共查询到20条相似文献,搜索用时 31 毫秒
1.
Dhurjati Prasad Datta Santanu Raut Anuja Raychoudhuri 《P-Adic Numbers, Ultrametric Analysis, and Applications》2011,3(1):7-22
A class of ultrametric Cantor sets (C, d
u
) introduced recently (S. Raut and D. P. Datta, Fractals 17, 45–52 (2009)) is shown to enjoy some novel properties. The ultrametric d
u
is defined using the concept of relative infinitesimals and an inversion rule. The associated (infinitesimal) valuation which turns out to be both scale and reparametrization invariant, is identified
with the Cantor function associated with a Cantor set $
\tilde C
$
\tilde C
, where the relative infinitesimals are supposed to live in. These ultrametrics are both metrically as well as topologically
inequivalent compared to the topology induced by the usual metric. Every point of the original Cantor set C is identified with the closure of the set of gaps of $
\tilde C
$
\tilde C
. The increments on such an ultrametric space is accomplished by following the inversion rule. As a consequence, Cantor functions
are reinterpreted as locally constant functions on these extended ultrametric spaces. An interesting phenomenon, called growth of measure, is studied on such an ultrametric space. Using the reparametrization invariance of the valuation it is shown how the scale
factors of a Lebesgue measure zero Cantor set might get deformed leading to a deformed Cantor set with a positive measure. The definition of a new valuated exponent is introduced which is shown to yield the fatness exponent in the case of a positive measure (fat) Cantor set. However, the
valuated exponent can also be used to distinguish Cantor sets with identical Hausdorff dimension and thickness. A class of
Cantor sets with Hausdorff dimension log3 2 and thickness 1 are constructed explicitly. 相似文献
2.
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
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.
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.
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
7.
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
8.
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
9.
Hongliang Yao 《Proceedings Mathematical Sciences》2010,120(2):199-207
Lin and Su classified A$
\mathcal{T}
$
\mathcal{T}
-algebras of real rank zero. This class includes all A$
\mathbb{T}
$
\mathbb{T}
-algebras of real rank zero as well as many C*-algebras which are not stably finite. An A$
\mathcal{T}
$
\mathcal{T}
-algebra often becomes an extension of an A$
\mathbb{T}
$
\mathbb{T}
-algebra by an AF-algebra. In this paper, we show that there is an essential extension of an A$
\mathbb{T}
$
\mathbb{T}
-algebra by an AF-algebra which is not an A$
\mathcal{T}
$
\mathcal{T}
-algebra. We describe a characterization of an extension E of an A$
\mathbb{T}
$
\mathbb{T}
-algebra by an AF-algebra if E is an A$
\mathcal{T}
$
\mathcal{T}
-algebra. 相似文献
10.
Assume that no cardinal κ < 2
ω
is quasi-measurable (κ is quasi-measurable if there exists a κ-additive ideal
$
\mathbb{I}
$
\mathbb{I}
of X contains uncountably many pairwise disjoint subfamilies
$
\mathbb{I}
$
\mathbb{I}
-Bernstein unions ∪
$
\mathbb{I}
$
\mathbb{I}
-Bernstein if A and X \ A meet each Borel $
\mathbb{I}
$
\mathbb{I}
-positive subset B ⊆ X). This result is a generalization of the Four Poles Theorem (see [1]) and results from [2] and [4]. 相似文献
11.
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
12.
Let A and B denote two families of subsets of an n-element set. The pair (A,B) is said to be ℓ-cross-intersecting iff |A∩B|=ℓ for all A∈ A and B∈B. Denote by P
e
(n) the maximum value of |A||B| over all such pairs. The best known upper bound on P
e
(n) is Θ(2
n
), by Frankl and R?dl. For a lower bound, Ahlswede, Cai and Zhang showed, for all n ≥ 2ℓ, a simple construction of an ℓ-cross-intersecting pair (A,B) with |A||B| = $
\left( {{*{20}c}
{2\ell } \\
\ell \\
} \right)
$
\left( {\begin{array}{*{20}c}
{2\ell } \\
\ell \\
\end{array} } \right)
2
n−2ℓ
= Θ(2
n
/$
\sqrt \ell
$
\sqrt \ell
), and conjectured that this is best possible. Consequently, Sgall asked whether or not P
e
(n) decreases with ℓ. 相似文献
13.
