21. Open Problems On Perfect Graphs unsolved problems on perfect graphs. http://www.cs.rutgers.edu/~chvatal/perfect/problems.html

PERFECT PROBLEMS Created on 22 August, 2000 Last updated on 11 February, 2003 The Strong Perfect Graph Conjecture has become 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

22. Unsolved Problems unsolved problems 7. The Geometry Junkyard unsolved problems http//www.ics.uci.edu/~eppstein/junkyard/open.htmlA list of unsolved problems in geometry. http://www.hypography.com/topics/unsolvedproblems.cfm

document.write('<');document.write('! '); home hypographies links quizzes ... about Tuesday, March 18, 2003 Not logged in Unsolved Problems In an age where scientific discovery is everyday news, there are in fact problems which have never been solved. Created by Tormod Guldvog Last updated September 14 2001 Viewed 5752 times. There are actually so many unsolved problems in all areas of science, that the task of creating a complete list of them would in fact be another unsolved problem. Many of these problems are well documented on the Internet. This hypography features web directories which have collected problems in areas like mathematics, astrophysics, physics and cosmology. Relevant keywords problems, conjectures, theories, unsolved Find similar content Take a quiz! Number Theory This quiz tests your knowledge about some famous numbers and theorists. Theories and People This quiz will test your knowledge about famous theories - and how much you actually know about the people behind them. More quizzes Open Questions and Unsolved Mysteries in Particle Physics and Cosmology http://www.thebigview.com/spacetime/questions.html This is a presentation of some of the fundamental problems in cosmology and related fields.

23. Unsolved Problem Of The Week Archive A list of unsolved problems published by MathPro Press during 1995. http://cage.rug.ac.be/~hvernaev/problems/archive.html

Unsolved Problem of the Week Archive Welcome to the archive for the Unsolved Math Problem of the Week Each week, for your edification, we publish a well-known unsolved mathematics problem. These postings are intended to inform you of some of the difficult, yet interesting, problems that mathematicians are investigating. We give a reference so that you can get more information about the topic. These problems can be understood by the average person. Nevertheless, we do not suggest that you tackle these problems, since mathematicians have been unsuccessfully working on these problems for many years. Should you wish to discuss aspects of these problems with others, one of the newsgroups, such as sci.math , might be the appropriate forum. 3-Sep-1995 Problem 36 : Primes of the form n^n+1 27-Aug-1995 Problem 35 : Must one of n points lie on n/3 lines? 20-Aug-1995 Problem 34 : Squares with Two Different Decimal Digits 13-Aug-1995 Problem 33 : Unit Triangles in a Given Area 6-Aug-1995 Problem 32 : Can the Cube of a Sum Equal their Product 30-Jul-1995 Problem 31 : Different Number of Distances 23-Jul-1995 Problem 30 : Sum of Four Cubes 16-Jul-1995 Problem 29 : Fitting One Triangle Inside Another 9-Jul-1995 Problem 28 : Expressing 3 as the Sum of Three Cubes 2-Jul-1995 Problem 27 : Factorial that are one less than a Square 25-Jun-1995 Problem 26 : Inscribing a Square in a Curve 18-Jun-1995 Problem 25 : The Collatz Conjecture 11-Jun-1995 Problem 24 : Primes Between Consecutive Squares 4-Jun-1995 Problem 23 : Thirteen Points on a Sphere 28-May-1995

24. Overview Of "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

Overview of "Mathematician's Secret Room" Challenges to the Unsolved Problems in Number Theory (September 07, 2002) (Chapter 2, 4, 9, 10, Appendix 1, 4 are translated in English. Other chapters are still written only in Japanese, sorry.) News (June 04, 2001) : In Chapter 7, new results by Tomas Oliveira and Silva. Their web site is here ( 3x+1 conjecture verification results Chapter 0 : Opening Why I had an interest in Number Theory. Chapter 1 : 4/n = 1/a + 1/b + 1/c whether do there exist the natural number solutions of above equation, or not. I found the construction method of the parameterize solution from arbitrary solutions. That is, Theorem : Let A, B, C in N be a solution of following Diophantine equation, m/P=1/A+1/B+1/C, B=kP (m=4, 5, 6, 7, P=prime, k in N (i.e. 2 of A, B, C can be divisable by P) Define a, b, c, d, e, f, c', d' as, c := B/P a := mk-1 b := a-(P mod a) n := (P+b)/a d := cn-A e := gcd(c,d) c':= c/e d':= d/e f := ke/(bc-ad) Then, m/(an-b)=1/e(c'n-d')+1/k(an-b)+1/f(an-b)(c'n-d') and P = an-b A = e(c'n-d') B = k(an-b) C = f(an-b)(c'n-d) If only 1 of A, B, C can be divisable by P, then there is another way to construct the parameterize solution heuristically.

