共查询到20条相似文献,搜索用时 296 毫秒
1.
Wolfgang Müller 《Monatshefte für Mathematik》2011,162(1):69-88
Denote by 0 = λ 0 < λ 1 ≤ λ 2 ≤ . . . the infinite sequence given by the values of a positive definite irrational quadratic form in k variables at integer points. For l ≥ 2 and an (l ?1)-dimensional interval I = I 2×. . .×I l we consider the l-level correlation function \({K^{(l)}_I(R)}\) which counts the number of tuples (i 1, . . . , i l ) such that \({\lambda_{i_1},\ldots,\lambda_{i_l}\leq R^2}\) and \({\lambda_{i_{j}}-\lambda_{i_{1}}\in I_j}\) for 2 ≤ j ≤ l. We study the asymptotic behavior of \({K^{(l)}_I(R)}\) as R tends to infinity. If k ≥ 4 we prove \({K^{(l)}_I(R)\sim c_l(Q)\,{\rm vol}(I)R^{lk-2(l-1)}}\) for arbitrary l, where c l (Q) is an explicitly determined constant. This remains true for k = 3 under the restriction l ≤ 3. 相似文献
2.
Let R be a prime ring with extended centroid F and let δ be an F-algebraic continuous derivation of R with the associated inner derivation ad(b). Factorize the minimal polynomial μ(λ) of b over F into distinct irreducible factors m(l)=?ipi(l)ni{\mu(\lambda)=\prod_i\pi_i(\lambda)^{n_i}} . Set ℓ to be the maximum of n
i
. Let R(d)=def.{x ? R | d(x)=0}{R^{(\delta)}{\mathop{=}\limits^{{\rm def.}}}\{x\in R\mid \delta(x)=0\}} be the subring of constants of δ on R. Denote the prime radical of a ring A by P(A){{\mathcal{P}}(A)} . It is shown among other things that
P(R(d))2l-1=0 \textand P(R(d))=R(d)?P(CR(b)){\mathcal{P}}(R^{(\delta)})^{2^\ell-1}=0\quad\text{and}\quad{\mathcal{P}}(R^{(\delta)})=R^{(\delta)}\cap {\mathcal{P}}(C_R(b)) 相似文献
3.
P. Erdös 《Israel Journal of Mathematics》1964,2(3):183-190
Anr-graph is a graph whose basic elements are its vertices and r-tuples. It is proved that to everyl andr there is anε(l, r) so that forn>n
0 everyr-graph ofn vertices andn
r−ε(l, r) r-tuples containsr. l verticesx
(j), 1≦j≦r, 1≦i≦l, so that all ther-tuples
occur in ther-graph. 相似文献
4.
Jun Wu 《Monatshefte für Mathematik》2006,54(4):259-264
For
log\frac1+?52 £ l* £ l* < ¥{\rm log}\frac{1+\sqrt{5}}{2}\leq \lambda_\ast \leq \lambda^\ast < \infty
, let E(λ*, λ*) be the set
{x ? [0,1): liminfn ? ¥\fraclogqn(x)n=l*, limsupn ? ¥\fraclogqn(x)n=l*}. \left\{x\in [0,1):\ \mathop{\lim\inf}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda_{\ast}, \mathop{\lim\sup}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda^{\ast}\right\}.
It has been proved in [1] and [3] that E(λ*, λ*) is an uncountable set. In the present paper, we strengthen this result by showing that
dimE(l*, l*) 3 \fracl* -log\frac1+?522l*\dim E(\lambda_{\ast}, \lambda^{\ast}) \ge \frac{\lambda_{\ast} -\log \frac{1+\sqrt{5}}{2}}{2\lambda^{\ast}} 相似文献
5.
