21. Unsolved Problems (Part 2) unsolved problems (Part 2). You can contact Stephen C. Locke at LockeS@fau.edu. Several people have asked me about unsolved problems. http://www.math.fau.edu/locke/Unsolv2.htm

Unsolved Problems (Part 2) You can contact Stephen C. Locke at LockeS@fau.edu 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 . I hope it will not annoy the authors of that text if I will reproduce that list here, and perhaps (eventually) add to it. Problems number above 50 are from other sources. 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 . Also, I'm not giving you all of the references in Bondy and Murty . You should get yourself a copy of that book. Problems 1-25 Problems 57-61 26. Prove that every n -chromatic graph G has r(G,G) >= r(n,n) Message from Stephan Brandt Disproved by Faudree and McKay [ J. Comb. Math. Comb. Comp. 13 Counterexample: Wheel with 5 spokes has Ramsey number 17 < r(4,4).

22. [gr-qc/0107090] Current Trends In Mathematical Cosmology A review of current unsolved problems in mathematical cosmology http://arxiv.org/abs/gr-qc/0107090

General Relativity and Quantum Cosmology, abstract gr-qc/0107090 From: Spiros Cotsakis [ view email ] Date ( ): Fri, 27 Jul 2001 17:32:02 GMT (13kb) Date (revised v2): Sat, 28 Jul 2001 14:53:55 GMT (13kb) Current Trends in Mathematical Cosmology Authors: Spiros Cotsakis Comments: 16 pages, LaTeX. To appear in the Proceedings of the 2nd Hellenic Cosmology Workshop, (Kluwer, 2001) We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current, seemingly unrelated trends of this subject. We discuss problems associated with the definition and asymptotic structure of the notion of cosmological solution and also problems related to the qualification of approximations and to the ranges of validity of given cosmologies. Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted);

23. Open Problems On Perfect Graphs This page has moved to http//www.cs.concordia.ca/~chvatal/per. .. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

24. Konrad Lorenz Institute For Ethology An Institute of the Austrian Academy of Sciences that investigates the major unsolved problems in behavioral and evolutionary ecology. http://www.oeaw.ac.at/klivv

A scientific institute devoted to the study of animal behavior, ecology, and evolutionary biology. We are located in the outskirts of Vienna, Austria, in the beautiful Vienna Woods. Konrad Lorenz Institute for Ethology an Institute of the Austrian Academy of Sciences News September'04 Chemical pollutants cause pathological effects on the behavior A recent paper by Sarah Zala and Dustin Penn, published in Animal Behaviour, reviews decades of work on how chemical pollutants, known as "endocrine disruptors," also cause pathological effects on the behavior of a wide variety of species. July 04 Public Information: From Nosy Neighbors to Cultural Evolution Richard Wagner has co-authored a review article in Science. More News and Press Releases Jobs Post-doctoral Scientist KLIVV is an Institute of the Austrian Academy of Sciences KLIVV - Savoyenstrasse 1a - 1160 Vienna - Austria Phone: (+43) (1) 515 81-2700, Fax: -2800

25. MathPuzzle.com Mazes Number Fun Parity Partridge Puzzle Path Problems Pentagon Tiling Can you find an improvement, or solve one of the unsolved cases? http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

26. Unsolved Problems In OR unsolved problems in OR. This page contains a list of open problems that I find intriguing. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

27. Hurricane Dennis Crisis Counseling Available unsolved problems caused by disasters can wear people down emotionally, said State Coordinating Officer Craig Fugate of the State Emergency http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

28. Clay Public Lecture: Are The Unsolved Problems In Mathematics — Barry Mazur CMI organizes public lectures on mathematics twice each year. This lecture by Barry Mazur fill focus on one of the great unsolved problems the Riemann http://www.claymath.org/public_lectures/mazur.php

Clay Mathematics Institute Dedicated to increasing and disseminating mathematical knowledge HOME ABOUT CMI PROGRAMS AWARDS ... PUBLICATIONS Are there unsolved problems about numbers? A public lecture Barry Mazur, Harvard University May 3, 2005 at 7pm Stata Center, MIT 32 Vassar Street, Cambridge Are there unsolved problems about numbers? The answer is yes, and we will discuss one of the most famous of these open problems, the Riemann hypothesis, which is about the hidden structure of the prime numbers 2, 3, 5, 7, ... . Primes are the "building blocks" of all numbers, and are key actors in a subject, central to mathematics, initiated two millennia ago by the Greeks. $1 million Millennium Prize Problems Prof. Mazur's lecture will be accessible to the general interested public. No calculus is required. Photos of Riemann's 1859 manuscript courtesy of of the . Go here for the full facsimilie. Clay Public Lectures Upcoming Lectures Escher and the Droste effect, Clay Public Lecture by Hendrik Lenstra of Leiden University. Harvard, October 25, 2005 Past Lectures: Are there unsolved problems about numbers?

