共查询到20条相似文献,搜索用时 31 毫秒
1.
Yoshihiro Takeyama 《The Ramanujan Journal》2012,27(1):15-28
We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV’s). In the limit q→1, it turns into Kawashima’s relation for multiple zeta values. As a corollary we find that qMZV’s satisfy the linear relation contained in Kawashima’s relation. In the proof we make use of a q-analogue of Newton series and Bradley’s duality formula for finite multiple harmonic q-series. 相似文献
2.
On the Equivalence and Generalized of Weyl Theorem Weyl Theorem 总被引:3,自引:0,他引:3
M. BERKANI 《数学学报(英文版)》2007,23(1):103-110
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a sinlilar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators. 相似文献
3.
The two-fold aim of the paper is to unify and generalize on the one hand the double integrals of Beukers for ζ(2) and ζ(3), and of the second author for Euler’s constant γ and its alternating analog ln (4/π), and on the other hand the infinite products of the first author for e, of the second author for π, and of Ser for e
γ
. We obtain new double integral and infinite product representations of many classical constants, as well as a generalization
to Lerch’s transcendent of Hadjicostas’s double integral formula for the Riemann zeta function, and logarithmic series for
the digamma and Euler beta functions. The main tools are analytic continuations of Lerch’s function, including Hasse’s series.
We also use Ramanujan’s polylogarithm formula for the sum of a particular series involving harmonic numbers, and his relations
between certain dilogarithm values.
相似文献
4.
Abraham Zaks 《Israel Journal of Mathematics》1980,37(4):281-302
LetR be a commutative domain with 1. We termR an HFD (Half-Factorial-Domain) provided the equality Π
i=1
n
χi=Π{f=1/m}y
f impliesm=n, whenever thex’s and they’s are non-zero, non-unit and irreducible elements ofR. The purpose of this note is to study HFD’s, in particular, Krull domains that are HFD’s, and to provide examples of HFD’s,
that contradict a conjecture of Narkiewicz. 相似文献
5.
Sheng Jun Fan 《数学学报(英文版)》2009,25(10):1681-1692
Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen's inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g(t, 0) = 0, a.s., a.e.. In this paper, based on Jiang's results, under the same assumptions as Jiang's, we investigate the necessary and sufficient condition on g under which Jensen's inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen's inequality for BSDEs. 相似文献
6.
F. Carbonell K. J. Worsley L. Galan 《Annals of the Institute of Statistical Mathematics》2011,63(1):1-27
The statistical problem addressed in this paper is to approximate the P value of the maximum of a smooth random field of Wilks’s Λ statistics. So far results are only available for the usual univariate
statistics (Z, t, χ2, F) and a few multivariate statistics (Hotelling’s T
2, maximum canonical correlation, Roy’s maximum root). We derive results for any differentiable scalar function of two independent
Wishart random fields, such as Wilks’s Λ random field. We apply our results to a problem in brain shape analysis. 相似文献
7.
Hai Jinke 《中国科学A辑(英文版)》2006,49(5):620-625
Let π be a set of primes and G a π-separable group. Isaacs defines the B
π
characters, which can be viewed as the “π-modular” characters in G, such that the B
p′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs’ work, Slattery has developed some Brauer’s ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer’s three main theorems to the π-blocks. In this paper, depending on Isaacs’ and Slattery’s work, we will extend the first main theorem for π-blocks. 相似文献
8.
Rade T. Živaljević 《Combinatorica》2010,30(4):471-484
L. Lovász (Matroids and Sperner’s Lemma, Europ. J. Comb.
1 (1980), 65–66) has shown that Sperner’s combinatorial lemma admits a generalization involving a matroid defined on the set of vertices of the associated triangulation. We prove that Ky Fan’s theorem admits an oriented matroid generalization of similar nature. Classical Ky Fan’s theorem is obtained as a corollary if the underlying oriented matroid
is chosen to be the alternating matroid C
m,r
. 相似文献
9.