Susana D. Moura J��lio S. Neves Cornelia Schneider 《Journal of Fourier Analysis and Applications》2011,17(5):777-800
We study necessary and sufficient conditions for embeddings of Besov and Triebel-Lizorkin spaces of generalized smoothness
B(n/p,Y)p,q(\mathbbRn)B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}) and
F(n/p,Y)p,q(\mathbbRn)F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}), respectively, into generalized H?lder spaces
L¥,rm(·)( \mathbb Rn)\Lambda_{\infty,r}^{\mu(\cdot)}(\ensuremath {\ensuremath {\mathbb {R}}^{n}}). In particular, we are able to characterize optimal embeddings for this class of spaces provided q>1. These results improve the embedding assertions given by the continuity envelopes of
B(n/p,Y)p,q(\mathbbRn)B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}) and
F(n/p,Y)p,q(\mathbbRn)F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}), which were obtained recently solving an open problem of D.D. Haroske in the classical setting. 相似文献
6.
We describe an algorithm for large-scale discrete ill-posed problems, called GKB-FP, which combines the Golub-Kahan bidiagonalization
algorithm with Tikhonov regularization in the generated Krylov subspace, with the regularization parameter for the projected
problem being chosen by the fixed-point method by Bazán (Inverse Probl. 24(3), 2008). The fixed-point method selects as regularization
parameter a fixed-point of the function ‖r
λ
‖2/‖f
λ
‖2, where f
λ
is the regularized solution and r
λ
is the corresponding residual. GKB-FP determines the sought fixed-point by computing a finite sequence of fixed-points of
functions ||rl(k)||2/||fl(k)||2\|r_{\lambda}^{(k)}\|_{2}/\|f_{\lambda}^{(k)}\|_{2}, where fl(k)f_{\lambda}^{(k)} approximates f
λ
in a k-dimensional Krylov subspace and rl(k)r_{\lambda}^{(k)} is the corresponding residual. Based on this and provided the sought fixed-point is reached, we prove that the regularized
solutions fl(k)f_{\lambda}^{(k)} remain unchanged and therefore completely insensitive to the number of iterations. This and the performance of the method when applied to
well-known test problems are illustrated numerically. 相似文献
7.
We consider the spectral decomposition of A, the generator of a polynomially bounded n-times integrated group whose spectrum set $\sigma(A)=\{i\lambda_{k};k\in\mathbb{\mathbb{Z}}^{*}\}
8.
We show that T is a surjective multiplicative (but not necessarily linear) isometry from the Smirnov class on the open unit disk, the ball, or the polydisk onto itself,
if and only if there exists a holomorphic automorphism Φ such that T(f)=f ○ Φ for every class element f or T(f) = [`(f° [`(j)] )]\overline {f^\circ \bar \varphi } for every class element f, where the automorphism Φ is a unitary transformation in the case of the ball and Φ(z
1, ..., z
n
) = (l1 zi1 ,...,ln zin )(\lambda _1 z_{i_1 } ,...,\lambda _n z_{i_n } ) for |λ
j
| = 1, 1 ≤ j ≤ n, and (i
1; ..., i
n
)is some permutation of the integers from 1through n in the case of the n-dimensional polydisk. 相似文献
9.
J. Hu 《Transformation Groups》2010,15(2):333-370
