61. Dynamical Systems Home Page Conference listings, survey articles, open problems, people, jobs, and seminars. http://www.math.sunysb.edu/dynamics/

Dynamical Systems Homepage Institute for Mathematical Sciences SUNY at Stony Brook A list of recent past conferences , and some upcoming conferences in the field. There is a special Joint Symplectic Topology/Dynamics Seminar held at Courant Institute or at Stony Brook every 3 weeks. Seminar schedules in the tri-state area. Take a look at the pictures from the conference "Around Dynamics" held in honor of Jack Milnor. A searchable list of people working in the field, and some other similar lists Browse our Thesis Server or submit your own work. The Dynamical Systems electronic preprint list at Stony Brook, has merged into the Dynamical Systems section of the XXX mathematics e-print server Here are several other electronic preprint servers We also have collected links to some survey articles in Dynamical Systems, available on-line. Programs :Links to a great variety of programs to draw pictures of dynamical objects. There is a bibliography list , constantly updating. Open problems in Dynamical Systems. Links to similar pages Leave a comment about these pages.

62. Generic Programming Projects And Open Problems Projects and open problems. David R. Musser1 Rensselaer Polytechnic InstituteTroy, New York 12180 musser@cs.rpi.edu Alexander A. Stepanov http://www.cs.rpi.edu/~musser/gp/pop/

Generic Programming Projects and Open Problems David R. Musser Rensselaer Polytechnic Institute Troy, New York 12180 musser@cs.rpi.edu Alexander A. Stepanov Silicon Graphics Inc. 2011 N. Shoreline Boulevard Mountain View, CA 94043-1389 stepanov@sgi.com Last updated: August 25, 1998 There is a At the Dagstuhl Seminar on Generic Programming The current state of this list should not, of course, be considered "complete" in any way. It is being made available on the WWW for the Dagstuhl participants and others to make additions or revisions. It will likely continually grow, but hopefully it can be pruned as projects are completed or open problems are solved! (These can be highlighted or maintained separately as a record of progress.) Suggestions are also sought for improving the level and type of information provided with projects and problems. For example, should there be a rating system to help readers understand the level of difficulty and/or importance attached to a project or problem by its proposer? Originally Alex Stepanov rated the projects on his list according to both difficulty and importance, each on a scale of 1 to 5. Those ratings are currently not included here, but if there is enough interest they could be added, perhaps after translation to an agreed-up scale. Revision History Postscript Version for Printing 1 Theory Concept Development ... Footnotes

63. Open Problems In Continuum Theory open problems in topology, Edited by Jan van Mill and George M. Reed. NorthHollandPublishing Co., Amsterdam, 1990 (H. Cook, WT Ingram and A. Lelek, http://web.umr.edu/~continua/

Open Problems in Continuum Theory FastCounter by bCentral Last Modified Monday, 18-Apr-2005 10:36:36 CDT Edited by Janusz R. Prajs Technical editor 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 and Statistics California State University, Sacramento 6000 J Street Sacramento, CA 95819-6051 prajs@csus.edu or J. Charatonik Department of Mathematics and Statistics University of Missouri-Rolla Rolla MO wjcharat@umr.edu News on the List August 31, 2004, Problem 32 was added. July 22, 2004, Problem 22 was positively solved by Francis Jordan. May 24, 2004 Problems 20, 21 and remarks by Jo Heath has been added. March 31, 2004 Problem 9 was solved in the negative by W. J. Charatonik.. March 29, 2004 Problem 25 was added. April 2, 2003 As you can see we have moved to a different account. Please change the address in your favorites list. March 13, 2003

64. COLT2003 Call For Open Problems The deadline for submission of open problems is May 10, 2003. On the subjectline please include open problem for colt2003. http://learningtheory.org/colt2003/OpenProblems/solicitation.html

COLT2003 Call for open problems COLT2003 will include a session devoted to the presentation of open problems. A two page description of the accepted problems will also appear in the COLT proceedings. The idea is to facilitate collaborations and to encourage new people to get into the field. The writeup of an open problem should include: A clear and self contained description of a single open problem. Motivation for the study of this problem. The current state of understanding for this problem, including known partial solutions and citations of published work. The deadline for submission of open problems is May 10, 2003. This description should be written in the COLT proceedings format ( LLNCS format Please submit the problem electronically to (my-last-name) at merl dot com On the subject line please include: open problem for colt2003 The submissions themselves should be in postscript (letter size page) and should be included as attachments to the email. Characteristics of a good open problem There is no requirement to satisfy all of these characterizations, but the more the better.

