共查询到20条相似文献,搜索用时 31 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.
Let K = $
k(\sqrt \theta )
$
k(\sqrt \theta )
be a real cyclic quartic field, k be its quadratic subfield and $
\tilde K = k(\sqrt { - \theta } )
$
\tilde K = k(\sqrt { - \theta } )
be the corresponding imaginary quartic field. Denote the class numbers of K, k and $
\tilde K
$
\tilde K
by h
K
, h
k
and {417-3} respectively. Here congruences modulo powers of 2 for h
− = h
K
/h
K
and $
\tilde h^ - = h_{\tilde K} /h_k
$
\tilde h^ - = h_{\tilde K} /h_k
are obtained via studying the p-adic L-functions of the fields. 相似文献
3.
4.
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
5.
In this paper, the authors consider the boundedness of generalized higher commutator of Marcinkiewicz integral μΩ^b, multilinear Marcinkiewicz integral μΩ^A and its variation μΩ^A on Herz-type Hardy spaces, here Ω is homogeneous of degree zero and satisfies a class of L^s-Dini condition. And as a special case, they also get the boundedness of commutators of Marcinkiewicz integrals on Herz-type Hardy spaces. 相似文献
6.
Jon Handy 《Journal d'Analyse Mathématique》2009,108(1):1-18
Let K be a square Cantor set, i.e., the Cartesian product K = E × E of two linear Cantor sets. Let δ
n
denote the proportion of the intervals removed in the nth stage of the construction of E. It is shown that if $
\delta _n = o(\frac{1}
{{\log \log n}})
$
\delta _n = o(\frac{1}
{{\log \log n}})
, then the corona theorem holds on the domain Ω = ℂ* \ K. 相似文献
7.
Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification $
\bar C
$
\bar C
(X) of C(X) such that the pair ($
\bar C
$
\bar C
(X), C(X)) is homeomorphic to (Q, s). In case X has no isolated points, this compactification $
\bar C
$
\bar C
(X) coincides with the space USCC
F
(X,
相似文献
8.
Coenraad C. A. Labuschagne Theresa M. Offwood 《Central European Journal of Mathematics》2010,8(6):1109-1119
Let Y be a Banach space, (Ω, Σ; μ) a probability space and φ a finite Young function. It is shown that the Y-valued Orlicz heart H
φ(μ, Y) is isometrically isomorphic to the l-completed tensor product $
H_\varphi \left( \mu \right)\tilde \otimes _l Y
$
H_\varphi \left( \mu \right)\tilde \otimes _l Y
of the scalar-valued Orlicz heart Hφ(μ) and Y, in the sense of Chaney and Schaefer. As an application, a characterization is given of the equality of $
\left( {H_\varphi \left( \mu \right)\tilde \otimes _l Y} \right)*
$
\left( {H_\varphi \left( \mu \right)\tilde \otimes _l Y} \right)*
and $
H_\varphi \left( \mu \right)*\tilde \otimes _l Y*
$
H_\varphi \left( \mu \right)*\tilde \otimes _l Y*
in terms of the Radon-Nikodym property on Y. Convergence of norm-bounded martingales in H
φ(μ, Y) is characterized in terms of the Radon-Nikodym property on Y. Using the associativity of the l-norm, an alternative proof is given of the known fact that for any separable Banach lattice E and any Banach space Y, E and Y have the Radon-Nikodym property if and only if $
E\tilde \otimes _l Y
$
E\tilde \otimes _l Y
has the Radon-Nikodym property. As a corollary, the Radon-Nikodym property in H
φ(μ, Y) is described in terms of the Radon-Nikodym property on H
φ(μ) and Y. 相似文献
9.
This note studies the Chern-Simons invariant of a closed oriented Riemannian 3-manifold M. The first achievement is to establish the formula CS(e) - CS(e) = degA, where e and e are two (global) frames of M, and A : M → SO(3) is the "difference" map. An interesting phenomenon is that the "jumps" of the Chern-Simons integrals for various frames of many 3-manifolds are at least two, instead of one. The second purpose is to give an explicit representation of CS(e+) and CS(e_), where e+ and e_ are the "left" and "right" quaternionic frames on M3 induced from an immersion M^3 → E^4, respectively. Consequently we find many metrics on S^3 (Berger spheres) so that they can not be conformally embedded in E^4. 相似文献
10.
We consider one-phase (formal) asymptotic solutions in the Kuzmak-Whitham form for the nonlinear Klein-Gordon equation and for the Korteweg-de Vries equation.
In this case, the leading asymptotic expansion term has the form X(S(x, t)/h+Φ(x, t), I(x, t), x, t) +O(h), where h ≪ 1 is a small parameter and the phase S}(x, t) and slowly changing parameters I(x, t) are to be found from the system of “averaged” Whitham equations. We obtain the equations for the phase shift Φ(x, t) by studying the second-order correction to the leading term. The corresponding procedure for finding the phase shift is
then nonuniform with respect to the transition to a linear (and weakly nonlinear) case. Our observation, which essentially
follows from papers by Haberman and collaborators, is that if we incorporate the phase shift Φ into the phase and adjust the
parameter Ĩ by setting $
\tilde S
$
\tilde S
= S +hΦ+O(h
2),Ĩ = I + hI
1 + O(h
2), then the functions $
\tilde S
$
\tilde S
(x, t, h) and Ĩ(x, t, h) become solutions of the Cauchy problem for the same Whitham system but with modified initial conditions. These functions
completely determine the leading asymptotic term, which is X($
\tilde S
$
\tilde S
(x, t, h)/h, Ĩ(x, t, h), x, t) + O(h). 相似文献
11.
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
12.
13.
For systems of second-order nonlinear ordinary differential equations with the Dirichlet boundary conditions, we develop generalized
three-point difference schemes of high-order accuracy on a nonuniform grid. The construction of the suggested schemes requires
solving four auxiliary Cauchy problems (two problems for systems of nonlinear ordinary differential equations and two problems
for matrix linear ordinary differential equations) on the intervals [x
j−1, x
j
] (forward) and [x
j
, x
j+1] (backward) at each grid point; this is done at each step by any single-step method of accuracy order $
\bar m
$
\bar m
= 2[(m+1)/2]. (Here m is a given positive integer, and [·] is the integer part of a number.) We prove that such three-point difference schemes
have the accuracy order $
\bar m
$
\bar m
for the approximation to both the solution u of the boundary value problem and the flux K(x)d
u/dx at the grid points. 相似文献
14.
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
15.
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
16.
Heinrich P. Lotz 《Israel Journal of Mathematics》2010,176(1):209-220
We consider a Dedekind σ-complete Banach lattice E whose dual is weakly sequentially complete. Suppose that E has a positive element u and a family of positive operators $
\mathcal{G}
$
\mathcal{G}
such that
(i) |
each T′, T ∈ $
\mathcal{G}
$
\mathcal{G}
, is a lattice homomorphism 相似文献
17.
The $
\vec E
$
\vec E
= (E, E(2-k
)) is a stably $
\vec E
$
\vec E
is $
\vec E
$
\vec E
is $
\vec E
$
\vec E
is -monotone, then either E = l
p (1 ≤ p < ∞) or E = c
0. 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
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |