Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out on the citizen supercomputer Ibercivis. Upon dilution, the pure model’s first-order transition becomes of the second order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their random field Ising model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states.

On a conjecture of Lapidus and van Frankenhuysen

In this paper it is shown that a conjecture of Lapidus and van Frankenhuysen of 2003 on the existence of a vertical line such that the density of the complex dimensions of nonlattice fractal strings with M scaling ratios off this line vanishes in the limit as M→∞, fails on the class of nonlattice self-similar fractal strings.

Three new Mersenne primes, and a conjecture /

Bibliography: leaf 6.

A feasibility conjecture related to the Hirsch conjecture.

Photocopy. [Washington?] Clearinghouse for Federal Scientific and Technical Information of the U. S. Dept. of Commerce [1966?]

Breadth-first search and the Andrews-Curtis conjecture

Andrews and Curtis conjectured in 1965 that every balanced presentation of the trivial group can be transformed into a standard presentation by a finite sequence of elementary transformations. Recent computational work by Miasnikov and Myasnikov on this problem has been based on genetic algorithms. We show that a computational attack based on a breadth-first search of the tree of equivalent presentations is also viable, and seems to outperform that based on genetic algorithms. It allows us to extract shorter proofs (in some cases, provably shortest) and to consider the length thirteen case for two generators. We prove that, up to equivalence, there is a unique minimum potential counterexample.

The Fa,b,c conjecture, I

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.

The Fa,b,c conjecture is true, II

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and subsequently two parts of the conjecture were proved. The conjecture completely determines all finite members of the family. Here we complete the proof of the conjecture by giving proofs for the remaining three parts. (c) 2006 Elsevier Inc. All rights reserved.

On some Results Related to Köthe's Conjecture

The Köthe conjecture states that if a ring R has no nonzero nil ideals then R has no nonzero nil one-sided ideals. Although for more than 70 years significant progress has been made, it is still open in general. In this paper we survey some results related to the Köthe conjecture as well as some equivalent problems.

Generalization of a Conjecture in the Geometry of Polynomials

In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros of the polynomials.

Toward Clemens' Conjecture in Degrees between 10 and 24

1 Supported in part by the Norwegian Research Council for Science and the Humanities. It is a pleasure for this author to thank the Department of Mathematics of the University of Sofia for organizing the remarkable conference in Zlatograd during the period August 28-September 2, 1995. It is also a pleasure to thank the M.I.T. Department of Mathematics for its hospitality from January 1 to July 31, 1993, when this work was started. 2Supported in part by NSF grant 9400918-DMS.

Hilbert-Smith Conjecture for K - Quasiconformal Groups

MSC 2010: 30C60

Remarks on the Nagata Conjecture

2000 Mathematics Subject Classification: 14C20, 14E25, 14J26.

Smale's Conjecture on Mean Values of Polynomials and Electrostatics

2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.

A Note About the Nowicki Conjecture on Weitzenböck Derivations

2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.