We introduce the class of operators on Banach spaces having property (H) and study Weyl’s theorems, and related results for operators which satisfy this property. We show that a- Weyl’s theorem holds for every decomposable operator having property (H). We also show that a-Weyl’s theorem holds for every multiplier T of a commutative semi-simple regular Tauberian Banach algebra. In particular every convolution operator Tμ of a group algebra L1(G), G a locally compact abelian group, satisfies a-Weyl’s theorem. Similar results are given for multipliers of other important commutative Banach algebras. 相似文献
10.
Mourad Oudghiri 《Integral Equations and Operator Theory》2005,53(4):535-545
In the present paper we examine the stability of Weyl’s theorem under perturbations. We show that if T is an isoloid operator on a Banach space, that satisfies Weyl’s theorem, and F is a bounded operator that commutes with T and for which there exists a positive integer n such that Fn is finite rank, then T + F obeys Weyl’s theorem. Further, we establish that if T is finite-isoloid, then Weyl’s theorem is transmitted from T to T + R, for every Riesz operator R commuting with T. Also, we consider an important class of operators that satisfy Weyl’s theorem, and we give a more general perturbation results
for this class. 相似文献
11.
V. M. Korchevsky 《Vestnik St. Petersburg University: Mathematics》2010,43(4):217-219
We investigate relationship between Kolmogorov–s condition and Petrov–s condition in theorems on the strong law of large numbers
for a sequence of independent random variables X
1, X
2, … with finite variances. The convergence (S
n
− ES
n
)/n → 0 holds a.s. (here, S
n
= Σ
k=1
n
X
k
), provided that Σ
n=1∞
DX
n
/n
2 < ∞ (Kolmogorov’s condition) or DS
n
= O(n
2/ψ(n)) for some positive non-decreasing function ψ(n) such that Σ1/(nψ(n)) < ∞ (Petrov’s condition). Kolmogorov’s condition is shown to follow from Petrov’s condition. Besides, under some additional
restrictions, Petrov’s condition, in turn, follows from Kolmogorov’s condition. 相似文献
12.
L. D. Faddeev 《Theoretical and Mathematical Physics》2011,166(3):279-290
We describe an alternative formalism for Einstein’s theory of gravity. The role of dynamical variables is played by a collection
of ten vector fields f
μ
A
, A = 1,..., 10. The metric is a composite variable, g
μν = f
μ
A
f
ν
A
. The proposed scheme may lead to further progress in a theory of gravity where Einstein’s theory is to play the role of an
effective theory, with Newton’s constant appearing by introducing an anomalous Green’s function. 相似文献
13.
Yanjun Liu 《Algebras and Representation Theory》2011,14(2):213-215
Our main purpose of this paper is to give π-block forms of Brauer’s k(B) −conjecture and Olsson’s conjecture for finite π −separable groups. 相似文献
14.
Constantine Sandis 《Acta Analytica》2006,21(2):30-40
This paper aims to explore the space of possible particularistic approaches to Philosophy of Science by examining the differences
and similarities between Jonathan Dancy’s moral particularism—as expressed in both his earlier writings (e.g., Moral Reasons, 1993), and, more explicitly defended in his book Ethics without Principles (2004)—and Nancy Cartwright’s particularism in the philosophy of science, as defended in her early collection of essays,
How the Laws of Physics Lie (1983), and her later book, The Dappled World: A Study of the Boundaries of Science (1999). I shall argue that Dancy’s particularism is more radical, but also more plausible, than Cartwright’s, concluding
that we have good reason to embrace a scientific particularism that is far closer to Dancy’s ethical particularism than any
view defended by Nancy Cartwright, or any other philosopher from the ‘Stanford school’ of scientific theory. 相似文献
15.
