共查询到20条相似文献,搜索用时 31 毫秒
1.
We give an Atkinson-type formula for the periodic zeta-function ζλ with rational parameter λ.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 4, pp. 504–516, October–December, 2007. 相似文献
2.
We consider a multiple interpolation by Padé simple partial fractions and propose a method for calculating the values of rational
functions and polynomials on the basis of approximation by special rational functions (their numerator and denominator are
represented as the differences between two simple partial fractions). We obtain an extrapolation formula for an analytic function
h(z) in a neighborhood of the origin. For an extrapolation tool we use the expressions Σ
k
λ
k
h(λ
k
z), where λ
k
are calculated by a certain algorithm and are independent of the choice of h. Bibliography: 17 titles. 相似文献
3.
By using the solution to the Helmholtz equation u-λu = 0(λ ≥ 0),the explicit forms of the so-called kernel functions and the higher order kernel functions are given.Then by the generalized Stokes formula,the integral representation formulas related with the Helmholtz operator for functions with values in C(V3,3) are obtained.As application of the integral representations,the maximum modulus theorem for function u which satisfies Hu = 0 is given. 相似文献
4.
5.
Abstract
We improve estimates for the distribution of primitive λ-roots of a composite modulus q yielding an asymptotic formula for the number of primitive λ-roots in any interval I of length ∣I∣ ≫ q
1/2+∈. Similar results are obtained for the distribution of ordered pairs (x, x
−1) with x a primitive λ-root, and for the number of primitive λ-roots satisfying inequalities such as |x − x
−1| ≤ B.
(Dedicated to Professor Wang Yuan on the occasion of his 75th birthday)
*Project supported by the National Natural Science Foundation of China (No.19625102) and the 973 Project of the Ministry of
Science and Technology of China. 相似文献
6.
Mascarenhas gave an instance of linear programming problems to show that the long-step affine scaling algorithm can fail
to converge to an optimal solution with the step-size λ=0.999 . In this note, we give a simple and clear geometrical explanation for this phenomenon in terms of the Newton barrier flow
induced by projecting the homogeneous affine scaling vector field conically onto a hyperplane where the objective function
is constant. Based on this interpretation, we show that the algorithm can fail for "any" λ greater than about 0.91 (a more precise value is 0.91071), which is considerably shorter than λ = 0.95 and 0.99 recommended for efficient implementations.
Accepted 17 February 1998 相似文献
7.
Karin Erdmann 《manuscripta mathematica》1995,88(1):357-386
LetK be an algebraically closed field of characteristic,p>0 and letD
λ be the simple modules of the symmetric groupS
r
overK where λ is a p-regular partition ofr. The dimensions ofD
λ for λ with at mostn parts are the same as the multiplicities of direct summands ofD
⊗r
whereE is the natural module for the groupGL
n
(K). Whenn=2 we determine generating functions for these multiplicities and hence for the dimensions ofD
λ for all partitions λ with two parts. These can be expressed as rational functions of Chebyshev polynomials; and we obtain
explicit formulae for the coefficients. 相似文献
8.
V. V. Shchigolev 《Journal of Mathematical Sciences》2007,142(2):2015-2019
In this paper, we calculate the space Ext
GL(n
1
)(L
n
(λ), L
n
(μ)), where GL(n) is the general linear group of degree n over an algebraically closed field of positive characteristic, L
n
(λ) and L
n
(μ) are rational irreducible GL(n)-modules with highest weights λ and μ, respectively, the restriction of L
n
(λ) to any Levi subgroup of GL(n) is semisimple, λ is a p-restricted weight, and μ does not strictly dominate λ.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 219–226, 2005. 相似文献
9.
Palle E. T. Jorgensen Keri A. Kornelson Karen L. Shuman 《Journal of Fourier Analysis and Applications》2011,17(3):431-456
We study the harmonic analysis of Bernoulli measures μ
λ
, a one-parameter family of compactly supported Borel probability measures on the real line. The parameter λ is a fixed number in the open interval (0,1). The measures μ
λ
may be understood in any one of the following three equivalent ways: as infinite convolution measures of a two-point probability
distribution; as the distribution of a random power series; or as an iterated function system (IFS) equilibrium measure determined
by the two transformations λ(x±1). For a given λ, we consider the harmonic analysis in the sense of Fourier series in the Hilbert space L
2(μ
λ
). For L
2(μ
λ
) to have infinite families of orthogonal complex exponential functions e
2πis(⋅), it is known that λ must be a rational number of the form
\fracm2n\frac{m}{2n}, where m is odd. We show that
L2(m\frac12n)L^{2}(\mu_{\frac{1}{2n}}) has a variety of Fourier bases; i.e. orthonormal bases of exponential functions. For some other rational values of λ, we exhibit maximal Fourier families that are not orthonormal bases. 相似文献
10.
We provide some more explicit formulae to facilitate the computation of Ohtsuki’s rational invariants λ
n
of integral homology 3-spheres extracted from Reshetikhin-TuraevSU(2) quantum invariants. Several interesting consequences will follow from our computation of λ2. One of them says that λ2 is always an integer divisible by 3. It seems interesting to compare this result with the fact shown by Murakami that λ1 is 6 times the Casson invariant. Other consequences include some general criteria for distinguishing homology 3-spheres obtained
from surgery on knots by using the Jones polynomial.
The first author is supported in part by NSF and the second author is supported by an NSF Postdoctoral Fellowship. 相似文献
11.
WuJunde 《高校应用数学学报(英文版)》2000,15(4):399-402
Let λ and μ be sequence spaces and have both the signed-weak gliding hump property, (λ,μ) the algebra of the infinite matrix operators which transform λ into μ. In this paper, it is proved that if λ and μ are β-spaces and λ^β and ,μ^β have also the signed-weak gliding hump property, then for any polar topology τ, ((λ,μ),τ) is always sequentially complete locally convex topological algebra. 相似文献
12.
We introduce the notion ofα, λ-absolute continuity for functions of several variables and we compare it with the Hencl’s definition. We obtain that eachα, λ-absolutely continuous function isn, λ-absolutely continuous in the sense of Hencl and hence is continuous, differentiable almost everywhere and satisfies change
of variables results based on a coarea formula and an area formula. 相似文献
13.
A multiplication on an H-space X has a left inverse λ and a right inverse ρ. They are mutual inverses and λ = ρ if and only if . In this paper we investigate the order of λ. We give an example of a multiplication with , and prove that for any finite H-complex X there are finitely many left inverses of finite order. Conditions are given for there to be infinitely many multiplications
on X with the same left inverse. We then give conditions for a left inverse to have infinite order. We apply these results to
specific Lie groups.
Received: 15 June 2001 相似文献
14.
Qiu Weisheng 《中国科学A辑(英文版)》2002,45(9):1117-1134
In this paper we improve the character approach to the multiplier conjecture that we presented after 1992, and thus we have
made considerable progress in the case of n = 3n1. We prove that in the case of n = 3n1 Second multiplier theorem remains true if the assumption “n1 > λ” is replaced by “(n1, λ) = 1”. Consequentially we prove that if we let D be a (v, k, λ)-difference set in an abelian group G, and n = 3pr for some prime p, (p,v) = 1, then p is a numerical multiplier of D. 相似文献
15.
Stephan Baier 《Acta Mathematica Hungarica》2006,113(1-2):39-49
Summary Suppose that 1/2 ≦ λ < 1. Balog and Harman proved that for any real θ there exist infinitely many primes p satisfying pλ-θ < p-(1-λ)/2+ ε (with an asymptotic result). In the present paper we establish that for almost all θ in the interval 0 ≦ θ < 1 there exist
infinitely many primes p such that {pλ-θ} < p-min{(2-λ)/6,(14-9λ)/32}+ε. Thus we obtain a better result for almost all θ than for a single θ if λ>1/2. 相似文献
16.
M. Vanninathan 《Proceedings Mathematical Sciences》1981,90(3):239-271
In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of
the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic
expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we
denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet:
λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).
Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in
the case of Neumann eigenvalue problem. 相似文献
17.
R. Monneau 《Journal of Geometric Analysis》2003,13(2):359-389
We study the obstacle problem in two dimensions. On the one hand we improve a result of L.A. Caffarelli and N.M. Rivière:
we state that every connected component of the interior of the coincidence set has at most N
0
singular points, where N
0
is only dependent on some geometric constants. Moreover, if the component is small enough, then this component has at most
two singular points. On the other hand, we prove in a simple case a conjecture of D.G. Schaeffer on the generic regularity
of the free boundary: for a family of obstacle problems in two dimensions continuously indexed by a parameter λ, the free
boundary of the solution uλ is analytic for almost every λ. Finally we present a new monotonicity formula for singular points.
Dedicated to Henri Berestycki and Alexis Bonnet. 相似文献
18.
M. Hărăguş 《Journal of Nonlinear Science》1998,8(4):353-374
Summary. For a certain class of partial differential equations in cylindrical domains, we show that all small time-dependent solutions
are described by a reduced system of equations on the real line, which contains nonlocal terms. As an application, we investigate
the system describing nonlinear water waves travelling on the free surface of an inviscid fluid. Two-dimensional gravity waves
are characterized by the parameter λ , the inverse square of the Froude number. For λ close to the critical value λ
0
=1 , we obtain a reduced system of four nonlocal equations. We show that the terms of lowest order in μ=λ-1 lead to the Korteweg—de Vries equation for the lowest-order approximation of the free surface.
Received February 23, 1994; final revision received October 13, 1997; accepted for publication October 16, 1997. 相似文献
19.
A mathematical program with a rational objective function may have irrational algebraic solutions even when the data are integral.
We suggest that for such problems the optimal solution will be represented as follows: If λ* denotes the optimal value there
will be given an intervalI and a polynomialP(λ) such thatI contains λ* and λ* is the unique root ofP(λ) inI. It is shown that with this representation the solutions to convex quadratic fractional programs and ratio games can be obtained
in polynomial time. 相似文献
20.
Ahmed M.K. Tarabia Hideaki Takagi A.H. El-Baz 《Mathematical Methods of Operations Research》2009,70(1):77-98
In this paper, we illustrate that a power series technique can be used to derive explicit expressions for the transient state
distribution of a queueing problem having “chemical” rules with an arbitrary number of customers present initially in the
system. Based on generating function and Laplace techniques Conolly et al. (in Math Sci 22:83–91, 1997) have obtained the
distributions for a non-empty chemical queue. Their solution enables us only to recover the idle probability of the system
in explicit form. Here, we extend not only the model of Conolly et al. but also get a new and simple solution for this model.
The derived formula for the transient state is free of Bessel function or any integral forms. The transient solution of the
standard M/M/1/∞ queue with λ = μ is a special case of our result. Furthermore, the probability density function of the virtual waiting time in a chemical
queue is studied. Finally, the theory is underpinned by numerical results.
相似文献