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1.
2.
We classify all connected subgroups of SO(2, n) that act irreducibly on ℝ2, n
. Apart from SO
0(2, n) itself these are U(1, n/2), SU(1, n/2), if n even, S
1 · SO(1, n/2) if n even and n ≥ 2, and SO
0(1, 2) for n = 3. Our proof is based on the Karpelevich Theorem and uses the classification of totally geodesic submanifolds of complex
hyperbolic space and of the Lie ball. As an application we obtain a list of possible irreducible holonomy groups of Lorentzian
conformal structures, namely SO
0(2, n), SU(1, n), and SO
0(1, 2). 相似文献
3.
We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best
uniform polynomial approximation of |x|
p
on two symmetric intervals. Note that, in addition, we get asymptotics for the polynomials themselves under a certain renormalization.
Also, we solve a problem on asymptotics of the best approximation of sgn(x) on [−1,−a]∪[a,1] by Laurent polynomials.
相似文献
4.
本文研究亚纯函数的值分布问题.利用值分布理论,获得了一个带精简密指量的模分布的不等式,改进了Xu和Yang等人的结果. 相似文献
5.
V. A. Belonogov 《Proceedings of the Steklov Institute of Mathematics》2009,264(Z1):60-71
In the author’s previous paper, the hypothesis that the alternating groups A
n
have no pairs of semiproportional irreducible characters is reduced to a hypothesis concerning the problem of describing
the pairs of irreducible characters of the symmetric group S
n
that are semiproportional on one of the sets A
n
or S
n
∖A
n
. In this hypothesis, properties of such a pair of characters are expressed in terms of Young’s diagrams corresponding to
these characters. The theorem proved in this paper allows one to exclude from consideration some stages of the verification
of this hypothesis. 相似文献
6.
V. Yu. Gubarev 《Siberian Mathematical Journal》2009,50(3):395-404
We take the exterior power ℝ4 ∧ ℝ4 of the space ℝ4, its mth symmetric power V = S
m
(∧2ℝ4) = (ℝ4 ∧ ℝ4) ∨ (ℝ4 ∧ ℝ4) ∨ ... ∨(ℝ4 ∧ ℝ4), and put V
0 = L((x ∧ y)∨ ... ∨(x ∧ y): x, y ∈ ℝ4). We find the dimension of V
0 and an algorithm for distinguishing a basis for V
0 efficiently. This problem arose in vector tomography for the purpose of reconstructing the solenoidal part of a symmetric
tensor field.
Original Russian Text Copyright ? 2009 Gubarev V. Yu.
The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant
NSh-344.2008.1).
__________
Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 3, pp. 503–514, May–June, 2009. 相似文献
7.
Samuel A. Ilori 《K-Theory》1989,2(5):623-624
We use the work of Karoubi and Mudrinski on the real Grothendieck's groups of certain complex projective bundles to show that the torsion of the KO
–i
groups of G
3(
n
), n odd, are related to the known torsion of the KO
–i
groups of G2(
n
). 相似文献
8.
Andreas Arvanitoyeorgos Ioannis Chrysikos Yusuke Sakane 《Annals of Global Analysis and Geometry》2010,38(4):413-438
We find the precise number of non-K?hler SO(2n)-invariant Einstein metrics on the generalized flag manifold M = SO(2n)/U(p)×U(n−p) with n ≥ 4 and 2 ≤ p ≤ n−2. We use an analysis on parametric systems of polynomial equations and we give some insight towards the study of such systems.
We also examine the isometric problem for these Einstein metrics. 相似文献
9.
The subgroups E(m,R) ⊗ E(n,R) ≤ H ≤ G = GL(mn,R) are studied under the assumption that the ring R is commutative and m, n ≥ 3. The group GL
m
⊗GL
n
is defined by equations, the normalizer of the group E(m,R) ⊗ E(n,R) is calculated, and with each intermediate subgroup H it is associated a uniquely determined lower level (A,B,C), where A,B,C are ideals in R such that mA,A
2 ≤ B ≤ A and nA,A
2 ≤ C ≤ A. The lower level specifies the largest elementary subgroup satisfying the condition E(m, n,R, A,B,C) ≤ H. The standard answer to this problem asserts that H is contained in the normalizer N
G
(E(m,n,R, A,B,C)). Bibliography: 46 titles. 相似文献
10.
Yasutsugu Fujita 《Periodica Mathematica Hungarica》2009,59(1):81-98
Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the product of any two of them increased by n is a perfect square. Let k be a positive integer. In this paper, we show that if {k
2, k
2 + 1, 4k
2 + 1, d} is a D(−k
2)-quadruple, then d = 1, and that if {k
2 − 1, k
2, 4k
2 − 1, d} is a D(k
2)-quadruple, then d = 8k
2(2k
2 − 1). 相似文献
11.