25. 2nd International Conference On: Unsolved Problems Of Noise And Fluctuations (UP 2nd International Conference on unsolved problems of Noise (UPoN '99). and fluctuationsin physics, high technology, information technology, biology . http://www.eleceng.adelaide.edu.au/Personal/dabbott/UPoN/uponhome.html

2nd International Conference on: Unsolved Problems of Noise (UPoN '99) and fluctuations in physics, high technology, information technology, biology.... 11-15th July 1999 ADELAIDE, AUSTRALIA Conference Director: Derek Abbott Technical Program Director: Laszlo B. Kiss Keynote Speaker SPONSORED BY: Inst. of Electrical and Electronic Eng. (IEEE) - USA Electron Devices Society (EDS) - USA US Office of Naval Research Field Office Asia (ONRIFO Asia) US Air Force Office of Scientific Research - Asian Office of Aerospace Research and Development (AFOSR-AOARD) ... Centre for Biomedical Engineering (CBME) - Proceedings published by: American Institute of Physics Welcome to UPoN '99 UPoN '99 Photo gallery Feedback: what people thought of UPoN'99 ... About The Solar System host for UPoN '99 Enquiries to: Dr. Derek Abbott Conference Director UPoN '99 Secretariat EEE Dept University of Adelaide SA 5005, AUSTRALIA. dabbott@eleceng.adelaide.edu.au Ph: +618-8303-5748 Fx: +618-8303-4360 Page hits before May 1999: 2348 Page hits since May 1999: Updated: 3rd July 1999

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

MathPages Wanted List The twenty-four mathematical problems and questions listed below have been studied by numerous people since they were first posted on the internet in 1995. In that time, Problems 1, 5, 7, 8, and 22 have been solved completely, and part of Question 12 has been answered. The other eighteen 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) Prove or disprove that there cannot be distinct colinear arrangements of points with the same multi-set of point-to-point distances. (Reflections are not counted as distinct.) Ref: Distinct Point Sets With Same Distances Variations and Comments on Problem 1 Relation to Golomb Rulers Generating Functions for Point Set Distances SOLVED: 4 Apr 97. Dan Hoey forwarded a couple of messages from John Scholes and Torsten Sillke each giving an example of isospectral sets in one dimension. (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:

27. 2nd International Conference On: Unsolved Problems Of Noise (UPoN '99) 2nd International Conference on unsolved problems of Noise (UPoN '99) and fluctuationsin physics, high technology, information technology, biology . http://www.eleceng.adelaide.edu.au/Personal/gpharmer/upon/uponcall.htm

2nd International Conference on: Unsolved Problems of Noise (UPoN '99) and fluctuations in physics, high technology, information technology, biology.... 11-15th July 1999, Adelaide, Australia INTERNATIONAL SCIENTIFIC ADVISORY COMMITTEE (Technical program and review panel) Abbott, D. (Uni. Adelaide, Australia) Bezrukov, S. (NIH, USA) Collins, J.J. (Boston Uni., USA) Danneville F. (Uni. Lille., Fr.) Davis, B.R. (Uni. Adelaide, Australia) Deen, J. (S.F. Uni., Canada) Doering, Ch. (Uni. Michigan, USA) Fuchikami, N. (TMU, Japan) Giordano, N. (Purdue Uni., USA) Hanggi, P. (Uni. Augsburb, Germany) Jones, B.K. (Lancaster Uni., UK) Kiss, L.B. (Uppsala Uni., Sweden) Koch, R. (IBM, NY, USA) Levinshtein, M.E. (Ioffe Ins., Russia) Moss, F. (UMSL, USA) Marchesoni, F. (Uni. Perugia, Italy) McClintock, P.V.E. (Lancaster Uni., UK) Parrondo, J.M.R. (Uni. Complutense, Spain) Reggiani, L. (Uni. Lec., Italy) Shlesinger, M. (ONR, USA) Vandamme, L.K.J. (Uni. Eindhoven, NL) Van Kampen, N.G.