Rèsumé. Dans cet article, nous montrons que l’indice cohomologique (construit dans [11]) d’un symbole transversalement elliptique
satisfait certaines propriétés fonctorielles. Nous calculons d’autre part l’indice cohomologique pour certains symboles transversalement
elliptiques particuliers. En reprenant les arguments donnés par Atiyah dans [1], on en déduit que l’indice cohomologique du
symbole d’un opérateur transversalement elliptique P est égal à l’indice analytique de P.
Oblatum 24-VII-1995 相似文献
Oblatum 24-VII-1995 相似文献
16.
We add two sections to [8] and answer some questions asked there. In the first section we give another derivation of Theorem
1.1 of [8], which reveals the relation between the entropy formula, (1.4) of [8], and the well-known Li-Yau ’s gradient estimate.
As a by-product we obtain the sharp estimates on ‘Nash’s entropy’ for manifolds with nonnegative Ricci curvature. We also
show that the equality holds in Li-Yau’s gradient estimate, for some positive solution to the heat equation, at some positive
time, implies that the complete Riemannian manifold with nonnegative Ricci curvature is isometric to ℝ
n
.In the second section we derive a dual entropy formula which, to some degree, connects Hamilton’s entropy with Perelman ’s
entropy in the case of Riemann surfaces. 相似文献
17.
For the regression parameter β
0 in the Cox model, there have been several estimators constructed based on various types of approximated likelihood, but none
of them has demonstrated small-sample advantage over Cox’s partial likelihood estimator. In this article, we derive the full
likelihood function for (β
0, F
0), where F
0 is the baseline distribution in the Cox model. Using the empirical likelihood parameterization, we explicitly profile out
nuisance parameter F
0 to obtain the full-profile likelihood function for β
0 and the maximum likelihood estimator (MLE) for (β
0, F
0). The relation between the MLE and Cox’s partial likelihood estimator for β
0 is made clear by showing that Taylor’s expansion gives Cox’s partial likelihood estimating function as the leading term of
the full-profile likelihood estimating function. We show that the log full-likelihood ratio has an asymptotic chi-squared
distribution, while the simulation studies indicate that for small or moderate sample sizes, the MLE performs favorably over
Cox’s partial likelihood estimator. In a real dataset example, our full likelihood ratio test and Cox’s partial likelihood
ratio test lead to statistically different conclusions. 相似文献
18.
Vivek V. Rane 《Proceedings Mathematical Sciences》2003,113(3):213-221
Euler-Maclaurin and Poisson analogues of the summations ε
a <n ≤b
χ(n)f(n), have been obtained in a unified manner, where (χ(n)) is a periodic complex sequence;d(n) is the divisor function andf(x) is a sufficiently smooth function on [a, b]. We also state a generalised Abel’s summation formula, generalised Euler’s summation formula and Euler’s summation formula
in several variables. 相似文献
19.
Graph factors 总被引:1,自引:0,他引:1
W. T. Tutte 《Combinatorica》1981,1(1):79-97
This exposition is concerned with the main theorems of graph-factor theory, Hall’s and Ore’s Theorems in the bipartite case,
and in the general case Petersen’s Theorem, the 1-Factor Theorem and thef-Factor Theorem. Some published extensions of these theorems are discussed and are shown to be consequences rather than generalizations
of thef-Factor Theorem. The bipartite case is dealt with in Section 2. For the proper presentation of the general case a preliminary
theory of “G-triples” and “f-barriers” is needed, and this is set out in the next three Sections. Thef-Factor Theorem is then proved by an argument of T. Gallai in a generalized form. Gallai’s original proof derives the 1-Factor
Theorem from Hall’s Theorem. The generalization proceeds analogously from Ore’s Theorem to thef-Factor Theorem. 相似文献
20.
Transformations for a bilateral 2
ψ
2-series are investigated by means of Abel’s lemma on summation by parts. Two q-extensions of Dougall’s classical identity for bilateral 2H2-sum are established. As by-products, the Rogers–Fine identity is recovered and a new proof is presented for Bailey’s identity
of bilateral well-poised 6
ψ
6-series. 相似文献