共查询到20条相似文献,搜索用时 600 毫秒
1.
Enrico Jabara 《Rendiconti del Circolo Matematico di Palermo》1995,44(1):107-112
An automorphism σ of order (a divisor of)n of the groupG is calledn-splitting if
for everyg∈G.
In this paper we prove that a 2-group admitting a 4-splitting automorphism, is locally finite. 相似文献
2.
Enrico Jabara 《Rendiconti del Circolo Matematico di Palermo》2003,52(1):158-162
LetG be a group andα εAut(G);α is calledn-splitting if ggα...gα
n-1=1 ∀g εG. In this note we study the structure of finite groups admitting an-splitting automorphism of orderp (p an odd prime number).
相似文献
3.
Enrico Jabara 《Rendiconti del Circolo Matematico di Palermo》1996,45(1):84-92
LetG be a group admitting a 4-splitting automorphism (i.e. an automorphism σ such that
for everyg∈G). In this paper we prove that ifG≠1 is solvable with derived lengthd thenG′ is nilpotent of class not greater than (4
d−1−1)/3. 相似文献
4.
V. V. Andrievskii 《Journal d'Analyse Mathématique》2005,96(1):283-295
LetG⊂C be a quasidisk,K ⊂ G be a compact set, andp
n be a non-constant complex polynomial of degree at mostn. We establish the inequality
whereα
n < 0 depends onn, K,
and the geometrical structure of ϖG. 相似文献
5.
We study the irrational factor function I(n) introduced by Atanassov and defined by , where is the prime factorization of n. We show that the sequence {G(n)/n}
n≧1, where G(n) = Π
ν=1
n
I(ν)1/n
, is convergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function
I(n).
Research of the third author is supported in part by NSF grant number DMS-0456615. 相似文献
6.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
7.
Yuexu Zhao 《Bulletin of the Brazilian Mathematical Society》2006,37(3):377-391
Let X1, X2, ... be i.i.d. random variables with EX1 = 0 and positive, finite variance σ2, and set Sn = X1 + ... + Xn. For any α > −1, β > −1/2 and for κn(ε) a function of ε and n such that κn(ε) log log n → λ as n ↑ ∞ and
, we prove that
*Supported by the Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. 20060237 and 20050494). 相似文献
8.
Two Inequalities for Convex Functions 总被引:1,自引:0,他引:1
Let a 0 < a 1 < ··· < a n be positive integers with sums $ {\sum\nolimits_{i = 0}^n {\varepsilon _{i} a_{i} {\left( {\varepsilon _{i} = 0,1} \right)}} } Let a
0 < a
1 < ··· < a
n
be positive integers with sums
distinct.
P. Erd?s conjectured that
The best known result along this line is that
of Chen: Let f be any given convex decreasing function on [A, B] with α
0, α
1, ... , α
n
, β
0, β
1, ... , β
n
being real numbers in [A, B] with α
0 ≤ α
1 ≤ ··· ≤ α
n
,
Then
In this paper, we obtain two generalizations of the above result; each is of
special interest in itself. We prove:
Theorem 1
Let f and g be two given non-negative convex decreasing functions on [A, B], and α
0, α
1, ... ,
α
n
, β
0, β
1, ... , β
n
, α'
0, α'
1, ... , α'
n
, β'
0
, β'
1
, ... , β'
n
be real numbers in [A, B] with
α
0 ≤ α
1 ≤ ··· ≤
α
n
,
α'
0 ≤ α'
1 ≤ ··· ≤ α'
n
,
Then
Theorem 2
Let f be any given convex decreasing function on [A, B] with
k
0, k
1, ... , k
n
being nonnegative
real numbers and
α
0, α
1, ... , α
n
, β
0, β
1, ... , β
n
being real numbers in [A, B] with
α
0 ≤ α
1 ≤
··· ≤ α
n
,
Then
相似文献
9.
