101. Open Problems In Science Open Problems in Science. This page will build a list of open research questions at the socalled bleeding edge of science. This page makes no attempt to be http://www.madscitech.org/open.html

Open Problems in Science This page will build a list of open research questions at the so-called bleeding edge of science. This page makes no attempt to be complete, or even up-to-date. I will attempt to address each science wherever I can dig up the most important problems. Archaeology How, and when, did agriculture develop? How can modern analytical techniques be used to gather information about artifacts? How did the first nations come into being? How do aboriginal cultures approach astronomy? How do complex societies come to be? How do human beings adapt? How do we accurately date artifacts? How do we reconstruction prehistoric and ancient life. In what ways did ancient peoples use plants? What were the environments of prehistoric and ancient humans like?. Astronomy Are there active galactic nuclei? Are there black holes? Are there dwarf galaxies? Can we use cosmic rays for imaging? How are elements created in a star? How are large-scale cosmic structures formed? How are black holes formed? How are neutron stars formed? How can we detect Doppler shifts of spectral lines in the X-ray spectra of clusters?

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

103. Five Open Problems Regarding Convex Polytopes | Combinatorics And More This entry was posted on May 7, 2008 at 900 pm and is filed under Combinatorics , Convex polytopes, Convexity, Open problems. You can follow any responses http://gilkalai.wordpress.com/2008/05/07/five-open-problems-regarding-convex-pol

104. Some Problems In Matroid Theory Thomas Zaslavsky of Binghamton State University of New York presents brief descriptions and references. Find information on Bonin s Projective Bound including the maximum r-flat, covering and packing by flats. 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.

105. Aims And Scope I J O P C M . Welcome to the Website of the International Center for Scientific Research and Studies. Aims and Scope. Editorial Board http://www.ijopcm.org/

Main - I J O P C M - Welcome to the Website of the International Center for Scientific Research and Studies Aims and Scope Editorial Board Assoc. Edit. Board Edit. Rev. Board Volumes ... Databases Your browser does not support inline frames or is currently configured not to display inline frames. Browse for Journals Journals Conferences Host Sponsors ... Contact Us Hit Counter

106. Unsolved Problems Including the list of 50 problems of Bondy and Murty with current status. Compiled by Stephen C. Locke. http://www.math.fau.edu/locke/unsolved.htm

Unsolved Problems How to contact me Several people have asked me about unsolved problems. I will take the easy way out: see the list of 50 problems in Bondy and Murty . You can now see the list as it originally appeard in the the text, Graph Theory with Applications December 2007 : I have now received a copy of the new text, GTM 244. and the authors revisit these unsolved problems in Appendix A, and have increased the number of unsolved problems to 100. Some of these problems have been solved (and thus the title is slightly incorrect) and I won't claim to be familiar with all current results. If you find that one of them has been solved (or even that some reasonable progress has been made), please e-mail me. ( How to contact me .) If I receive comments on these new problems, I will of course post those that seem suitable (and, at that point, I would presumably post the problem to which the comment refers). Note, however, the publisher does have a site for the text, http://blogs.springer.com/bondyandmurty/ , and it would seem reasonable that one should post comments there. Also, I'm not giving you all of the references in

107. Web Service Composition - Current Solutions And Open Problems File Format PDF/Adobe Acrobat Quick View http://www.zurich.ibm.com/pdf/ebizz/icaps-ws.pdf

108. Games On Graphs Students can understand and work on an unsolved problem in mathematics. http://www.c3.lanl.gov/mega-math/workbk/graph/grthree.html

Three for the Money: The Degree/Diameter Problem Description Students can understand and work on an unsolved problem in mathematics. There is a good chance that this problem can be solved by someone who spends enough time experimenting with it. The only skills required to work on it are the ability to draw dots and connect them with lines, and the understanding of four ideas related to graphs: degree diameter planarity , and size . (These concepts can be explored in the story Superperson Saves the Monster Materials Instructions Ideas for discussion Materials One large copy of the puzzle graph that all students can see, such as one that is drawn on the floor with masking tape, or a copy for each student or group of students. Paper and pencil should be handy so students can experiment and draw their own solutions to the problem. Instructions Explain to students that you are going to tell them about a problem in mathematics that is easy to understand that no one has solved yet. There is no reason why one of them could not be the person to solve it. A famous mathematician, Paul Erdos, has offered a large cash prize for the person who succeeds in drawing the graph that solves this problem. They could win it.