29. Open Problems On Perfect Graphs unsolved problems on perfect graphs. http://www.cs.concordia.ca/~chvatal/perfect/problems.html

PERFECT PROBLEMS Created on 22 August, 2000 Last updated on 28 November, 2004 In May 2002, the Strong Perfect Graph Conjecture became the Strong Perfect Graph Theorem Details are here. As a part of the 1992 1993 Special Year on Combinatorial Optimization at DIMACS ftp://dimacs.rutgers.edu/pub/perfect/problems.tex If you have information on progress towards solving these problems or complaints in case I did not give credit where credit was due or suggestions for problems to add, please, send them to me Related pages: Problems from the AIM Workshop on Perfect Graphs (compiled by Maria Chudnovsky) A bibliography on perfect graphs Home pages of people interested in perfect graphs This collection is written for people with at least a basic knowledge of perfect graphs. Uninformed neophytes may look up the missing definitions on the web in Alexander Schrijver's lecture notes or in Jerry Spinrad's draft of a book on efficient graph representations etc. or in Eric Weisstein's World of Mathematics . Books on perfect graphs include M. C. Golumbic

30. Ultimate Boot CD - Unsolved Problems unsolved problems. The following problems have been reported from users and have no workaround/solution yet. If you have any answers or suggestions, http://www.ultimatebootcd.com/problems.html

Mirror Sites Mirror Site #1 Mirror Site #2 Mirror Site #3 Mirror Site #4 ... Mirror Site #6 Table of Content Overview News Download UBCD Download CDR Labels ... Known Bugs Unsolved Problems Rejected Software You Can Help! How it all started Acknowledgements ... Useful Links Unsolved Problems The following problems have been reported from users and have no workaround/solution yet. If you have any answers or suggestions, be sure to post them to the document.write(''); document.write('ubcd-support'); document.write(''); mailing list. In addition, the ISOLINUX website has some information on hardware that does not play well. Be sure to check it out too! Version 3.2 Daniel Nelson: Victor: Could those having this problem trying launching Segate DiscWizard with diskemu or bcdw, and let me know whether it works? Version 2.4 Pellegrino Sylvain: I was unable to boot on IBM ThinkCenter 8183, NetVista old and new generation but the same CD works with other computers, as if the BIOS can't find the CD boot sector. I tried many things: a CD with just the original cdshell (works), then with just the /boot folder (works), so I tried to add other folders. The CD didn't boot when I add /docs. Why? Dave Higham: Great CD, but I have a problem with part of it. When I try to run the diagnostic section for Western Digital hard drives, I get a message saying "Panic: MCB chain corrupted, system halted". This only happens with Western Digital hard drives. Am I doing some thing wrong?

31. MathPages Wanted List Elementary unsolved problems in mathematics, listed at the MathPages archive. http://mathpages.com/home/mwlist.htm

MathPages Wanted List The twenty-five mathematical problems and questions listed below were first posted on the internet in 1995. Since that time, Problems 5, 7, 8, and 22 have been solved completely, and part of Question 12 has been answered. The other problems remain unsolved. The links in this list point to articles on the MathPages web site containing more background on each problem, and partial or related results. (1) If each "1" in the binary representation of the integer x signifies a point in the corresponding position on a linear lattice, and if x' denotes the binary digit reversal of x, prove or disprove that the equality xx' = yy' implies that x and y have the same multi-set of point-to point distances. Ref: Generating Functions for Point Set Distances Isospectral Point Sets in Higher Dimensions (2) Find an elementary proof that x^2 + y^2 and x^2 + 103y^2 cannot both be squares for non-zero integers x,y. Ref: Concordant Forms (3) Prove (or disprove) that the only solutions of ab = c (mod a+b) ac = b (mod a+c) bc = a (mod b+c) in positive coprime integers are (1,1,1) and (5,7,11). Ref: A Knot of Congruences Limit Cycles of xy (mod x+y) More Results on the Form xy (mod x+y) Permutation Loops ... String Algebra (5) In how many distinct ways can the integers through 15 be arranged in a 4x4 array such that the bitwise OR over each row, column, and diagonal is 15, and the bitwise AND over each row, column, and diagonal is 0? Ref:

