Zobrazeno 1 - 10
of 181
pro vyhledávání: '"Lagarias, J. C."'
Autor:
Lagarias, J. C., Soundararajan, K.
Publikováno v:
Proc. London Math. Soc. (3) 104 (2012), no. 4, 770--798
This paper studies integer solutions to the Diophantine equation A+B=C in which none of A, B, C have a large prime factor. We set H(A, B,C) = max(|A|, |B|, |C|), and consider primitive solutions (gcd}(A, B, C)=1) having no prime factor p larger than
Externí odkaz:
http://arxiv.org/abs/1102.4911
Autor:
Lagarias, J. C.
Binary quadratic Diophantine equations are of interest from the viewpoint of computational complexity theory. They contain as special cases many examples of natural problems apparantly occupying intermediate stages in the P-NP hierarchy, i.e. problem
Externí odkaz:
http://arxiv.org/abs/math/0611209
Autor:
Lagarias, J. C., Sloane, N. J. A.
Publikováno v:
Experimental Math. 13 (2004), 113--128.
We study the ``approximate squaring'' map f(x) := x ceiling(x) and its behavior when iterated. We conjecture that if f is repeatedly applied to a rational number r = l/d > 1 then eventually an integer will be reached. We prove this when d=2, and prov
Externí odkaz:
http://arxiv.org/abs/math/0309389
Publikováno v:
Experimental Math. Vol. 11, No. 3 (2002), 437-446.
The EKG or electrocardiogram sequence is defined by a(1) = 1, a(2) = 2 and, for n >= 3, a(n) is the smallest natural number not already in the sequence with the property that gcd {a(n-1), a(n)} > 1. In spite of its erratic local behavior, which when
Externí odkaz:
http://arxiv.org/abs/math/0204011
Autor:
Lagarias, J. C., Pleasants, P. A. B.
Publikováno v:
Canad. Math. Bull. Vol 48 (4), 2002 pp. 634-652
This paper characterizes when a Delone set X is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the hetereogeneity of their distribution. Let N(T) count the number of translation-inequivalent patches
Externí odkaz:
http://arxiv.org/abs/math/0105088
Publikováno v:
Discrete and Computational Geometry, 35: 37-72(2006)
This paper gives $n$-dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space $\sM_{\dd}^n$ of all $n$-dimensional oriented Descartes configurations parametrized in a coordinate system, ACC-coordinates, as those
Externí odkaz:
http://arxiv.org/abs/math/0010324
Publikováno v:
Discrete and Computational Geometry, 35: 1-36(2006)
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain. It observed there exist i
Externí odkaz:
http://arxiv.org/abs/math/0010302
Publikováno v:
Discrete and Computational Geometry, 34: 547-585(2005)
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles
Externí odkaz:
http://arxiv.org/abs/math/0010298
Publikováno v:
J. Number Theory 100 (2003), 1--45
Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. It is possible for every circle in such a packing to have integer radius of curvature, and we call such a packing an
Externí odkaz:
http://arxiv.org/abs/math/0009113
Publikováno v:
Mathematics of Operations Research, 1999 May 01. 24(2), 362-382.
Externí odkaz:
https://www.jstor.org/stable/3690489