109. Open Problems In Continuum Theory Apr 3, 2010 Open problems in topology, Edited by Jan van Mill and George M. Reed, North Holland Publishing Co., Amsterdam, 1990 (H. Cook, W. T. Ingram http://web.mst.edu/~continua/

Open Problems in Continuum Theory, nd Edition st Edition Solved Problems Last Modified Saturday, 03-Apr-2010 14:05:33 CDT Edited by Janusz R. Prajs In the first half of the twentieth century, when foundations of general topology had been established, many famous topologists were particularly interested in the properties of compact connected metric spaces called continua . It seems that studying continua was for them a major source of new ideas. These new ideas were later generalized and formed into developed topological theories. What emerged as continuum theory is a continuation of this early study of continua. Continuum theory is not exactly a "theory" separated from other areas of topology and mathematics by a fixed set of axioms or specific methods. Its identity is rather defined by special type of questions asked in this area. Now, when basic general topology is already established, many deep but naturally and simply formulated problems in continuum theory still remain open. Due to these problems, continuum theory remains a remarkably fresh area in topology. We consider these problems interesting and important. We think that it would be useful to find a place where they could be continuously exposed and updated. Therefore, we have decided to present this web site so that everyone interested, especially beginners, can find them together with some basic information necessary to start working on these problems. This is the second edition of our list. The last version of the previous edition can be found

110. Problems In Topological Graph Theory Web text by Dan Archdeacon with a list of open questions in topological graph theory. http://www.emba.uvm.edu/~archdeac/newlist/problems.html

Problems in Topological Graph Theory Go to the Table of Contents Compiled by Dan Archdeacon List Started: August 5, 1995 Converted to the web: September 1, 1998 Last modified: November 15, 1998 E-Mail: dan.archdeacon@uvm.edu Postal Mail: Dan Archdeacon Dept. of Math. and Stat. University of Vermon t Burlington VT 05401-1455 USA Abstract Do you think you've got problems? I know I do. This paper contains an ongoing list of open questions in topological graph theory. If you are interested in adding a problem to this list please contact me at the addresses above. The spirit is inclusive-don't submit a problem you're saving for your graduate student. If it appears here, it's fair game. If you solve one of the problems, know some additional history, or recognize it as misphrased or just a stupid question, please let me know so that I can keep the list up-to-date. I've taken quite a bit of liberty editing the submissions. I apologize for any errors introduced. Enjoy my problems-I do! Table of Contents Classical questions on genus Coloring graphs and maps Drawings and crossings Paths, cycles, and matchings

111. Open Problems In Costas Arrays File Format PDF/Adobe Acrobat Quick View http://www.costasarrays.org/costasrefs/rickard06open.pdf

112. Graph Coloring Problems -- The Archive. Archive for the book Graph Coloring Problems by Tommy R. Jensen and Bjarne Toft (Wiley Interscience 1995), dedicated to Paul Erd s. Gives progress and new problems. http://www.imada.sdu.dk/Research/Graphcol/

IMADA Research activities Graph Coloring Problems Here are the archives for the book "Graph Coloring Problems" by Tommy R. Jensen and Bjarne Toft (Wiley Interscience 1995), dedicated to Overview New problems Reviews Kenneth I. Appel, Bull. Amer. Math. Soc. 33 (1996), pp.287-288. Ron Read, ... James Arvo, www.amazon.com, July 2003. Contributions to be considered for inclusion into the archives may be sent by e-mail to graphcol@imada.sdu.dk An interesting graph coloring link is Joseph Culberson's Graph Coloring Page . It contains links to numerous other sites with material of interest for graph coloring. For general information related to combinatorial mathematics, consult the World Combinatorics Exchange Graph Theory with Applications by J.A. Bondy and U.S.R. Murty (Macmillan 1976) was for many years a much used standard graph theory text. It is available on-line - its Appendix IV is a list of 50 unsolved problems (1976). Introduction to Graph Theory by Douglas West (Prentice Hall 1996 and 2001) is a standard textbook, used in many places, with a well written chapter on graph coloring, but colorings appear also in several other places in the book. It has a final chapter with more advanced material. Douglas west also maintains a webpage with open problems.

