共查询到20条相似文献,搜索用时 15 毫秒
1.
Hüseyin Bor 《Rendiconti del Circolo Matematico di Palermo》2007,56(2):198-206
In the present paper, a general theorem on summability factors of infinite series has been proved. Also we have obtained a new result concerning the |C,1;δ|
k
summability factors. 相似文献
2.
Hüseyin Bor 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):358-368
In the present paper, two general theorems on summability factors of infinite series which generalize some known results, have been proved. Also we have obtained two new
results concerning the |C,1;δ|
k
summability factors. 相似文献
3.
It is proved that for any two subsets A and B of an arbitrary finite field $
\mathbb{F}_q
$
\mathbb{F}_q
such that |A||B| > q, the identity 10AB = $
\mathbb{F}_q
$
\mathbb{F}_q
holds. Under the assumption |A||B| ⩾2q, this improves to 8AB = $
\mathbb{F}_q
$
\mathbb{F}_q
. 相似文献
4.
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
5.
Bohui Chen 《数学学报(英文版)》2010,26(2):209-240
The bubble tree compactified instanton moduli space -Mκ (X) is introduced. Its singularity set Singκ(X) is described. By the standard gluing theory, one can show that- Mκ(X) - Singκ(X) is a topological orbifold. In this paper, we give an argument to construct smooth structures on it. 相似文献
6.
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
7.
In the study of two-dimensional compact toric varieties, there naturally appears a set of coordinate planes of codimension
two $
Z = {*{20}c}
\cup \\
{1 < \left| {i - j} \right| < d - 1} \\
\{ z_i = z_j = 0\}
$
Z = \begin{array}{*{20}c}
\cup \\
{1 < \left| {i - j} \right| < d - 1} \\
\end{array} \{ z_i = z_j = 0\}
in ℂ
d
. Based on the Alexander-Pontryagin duality theory, we construct a cycle that is dual to the generator of the highest dimensional
nontrivial homology group of the complement in ℂ
d
of the set of planes Z. We explicitly describe cycles that generate groups H
d+2(ℂ
d
\ Z) and H
d−3($
\bar Z
$
\bar Z
), where $
\bar Z
$
\bar Z
= Z ∪ {∞}. 相似文献
8.
Let ξ, ξ1, ξ2, ... be independent identically distributed random variables, and S
n
:=Σ
j=1
n
,ξ
j
, $
\bar S
$
\bar S
:= sup
n≥0
S
n
. If Eξ = −a < 0 then we call transient those phenomena that happen to the distribution $
\bar S
$
\bar S
as a → 0 and $
\bar S
$
\bar S
tends to infinity in probability. We consider the case when Eξ fails to exist and study transient phenomena as a → 0 for the following two random walk models:
9.
Hassen AYDI 《数学年刊B辑(英文版)》2011,32(1):15-26
In the presence of applied magnetic fields H such that |lnε| 《H 《1/ε2,the author evaluates the minimal Ginzburg-Landau energy with discontinuous constraint.Its expression is analogous to the work of Sandier and Serfaty. 相似文献
10.
Approximation to the function |x| plays an important role in approximation theory. This paper studies the approximation to the function xαsgn x, which equals |x| if α = 1. We construct a Newman Type Operator rn(x) and prove max |x|≤1|xαsgn x-rn(x)|~Cn1/4e-π1/2(1/2)αn. 相似文献
11.
Péter Kevei 《Periodica Mathematica Hungarica》2010,60(1):25-36
Let X1,X2, ... be iid random variables, and let a
n
= (a
1,n, ..., a
n,n
) be an arbitrary sequence of weights. We investigate the asymptotic distribution of the linear combination $
S_{a_n }
$
S_{a_n }
= a
1,n
X
1 + ... + a
n,n
X
n
under the natural negligibility condition lim
n→∞
max{|a
k,n
|: k = 1, ..., n} = 0. We prove that if $
S_{a_n }
$
S_{a_n }
is asymptotically normal for a weight sequence a
n
, in which the components are of the same magnitude, then the common distribution belongs to $
\mathbb{D}
$
\mathbb{D}
(2). 相似文献
12.
