verified using process algebraic methods, and/or analyzed using the aforementioned tool sets. The aim of this workshop will be to highlight the most important open problems in the field of process algebra, and to stimulate international cooperation on their solutions. Special emphasis will also be given to future directions in the study of process algebra, and to new application areas.

40. Open Problems Articles in PostScript format. http://www.cecm.sfu.ca/personal/pborwein/CA_MOSAIC/PROBLEMS/A_PROBLEMS.html

Problems Each entry includes a postscript version of the paper and a discussion section. The problems are available online only in postscript form. If you have solutions, references or additional comments please send them to pborwein@cecm.sfu.ca. Online Problems P95-1: Some old and new problems in approximation theory P95-2: Two problems on interpolation P96-1: A convergence problem for rational interpolants P96-4: Bivariate segment approximation and free knot splines ... P97-2: Conjectures around the Baker-Gammel-Wills conjecture

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