65. Steiner Trees: Open Problems open problems with Steiner Trees, maintained by Joe Ganley. http://ganley.org/steiner/open.html

ganley.org The Steiner Tree Page Open Problems Of course, there are probably about a zillion open problems related to Steiner trees, but here are a few I've thought about. Full trees Hwang's theorem allows us to construct an optimal rectilinear Steiner tree of a full set in linear time. I know of no other metric or type of graph in which computing the optimal Steiner tree of a full set is polynomial-time solvable but computing a general Steiner tree is NP-hard. Note that there isn't even a sufficiently strong analogue of Hwang's theorem for rectilinear Steiner trees in three dimensions. Multidimensional rectilinear Steiner ratio . What is the rectilinear Steiner ratio in arbitrary dimension d ? It is at least 2-1/ d , as the d -dimensional analogue of the "cross" has this ratio. It is obviously at most 2. It is generally believed that the lower bound is correct, but this hasn't been proven. Even an upper bound lower than 2 would be interesting. Rectilinear Steiner arborescence . These are Steiner-like trees on points in the (first quadrant of the) plane, in which every segment in the tree is directed left to right or bottom to top. It is unknown whether computing an RSA is NP-complete. (A good reference to start with is Rao, Sadayappan, Hwang, and Shor

66. The Valuation Theory Home Page - Open Problems Possible applications To the open problem whether the power series field This is an open problem about finite extensions of a valued field (K,v) within 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.

67. Open Problems In Mathematical Systems And Control Theory There are several resources containing description of open problems in mathematicalsystems That book contains descriptions of about 50 open problems. http://www.inma.ucl.ac.be/~blondel/op/

Open Problems in Mathematical Systems and Control Theory There are several resources containing description of open problems in mathematical systems and control theory. The most recent resource is the book: Unsolved problems in mathematical systems and control theory, Vincent Blondel, Alexander Megretski (Eds), Princeton University Press, 2004 . That book was published by Princeton University Press in July 2004 and contains more than 60 problems (see the call for submission ). The book is for sale at a price of 40 USD. A PDF electronic version of the book can also be downloaded for free from the publisher's website. Updates on the status of the problems will be posted on the PUP book website and on the editors book website . These websites are maintained by Dr Roland Hildebrand. The book published by Princeton University Press is based in part on problems that were presented in August 2002 at a "Workshop on open problems in system theory" held during the Symposium MTNS 2002 at the University of Notre-Dame (USA). A booklet with descriptions of about 40 problems presented at that symposium is available here for download (the PDF file weights 956K):

68. Uni Dortmund, Informatik 2: BDD-Book Solutions By Ingo Wegener (SIAM, 2000). Errata, solutions to exercises, updates on open problems. http://ls2-www.cs.uni-dortmund.de/monographs/bdd/

LS 2 Home Lehre Service Anreise Mitarbeiter Kontakt Interna Externe Links Fachbereich Informatik SFB 531 SFB 475 DFG-Schwerp. Nr. 1126 Studieninformation Branching Programs and Binary Decision Diagrams by Ingo Wegener The book is available from the Society of Industrial and Applied Mathematics. The official SIAM homepage includes an abstract and an order form. Resources PostScript PDF Last update Solutions of Exercises 2000-August-24 Solutions of Open Problems 2005-Mar-16 Errors and Misprints 2004-Aug-17 If you find typos etc. or if you have remarks, please contact the author. Other monographs by authors at Lehrstuhl Informatik 2.