28. Jonathan D. Victor: Unsolved Problems Unsolved mathematical problems. Here are some unsolved mathematical problemswith potential impact for neuroscience. Not all are tightly posed. http://www-users.med.cornell.edu/~jdvicto/jdvunso.html

Unsolved mathematical problems Here are some unsolved mathematical problems with potential impact for neuroscience. Not all are tightly posed. Any feedback , not limited to brilliant ideas, is always appreciated and will be gratefully acknowledged. spike metrics nonlinear dynamics isodipole textures point processes ... Home Page Spike metrics brief background key reference further reading Develop a computationally efficient algorithm for D motif . Maybe this is a well-known problem in dynamic programming algorithms. Develop a computationally efficient algorithm for combinations of D spike , D interval , and D motif . Maybe this is also a well-known problem in dynamic programming algorithms. Progress (8/2002) for combinations of D spike and D interval : Perhaps any optimal path from spike train A to spike train B can be reorganized as an equal-cost path from spike train A to spike train X, then from X to B, in which A to X only uses the transformations of D spike , and X to B only uses the transformations of D interval . Then, find a DP algorithm that finds X. Unfortunately, such reorganizations cannot be guaranteed. This idea makes use of the "algebraic" properties of the transformations. For general inspiration, see the algebraic dynamic programming work of

29. Unsolved Problems next up previous contents Next Does there exist a Up Famous Problemsin Mathematics Previous Which are the. unsolved problems. http://db.uwaterloo.ca/~alopez-o/math-faq/node59.html

Next: Does there exist a Up: Famous Problems in Mathematics Previous: Which are the Unsolved Problems Does there exist a number that is perfect and odd? Collatz Problem Goldbach's conjecture Twin primes conjecture Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

30. Unsolved Problems unsolved problems. Does there exist a number that is perfect and odd? References.unsolved problems in Number Theory. Richard K Guy. Springer, Problem E16. http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node30.html

Next: Mathematical Games Up: Famous Problems in Mathematics Previous: Which are the 23 Unsolved Problems Does there exist a number that is perfect and odd? A given number is perfect if it is equal to the sum of all its proper divisors. This question was first posed by Euclid in ancient Greece. This question is still open. Euler proved that if N is an odd perfect number, then in the prime power decomposition of N , exactly one exponent is congruent to 1 mod 4 and all the other exponents are even. Furthermore, the prime occurring to an odd power must itself be congruent to 1 mod 4. A sketch of the proof appears in Exercise 87, page 203 of Underwood Dudley's Elementary Number Theory. It has been shown that there are no odd perfect numbers Collatz Problem Take any natural number n : = m; repeat n is odd) then n : = 3*n + 1 ; else n : = n/2 until ( n==1 Conjecture 1. For all positive integers m, the program above terminates. The conjecture has been verified for all numbers up to References Unsolved Problems in Number Theory.

31. MATH-abundance See Copying Conditions. TUTORIAL Topics; Solved and unsolved problems. Othersolved and unsolved problems on the net. Exercises in math readiness. http://www.ping.be/~ping1339/

MATH-abundance Main Purpose = MATH TUTORIAL TUTORIAL : Topics; Solved and unsolved problems Math links to links to math links ... Other Tutorials ... Many other math links J.C.'s Math Home Page = http://home.planetinternet.be/~ping1339 Last update: 29 jul 2002 Main Purpose = MATH TUTORIAL The main purpose of this site is to provide the net with a 'upper secondary' MATH TUTORIAL The order of the topics is not random. Most of them appeal on the properties and formulas stated in a preceding topic. You can find headword-links of the tutorial in the MATH-TUTORIAL INDEX Download Since each topic is in 1 file, it is easy to download the file and to study the subject off line. See Copying Conditions TUTORIAL : Topics; Solved and unsolved problems Trigonometry Vectors Lines - orthogonality ; distance (in a plane) Complex numbers ... Miscellaneous Problems about all topics Additionally, I can give a number of math links to math related links to math links... Math links to links to math links ... Other Tutorials Lessons, Tutorials and Lecture Notes