32. Unsolved Problems In Physics - Wikipedia, The Free Encyclopedia This is an incomplete list of some of the unsolved problems in physics. Some of these problems are theoretical, meaning that existing theories seem http://en.wikipedia.org/wiki/Unsolved_problems_in_physics

Unsolved problems in physics From Wikipedia, the free encyclopedia. This is an incomplete list of some of the unsolved problems in physics . Some of these problems are theoretical , meaning that existing theories seem incapable of explaining some observed phenomenon or experimental result. Others are experimental , meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail. Accretion disc jets: Why do the accretion discs surrounding certain astronomical objects, such as the nuclei of active galaxies , emit relativistic jets along their polar axes? Accelerating universe : Why is the expansion of the universe accelerating, as we have observed? What is the nature of the dark energy driving this acceleration? If it is due to a cosmological constant , why is the constant so small, yet non-zero? Why isn't it huge, as predicted by most quantum field theories , or zero for some yet unknown symmetry reason? What is the ultimate fate of the universe Amorphous solids : What is the nature of the transition between a fluid or regular solid and a glassy phase ? What are the physical processes giving rise to the general properties of glasses? Arrow of time : Why did the universe have such low entropy in the past, resulting in the distinction between

33. List Of Unsolved Problems - Wikipedia, The Free Encyclopedia This is a list of lists of unsolved problems in various subjects. unsolved problems in biology unsolved problems in chemistry unsolved problems in http://en.wikipedia.org/wiki/List_of_unsolved_problems

List of unsolved problems From Wikipedia, the free encyclopedia. This is a list of lists of unsolved problems in various subjects: Unsolved problems in biology Unsolved problems in chemistry Unsolved problems in cognitive science Unsolved problems in computer science ... Unsolved problems in physics (incl. astrophysics) Unsolved problems in religion Unsolved problems in software engineering edit See also Open problem Encyclopedia of World Problems and Human Potential edit External links New York Times article on leading unsolved questions in science Retrieved from " http://en.wikipedia.org/wiki/List_of_unsolved_problems Categories Unsolved problems Culture lists 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 In other languages Espa±ol Portuguªs This page was last modified 15:23, 26 August 2005. All text is available under the terms of the GNU Free Documentation License (see for details).

34. Unsolved Problems Some Simple unsolved problems. One of the things that turned me on to math were some simple sounding but unsolved problems that were easy for a high school http://www.math.utah.edu/~pa/math/conjectures.html

Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah Some Simple Unsolved Problems One of the things that turned me on to math were some simple sounding but unsolved problems that were easy for a high school student to understand. This page lists some of them. Prime Number Problems To understand them you need to understand the concept of a prime number A prime number is a natural number greater than 1 that can be divided evenly only by 1 and itself. Thus the first few prime numbers are You can see a longer list of prime numbers if you like. The Goldbach Conjecture. Named after the number theorist Christian Goldbach (1690-1764). The problem: is it possible to write every even number greater than 2 as the sum of two primes? The conjecture says "yes", but nobody knows. You can explore the Goldbach conjecture interactively with the Prime Machine applet.

35. Full Text Online Of Blondel, V.D. And Megretski, A., Eds.: Unsolved Problems In Table of Contents for unsolved problems in Mathematical Systems and Control Theory by Blondel, VD and Megretski, A., eds., published by Princeton University http://www.pupress.princeton.edu/math/blondel/

SEARCH: Keywords Author Title More Options Power Search Search Hints SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Unsolved Problems in Mathematical Systems and Control Theory Edited by Vincent D. Blondel and Alexandre Megretski Book Description Endorsements Table of Contents To Order ... Class Use and other Permissions . For more information, send e-mail to permissions@pupress.princeton.edu Full text online (PDF format): Entire book as one file (1.4 MB) (Separate files for each section follow below) Frontmatter Preface xiii Associate Editors xv Website xvii PART 1. LINEAR SYSTEMS Problem 1.1. Stability and composition of transfer functions Problem 1.2. The realization problem for Herglotz-Nevanlinna functions Seppo Hassi, Henk de Snoo, Eduard Tsekanovskii Problem 1.3. Does any analytic contractive operator function on the polydisk have a dissipative scattering nD realization? Dmitry S. Kalyuzhniy-Verbovetzky Problem 1.4. Partial disturbance decoupling with stability Problem 1.5. Is Monopoli's model reference adaptive controller correct?

