共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we study the central values of L-functions associated to a large class of algebraic Hecke characters of imaginary quadratic fields. When these central values
are nonzero, the Bloch–Kato conjecture predicts an exact formula for the algebraic parts of the central values in terms of
periods and arithmetic data, most notably the Selmer groups corresponding to the Hecke characters. We investigate the nonvanishing
of these central values, and prove the p-part of the Bloch–Kato conjecture in these cases for primes p which split in K. 相似文献
2.
We incorporate the non-critical values of L-functions of cusp forms into a cohomological set-up analogous to the one of Eichler, Manin and Shimura. We use the 1-cocycles
we associate in this way to non-critical values to prove an expression for such values which is similar in structure to Manin’s
formula for the critical value of the L-function of a weight 2 cusp form.
YoungJu Choie is partially supported by KOSEF R01-2003-00011596-0 and by ITRC Research Fund.
N. Diamantis is partially supported by EPSRC grant EP/D032350/1. 相似文献
3.
K. Y. Cheung Stephen M. S. Lee 《Annals of the Institute of Statistical Mathematics》2005,57(2):279-290
We consider the problem of estimating the variance of a sample quantile calculated from a random sample of sizen. Ther-th-order kernel-smoothed bootstrap estimator is known to yield an impressively small relative error of orderO(n
−r/(2r+1)
). It nevertheless requires strong smoothness conditions on the underlying density function, and has a performance very sensitive
to the precise choice of the bandwidth. The unsmoothed bootstrap has a poorer relative error of orderO(n
−1/4), but works for less smooth density functions. We investigate a modified form of the bootstrap, known as them out ofn bootstrap, and show that it yields a relative error of order smaller thanO(n
−1/4) under the same smoothness conditions required by the conventional unsmoothed bootstrap on the density function, provided
that the bootstrap sample sizem is of an appropriate order. The estimator permits exact, simulation-free, computation and has accuracy fairly insensitive
to the precise choice ofm. A simulation study is reported to provide empirical comparison of the various methods.
Supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU
7131/00P). 相似文献
4.
A. Fujii, and later J. Steuding, considered an asymptotic formula for the sum of values of the Dirichlet L-function taken at the nontrivial zeros of another Dirichlet L-function. Here we improve the error term of this asymptotic formula. 相似文献
5.
In this paper, the exact solutions of the L∝ norm on some classes of monosplines with free knots on the real axis are obtained, and the optimal quadrature formula and optimal error on the convolution class taking a PF density as its kernal are given. 相似文献
6.
Abdullo Rakhmonovich Hayotov Gradimir V. Milovanović Kholmat Mahkambaevich Shadimetov 《Numerical Algorithms》2011,57(4):487-510
In this paper we construct an optimal quadrature formula in the sense of Sard in the Hilbert space K
2(P
2). Using S.L. Sobolev’s method we obtain new optimal quadrature formula of such type and give explicit expressions for the
corresponding optimal coefficients. Furthermore, we investigate order of the convergence of the optimal formula and prove
an asymptotic optimality of such a formula in the Sobolev space L2(2)(0,1)L_2^{(2)}(0,1). The obtained optimal quadrature formula is exact for the trigonometric functions sinx and cosx. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula. 相似文献
7.
Shu Tezuka 《Mathematica Slovaca》2009,59(3):379-386
In this paper, we consider Owen’s scrambling of an (m−1, m, d)-net in base b which consists of d copies of a (0, m, 1)-net in base b, and derive an exact formula for the gain coefficients of these nets. This formula leads us to a necessary and sufficient
condition for scrambled (m − 1, m, d)-nets to have smaller variance than simple Monte Carlo methods for the class of L
2 functions on [0, 1]
d
. Secondly, from the viewpoint of the Latin hypercube scrambling, we compare scrambled non-uniform nets with scrambled uniform
nets. An important consequence is that in the case of base two, many more gain coefficients are equal to zero in scrambled
(m − 1, m, d)-nets than in scrambled Sobol’ points for practical size of samples and dimensions.
相似文献
8.