32. Bahcall, J.N. And Ostriker, J.P., Eds.: Unsolved Problems In Astrophysics. of the book unsolved problems in Astrophysics by Bahcall,JN and Ostriker, JP, eds., published by Princeton University Press....... http://pup.princeton.edu/titles/5988.html

PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Winner of the 1999 Henry Norris Russell Lectureship sponsored by the American Astronomical Society Unsolved Problems in Astrophysics Edited by John N. Bahcall and Jeremiah P. Ostriker Shopping Cart Reviews Table of Contents The field of astrophysics is in the midst of a technologically driven renaissance, as fundamental discoveries are being made with astonishing frequency. In the last decade, new detectors in space, on earth, and deep underground have, when coupled with the computational power of modern computers, revolutionized our knowledge and understanding of the astronomical world. This is a great time for a student of any age to become acquainted with the remarkable universe in which we live. This volume is a collection of essays, originally presented orally to a diverse group of students and professionals, which reveal the most fertile areas for future study of astronomy and astrophysics. The emphasis of this work is on the clear description of the current state of our knowledge as a preparation for the future unraveling of the mysteries of the universe that appear today as most fundamental and most amenable to solution. A stellar group of astronomers and astrophysicists describes the directions and styles of work that they think are most likely to lead to progress. Bibliographical notes at the end of each presentation provide guidance for the reader who wishes to go more deeply into a given subject.

33. Old And New Unsolved Problems Old and New unsolved problems Problems in Plane Geometry and NumberTheory. Victor Klee and Stan Wagon. Series Dolciani Mathematical http://www.maa.org/pubs/books/dol11.html

Old and New Unsolved Problems Problems in Plane Geometry and Number Theory Victor Klee and Stan Wagon Series: Dolciani Mathematical Expositions The book will serve well as a point of entry for students who want to know more about a celebrated question, or simply take in the vistas. Choice This is a book that not only belongs in every university, college, and high school library, it very definitely belongs in every public library. Mathematical Reviews. The book is well-written and readable. Each part of each section concludes with a nice selection of exercises. The authors have appended a useful bibliography to each chapter. It is compulsive reading and will fill your mind with problems that will come back to haunt you again and again during idle moments. The Mathematical Intelligencer Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. Part Two contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions.

34. Unsolved Problems In Playing-Card Research unsolved problems in PlayingCard Research. Submissions by Sir Michael Dummett,February 10th, 1999. unsolved problems concerning Tarot and Italian Cards. http://www.pagat.com/ipcs/problist.html

[Note: This page is written in the Unicode character set, and employs characters which may not be properly displayed without an adequate Unicode font. A downgrade to an ISO Latin 1 version of this document may be viewed, with some loss of precision.] Unsolved Problems in Playing-Card Research Submissions by Sir Michael Dummett, February 10th, 1999 Unsolved Problems concerning Tarot and Italian Cards Can definite evidence be found to assign the standard pattern exemplified by early Trappola cards from north of the Alps to Venice, or perhaps to Trent or some other city? Two questions relate to Piedmont. The first is this: Various features of Tarot games played in Piedmont indicate a connection with Bologna: Papi the superiority of the Angel to the World. Can any early connection be found between Bologna and Piedmont, or Tarot players in both places, be discovered to account for this? Can any pre-XVIIIth-century tarocchi What were the origins of the pattern (for regular cards) we know as Venetian, and when did it originate? Papi Is it possible to discover any Sicilian Minchiate cards (known there as Gallerini ), which would have been manufactured up to about 1770? The game differed from Florentine

35. UNSOLVED PROBLEMS OF NOISE IN PHYSICS, BIOLOGY, ELECTRONIC TECHNOLOGY AND INFORM unsolved problems OF NOISE IN PHYSICS, BIOLOGY, ELECTRONICTECHNOLOGY AND INFORMATION TECHNOLOGY. http://www.wspc.com/books/physics/3532.html

Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Keyword Author Concept ISBN Series New Titles Editor's Choice Bestsellers Book Series ... Join Our Mailing List UNSOLVED PROBLEMS OF NOISE IN PHYSICS, BIOLOGY, ELECTRONIC TECHNOLOGY AND INFORMATION TECHNOLOGY Proceedings of the First International Conference (UPoN '96) Szeged, Hungary 3 - 7 September 1996 edited by Ch R Doering (University of Michigan, USA) , L B Kiss (University of Uppsala, Sweden) (Office of Naval Research., USA) Much has been learned about the subject of noise and random fluctuations over the last 170 years (some old milestones: Brownian motion, 1826; Einstein's diffusion theory, 1905; Johnson–Nyquist thermal noise, 1926), but much remains to be known. This volume will be interesting reading for physicists, engineers, mathematicians, biologists and PhD students. The invited papers in the volume survey classical unsolved problems while the regular papers present new problems and paradoxes. Contents: Fundamental Problems of Random Processes: A Brief History of Random Processes (M F Shlesinger) The Fokker–Planck Boundary Layer, Recurrence Times, and Wang and Uhlenbeck's Unsolved Problems (Ch R Doering)

36. Sci.math FAQ: Unsolved Problems sci.math FAQ unsolved problems. The conjecture has been verified up to 7 *10^(11) . References unsolved problems in Number Theory. Richard K Guy. http://www.faqs.org/faqs/sci-math-faq/unsolvedproblems/

sci.math FAQ: Unsolved Problems Newsgroups: sci.math sci.answers news.answers From: alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz) Subject: sci.math DI76LD.Fnt@undergrad.math.uwaterloo.ca alopez-o@neumann.uwaterloo.ca Organization: University of Waterloo Followup-To: sci.math hv@cix.compulink.co.uk (Hugo van der Sanden): To the best of my knowledge, the House of Commons decided to adopt the US definition of billion quite a while ago - around 1970? - since which it has been official government policy. dik@cwi.nl (Dik T. Winter): The interesting thing about all this is that originally the French used billion to indicate 10^9, while much of the remainder of Europe used billion to indicate 10^12. I think the Americans have their usage from the French. And the French switched to common European usage in 1948. gonzo@ing.puc.cl alopez-o@barrow.uwaterloo.ca By Archive-name By Author ... Help Send corrections/additions to the FAQ Maintainer: alopez-o@neumann.uwaterloo.ca Last Update March 05 2003 @ 01:20 AM

37. KLUWER Academic Publishers | Unsolved Problems Of The Milky Way Books » unsolved problems of the Milky Way. unsolved problems ofthe Milky Way. Kluwer Academic Publishers is pleased to make this http://www.wkap.nl/prod/b/0-7923-4039-6

Title Authors Affiliation ISBN ISSN advanced search search tips Books Unsolved Problems of the Milky Way Unsolved Problems of the Milky Way Kluwer Academic Publishers is pleased to make this title available as a special Printing on Demand (PoD) edition. PoD books will be sent to you within 6-9 weeks of receipt of your order. Firm orders only!: returns cannot be accepted as PoD books are only printed on request. Add to cart Proceedings of the 169th Symposium of the International Astronomical Union, held in The Hague, the Netherlands, August 23-29, 1994 edited by Leo Blitz Dept. of Astronomy, University of Maryland, College Park, USA Peter Teuben Dept. of Astronomy, University of Maryland, College Park, USA Book Series: INTERNATIONAL ASTRONOMICAL UNION SYMPOSIA Volume 169 Although the Milky Way is the most studied and best understood galactic system, there are many fundamental questions about our Galaxy that remain unanswered. This book concentrates on those questions which have the widest applicability in all of astrophysics, and for which answers are most likely to be forthcoming in the next few years. Is the Milky Way a barred spiral, and if so, what are its properties? Is the disk of the Milky Way axisymmetric and what does the answer tell us about its dynamical history? Is there a black hole at the center of the Galaxy? How far does the Galaxy extend? How much dark matter is there in the Milky Way system? And more. Contents Kluwer Academic Publishers, Dordrecht