36. Blondel, VD And Megretski, A., Eds. Unsolved Problems In of the book unsolved problems in Mathematical Systems and Control Theory by Blondel, VD and Megretski, A., eds., published by Princeton...... http://www.pupress.princeton.edu/titles/7790.html

37. Unsolved Problems In Biology - Wikibooks 4th International Conference on unsolved problems of Noise4th International Conference on unsolved problems of Noise and Fluctuations in Physics, Biology High Technology. Gallipoli (Lecce), Conference Centre http://en.wikibooks.org/wiki/Unsolved_problems_in_biology

Unsolved problems in biology From Wikibooks This biology textbook originated in Wikipedia with the article Unsolved problems in biology (started 08:56, 27 Jun 2003 . . Ike9898). On January 8, 2005 that Wikipedia page looked like this archive page Contents The endless frontier. Some unsolved problems in biology include: Chapters External links ... edit The endless frontier. No matter how much we know about living organisms, there is always more to learn. This book is dedicated to the idea that asking questions is important. We welcome contributions of new questions about biology on the Grist page. Answers to all questions about biology can start with what is already known and then move on to what remains to be discovered, what remains unsolved. The goal of this textbook is to serve as an unorthodox introduction to biology. Each chapter starts with a question, maybe the sort of question a small child would ask, and explores the implications of that question out to the limits of the current state of research and then moves on into speculation about what might be discovered in the future. What is life?

38. Unsolved Problems In Number Theory (Guy)-Springer Number Theory Book Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of http://www.springeronline.com/sgw/cda/frontpage/0,11855,5-10048-22-34511272-0,00

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39. Prime Numbers Some unsolved problems. The Twin Primes Conjecture that there are infinitely many pairs of primes only 2 apart. Goldbach s Conjecture (made in a letter by C http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html

Prime numbers Number theory index History Topics Index Version for printing Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. The mathematicians of Pythagoras 's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers. A perfect number is one whose proper divisors sum to the number itself. e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors 1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28. A pair of amicable numbers is a pair like 220 and 284 such that the proper divisors of one number sum to the other and vice versa. You can see more about these numbers in the History topics article Perfect numbers By the time Euclid 's Elements appeared in about 300 BC, several important results about primes had been proved. In Book IX of the Elements Euclid proves that there are infinitely many prime numbers. This is one of the first proofs known which uses the method of contradiction to establish a result. Euclid also gives a proof of the Fundamental Theorem of Arithmetic: Every integer can be written as a product of primes in an essentially unique way.

40. Dantzig_George To make a long story short, the problems on the blackboard which I had they were homework were in fact two famous unsolved problems in statistics. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dantzig_George.html

George Dantzig Born: 8 Nov 1914 in Portland, Oregon, USA Click the picture above to see two larger pictures Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing George Dantzig 's parents were Tobias Dantzig and Anja Ourisson. Tobias was born in Russia, but went to France where he studied mathematics in Paris being taught there by . At this time Tobias met Anja who was at the Sorbonne at this time also studying mathematics. They married and emigrated to the United States, settling in Oregon. Tobias believed that his strong Russian accent would prevent him from obtaining jobs other than as a labourer, and at first his jobs included that of lumberjack, road builder and painter. It was into this very poor family that George was born. Tobias and Anja chose names for their children hoping that these would influence their future careers. George was named "George Bernard" after George Bernard Shaw since his parents hoped their first child would become a writer. Similarly George's younger brother was named Henry after , and he did indeed become a mathematician. Tobias was fortunate to gain the chance of reading for a Ph.D. in mathematics at the University of Indiana, while Anja obtained a Master's degree in French becoming a linguist at the Library of Congress in Washington D.C.

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