We generalize the results of [11] and [12] for the unit ball $
\mathbb{B}_d
$
\mathbb{B}_d
of ℂ
d
. In particular, we show that under the weight condition (B) the weighted H
∞-space on $
\mathbb{B}_d
$
\mathbb{B}_d
is isomorphic to ℓ∞ and thus complemented in the corresponding weighted L
∞-space. We construct concrete, generalized Bergman projections accordingly. We also consider the case where the domain is
the entire space ℂ
d
. In addition, we show that for the polydisc $
\mathbb{D}^d
$
\mathbb{D}^d
d
, the weighted H
∞-space is never isomorphic to ℓ∞. 相似文献
14.
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
15.
Rumi Shindo 《Central European Journal of Mathematics》2010,8(1):135-147
Let A and B be uniform algebras. Suppose that α ≠ 0 and A
1 ⊂ A. Let ρ, τ: A
1 → A and S, T: A
1 → B be mappings. Suppose that ρ(A
1), τ(A
1) and S(A
1), T(A
1) are closed under multiplications and contain expA and expB, respectively. If ‖S(f)T(g) − α‖∞ = ‖ρ(f)τ(g) − α‖∞ for all f, g ∈ A
1, S(e
1)−1 ∈ S(A
1) and S(e
1) ∈ T(A
1) for some e
1 ∈ A
1 with ρ(e
1) = 1, then there exists a real-algebra isomorphism $
\tilde S
$
\tilde S
: A → B such that $
\tilde S
$
\tilde S
(ρ(f)) = S(e
1)−1
S(f) for every f ∈ A
1. We also give some applications of this result. 相似文献
16.
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
17.
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
18.
This note continues some previous studies by the authors. We consider a linear-fractional mapping $
F_A :K \to K
$
F_A :K \to K
generated by a triangular operator, where $
K
$
K
is the unit operator ball and the fixed point C of the extension of $
F_A
$
F_A
to $
\overline K
$
\overline K
is either an isometry or a coisometry. Under some natural restrictions on one of the diagonal entries of the operator matrix
A, the structure of the other diagonal entry is investigated completely. It is shown that generally C cannot be replaced in all these considerations by an arbitrary point of the unit sphere. Some special cases are studied in
which this is nevertheless possible. 相似文献
19.
S. K. Godunov A. N. Malyshev 《Computational Mathematics and Mathematical Physics》2008,48(7):1089-1099
Let $ \tilde \lambda Let be an approximate eigenvalue of multiplicity m
c
= n − r of an n × n real symmetric tridiagonal matrix T having nonzero off-diagonal entries. A fast algorithm is proposed (and numerically tested) for deleting m
c
rows of T−
I so that the condition number of the r × n matrix B formed of the remaining r rows is as small as possible. A special basis of m
c
vectors with local supports is constructed for the subspace kerB. These vectors are approximate eigenvectors of T corresponding to . Another method for deleting m
c
rows of T−
I is also proposed. This method uses a rank-revealing QR decomposition; however, it requires a considerably larger number of
arithmetic operations. For the latter algorithm, the condition number of B is estimated, and orthogonality estimates for vectors of the special basis of kerB are derived.
Original Russian Text ? S.K. Godunov, A.N. Malyshev, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi
Fiziki, 2008, Vol. 48, No. 7, pp. 1156–1166. 相似文献
20.
T. A. Suslina 《Functional Analysis and Its Applications》2012,46(3):234-238
In a bounded domain O ⊂ ℝd with C 1,1 boundary a matrix elliptic second-order operator A D,ɛ with Dirichlet boundary condition is studied. The coefficients of this operator are periodic and depend on x/ɛ, where ɛ s 0 is a small parameter. The sharp-order error estimate $
\left\| {A_{D,\varepsilon }^{ - 1} - \left( {A_D^0 } \right)^{ - 1} } \right\|\left. {L_2 \to L_2 \leqslant C\varepsilon } \right|
$
\left\| {A_{D,\varepsilon }^{ - 1} - \left( {A_D^0 } \right)^{ - 1} } \right\|\left. {L_2 \to L_2 \leqslant C\varepsilon } \right|
相似文献