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51.
In this paper we obtain some metrics results about large partial quotients in the continued fraction expansion. 相似文献
52.
R. Weidmann 《Archiv der Mathematik》2003,81(5):589-595
We describe a family of graph manifolds that have 2-generated
fundamental group but do not admit a Heegaard splitting of genus 2. They are
closely related to the examples provided by Boileau and Zieschang if these are
considered as (non-proper) graph manifolds.Received: 14 August 2002 相似文献
53.
Summary. We consider the spline collocation method for a class of parabolic pseudodifferential operators. We show optimal order convergence
results in a large scale of anisotropic Sobolev spaces. The results cover the classical boundary integral equations for the
heat equation in the general case where the spatial domain has a smooth boundary in the plane. Our proof is based on a localization
technique for which we use our recent results proved for parabolic pseudodifferential operators. For the localization we need
also some special spline approximation results in anisotropic Sobolev spaces.
Received May 17, 2001 / Revised version received February 19, 2002 / Published online April 17, 2002 相似文献
54.
Yong-Gao Chen 《Journal of Number Theory》2003,98(2):310-319
In this paper we prove that if (r,12)?3, then the set of positive odd integers k such that kr−2n has at least two distinct prime factors for all positive integers n contains an infinite arithmetic progression. The same result corresponding to kr2n+1 is also true. 相似文献
55.
We studied the low speed fracture regime (10−4-10−9 m s−1) in different glassy materials (soda-lime glass, glass ceramics) with variable but controlled length scale of heterogeneity. The chosen mechanical system enabled us to work in pure mode I (tensile) and at a fixed load on double cleavage drilled compression specimen. The internal residual stresses of studied samples were carefully relaxed by appropriate thermal treatment. By means of optical and atomic force microscopy techniques fracture surfaces have been examined. We have shown for the first time that the crack front line underwent an out-of-plane oscillating behavior as a result of a reproducible sequence of instabilities. The wavelength of such a phenomenon is in the micrometer range and its amplitude in the nanometer range. These features were observed for different glassy materials providing that a typical length scale characterizing internal heterogeneities was lower than a threshold limit estimated to few nanometers. This effect is the first clear experimental evidence of crack path instabilities in the low speed regime in a uniaxial loading experiment. This phenomenon has been interpreted by referring to the stability criterion for a straight crack propagation as presented by Adda-Bedia et al. [Phys. Rev. Lett. 76 (1996) 1497]. 相似文献
56.
Parameters of Gaussian multivariate models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical when the sample size is very large, as, for example, in the case of massive georeferenced data sets. In this paper, we study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, designed to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first-order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations. 相似文献
57.
Yasufumi Hashimoto 《Journal of Number Theory》2007,122(2):324-335
In [P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982) 229-247], it was proved that the Selberg zeta function for SL2(Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms. The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg zeta functions for congruence subgroups of SL2(Z). As applications, we study the Brun-Titchmarsh type prime geodesic theorem and the asymptotic formula of the sum of the class number. 相似文献
58.
Clemens Amstler 《Monatshefte für Mathematik》1995,119(3):177-186
In this paper we establish an inequality of Koksma-Hlawka-type for compact groups. We first define a discrepancy for compact groups based on discrepancy operators introduced by W. Fleischer and show the relation to the classicalL
2-discrepancy. Then we prove the inequality for functions in a weightedL
2-space. 相似文献
59.
Yuk-Kam Lau 《Archiv der Mathematik》2003,81(2):169-174
We establish a mean square estimate on the weight aspect for
symmetric square L-functions at every point
on the critical line.
Received: 15 February 2002 相似文献
60.
Takashi Kishimoto 《Journal of Pure and Applied Algebra》2007,208(1):189-204
Let X?(T,D) be a compactification of an affine 3-fold X into a smooth projective 3-fold T such that the (reduced) boundary divisor D is SNC. In this paper, as an affine counterpart to the work due to S. Mori (cf. [S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982) 133-176]), we shall classify (K+D)-negative extremal rays on T. In particular, if such an extremal ray R=R+[C] intersects K non-negatively, we shall describe the log flips and divisorial contractions appearing explicitly. 相似文献