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81.
82.
In 1934, Romanoff proved that there are a positive proportion natural numbers which can be expressed as the sum of a prime and a power of 2. In this paper, a quantitative version of this theorem is given. We show that the proportion is larger than 0.0868 and for a positive proportion of odd integers the number of such representations is between 1 and 16. 相似文献
83.
Hirofumi Tsumura 《Journal of Number Theory》2004,106(1):155-168
In this paper, we define the multiple Euler numbers and consider some multiple harmonic series of Mordell-Tornheim's type, which is a partial sum of the Mordell-Tornheim zeta series defined by Matsumoto. Indeed, we prove a certain reducibility of these series as well as the multiple zeta values. 相似文献
84.
Huazhong Tang Tao Tang Kun Xu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(3):365-382
In this paper, the Kinetic Flux Vector Splitting (KFVS)
scheme is extended to solving the shallow water equations with
source terms. To develop a well-balanced scheme between the source
term and the flow convection, the source term effect is accounted
in the flux evaluation across cell interfaces. This leads to a
modified gas-kinetic scheme with particular application to the
shallow water equations with bottom topography. Numerical
experiments show better resolution of the unsteady solution than
conventional finite difference method and KFVS method with little
additional cost. Moreover, some positivity properties of the
gas-kinetic scheme is established. 相似文献
85.
86.
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
87.
Toshiyuki Sugawa 《Monatshefte für Mathematik》2003,139(1):61-68
The inner radius of univalence of a domain D with Poincaré density ρ
D
is the possible largest number σ such that the condition ∥ S
f
∥
D
= sup
w∈ D
ρ
D
(w)
−2∥ S
f
(z) ∥ ≤ σ implies univalence of f for a nonconstant meromorphic function f on D, where S
f
is the Schwarzian derivative of f. In this note, we give a lower bound of the inner radius of univalence for strongly starlike domains of order α in terms
of the order α.
The author was partially supported by the Ministry of Education, Grant-in-Aid for Encouragement of Young Scientists, 11740088.
A part of this work was carried out during his visit to the University of Helsinki under the exchange programme of scientists
between the Academy of Finland and the JSPS.
Received November 26, 2001; in revised form September 24, 2002
Published online May 9, 2003 相似文献
88.
One of the open questions in the geometry of line arrangements is to what extent does the incidence lattice of an arrangement determine its fundamental group. Line arrangements of up to 6 lines were recently classified by K.M. Fan (Michigan Math. J. 44(2) (1997) 283), and it turns out that the incidence lattice of such arrangements determines the projective fundamental group. We use actions on the set of wiring diagrams, introduced in (Garber et al. (J. Knot Theory Ramf.), to classify real arrangements of up to 8 lines. In particular, we show that the incidence lattice of such arrangements determines both the affine and the projective fundamental groups. 相似文献
89.
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
90.
Franc Forstnerič 《Mathematische Annalen》1992,292(1):163-180