共查询到20条相似文献,搜索用时 46 毫秒
1.
In this paper, we introduce the subfamilies H
m
($
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n)) of holomorphic mappings defined on the Lie ball $
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n) which reduce to the family of holomorphic mappings and the family of locally biholomorphic mappings when m = 1 and m → +∞, respectively. Various distortion theorems for holomophic mappings H
m
($
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n)) are established. The distortion theorems coincide with Liu and Minda’s as the special case of the unit disk. When m = 1 and m → +∞, the distortion theorems reduce to the results obtained by Gong for $
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n), respectively. Moreover, our method is different. As an application, the bounds for Bloch constants of H
m
($
\mathcal{R}_{IV}
$
\mathcal{R}_{IV}
(n)) are given. 相似文献
2.
Sebahattin Ikikardes Recep Sahin I. Naci Cangul 《Bulletin of the Brazilian Mathematical Society》2009,40(4):479-494
In this paper, first, we determine the quotient groups of the Hecke groups H(λ
q
), where q ≥ 7 is prime, by their principal congruence subgroups H
p
(λ
q
) oflevel p, where p is also prime. We deal with the case of q = 7 separately, because of its close relation with the Hurwitz groups. Then, using the obtained results, we find the principal
congruence subgroups of the extended Hecke groups $
\overline H
$
\overline H
(λ
q
) for q ≥ 5 prime. Finally, we show that some of the quotient groups of the Hecke group H(λ
q
) and the extended Hecke group $
\overline H
$
\overline H
(λ
q
), q ≥ 5 prime, by their principal congruence subgroups H
p
(λ
q
) are M*-groups. 相似文献
3.
S. Plancade 《Mathematical Methods of Statistics》2009,18(4):341-374
This paper presents two results: a density estimator and an estimator of regression error density. We first propose a density
estimator constructed by model selection, which is adaptive for the quadratic risk at a given point. Then we apply this result
to estimate the error density in a homoscedastic regression framework Y
i
= b(X
i
) + ε
i
from which we observe a sample (X
i
, Y
i
). Given an adaptive estimator $
\hat b
$
\hat b
of the regression function, we apply the density estimation procedure to the residuals $
\hat \varepsilon _i = Y_i - \hat b(X_i )
$
\hat \varepsilon _i = Y_i - \hat b(X_i )
. We get an estimator of the density of ε
i
whose rate of convergence for the quadratic pointwise risk is the maximum of two rates: the minimax rate we would get if
the errors were directly observed and the minimax rate of convergence of $
\hat b
$
\hat b
for the quadratic integrated risk. 相似文献
4.
Mei-Chu Chang 《Combinatorica》2009,29(6):629-635
In this note, we use ‘classical’ methods to obtain sum-product theorems for subsets A⊂$
\mathbb{F}
$
\mathbb{F}
p
. 相似文献
5.
Let M be a smooth manifold with a regular foliation $
\mathcal{F}
$
\mathcal{F}
and a 2-form ω which induces closed forms on the leaves of $
\mathcal{F}
$
\mathcal{F}
in the leaf topology. A smooth map f: (M, $
\mathcal{F}
$
\mathcal{F}
) → (N, σ) in a symplectic manifold (N, σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the restriction of f*σ is the same as the restriction of ω on each leaf of the foliation.
If f is a foliated symplectic immersion then the derivative map Df gives rise to a bundle morphism F: TM → T N which restricts to a monomorphism on T
$
\mathcal{F}
$
\mathcal{F}
⊆ T M and satisfies the condition F*σ = ω on T
$
\mathcal{F}
$
\mathcal{F}
. A natural question is whether the existence of such a bundle map F ensures the existence of a foliated symplectic immersion f. As we shall see in this paper, the obstruction to the existence of such an f is only topological in nature. The result is proved using the h-principle theory of Gromov. 相似文献
6.
7.
Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated explicitly. And the cyclic homology of∧ can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from i≥1 HH^i(∧) to i≥1 HH^i(∧). 相似文献
8.
K. Zh. Kudaibergenov 《Siberian Advances in Mathematics》2010,20(1):58-67
We introduce the notion of a superstructure over a model. This is a generalization of the notion of the hereditarily finite
superstructure ℍ$
\mathbb{F}\mathfrak{M}
$
\mathbb{F}\mathfrak{M}
over a model $
\mathfrak{M}
$
\mathfrak{M}
. We consider the question on cardinalities of definable (interpretable) sets in superstructures over λ-homogeneous and λ-saturated models. 相似文献
9.