69. Open Problems In Mathematical Systems And Control Theory Open Problem 1 The static output feedback problem is the problem of deciding Open Problem 2 For what values of n and m is ``stability of all infinite http://www.inma.ucl.ac.be/~blondel/books/openprobs/

Open Problems in Mathematical Systems and Control Theory Vincent D. Blondel Eduardo D. Sontag M. Vidyasagar Jan C. Willems Springer Verlag, London, 1999 Communication and Control Engineering Series, ISBN: 1-85233-044-9 From the cover: "This volume collects a discussion of more than fifty open problems which touch upon a variety of subfields, including: chaotic observers, nonlinear controllability, discrete event and hybrid systems, neural network learning, matrix inequalities, Lyapunov exponents, and many other issues. Proposed and explained by leading researchers, they are offered with the intention of generating further work, as well as inspiration for many other similar problems." From Zentralblatt Math review 0945.93005: "History will tell if the proposed problems will be solved through tricks or will open vast areas of knowledge and if the relatively recent domain of systems science is mature enough so that the open problems have the expected depth. At any rate, this book provides a welcome goal-oriented research drive to the field.'' 1. Uniform asymptotic stability of linear time-varying systems

70. Open Problems On Perfect Graphs This page has moved to http//www.cs.concordia.ca/~chvatal/perfect/problems.html. http://www.cs.rutgers.edu/~chvatal/perfect/problems.html

This page has moved to http://www.cs.concordia.ca/~chvatal/perfect/problems.html

71. List Of Open Problems In Computer Science - Wikipedia, The Free Encyclopedia List of open problems in computer science A solution to the problems in thislist will have a major impact of the field of study to which they belong. http://en.wikipedia.org/wiki/List_of_open_problems_in_computer_science

List of open problems in computer science From Wikipedia, the free encyclopedia. This is a list of unsolved problems in computer science . A solution to the problems in this list will have a major impact of the field of study to which they belong. Contents Computational complexity theory Cryptography High performance computing See also ... P versus NP Source: S. A. Cook Proceedings of the 3rd Annual ACM Symposium on Theory of Computing (1971), pp. 151158. Description: P is the class of problems whose solution can be found in polynomial time. NP is the class of problems whose solution can be verified in polynomial time. Naturally, any problem in P is also in NP. The P versus NP question is whether NP is in P, hence the classes are equal. One can see the question as a specific case of the problem in proving lower bounds for computational problems. Importance: If the classes are equal then we can solve many problems that are currently considered intractable. If they are not, then NP-complete problems are problems that are provably hard. Current conjecture: Though the question is far from being settled, it seems that the classes are different.

72. The Open Problems Project A project to record open problems of interest to researchers in computational geometry and related fields. http://www.cs.smith.edu/~orourke/TOPP/

Next: Numerical List of All The Open Problems Project edited by Erik D. Demaine Joseph S. B. Mitchell Joseph O'Rourke Introduction This is the beginning of a project to record open problems of interest to researchers in computational geometry and related fields. It commenced with the publication of thirty problems in Computational Geometry Column 42 [ ] (see Problems 1-30 ), but has grown much beyond that. We encourage correspondence to improve the entries; please send email to TOPP@cs.smith.edu . If you would like to submit a new problem, please fill out this template Each problem is assigned a unique number for citation purposes. Problem numbers also indicate the order in which the problems were entered. Each problem is classified as belonging to one or more categories. The problems are also available as a single Postscript or PDF file. To begin navigating through the open problems, you may select from a category of interest below, or view a list of all problems sorted numerically Categorized List of All Problems Below, each category lists the problems that are classified under that category. Note that each problem may be classified under several categories.

73. Open Problem - Wikipedia, The Free Encyclopedia It is common in graduate schools to point out open problems to students in the hopes Examples of formerly open problems that have been closed since 1975 http://en.wikipedia.org/wiki/Open_problem

Open problem From Wikipedia, the free encyclopedia. An open problem is a problem that can be formally stated and for which a solution is known to exist but which has not yet been solved. It is common in graduate schools to point out open problems to students. However, Fermat's last theorem and the Four color theorem are two notable open problems that have been closed or solved by faculty members, as they would have more expertise and resources than students. Important open problems exist in many fields, such as in the field of theoretical computer science, computer scheduling, and real-time computing. edit See also List of unsolved problems Retrieved from " http://en.wikipedia.org/wiki/Open_problem Categories Unsolved problems Views Article Discussion Edit this page History Personal tools Create account / log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 20:19, 11 September 2005. All text is available under the terms of the GNU Free Documentation License (see for details).