A. I. Vagabov 《Differential Equations》2012,48(4):477-485
For a linear differential expression with matrix coefficients in the class L p , p ≥ 2, and with a parameter λ, we consider a boundary value problem with boundary conditions at the endpoints of the interval [a, b]. Under the condition that the problem is regular, we obtain a formula for the Fourier series expansion of an arbitrary vector function of the class L p in the root functions of the problem. 相似文献
9.
Benjamin Howard 《Mathematische Annalen》2007,339(4):803-818
We prove a result of the following type: given a Hida family of modular forms, if there exists a weight two form in the family
whose L-function vanishes to exact order one at s = 1, then all but finitely many weight two forms in the family enjoy this same property. The analogous result for order of
vanishing zero is also true, and is an easy consequence of the existence of the Mazur–Kitagawa two-variable p-adic L-function.
This research was supported in part by NSF grant DMS-0556174. 相似文献
10.
The kernel estimator of a multivariate probability density function is studied. An asymptotic upper bound for the expected L1 error of the estimator is derived. An asymptotic lower bound result and a formula for the exact asymptotic error are also given. The goodness of the smoothing parameter value derived by minimizing an explicit upper bound is examined in numerical simulations that consist of two different experiments. First, the L1 error is estimated using numerical integration and, second, the effect of the choice of the smoothing parameter in discrimination tasks is studied. 相似文献
11.
W. L. Pearn Ching-Ho Yen Dong-Yuh Yang 《Central European Journal of Operations Research》2012,20(1):65-85
Process yield is an important criterion used in the manufacturing industry for measuring process performance. Methods for
measuring yield for processes with single characteristic have been investigated extensively. However, methods for measuring
yield for processes with multiple characteristics have been comparatively neglected. Chen et al. (Qual Reliab Eng Int 19:101–110,
2003) proposed a measurement formula called SpkT{S_{pk}^T } , which provides an exact measure of the overall process yield, for processes with multiple characteristics. In this paper,
we considered the natural estimator of SpkT{S_{pk}^T } under multiple samples, and derived the asymptotic distribution for the estimator. In addition, a comparison between the
SB (standard bootstrap) and the proposed method based on the lower confidence bound is executed. Generally, the result indicates
that the proposed approach is more reliable than the standard bootstrap method. 相似文献
12.
For a finite lattice L, let $ \trianglelefteq_L $ denote
the reflexive and transitive closure of the join-dependency relation on L,
defined on the set J(L) of all join-irreducible elements of L.
We characterize the relations of the form $ \trianglelefteq_L $, as follows:
Theorem. Let $ \trianglelefteq $ be a quasi-ordering on
a finite set P. Then the following conditions are
equivalent:(i) There exists a finite lattice L such that $ \langle J(L), \trianglelefteq_L $ is
isomorphic to the quasi-ordered set $ \langle P, \trianglelefteq \rangle $.(ii) $ |\{x\in P|p \trianglelefteq x\}| \neq 2 $, for any $ p \in P $.For a finite lattice L,
let $ \mathrm{je}(L) = |J(L)|-|J(\mathrm{Con} L)| $ where Con L
is the congruence lattice of L. It is well-known that the
inequality $ \mathrm{je}(L) \geq 0 $ holds. For a finite distributive
lattice D, let us define the join-
excess function:$ \mathrm{JE}(D) =\mathrm{min(je} (L) | \mathrm{Con} L \cong D). $We provide a formula for computing the join-excess function of a finite distributive lattice
D. This formula implies that $ \mathrm{JE}(D) \leq (2/3)| \mathrm{J}(D)|$
, for any finite distributive lattice D;
the constant 2/3 is best possible.A special case of this formula gives a characterization of congruence lattices of finite
lower bounded lattices.Dedicated to the memory of Gian-Carlo Rota 相似文献
13.
Arup Bose 《中国科学A辑(英文版)》2009,52(6):1251-1261
We study the asymptotic distribution of the L
1 regression estimator under general conditions with matrix norming and possibly non i.i.d. errors. We then introduce an appropriate
bootstrap procedure to estimate the distribution of this estimator and study its asymptotic properties. It is shown that this
bootstrap is consistent under suitable conditions and in other situations the bootstrap limit is a random distribution.