113. Mathematician's Secret Room Unsolved problems in Number Theory. English and Japanese text by Hisanori Mishima. http://www.asahi-net.or.jp/~KC2H-MSM/mathland/overview.htm

Mathematician's Secret Room Challenges to Unsolved Problems in Number Theory Contents What's new (July 22, 2009) Chapter 0 : Opening - Why I am interested in Number Theory. Chapter 1 : 4/n = 1/a + 1/b + 1/c [D11] Chapter 2 : Squares consisted of 3 different digits [F24] Chapter 3 : n = (x + y + z)(1/x + 1/y + 1/z) Chapter 4 : n = x + y + z Chapter 5 : Repeating Decimals [A3] Chapter 6 : Additive Palindromicness of Natural Numbers [F32] Chapter 7 : Collatz's Conjecture [E16] Chapter 8 : Continued Fraction and Pell's Equation Chapter 9 : Amicable Numbers [B4][B5] Chapter 10 : Congruent Numbers (Congruum) [D27] Chapter 11 : Number Theoretic Algorithms [A3] [B45] [F10] Chapter 12 : Integer Factorization Algorithms Appendix 1 : WIFC (World Integer Factorization Center) Appendix 2 : Bibliography Appendix 3 : How to join in the Factorization Project Appendix 4 : Benchmark of Tomabechi's "ppmpqs.exe" Appendix 5 (new !) Prime table (Primes near to 2 n n , factorial, primorial and compositorial) [nn] denote the number in Richard K. Guy

114. Process Algebra Open Problems And Future Directions PA 03 File Format PDF/Adobe Acrobat http://www.brics.dk/NS/03/3/BRICS-NS-03-3.pdf

115. F. Conjectures (Math 413, Number Theory) A collection of easily stated conjectures which are still open. Each conjecture is stated along with a collection of references. http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html

F. Conjectures Number Theory, Math 413, Fall 1998 A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references. The Riemann Hypothesis Fermat Numbers Goldbach's Conjecture Catalan's Conjecture ... The Collatz Problem The Riemann Hypothesis Def: Riemann's Zeta function, Z(s), is defined as the analytic extension of sum n infty n s Thm: Z( s )=prod i infty p i s , where p i is the i th prime. Thm: The only zeros of Z( s ) are at s s Conj: The only zeros of Z( s ) are at s =-2, -4, -6, ... and on the line Re( s Thm: The Riemann Conjecture is equivalent to the conjecture that for some constant c x )-li( x c sqrt( x )ln( x where pi( x ) is the prime counting function. Refs: Unsolved Problems Elementary Number Theory http://www.utm.edu/research/primes/notes/rh.html (notes in Chris Caldwell's Prime Pages) http://match.stanford.edu/rh/ (Dan Bump's notes) Def: n is perfect if it is equal to the sum of its divisors (except itself). Examples are 6=1+2+3, 28, 496, 8128, ... Def: The n th Mersenne Number, M

116. A Few Results And Open Problems Regarding Incompressible Fluids File Format PDF/Adobe Acrobat Quick View http://www.csam.montclair.edu/~yecko/fluids/constant.pdf

117. Catalan's Conjecture -- From Wolfram MathWorld Features an explanation of the equation and offers bibliographic references. http://mathworld.wolfram.com/CatalansConjecture.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Pegg Catalan's Conjecture and ) are the only consecutive powers (excluding and 1). In other words, is the only nontrivial solution to Catalan's Diophantine problem The special case and is the case of a Mordell curve Interestingly, more than 500 years before Catalan formulated his conjecture, Levi ben Gerson (1288-1344) had already noted that the only powers of 2 and 3 that apparently differed by 1 were and (Peterson 2000). three consecutive powers exist (Ribenboim 1996), and it was also known that 8 and 9 are the only consecutive cubic and square numbers Tijdeman (1976) showed that there can be only a finite number of exceptions should the conjecture not hold. More recent progress showed the problem to be decidable in a finite (but more than astronomical) number of steps and that, in particular, if and are powers , then (Guy 1994, p. 155). In 1999, M. Mignotte showed that if a nontrivial solution exists, then (Peterson 2000). It had also been known that if additional solutions to the equation exist

118. Open Problems From Dagstuhl Seminar 09511 Parameterized File Format PDF/Adobe Acrobat Quick View http://drops.dagstuhl.de/opus/volltexte/2010/2499/pdf/09511.SWM.Paper.2499.pdf

119. The Prime Glossary: Catalan's Problem Entry in the Prime Glossary with description, brief history and references. http://primes.utm.edu/glossary/page.php?sort=CatalansProblem

120. Computability, Reverse Mathematics And Combinatorics Open File Format PDF/Adobe Acrobat Quick View http://robson.birs.ca/~08w5019/problems.pdf

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