Let λ be a real number such that 0 < λ < 1. We establish asymptotic formulas for the weighted real moments Σ
n≤x
R
λ
(n)(1 − n/x), where R(n) =$
\prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu - 1} }
$
\prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu - 1} }
is the Atanassov strong restrictive factor function and n =$
\prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu } }
$
\prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu } }
is the prime factorization of n. 相似文献
10.
Spiros A. Argyros Irene Deliyanni Andreas G. Tolias 《Israel Journal of Mathematics》2011,181(1):65-110
We provide a characterization of the Banach spaces X with a Schauder basis (e
n
)
n∈ℕ which have the property that the dual space X* is naturally isomorphic to the space L
diag(X) of diagonal operators with respect to (e
n
)
n∈ℕ. We also construct a Hereditarily Indecomposable Banach space $
\mathfrak{X}
$
\mathfrak{X}
D with a Schauder basis (e
n
)
n∈ℕ such that $
\mathfrak{X}
$
\mathfrak{X}
*D is isometric to L
diag($
\mathfrak{X}
$
\mathfrak{X}
D) with these Banach algebras being Hereditarily Indecomposable. Finally, we show that every T ∈ L
diag($
\mathfrak{X}
$
\mathfrak{X}
D) is of the form T = λI + K, where K is a compact operator. 相似文献
11.
Let $
\mathfrak{S}
$
\mathfrak{S}
be a locally compact semigroup, ω be a weight function on $
\mathfrak{S}
$
\mathfrak{S}
, and M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) be the weighted semigroup algebra of $
\mathfrak{S}
$
\mathfrak{S}
. Let L
0∞ ($
\mathfrak{S}
$
\mathfrak{S}
; M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)) be the C*-algebra of all M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)-measurable functions g on $
\mathfrak{S}
$
\mathfrak{S}
such that g/ω vanishes at infinity. We introduce and study a strict topology β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω) on M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) and show that the Banach space L
0∞ ($
\mathfrak{S}
$
\mathfrak{S}
; M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)) can be identified with the dual of M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) endowed with β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω). We finally investigate some properties of the locally convex topology β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω) on M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω). 相似文献
12.
We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-Xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in S n+1 satisfying Sf 4 f_3~2 ≤ 1/n S~3 , where S is the squared norm of the second fundamental form of M, and f_k =sum λ_i~k from i and λ_i (1 ≤ i ≤ n) are the principal curvatures of M. We prove that there exists a positive constant δ(n)(≥ n/2) depending only on n such that if n ≤ S ≤ n + δ(n), then S ≡ n, i.e., M is one of the Clifford torus S~k ((k/n)~1/2 ) ×S~... 相似文献
13.
We obtain characterizations (and prove the corresponding equivalence of norms) of function spaces B
pq
sm
($
\mathbb{I}
$
\mathbb{I}
k
) and L
pq
sm
($
\mathbb{I}
$
\mathbb{I}
k
) of Nikol’skii-Besov and Lizorkin-Triebel types, respectively, in terms of representations of functions in these spaces by
Fourier series with respect to a multiple system $
\mathcal{W}_m^\mathbb{I}
$
\mathcal{W}_m^\mathbb{I}
of Meyer wavelets and in terms of sequences of the Fourier coefficients with respect to this system. We establish order-sharp
estimates for the approximation of functions in B
pq
sm
($
\mathbb{I}
$
\mathbb{I}
) and L
pq
sm
($
\mathbb{I}
$
\mathbb{I}
k
) by special partial sums of these series in the metric of L
r
($
\mathbb{I}
$
\mathbb{I}
k
) for a number of relations between the parameters s, p, q, r, and m (s = (s
1, ..., s
n
) ∈ ℝ+
n
, 1 ≤ p, q, r ≤ ∞, m = (m
1, ..., m
n
) ∈ ℕ
n
, k = m
1 +... + m
n
, and $
\mathbb{I}
$
\mathbb{I}
= ℝ or $
\mathbb{T}
$
\mathbb{T}
). In the periodic case, we study the Fourier widths of these function classes. 相似文献
14.