This work was supported by J.C. Bose National Fellowship, Government of India 相似文献
14.
Abir Nour 《Mathematical Logic Quarterly》1999,45(4):457-466
In order to modelize the reasoning of an intelligent agent represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems a set of constants constitutes a fundamental tool. In this papers, we consider logic systems called L′T without this kind of constants but limited to the case where T is a finite poset. We prove a weak deduction theorem. We introduce also an algebraic semantics using Hey ting algebra with operators. To prove the completeness theorem of the L′T system with respect to the algebraic semantics, we use the method of H. Rasiowa and R. Sikorski for first order logic. In the propositional case, a corollary allows us to assert that it is decidable to know “if a propositional formula is valid”. We study also certain relations between the L′T logic and the intuitionistic and classical logics. 相似文献
15.
Takeshi Saito 《Commentarii Mathematici Helvetici》1995,70(1):507-515
Henniart has computed the local constant ε (Ind
K
L
1) for an extensionL overK of local fields of odd degree in [H]. In this paper, we show that his formula is a consequence of results of Serre [S4] and
of Deligne [D2]. Further we compute the local constant for an extension of even degree, assuming the residual characteristic
is not equal to 2. 相似文献
16.
We investigate the second order accuracy of the M out of N bootstrap for a Studentized trimmed mean using the Edgeworth expansion derived in a previous paper. Some simulations, which
support our theoretical results, are also given. The effect of extrapolation in conjunction with the M out of N bootstrap for Studentized trimmed means is briefly discussed. As an auxiliary result we obtain a Bahadur’s type representation
for an M out of N bootstrap quantile.
Our results supplement previous work on (Studentized) trimmed means by Hall and Padmanabhan [13], Bickel and Sakov [7], and
Gribkova and Helmers [11].
相似文献
17.
François Laudenbach 《Commentarii Mathematici Helvetici》1995,70(1):558-614
Let }L
t{,t ∈ [0, 1], be a path of exact Lagrangian submanifolds in an exact symplectic manifold that is convex at infinity and of dimension
≥6. Under some homotopy conditions, an engulfing problem is solved: the given path }L
t{ is conjugate to a path of exact submanifolds inT
*Lo. This impliesL
t must intersectL
o at as many points as known by the generating function theory. Our Engulfing theorem depends deeply on a new flexibility property
of symplectic structures which is stated in the first part of this work.
相似文献
18.
Arindam Chatterjee 《Annals of the Institute of Statistical Mathematics》2011,63(1):157-179
In this paper we consider the problem of estimating quantiles of a finite population of size N on the basis of a finite sample of size n selected without replacement. We prove the asymptotic normality of the sample quantile and show that the scaled variance
of the sample quantile converges to the asymptotic variance under a slight moment condition. We also consider the performance
of the bootstrap in this case, and find that the usual (Efron’s) bootstrap method fails to be consistent, but a suitably modified
version of the bootstrapped quantile converges to the same asymptotic distribution as the sample quantile. Consistency of
the modified bootstrap variance estimate is also proved under the same moment conditions. 相似文献
19.
We deduce the exact Jackson-type inequalities for the approximations of functions ƒ ∈ L
2(ℝ) in L
2(ℝ) by using partial sums of wavelet series in the cases of Meyer and Shannon-Kotelnikov wavelets.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 8, pp. 1119–1127, August, 2008. 相似文献
20.
In applications of branching processes, usually it is hard to obtain samples of a large size. Therefore, a bootstrap procedure allowing inference based on a small sample size is very useful. Unfortunately, in the critical branching process with stationary immigration the standard parametric bootstrap is invalid. In this paper, we consider a process with non-stationary immigration, whose mean and variance vary regularly with nonnegative exponents α and β, respectively. We prove that 1+2α is the threshold for the validity of the bootstrap in this model. If β<1+2α, the standard bootstrap is valid and if β>1+2α it is invalid. In the case β=1+2α, the validity of the bootstrap depends on the slowly varying parts of the immigration mean and variance. These results allow us to develop statistical inferences about the parameters of the process in its early stages. 相似文献