Let V be a 2m-dimensional symplectic vector space over an algebraically closed field K. Let $ \mathfrak{B}_n^{(f)} | / | \vphantom V ?n V ?n V ?n\mathfrakBn(f) ) {\text{En}}{{\text{d}}_{K{\text{Sp}}(V)}}\left( {{{{V^{ \otimes n}}} \mathord{\left/{\vphantom {{{V^{ \otimes n}}} {{V^{ \otimes n}}}}} \right.} {{V^{ \otimes n}}}}\mathfrak{B}_n^{(f)}} \right) are both independent of K, and the natural homomorphism from \mathfrakBn( - 2m ) \mathord | / | \vphantom ( - 2m ) \mathfrakBn(f) \mathfrakBn(f) {\mathfrak{B}_n}{{\left( { - 2m} \right)} \mathord{\left/{\vphantom {{\left( { - 2m} \right)} {\mathfrak{B}_n^{(f)}}}} \right.} {\mathfrak{B}_n^{(f)}}} to \textEn\textdK\textSp(V)( V ?n \mathord | / | \vphantom V ?n V ?n V ?n\mathfrakBn(f) ) {\text{En}}{{\text{d}}_{K{\text{Sp}}(V)}}\left( {{{{V^{ \otimes n}}} \mathord{\left/{\vphantom {{{V^{ \otimes n}}} {{V^{ \otimes n}}}}} \right.} {{V^{ \otimes n}}}}\mathfrak{B}_n^{(f)}} \right) is always surjective. We show that HTf ?n \mathcal{H}\mathcal{T}_f^{ \otimes n} has a Weyl filtration and is isomorphic to the dual of V ?n\mathfrakBn(f) \mathord | / | \vphantom V ?n\mathfrakBn(f) V V ?n\mathfrakBn( f + 1 ) {{{{V^{ \otimes n}}\mathfrak{B}_n^{(f)}} \mathord{\left/{\vphantom {{{V^{ \otimes n}}\mathfrak{B}_n^{(f)}} V}} \right.} V}^{ \otimes n}}\mathfrak{B}_n^{\left( {f + 1} \right)} as an \textSp(V) - ( \mathfrakBn( - 2m ) \mathord | / |
\vphantom ( - 2m ) \mathfrakBn( f + 1 ) \mathfrakBn( f + 1 ) ) {\text{Sp}}(V) - \left( {{\mathfrak{B}_n}{{\left( { - 2m} \right)} \mathord{\left/{\vphantom {{\left( { - 2m} \right)} {\mathfrak{B}_n^{\left( {f + 1} \right)}}}} \right.} {\mathfrak{B}_n^{\left( {f + 1} \right)}}}} \right) -bimodule. We obtain an
\textSp(V) - \mathfrakBn {\text{Sp}}(V) - {\mathfrak{B}_n} -bimodules filtration of V
⊗n
such that each successive quotient is isomorphic to some
?( l) ?zg,l\mathfrakBn \nabla \left( \lambda \right) \otimes {z_{g,\lambda }}{\mathfrak{B}_n} with λ ⊢ n 2g, ℓ(λ)≤m and 0 ≤ g ≤ [n/2], where ∇(λ) is the co-Weyl module associated to λ and z
g,λ is an explicitly constructed maximal vector of weight λ. As a byproduct, we show that each right
\mathfrakBn {\mathfrak{B}_n} -module
zg,l\mathfrakBn {z_{g,\lambda }}{\mathfrak{B}_n} is integrally defined and stable under base change. 相似文献
10.
Yu Liu 《Monatshefte für Mathematik》2012,127(2):41-56
Let
Lf(x)=-\frac1w?i,j ?i(ai,j(·)?jf)(x)+V(x)f(x){\mathcal{L}f(x)=-\frac{1}{\omega}\sum_{i,j} \partial_i(a_{i,j}(\cdot)\partial_jf)(x)+V(x)f(x)} with the non-negative potential V belonging to reverse H?lder class with respect to the measure ω(x)dx, where ω(x) satisfies the A
2 condition of Muckenhoupt and a
i,j
(x) is a real symmetric matrix satisfying l-1w(x)|x|2 £ ?ni,j=1ai,j(x)xixj £ lw(x)|x|2.{\lambda^{-1}\omega(x)|\xi|^2\le \sum^n_{i,j=1}a_{i,j}(x)\xi_i\xi_j\le\lambda\omega(x)|\xi|^2. } We obtain some estimates for VaL-a{V^{\alpha}\mathcal{L}^{-\alpha}} on the weighted L
p
spaces and we study the weighted L
p
boundedness of the commutator [b, Va L-a]{[b, V^{\alpha} \mathcal{L}^{-\alpha}]} when b ? BMOw{b\in BMO_\omega} and 0 < α ≤ 1. 相似文献
11.
H. A. Dzyubenko 《Ukrainian Mathematical Journal》2009,61(4):519-540
In the case where a 2π-periodic function f is twice continuously differentiable on the real axis ℝ and changes its monotonicity at different fixed points y
i
∈ [− π, π), i = 1,…, 2s, s ∈ ℕ (i.e., on ℝ, there exists a set Y := {y
i
}
i∈ℤ of points y
i
= y
i+2s
+ 2π such that the function f does not decrease on [y
i
, y
i−1] if i is odd and does not increase if i is even), for any natural k and n, n ≥ N(Y, k) = const, we construct a trigonometric polynomial T
n
of order ≤n that changes its monotonicity at the same points y
i
∈ Y as f and is such that
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