共查询到20条相似文献,搜索用时 889 毫秒
1.
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
2.
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
3.
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
4.
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
5.
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:
We obtain some results for identically and differently distributed ξ
j
. 相似文献
1. | The first model assumes that ξ j can be represented as ξ j = ζ j + αη j , where ζ1, ζ 2 , ... and η 1, η 2, ... are two independent sequences of independent random variables, identically distributed in each sequence, such that supn≥0Σ j=1 n ζ j = ∞, sup n≥0Σ j=1 n η j < ∞, and $ \bar S $ \bar S < ∞ almost surely. |
2. | In the second model we consider a triangular array scheme with parameter a and assume that the right tail distribution P(ξ j ≥ t) ∼ V (t) as t→∞ depends weakly on a, while the left tail distribution is P(ξ j < −t) = W(t/a), where V and W are regularly varying functions and $ \bar S $ \bar S < ∞ almost surely for every fixed α > 0. |
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.
Dong Sheng Kang 《数学学报(英文版)》2009,25(3):435-444
Suppose Ω belong to R^N(N≥3) is a smooth bounded domain,ξi∈Ω,0〈ai〈√μ,μ:=((N-1)/2)^2,0≤μi〈(√μ-ai)^2,ai〈bi〈ai+1 and pi:=2N/N-2(1+ai-bi)are the weighted critical Hardy-Sobolev exponents, i = 1, 2,..., k, k ≥ 2. We deal with the conditions that ensure the existence of positive solutions to the multi-singular and multi-critical elliptic problem ∑i=1^k(-div(|x-ξi|^-2ai△↓u)-μiu/|x-ξi|^2(1+ai)-u^pi-1/|x-ξi|^bipi)=0with Dirichlet boundary condition, which involves the weighted Hardy inequality and the weighted Hardy-Sobolev inequality. The results depend crucially on the parameters ai, bi and #i, i -- 1, 2,..., k. 相似文献
8.
A. V. Zheleznyak 《Vestnik St. Petersburg University: Mathematics》2009,42(4):269-274
In the middle of the 20th century Hardy obtained a condition which must be imposed on a formal power series f(x) with positive coefficients in order that the series f
−1(x) = $
\sum\limits_{n = 0}^\infty {b_n x^n }
$
\sum\limits_{n = 0}^\infty {b_n x^n }
b
n
x
n
be such that b
0 > 0 and b
n
≤ 0, n ≥ 1. In this paper we find conditions which must be imposed on a multidimensional series f(x
1, x
2, …, x
m
) with positive coefficients in order that the series f
−1(x
1, x
2, …, x
m
) = $
\sum i_1 ,i_2 , \ldots ,i_m \geqslant 0^b i_1 ,i_2 , \ldots ,i_m ^{x_1^{i_1 } x_2^{i_2 } \ldots x_m^{i_m } }
$
\sum i_1 ,i_2 , \ldots ,i_m \geqslant 0^b i_1 ,i_2 , \ldots ,i_m ^{x_1^{i_1 } x_2^{i_2 } \ldots x_m^{i_m } }
satisfies the property b
0, …, 0 > 0, $
bi_1 ,i_2 , \ldots ,i_m
$
bi_1 ,i_2 , \ldots ,i_m
≤ 0, i
12 + i
22 + … + i
m
2 > 0, which is similar to the one-dimensional case. 相似文献
9.
10.
The $
\bar \partial
$
\bar \partial
-closed differential forms with smooth coefficients are studied in the closure of a bounded domain D ⊂ ℂ
n
. It is demonstrated that the condition of $
\bar \partial
$
\bar \partial
-closedness can be replaced with a weaker differential condition in the domain and differential conditions on the boundary.
In particular, for the forms with harmonic coefficients the $
\bar \partial
$
\bar \partial
-closedness is equivalent to some boundary relations. This allows us to treat the results as conditions for the $
\bar \partial
$
\bar \partial
-closedness of an extension of a form from the boundary. 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.
S. V. Poborchii 《Vestnik St. Petersburg University: Mathematics》2010,43(3):175-182
The problem of representing the solution of the Dirichlet problem for the Laplace equation as a single-layer potential V
ϱ with unknown density ϱ is known to lead to the equation V
ϱ = f for density ϱ, where f is the Dirichlet boundary data. Let Γ be the boundary of a bounded planar domain with an outward or inward peak and T(Γ) be the space of the traces on Γ of functions with finite Dirichlet integral over R
2. It is shown that the operator $
L_2 \left( \Gamma \right) \ominus 1 \mathrel\backepsilon \varrho \to V\left. \varrho \right|\Gamma \in T\left( \Gamma \right)
$
L_2 \left( \Gamma \right) \ominus 1 \mathrel\backepsilon \varrho \to V\left. \varrho \right|\Gamma \in T\left( \Gamma \right)
is continuous, and the operator $
\varrho \to V\varrho - \overline {V\varrho }
$
\varrho \to V\varrho - \overline {V\varrho }
(where $
\bar u
$
\bar u
denotes u averaged over Γ) can be uniquely extended to the isomorphism
相似文献
13.
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
14.
A. V. Parfenenkov 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):194-204
We study the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
of algebraic polynomials P
n
(x, y) in two variables of total degree n whose uniform norm on the unit circle Γ1 centered at the origin is at most 1: $
\left\| {P_n } \right\|_{C(\Gamma _1 )}
$
\left\| {P_n } \right\|_{C(\Gamma _1 )}
≤ 1. The extension of polynomials from the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
to the plane with the least uniform norm on the concentric circle Γ
r
of radius r is investigated. It is proved that the values θ
n
(r) of the best extension of the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
satisfy the equalities θ
n
(r) = r
n
for r > 1 and θ
n
(r) = r
n−1 for 0 < r < 1. 相似文献
15.
I. E. Zuber 《Vestnik St. Petersburg University: Mathematics》2010,43(3):139-142
A control of an nth-order discrete system under an external perturbation is considered. The elements of the matrix of the system are functionals
of any nature. The observation matrix is constant and has arbitrary size m × n. A control ensuring the independence of the output σ
k
on the external perturbation ψ
k
is synthesized; moreover,
|