74. FoIKS - Intro International Symposium on Foundations of Information and Knowledge Systems. Burg (Spreewald), Germany; 1417 February 2000. List of open problems. http://www.informatik.tu-cottbus.de/~foiks/

International Symposium on Foundations of Information and Knowledge Systems (FoIKS 2000) next FoIKS will be held in february/march 2002

75. Open Problems In Graph Theory Involving Steiner Distance open problems involving Steiner distance. http://io.uwinnipeg.ca/~ooellerm/open_problems/index.html

Some Open Problems in Graph Theory It has been shown by Chartrand, Oellermann, Tian, and Zou that, for a tree T: diam n n This inequality does not hold for graphs in general as was shown by Henning, Oellermann, and Swart . It was shown in the same paper that for a graph G and n=3 and 4: diam n n G. It was shown by Oellermann and Tian that for a tree T: C n-1 (T) is contained in C n It remains an open problem to determine whether this containment holds for general graphs. In other words, it is not known if the Steiner (n-1)-center of a graph is contained in its Steiner n-center. It was shown by Beineke, Oellermann and Pippert that if T is a tree, then M n-1 (T) is contained in M n It remains an open problem to determine whether this containment holds for general graphs. In other words, it is not known if the Steiner (n-1)-median of a graph is contained in its Steiner n-median. Oellermann and Tian ). It is known that every graph is the 2-median of some graph (see Holbert ,and Hendry ). Steiner n-medians of trees have been completely characterized by

76. Computational Algebraic Statistics This web page highlights some of the conjectures and open problems concerning open problems. The individual participant contributions may have problems http://www.aimath.org/WWN/compalgstat/

Computational Algebraic Statistics This web page highlights some of the conjectures and open problems concerning Computational Algebraic Statistics. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. A list of participants is available. You may also wish to view the homework from Bernd Sturmfels Material from several workshop presentations is being compiled. Open problems 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.

77. Open Problems 5 open problems. Of course, the author would like to receive feedback. In addition,at least let me know if you have fixes for one of these open problems http://www.freebsd.org/doc/en_US.ISO8859-1/articles/euro/x200.html

78. DI & CoS - Current Research Topics And Open Problems The following pages contain interesting open problems related to those in this page, I think the two most important `open problems´ are at the same time http://alessio.guglielmi.name/res/cos/crt.html

Alessio Guglielmi's Research Deep Inference and the Calculus of Structures / Current Research Topics and Open Problems Deep Inference and the Calculus of Structures Current Research Topics and Open Problems In this page I list all open and currently explored research subjects I am aware of, in the area of deep inference and closely related matters. The solutions to most of these problems are instrumental in reaching the common goal of a comprehensive bureaucracy-free proof theory based on geometric methods. This page is incomplete and uneven: I'm working on it and I'm expecting quick feedback from my colleagues in order to complete it as soon as possible. Contents Introduction Calculus of Structures Calculus of structures without involutive negation Designing term calculi for systems in the calculus of structures ... Describing causal quantum evolution Introduction In very few words, what we do is looking for the best syntax and the best semantics for proofs (notice that semantics of proofs is a very different thing from semantics of formulae!). It is necessary to improve on the current state of the art in structural proof theory in order to solve important open problems like that of identity of proofs . By employing deep inference, which yields the necessary flexibility for the task, we are making very fast progress.

79. Perfect Graphs Conjectures and open problems, maintained at the AIM. http://www.aimath.org/WWN/perfectgraph/

Perfect Graphs This web page highlights some of the conjectures and open problems concerning Perfect Graphs. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Recognition of Perfect Graphs Polynomial Recognition Algorithm Found Interaction Between Skew-Partitions and 2-joins The Perfect-Graph Robust Algorithm Problem ... A Possible New Problem Skew-Partitions Extending a Skew -Partition Graphs Without Skew-Partitions Graphs Without Star Cutsets Finding Skew-Partitions in Berge Graphs ... beta-perfect graphs Partitionable Graphs Perfect, Partitionable, and Kernel-Solvable Graphs Partitionable graphs and odd holes A Property of Partitionable Graphs Small Transversals in Partitionable Graphs ... The Imperfection Ratio Integer Programming Partitionable Graphs as Cutting Planes for Packing Problems? Feasibility/Membership Problem For the Theta Body Balanced Graphs Balanced circulants ... P4-structure and Its Relatives 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.

80. Open Problems In Knot Theory A List of Approachable open problems in Knot Theory (To show it s false, it senough to show that an open knot is tricolorable if and only if its 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.)

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