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1.
J. Harrison 《Constructive Approximation》1989,5(1):99-115
A continued fractal
is a curve which is associated to a real number[0, 1]. Properties of the continued fraction expansion of appear as geometrical properties ofQ
. It is shown how number theoretic properties of affect topological and geometric properties ofQ
such as existence, continuity, Hausdorff dimension, and embeddedness.Communicated by Michael F. Barnsley. 相似文献
2.
Let be a positive number, and letE
n,n
(x
;[0,1]) denote the error of best uniform rational approximation from
n,n
tox
on the interval [0,1]. We rigorously determined the numbers {E
n,n
(x
;[0,1])}
n
=1/30
for six values of in the interval (0, 1), where these numbers were calculated with a precision of at least 200 significant digits. For each of these six values of , Richardson's extrapolation was applied to the products
to obtain estimates of
相似文献
3.
E. M. Matveev 《Mathematical Notes》1996,59(3):293-297
In this note we show that in the well-known Dobrowolski estimate lnM() (ln lnd/ lnd)3,d , where is a nonzero algebraic number of degreed that is not a root of unity andM() is its Mahler measure, the parameterd can be replaced by the quantity=d/()
1/d, where () is the modulus of the discriminant of. To this end, must satisfy the condition deg
p=deg for any primep.Translated fromMatematicheskie Zametki, Vol. 59, No. 3, pp. 415–420, March, 1996. 相似文献
4.
Ján Jakubík 《Czechoslovak Mathematical Journal》2003,53(3):641-653
In this paper we deal with the (, )-distributivity of an MV-algebra
, where and are nonzero cardinals. It is proved that if
is singular and (, 2)-distributive, then it is (, )-distributive. We show that if
is complete then it can be represented as a direct product of MV-algebras which are homogeneous with respect to higher degrees of distributivity. 相似文献
5.
We study the large-time behavior and rate of convergence to the invariant measures of the processes dX
(t)=b(X)
(t)) dt + (X
(t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/2 , the transition density has a good lower bound and when the process has run for about exp( – )/2, it is very close to the invariant measure. LetL
=(2/2) – U · be a second-order differential operator on d. Under suitable conditions,L
z has the discrete spectrum
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