共查询到20条相似文献,搜索用时 31 毫秒
1.
Let k be a field and E(n) be the 2
n+1-dimensional pointed Hopf algebra over k constructed by Beattie, Dăscălescu and Grünenfelder [J. Algebra, 2000, 225: 743–770]. E(n) is a triangular Hopf algebra with a family of triangular structures R
M
parameterized by symmetric matrices M in M
n
(k). In this paper, we study the Azumaya algebras in the braided monoidal category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
and obtain the structure theorems for Azumaya algebras in the category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
, where M is any symmetric n×n matrix over k. 相似文献
2.
In previous papers, we have constructed and studied mappings d
k
: M × M → ℝ called the H
k
-distance functions. The main result of this paper is a theorem on realizability of the generalized distances d
k
(υ, w), υ, w ∈ M, by critical values of the length functional L: Ω(M, υ, w) → ℝ generated by nontrivial homology classes of the space Ω(M, υ, w) of paths joining the points υ and w. 相似文献
3.
Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L
2 normalized family of functions such that P(h)u(h) is O(h) in L
2(M) as h↓0. Let H⊂M be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L
p
norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch
−δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator. 相似文献
4.
Morten Nielsen 《Journal of Geometric Analysis》2012,22(1):12-22
We consider a periodic matrix weight W defined on ℝ
d
and taking values in the N×N positive-definite matrices. For such weights, we prove transference results between multiplier operators on L
p
(ℝ
d
;W) and
Lp(\mathbb Td;W)L_{p}(\mathbb {T}^{d};W), 1<p<∞, respectively. As a specific application, we study transference results for homogeneous multipliers of degree zero. 相似文献
5.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献
6.
For 0 < α < mn and nonnegative integers n ≥ 2, m ≥ 1, the multilinear fractional integral is defined by
where = (y
1,y
2, ···, y
m
) and denotes the m-tuple (f
1,f
2, ···, f
m
). In this note, the one-weighted and two-weighted boundedness on L
p
(ℝ
n
) space for multilinear fractional integral operator I
α(m) and the fractional multi-sublinear maximal operator M
α(m) are established respectively. The authors also obtain two-weighted weak type estimate for the operator M
α(m).
Supported in Part by the NNSF of China under Grant #10771110, and by NSF of Ningbo City under Grant #2006A610090. 相似文献
7.
Let ( Y,d,dl )\left( {\mathcal{Y},d,d\lambda } \right) be (ℝ
n
, |·|, μ), where |·| is the Euclidean distance, μ is a nonnegative Radon measure on ℝ
n
satisfying the polynomial growth condition, or the Gauss measure metric space (ℝ
n
, |·|, d
λ
), or the space (S, d, ρ), where S ≡ ℝ
n
⋉ ℝ+ is the (ax + b)-group, d is the left-invariant Riemannian metric and ρ is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces
{ Xs ( Y ) }0 < s \leqslant ¥\left\{ {X_s \left( \mathcal{Y} \right)} \right\}_{0 < s \leqslant \infty } and the BMO-type spaces
{ BMO( Y, s ) }0 < s \leqslant ¥\left\{ {BMO\left( {\mathcal{Y}, s} \right)} \right\}_{0 < s \leqslant \infty }. Let H
1
( Y )\left( \mathcal{Y} \right) be the known atomic Hardy space and L
01
( Y )\left( \mathcal{Y} \right) the subspace of f ∈ L
1
( Y )\left( \mathcal{Y} \right) with integral 0. The authors prove that the dual space of X
s
( Y )\left( \mathcal{Y} \right) is BMO( Y,s )BMO\left( {\mathcal{Y},s} \right) when s ∈ (0,∞), X
s
( Y )\left( \mathcal{Y} \right) = H
1
( Y )\left( \mathcal{Y} \right) when s ∈ (0, 1], and X
∞
( Y )\left( \mathcal{Y} \right) = L
01
( Y )\left( \mathcal{Y} \right) (or L
1
( Y )\left( \mathcal{Y} \right)). As applications, the authors show that if T is a linear operator bounded from H
1
( Y )\left( \mathcal{Y} \right) to L
1
( Y )\left( \mathcal{Y} \right) and from L
1
( Y )\left( \mathcal{Y} \right) to L
1,∞
( Y )\left( \mathcal{Y} \right), then for all r ∈ (1,∞) and s ∈ (r,∞], T is bounded from X
r
( Y )\left( \mathcal{Y} \right) to the Lorentz space L
1,s
( Y )\left( \mathcal{Y} \right), which applies to the Calderón-Zygmund operator on (ℝ
n
, |·|, μ), the imaginary powers of the Ornstein-Uhlenbeck operator on (ℝ
n
, |·|, d
γ
) and the spectral operator associated with the spectral multiplier on (S, d, ρ). All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces. 相似文献
8.