Let K be a field of characteristic 0 and let p, q, G 0 , G 1 , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G n (x)) n=0 ∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G n (x) = G m (P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we present also bounds for the cardinality of the set
相似文献
12.
13.
Let K be a field of characteristic 0 and let p, q, G
0
, G
1
, P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G
n
(x))
n=0
∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G
n
(x) = G
m
(P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we
present also bounds for the cardinality of the set
In the last part we specialize our results to certain families of orthogonal polynomials.
This work was supported by the Austrian Science Foundation FWF, grant S8307-MAT.
The second author was supported by the Hungarian National Foundation for Scientific Research Grants No 16741 and 38225.
Received June 5, 2001; in revised form February 26, 2002
RID="a"
ID="a" Dedicated to Edmund Hlawka on the occasion of his 85th birthday 相似文献
14.
Ayelet Lindenstrauss 《K-Theory》1996,10(3):239-265
Topological Hochschild homology is calculated for the rings /p[x]/(f(x)) (where p is prime and f(x) /p[x] any polynomial), [x]/(x
n) and [x]/(x
n–1). A spectral sequence argument is used for calculating the homology of the topological Hochschild homology spectrum, from which its stable homotopy structure can be read off since the spectrum is known for a priori reasons to be a restricted product of Eilenberg-MacLane spectra. 相似文献
15.
Oleg Okunev 《Central European Journal of Mathematics》2011,9(5):978-983
We prove that if X is a strongly zero-dimensional space, then for every locally compact second-countable space M, C
p
(X, M) is a continuous image of a closed subspace of C
p
(X). It follows in particular, that for strongly zero-dimensional spaces X, the Lindel?f number of C
p
(X)×C
p
(X) coincides with the Lindel?f number of C
p
(X). We also prove that l(C
p
(X
n
)κ) ≤ l(C
p
(X)κ) whenever κ is an infinite cardinal and X is a strongly zero-dimensional union of at most κcompact subspaces. 相似文献
16.
D. M. Dyachenko 《Moscow University Mathematics Bulletin》2008,63(3):99-106
The class of functions H
ω
is considered, where ω(t) is a continuity modulus monotone in the sense of Hardy and satisfying some condition C. The behavior of the value is obtained, where is the sum of absolute values of Fourier coefficients of a function f ∈ L(T
m
) in pth power.
Original Russian Text ? D.M. D’yachenko, 2008, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2008,
Vol. 63, No. 3, pp. 19–26. 相似文献
17.
18.
D. M. D’yachenko 《Moscow University Mathematics Bulletin》2011,66(1):1-7
Two-side estimates of sums of absolute values of Fourier coefficients for functions of many variables from the classes H
ω
(T
m
) are established in the paper with the help of partial moduli of smoothness. 相似文献
19.
Song Li 《中国科学A辑(英文版)》2003,46(3):364-375
The purpose of this paper is to investigate the refinement equations of the form
where the vector of functions ϕ=(ϕ
1..., ϕ
r
)
T
is in (L
p
(ℝ
s
))
r
, 1⩽p⩽∞, a(α), α∈ℤ
s
is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim→∞ M-n = 0. In order to solve the refinement equation mentioned above, we start with a vector of compactly supported functions φ
0∈(L
p
(ℝ
s
))
r
and use the iteration schemes f
n
:=Q
a
n
φ
0, n=1,2,..., where Q
n
is the linear operator defined on (L
p
(ℝ
s
))
r
given by
This iteration scheme is called a subdivision scheme or cascade algorithm. In this paper, we characterize the Lp-convergence of subdivision schemes in terms of the p-norm joint spectral radius of a finite collection of some linear operators
determined by the sequence a and the set B restricted to a certain invariant subspace, where the set B is a complete set of representatives of the distinct cosets of the quotient group ℤs/Mℤs containing 0. 相似文献
20.
Mark L. Agranovsky 《Journal d'Analyse Mathématique》2011,113(1):293-304
Let f ∈ C ω (∂B n ), where B n is the unit ball of ℂ n . We prove that if a,b ? [`(B)] na,b in {overline B ^n}, a ≠ b, for every complex line L passing through one of a or b, the restricted function f|L ??Bnf{|_{L cap partial {B^n}}} has a holomorphic extention to the cross-section L∩B n , then f is the boundary value of a holomorphic function in B n . 相似文献