A. V. Stolyarov 《Russian Mathematics (Iz VUZ)》2010,54(11):56-65
In this paper, the following results are obtained: 1) It is proved that, in the fourth order differential neighborhood, a
regular hypersurface V
n−1 embedded into a projective-metric space K
n
, n ≥ 3, intrinsically induces a dual projective-metric space $
\bar K_n
$
\bar K_n
. 2) An invariant analytical condition is established under which a normalization of a hypersurface V
n−1 ⊂ K
n
(a tangential hypersurface $
\bar V_{n - 1}
$
\bar V_{n - 1}
⊂ $
\bar K_n
$
\bar K_n
) by quasitensor fields H
n
i
, H
i
($
\bar H_n^i
$
\bar H_n^i
, $
\bar H_i
$
\bar H_i
) induces a Riemannian space of constant curvature. If the two conditions are fulfilled simultaneously, the spaces R
n−1 and $
\bar R_{n - 1}
$
\bar R_{n - 1}
are spaces of the same constant curvature $
K = - \tfrac{1}
{c}
$
K = - \tfrac{1}
{c}
. 3) Geometric interpretations of the obtained analytical conditions are given. 相似文献
15.
If the second order problem u(t) + Bu(t) + Au(t) = f(t), u(0) =u(0) = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ(λ^2 + λB + A)^-1‖ and ‖B(λ^2 + λB + A)^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0. 相似文献
16.
The set of all m × n Boolean matrices is denoted by $
\mathbb{M}
$
\mathbb{M}
m,n
. We call a matrix A ∈ $
\mathbb{M}
$
\mathbb{M}
m,n
regular if there is a matrix G ∈ $
\mathbb{M}
$
\mathbb{M}
n,m
such that AGA = A. In this paper, we study the problem of characterizing linear operators on $
\mathbb{M}
$
\mathbb{M}
m,n
that strongly preserve regular matrices. Consequently, we obtain that if min{m, n} ⩽ 2, then all operators on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserve regular matrices, and if min{m, n} ⩾ 3, then an operator T on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserves regular matrices if and only if there are invertible matrices U and V such that T(X) = UXV for all X ε $
\mathbb{M}
$
\mathbb{M}
m,n
, or m = n and T(X) = UX
T
V for all X ∈ $
\mathbb{M}
$
\mathbb{M}
n
. 相似文献
17.
A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: $
\mathbb{I}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M there exists a map g′: $
\mathbb{I}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M such that g′ is ɛ-homotopic to g and dim g′ ({z} × $
\mathbb{I}
$
\mathbb{I}
n
) ≤ n for all z ∈ $
\mathbb{I}
$
\mathbb{I}
m
. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij
[11] and Tuncali-Valov [10]. 相似文献
18.
Let E be a cookie-cutter set with dimH E =s. It is known that the Hausdorff s-measure and the packing s-measure of the set E are positive and finite. In this paper, we prove that for a gauge function g the set E has positive and finite Hausdorff g-measure if and only if 0 〈 liminft→0 g(t)/ts 〈 ∞. Also, we prove that for a doubling gauge function g the set E has positive and finite packing g-measure if and only if 0 〈 lim supt→0 g(t)/ts 〈 ∞. 相似文献
19.
Marcio Colombo Fenille Oziride Manzoli Neto 《Central European Journal of Mathematics》2010,8(3):421-429
Given a model 2-complex K
P
of a group presentation P, we associate to it an integer matrix Δ
P
and we prove that a cellular map f: K
P
→ S
2 is root free (is not strongly surjective) if and only if the diophantine linear system Δ
P
Y = $
\overrightarrow {deg}
$
\overrightarrow {deg}
(f) has an integer solution, here $
\overrightarrow {deg}
$
\overrightarrow {deg}
(f)is the so-called vector-degree of f 相似文献
20.
Laurian Suciu 《Israel Journal of Mathematics》2009,174(1):419-443
For two bounded linear operators A and T on a complex Hilbert space H (A being positive) which satisfy the inequality T*AT ≤ A, we study the maximum subspace ℳ0 which reduces A and T, on which the equality T*AT = A holds. We show that in some cases involving the condition AT = A
1/2
TA
1/2, ℳ0 can be expressed in terms of the minimal isometric dilation of the contraction $
\hat T
$
\hat T
on $
\overline {R(A)}
$
\overline {R(A)}
associated to T by the condition $
\hat T
$
\hat T
A
1/2 = A
1/2
T. As application we find a concrete representation for ℳ0 when T is a contraction with S
T
= S
T
2, where S
T is the strong limit of the sequence [T
*n
T
n
: n ≥ 1]. Also, we derive some applications for hyponormal contractions and quasi-isometries. 相似文献