91,699 research outputs found
Weighted first moments of some special quadratic Dirichlet -functions
In this paper, we obtain asymptotic formulas for weighted first moments of
central values of families of primitive quadratic Dirichlet -functions whose
conductors comprise only primes that split in a given quadratic number field.
We then deduce a non-vanishing result of these -functions at the point
.Comment: 7 page
First Moment of Hecke -functions with quartic characters at the central point
In this paper, we study the first moment of central values of Hecke
-functions associated with quartic characters.Comment: 11 page
A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution
Soil fabric and its evolving nature underpin the non-coaxial, anisotropic mechanical behaviour of sand, which has not been adequately recognized by past studies on constitutive modelling. A novel three-dimensional constitutive model is proposed to describe the non-coaxial behaviour of sand within the framework of anisotropic critical state theory. The model features a plastic potential explicitly expressed in terms of a fabric tensor reflecting the anisotropy of soil structure and an evolution law for it. Under monotonic loading, the fabric evolution law characterizes a general trend of the fabric change to gradually become co-directional with the loading direction before the soil reaches the critical state. When sand is subjected to rotation of principal stress directions, the fabric evolves with the plastic strain increment which is further dependent on the current stress state, the current fabric and the direction of stress increment. During its evolution, the fabric rotates towards the loading direction and reaches a final degree of anisotropy proportional to a normalized stress ratio. With the incorporation of fabric and fabric evolution, the non-coaxial sand behaviour can be easily captured, and the model response converges to be coaxial at the critical state when the stress and fabric are co-directional. The model has been used to simulate the mechanical behaviour of sand subjected to either monotonic loading or continuous rotation of principal stress directions. The model predictions agree well with test data
One level density of low-lying zeros of quadratic and quartic Hecke -functions
In this paper, we prove some one level density results for the low-lying
zeros of famliies of quadratic and quartic Hecke -functions of the Gaussian
field. As corollaries, we deduce that, respectively, at least and
of the members of the quadratic family and the quartic family do not
vanish at the central point.Comment: 25 pages. arXiv admin note: text overlap with arXiv:0910.506
Unified anisotropic elastoplastic model for sand
This paper presents a unified approach to model the influence of fabric anisotropy and its evolution on both the elastic and plastic responses of sand. A physically based fabric tensor is employed to characterize the anisotropic internal structure of sand. It is incorporated into the nonlinear elastic stiffness tensor to describe anisotropic elasticity, and is further included explicitly in the yield function, the dilatancy relation, and the flow rule to characterize the anisotropic plastic sand response. The physical change of fabric with loading is described by a fabric evolution law driven by plastic strain, which influences both the elastic and the plastic sand behavior. The proposed model furnishes a comprehensive consideration of both anisotropic elasticity and anisotropic plasticity, particularly the nonlinear change of elastic stiffness with the evolution of fabric during the plastic deformation of sand. It offers a natural and rational way to capture the noncoaxial behavior in sand caused by anisotropy. It also facilitates easy determination of the initial anisotropy in sand based on simple laboratory tests and avoids the various arbitrary assumptions on its value made by many previous studies. The model predictions on sand behavior compare well with test data
Delta method in large deviations and moderate deviations for estimators
The delta method is a popular and elementary tool for deriving limiting
distributions of transformed statistics, while applications of asymptotic
distributions do not allow one to obtain desirable accuracy of approximation
for tail probabilities. The large and moderate deviation theory can achieve
this goal. Motivated by the delta method in weak convergence, a general delta
method in large deviations is proposed. The new method can be widely applied to
driving the moderate deviations of estimators and is illustrated by examples
including the Wilcoxon statistic, the Kaplan--Meier estimator, the empirical
quantile processes and the empirical copula function. We also improve the
existing moderate deviations results for -estimators and -statistics by
the new method. Some applications of moderate deviations to statistical
hypothesis testing are provided.Comment: Published in at http://dx.doi.org/10.1214/10-AOS865 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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