Humio Ichimura 《Archiv der Mathematik》2011,96(6):555-563
Let p be an odd prime number, and pn0{p^{n_0}} the highest power of p dividing 2
p−1 − 1. Let Kn=Q(zpn+1){K_n={\bf Q}(\zeta_{p^{n+1}})} and Ln,j=Kn+(z2j+2){L_{n,j}=K_n^+(\zeta_{2^{j+2}})} for j ≥ 0. Let hn*{h_n^*} be the relative class number of K
n
, and h
n,j
the class number of L
n,j
, respectively. Let n be an integer with n ≥ n
0. We prove that if the ratio hn*/hn-1*{h_n^*/h_{n-1}^*} is odd, then h
n,j
/h
n−1,j
is odd for any j ≥ 0. 相似文献
9.
L
p
approximation capability of radial basis function (RBF) neural networks is investigated. If g: R
+1 → R
1 and ∈ L
loc
p
(R
n
) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L
p
(K) with any accuracy for any compact set K in R
n
, if and only if g(x) is not an even polynomial.
Partly supported by the National Natural Science Foundation of China (10471017) 相似文献
10.
Let E be a Galois extension of ℚ of degree l, not necessarily solvable. In this paper we first prove that the L-function L(s, π) attached to an automorphic cuspidal representation π of cannot be factored nontrivially into a product of L-functions over E.
Next, we compare the n-level correlation of normalized nontrivial zeros of L(s, π1)…L(s, π
k
), where π
j
, j = 1,…, k, are automorphic cuspidal representations of , with that of L(s,π). We prove a necessary condition for L(s, π) having a factorization into a product of L-functions attached to automorphic cuspidal representations of specific , j = 1,…,k. In particular, if π is not invariant under the action of any nontrivial σ ∈ Gal
E/ℚ, then L(s, π) must equal a single L-function attached to a cuspidal representation of and π has an automorphic induction, provided L(s, π) can factored into a product of L-functions over ℚ. As E is not assumed to be solvable over ℚ, our results are beyond the scope of the current theory of base change and automorphic
induction.
Our results are unconditional when m,m
1,…,m
k
are small, but are under Hypothesis H and a bound toward the Ramanujan conjecture in other cases.
The first author was supported by the National Basic Research Program of China, the National Natural Science Foundation of
China (Grant No. 10531060), and Ministry of Education of China (Grant No. 305009). The second author was supported by the
National Security Agency (Grant No. H98230-06-1-0075). The United States Government is authorized to reproduce and distribute
reprints notwithstanding any copyright notation herein 相似文献
11.
In this paper, the authors give the L
p
(1 < p < ∞ ) boundedness of the k-th order commutator of parabolic singular integral with the kernel function Ω ∈ L(log +
L)
k + 1(S
n − 1). The result in this paper is an extension of some known results.
The research was supported by NSF of China (Grant: 10571015) and SRFDP of China (Grant: 20050027025). 相似文献
12.
Ismael G. Yero Sergio Bermudo Juan A. Rodríguez-Velázquez José M. Sigarreta 《数学学报(英文版)》2011,27(1):73-82
A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph
into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψ
k
gd
(Γ)) ψ
k
d
(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψ
k
d
(Θ) and ψ
k
gd
(Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity
and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of Γ1 × Γ2 into (global) defensive (k
1 + k
2)-alliances and partitions of Γ
i
into (global) defensive k
i
-alliances, i ∈ {1, 2}. 相似文献
13.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
and acting in spaces Lp(X, μ), where X is a compact topological space, φk∈C(X), φ = (φk)k=1N∈C(X)N, and
are linear positive operators (Ukf≥ 0 for f≥ 0). We consider the spectral exponent ln r(Aφ) as a functional depending on vector-function φ. We prove that ln r(Aφ) is continuous and on a certain subspace
of C(X)N is also convex. This yields that the spectral exponent is the Fenchel-Legendre transform of a convex functional
defined on a set
of continuous linear positive and normalized functionals on the subspace
of coefficients φ that is
相似文献
14.