B. Wróbel 《Acta Mathematica Hungarica》2009,124(4):333-351
Imaginary powers associated to the Laguerre differential operator $
L_\alpha = - \Delta + |x|^2 + \sum _{i = 1}^d \frac{1}
{{x_i^2 }}(\alpha _i^2 - 1/4)
$
L_\alpha = - \Delta + |x|^2 + \sum _{i = 1}^d \frac{1}
{{x_i^2 }}(\alpha _i^2 - 1/4)
are investigated. It is proved that for every multi-index α = (α1,...α
d
) such that α
i
≧ −1/2, α
i
∉ (−1/2, 1/2), the imaginary powers $
\mathcal{L}_\alpha ^{ - i\gamma } ,\gamma \in \mathbb{R}
$
\mathcal{L}_\alpha ^{ - i\gamma } ,\gamma \in \mathbb{R}
, of a self-adjoint extension of L
α, are Calderón-Zygmund operators. Consequently, mapping properties of $
\mathcal{L}_\alpha ^{ - i\gamma }
$
\mathcal{L}_\alpha ^{ - i\gamma }
follow by the general theory. 相似文献
13.
Considering the positive d-dimensional lattice point Z
+
d
(d ≥ 2) with partial ordering ≤, let {X
k: k ∈ Z
+
d
} be i.i.d. random variables taking values in a real separable Hilbert space (H, ‖ · ‖) with mean zero and covariance operator Σ, and set $
S_n = \sum\limits_{k \leqslant n} {X_k }
$
S_n = \sum\limits_{k \leqslant n} {X_k }
, n ∈ Z
+
d
. Let σ
i
2, i ≥ 1, be the eigenvalues of Σ arranged in the non-increasing order and taking into account the multiplicities. Let l be the dimension of the corresponding eigenspace, and denote the largest eigenvalue of Σ by σ
2. Let logx = ln(x ∨ e), x ≥ 0. This paper studies the convergence rates for $
\sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}} P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt {2\left| n \right|\log \log \left| n \right|} } \right)
$
\sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}} P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt {2\left| n \right|\log \log \left| n \right|} } \right)
. We show that when l ≥ 2 and b > −l/2, E[‖X‖2(log ‖X‖)
d−2(log log ‖X‖)
b+4] < ∞ implies $
\begin{gathered}
\mathop {\lim }\limits_{\varepsilon \searrow \sqrt {d - 1} } (\varepsilon ^2 - d + 1)^{b + l/2} \sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt 2 \left| n \right|\log \log \left| n \right|} \right)} \hfill \\
= \frac{{K(\Sigma )(d - 1)^{\frac{{l - 2}}
{2}} \Gamma (b + l/2)}}
{{\Gamma (l/2)(d - 1)!}} \hfill \\
\end{gathered}
$
\begin{gathered}
\mathop {\lim }\limits_{\varepsilon \searrow \sqrt {d - 1} } (\varepsilon ^2 - d + 1)^{b + l/2} \sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt 2 \left| n \right|\log \log \left| n \right|} \right)} \hfill \\
= \frac{{K(\Sigma )(d - 1)^{\frac{{l - 2}}
{2}} \Gamma (b + l/2)}}
{{\Gamma (l/2)(d - 1)!}} \hfill \\
\end{gathered}
, where Γ(·) is the Gamma function and $
\prod\limits_{i = l + 1}^\infty {((\sigma ^2 - \sigma _i^2 )/\sigma ^2 )^{ - {1 \mathord{\left/
{\vphantom {1 2}} \right.
\kern-\nulldelimiterspace} 2}} }
$
\prod\limits_{i = l + 1}^\infty {((\sigma ^2 - \sigma _i^2 )/\sigma ^2 )^{ - {1 \mathord{\left/
{\vphantom {1 2}} \right.
\kern-\nulldelimiterspace} 2}} }
. 相似文献
14.
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
15.
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
16.
Hüseyin Bor 《Proceedings Mathematical Sciences》1994,104(2):367-372
In this paper using δ-quasi-monotone sequences a theorem on
summability factors of infinite series, which generalizes a theorem of Bor [4] on
summability factors of infinite series, is proved. Also, in the special case this theorem includes a result of Mazhar [8]
on |C, 1|k summability factors. 相似文献
17.
We classify deformations of the standard embedding of the Lie superalgebra $
\mathcal{K}
$
\mathcal{K}
(2) of contact vector fields on the (1, 2)-dimensional supercircle into the Lie superalgebra SΨD(S
1|2
) of pseudodifferential operators on the supercircle S
1|2
. The proposed approach leads to the deformations of the central charge induced on $
\mathcal{K}
$
\mathcal{K}
(2) by the canonical central extension of SΨD(S
1|2
). 相似文献
18.
This work is a continuation of paper [1], where was considered analog of the problem of the first return for ultrametric diffusion.
The main result of this paper consists in construction and investigation of stochastic quantity $
\tau _{B_r (a)}
$
\tau _{B_r (a)}
(ω), which has meaning of the first passage time into domain B
r
(a) by trajectories of the Markov stochastic process ζ(t, ω).Markov stochastic process is given by distribution density f(x, t), x ∈ ℚ
p
, t ∈ R
+, which is solution of the Cauchy problem
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