By J. Steuding 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2001,71(1):113-121
We consider the value distribution of Hurwitz zeta-functions
at the nontrivial zeros ϱ= β + iγ of the Riemann zeta-function ζ (s):= ζ (s, 1). Using the method of Conrey, Ghosh and Gonek we prove for fixed 0< α< 1 andH ≤T that
with some absolute constantC > 0 (a similar result was first proved by Fujii [4] under assumption of the Riemann hypothesis). It follows that
is an entire function if and only if α = 1/2 or α = l. Further, we prove for α ≠ 1/2, 1 the existence of zeros ϱ = β +iγ withT < γ ≤T + T3/4, 1/2 β ≤ 9/10+ ε and ζ(ϱ,α)≠0. 相似文献
10.
G. Harman 《Acta Mathematica Hungarica》2009,124(3):289-298
We continue the study of sums of the form
begun by Indlekofer and Kátai. Here |Y
n
|,|X
p
| ≦ 1 and α is irrational. We prove one conjecture of Kátai, disprove another by both authors, and give what may be a close to best possible
result valid for all irrational α.
相似文献
11.
Claude Tardif 《Combinatorica》2005,25(5):625-632
We prove that the identity
holds for all directed graphs G and H. Similar bounds for the usual chromatic number seem to be much harder to obtain: It is still not known whether there exists
a number n such that χ(G×H) ≥ 4 for all directed graphs G, H with χ(G) ≥ χ(H) ≥ n. In fact, we prove that for every integer n ≥ 4, there exist directed graphs Gn, Hn such that χ(Gn) = n, χ(Hn) = 4 and χ(Gn×Hn) = 3. 相似文献
12.
We investigate the correlation between the constants K(ℝn) and
, where
is the exact constant in a Kolmogorov-type inequality, ℝ is the real straight line,
, L
l
p, p
(G
n) is the set of functions ƒ ∈ L
p
(G
n
) such that the partial derivative
belongs to L
p
(G
n
),
, 1 ≤ p ≤ ∞, l ∈ ℕn, α ∈ ℕ
0
n
= (ℕ ∪ 〈0〉)n, D
α
f is the mixed derivative of a function ƒ, 0 < μi < 1,
, and ∑
i=0
n
. If G
n
= ℝ, then μ0=1−∑
i=0
n
(α
i
/l
i
), μi = αi/l
i
,
if
, then μ0=1−∑
i=0
n
(α
i
/l
i
) − ∑
i=0
n
(λ/l
i
), μi = αi/ l
i
+ λ/l
i
,
, λ ≥ 0. We prove that, for λ = 0, the equality
is true.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 597–606, May, 2006. 相似文献
13.
We present a new explicit construction for expander graphs with nearly optimal spectral gap. The construction is based on
a series of 2-lift operations. Let G be a graph on n vertices. A 2-lift of G is a graph H on 2n vertices, with a covering map π :H →G. It is not hard to see that all eigenvalues of G are also eigenvalues of H. In addition, H has n “new” eigenvalues. We conjecture that every d-regular graph has a 2-lift such that all new eigenvalues are in the range
(if true, this is tight, e.g. by the Alon–Boppana bound). Here we show that every graph of maximal degree d has a 2-lift such that all “new” eigenvalues are in the range
for some constant c. This leads to a deterministic polynomial time algorithm for constructing arbitrarily large d-regular graphs, with second eigenvalue
.
The proof uses the following lemma (Lemma 3.3): Let A be a real symmetric matrix with zeros on the diagonal. Let d be such that the l1 norm of each row in A is at most d. Suppose that
for every x,y ∈{0,1}n with ‹x,y›=0. Then the spectral radius of A is O(α(log(d/α)+1)). An interesting consequence of this lemma is a converse to the Expander Mixing Lemma.
* This research is supported by the Israeli Ministry of Science and the Israel Science Foundation. 相似文献
14.