Carlo Magagna 《Monatshefte für Mathematik》2008,153(1):59-81
For a positive integer N, we define the N-rank of a non singular integer d × d matrix A to be the maximum integer r such that there exists a minor of order r whose determinant is not divisible by N. Given a positive integer r, we study the growth of the minimum integer k, such that A
k
− I has N-rank at most r, as a function of N. We show that this integer k goes to infinity faster than log N if and only if for every eigenvalue λ which is not a root of unity, the sum of the dimensions of the eigenspaces relative
to eigenvalues which are multiplicatively dependent with λ and are not roots of unity, plus the dimensions of the eigenspaces
relative to eigenvalues which are roots of unity, does not exceed d − r − 1. This result will be applied to recover a recent theorem of Luca and Shparlinski [6] which states that the group of rational
points of an ordinary elliptic curve E over a finite field with q
n
elements is almost cyclic, in a sense to be defined, when n goes to infinity. We will also extend this result to the product of two elliptic curves over a finite field and show that
the orders of the groups of
rational points of two non isogenous elliptic curves are almost coprime when n approaches infinity.
Author’s address: Dipartimento di Matematica e Informatica, Via Delle Scienze 206, 33100 Udine, Italy 相似文献
15.
In (k, n) visual cryptographic schemes (VCS), a secret image is encrypted into n pages of cipher text, each printed on a transparency sheet, which are distributed among n participants. The image can be visually decoded if any k(≥2) of these sheets are stacked on top of one another, while this is not possible by stacking any k − 1 or fewer sheets. We employ a Kronecker algebra to obtain necessary and sufficient conditions for the existence of a (k, n) VCS with a prior specification of relative contrasts that quantify the clarity of the recovered image. The connection of
these conditions with an L
1-norm formulation as well as a convenient linear programming formulation is explored. These are employed to settle certain
conjectures on contrast optimal VCS for the cases k = 4 and 5. Furthermore, for k = 3, we show how block designs can be used to construct VCS which achieve optimality with respect to the average and minimum
relative contrasts but require much smaller pixel expansions than the existing ones. 相似文献
16.
P. Kórus 《Acta Mathematica Hungarica》2010,126(4):369-380
Chaundry and Jolliffe [1] proved that if a
k
is a nonnegative sequence tending monotonically to zero, then a necessary and sufficient condition for the uniform convergence
of the series Σ
k=1∞
a
k
sin kx is lim
k→∞
ka
k
= 0. Lately, S. P. Zhou, P. Zhou and D. S. Yu [4] generalized this classical result. In this paper we propose new classes
of sequences for which we get the extended version of their results. Moreover, we generalize the results of S. Tikhonov [2]
on the L
1-convergence of Fourier series. 相似文献
17.
F. Galaz-Fontes 《Positivity》2010,14(4):715-729
For a vector measure ν having values in a real or complex Banach space and \({p \in}\) [1, ∞), we consider L p (ν) and \({L_{w}^{p}(\nu)}\), the corresponding spaces of p-integrable and scalarly p-integrable functions. Given μ, a Rybakov measure for ν, and taking q to be the conjugate exponent of p, we construct a μ-Köthe function space E q (μ) and show it is σ-order continuous when p > 1. In this case, for the associate spaces we prove that L p (ν) × = E q (μ) and \({E_q(\mu)^\times = L_w^p(\nu)}\). It follows that \({L_p (\nu) ^{**} = L_w^p (\nu)}\). We also show that L 1 (ν) × may be equal or not to E ∞ (μ). 相似文献
18.
Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp(0〈p〈1)Spaces 总被引:1,自引:0,他引:1
SongLI 《数学学报(英文版)》2003,19(1):97-106
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ
1, ..., ϕ
r
)
T
is unknown, g is a given vector of compactly supported functions on ℝ
s
, a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite
interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ
n
, n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ
0. We characterize the L
p
-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness
property of the solutions of the refinement equations associated with the homogeneous refinement equation.
This project is supported by the NSF of China under Grant No. 10071071 相似文献
19.
Let G be a locally compact group. For 1 < p < ∞, it is well-known that f * g exists and belongs to Lp(G) for all f, g
Lp
(G) if and only if G is compact. Here, for 2 < p < ∞, we show that f * g exists for all f, g
Lp(G) if and only if G is compact. We also show that this result does not remain true for 1 < p ≤ 2.
Received: 23 April 2006 相似文献
20.
Yun Qing Xu 《数学学报(英文版)》2009,25(8):1325-1336
A Latin squares of order v with ni missing sub-Latin squares (holes) of order hi (1 〈= i 〈 k), which are disjoint and spanning (i.e. ∑k i=l1 nihi = v), is called a partitioned incomplete Latin squares and denoted by PILS. The type of PILS is defined by (h1n1 h2n2…hknk ). If any two PILS inaset of t PILS of type T are orthogonal, then we denote the set by t-HMOLS(T). It has been proved that 3-HMOLS(2n31) exist for n ≥6 with 11 possible exceptions. In this paper, we investigate the existence of 3-HMOLS(2nu1) with u ≥ 4, and prove that 3-HMOLS(2~u1) exist if n ≥ 54 and n ≥7/4u + 7. 相似文献