38. KLUWER Academic Publishers | Unsolved Problems Of The Milky Way Books » unsolved problems of the Milky Way. unsolved problems ofthe Milky Way. Add to cart. Proceedings of the 169th Symposium of http://www.wkap.nl/prod/b/0-7923-4040-X

Title Authors Affiliation ISBN ISSN advanced search search tips Books Unsolved Problems of the Milky Way Unsolved Problems of the Milky Way Add to cart Proceedings of the 169th Symposium of the International Astronomical Union, held in The Hague, the Netherlands, August 23-29, 1994 edited by Leo Blitz Dept. of Astronomy, University of Maryland, College Park, USA Peter Teuben Dept. of Astronomy, University of Maryland, College Park, USA Book Series: INTERNATIONAL ASTRONOMICAL UNION SYMPOSIA Volume 169 Although the Milky Way is the most studied and best understood galactic system, there are many fundamental questions about our Galaxy that remain unanswered. This book concentrates on those questions which have the widest applicability in all of astrophysics, and for which answers are most likely to be forthcoming in the next few years. Is the Milky Way a barred spiral, and if so, what are its properties? Is the disk of the Milky Way axisymmetric and what does the answer tell us about its dynamical history? Is there a black hole at the center of the Galaxy? How far does the Galaxy extend? How much dark matter is there in the Milky Way system? And more. Contents Kluwer Academic Publishers, Dordrecht

39. Unsolved Problems Deficient Stars unsolved problems. Since the discovery of RCrB itself,the mechanism that produces fadings has been elusive. Primary http://star.arm.ac.uk/~csj/rcrb_rev/node15.html

Next: Bibliography Up: R Coronae Borealis Stars Previous: Other Hydrogen-Deficient Stars Unsolved Problems Since the discovery of RCrB itself, the mechanism that produces fadings has been elusive. Primary data connecting pulsation phase and the trigger for fadings exists for only two RCBs (V854Cen and RYSgr), and protracted photometry of several RCBs will be necessary to establish any connection firmly. A second difficulty is encountered by the physical conditions necessary for dust to condense above the surface of the star. The frequency and duration of fading events implies a geometry in which the dust clouds form within two stellar radii (2 R ). Under normal conditions, the local temperature would be too high for dust to condense at this distance, and a condensation distance of 20 R would be expected. Recent models treat the chemistry, energy balance and dust nucleation in pulsating star atmospheres in considerable detail. They show that excess cooling can occur during adiabatic expansion after the passage of a shock wave, reducing the local temperature to about 1500K within 1.5-3 R . It remains to be shown that pulsations in all RCB stars provide the necessary conditions for dust nucleation to occur at this distance. The RCB carbon abundance remains an enigma. If it is

40. UNSOLVED PROBLEMS again stars unsolved problems. Since the discovery of RCrB itself,the mechanism that produces fadings has been elusive. Primary http://star.arm.ac.uk/~csj/research/rcb_review/node20.html

Next: Conclusion Up: R CORONAE BOREALIS STARS Previous: Born-again stars UNSOLVED PROBLEMS Since the discovery of RCrB itself, the mechanism that produces fadings has been elusive. Primary data connecting pulsation phase and the trigger for fadings exists for only two RCBs (V854Cen and RYSgr, [ Lawson et al. 1992 Pugach 1977 ]), and protracted photometry of several RCBs will be necessary to establish any connection firmly. A second difficulty is encountered by the physical conditions necessary for dust to condense above the surface of the star. The frequency and duration of fading events implies a geometry in which the dust clouds form within two stellar radii (2 R Clayton et al. 1992 ]). Under normal conditions, the local temperature would be too high for dust to condense at this distance, and a condensation distance of 20 R would be expected ([ Fadeyev 1986 ]). Recent models treat the chemistry, energy balance and dust nucleation in pulsating star atmospheres in considerable detail ([ Woitke et al. 1996a ], 1996b). They show that excess cooling can occur during adiabatic expansion after the passage of a shock wave, reducing the local temperature to about 1500K within 1.5-3 R . It remains to be shown that pulsations in all RCB stars provide the necessary conditions for dust nucleation to occur at this distance. The RCB carbon abundance remains an enigma ([ Asplund et al. 2000

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