Zamira Abdikalikova Ryskul Oinarov Lars-Erik Persson 《Czechoslovak Mathematical Journal》2011,61(1):7-26
We consider a new Sobolev type function space called the space with multiweighted derivatives $
W_{p,\bar \alpha }^n
$
W_{p,\bar \alpha }^n
, where $
\bar \alpha
$
\bar \alpha
= (α
0, α
1,…, α
n
), α
i
∈ ℝ, i = 0, 1,…, n, and $
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
$
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
,
$
D_{\bar \alpha }^0 f(t) = t^{\alpha _0 } f(t),D_{\bar \alpha }^i f(t) = t^{\alpha _i } \frac{d}
{{dt}}D_{\bar \alpha }^{i - 1} f(t),i = 1,2,...,n
$
D_{\bar \alpha }^0 f(t) = t^{\alpha _0 } f(t),D_{\bar \alpha }^i f(t) = t^{\alpha _i } \frac{d}
{{dt}}D_{\bar \alpha }^{i - 1} f(t),i = 1,2,...,n
相似文献
15.
I. I. Sharapudinov 《Mathematical Notes》1997,62(4):501-512
Suppose that 0<δ≤1,N=1/δ, and α, ga≥0, is an integer. For the classical Meixner polynomials
orthonormal on the gird {0, δ, 2δ, ...} with weight ρ(x)=(1-e
−δ)αг(Nx+α+ 1)/г(Nx+1), the following asymptotic formula is obtained:
. The remainderv
n,N
α
(z) forn≤λN satisfies the estimate
16.
Francesco Leonetti 《Annali dell'Universita di Ferrara》1985,31(1):169-184
Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali
dei funzionali
sotto opportune ipotesi suA
ij
αβ
e sug.
Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA ij αβ andg.相似文献 17.
Xiao Chun FANG Shu Dong LIU 《数学学报(英文版)》2007,23(10):1745-1750
Let A be a separable unital nuclear simple C*-algebra with torsion K0 (A), free K1 (A) and with the UCT. Let T : A→M(K)/K be a unital homomorphism. We prove that every unitary element in the commutant of T(A) is an exponent, thus it is liftable. We also prove that each automorphism α on E with α ∈ Aut0(A) is approximately inner, where E is a unital essential extension of A by K and α is the automorphism on A induced by α. 相似文献
18.
For 0 < α < mn and nonnegative integers n ≥ 2, m ≥ 1, the multilinear fractional integral is defined by
19.
Cao Jiading 《分析论及其应用》1989,5(2):99-109
Let an≥0 and F(u)∈C [0,1], Sikkema constructed polynomials:
, ifα
n
≡0, then Bn (0, F, x) are Bernstein polynomials.
Let
, we constructe new polynomials in this paper:
Q
n
(k)
(α
n
,f(t))=d
k
/dx
k
B
n+k
(α
n
,F
k
(u),x), which are called Sikkema-Kantorovic polynomials of order k. Ifα
n
≡0, k=1, then Qn
(1) (0, f(t), x) are Kantorovič polynomials Pn(f). Ifα
n
=0, k=2, then Qn
(2), (0, f(t), x) are Kantorovič polynomials of second order (see Nagel). The main result is:
Theorem 2. Let 1≤p≤∞, in order that for every f∈LP [0, 1],
, it is sufficient and necessary that
,
§ 1. Let f(t) de a continuous function on [a, b], i. e., f∈C [a, b], we define[1–2],[8–10]:
.
As usual, for the space Lp [a,b](1≤p<∞), we have
and L[a, b]=l1[a, b].
Letα
n
⩾0and F(u)∈C[0,1],Sikkema-Bernstein polynomials
[3] [4].
The author expresses his thanks to Professor M. W. Müller of Dortmund University at West Germany for his supports. 相似文献
20.
M. Felten 《Acta Mathematica Hungarica》2008,118(3):265-297
The paper is concerned with bounds for integrals of the type
|