共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove that if ${\mu _{a}\,{=}\,m_{K}*\delta _{a}*m_{K}}$ is the K-bi-invariant measure supported on the double coset ${KaK\subseteq SU(n)}$ , for K = SO(n), then ${\mu _{a}^{k}}$ is absolutely continuous with respect to the Haar measure on SU(n) for all a not in the normalizer of K if and only if k ≥ n. The measure, μ a , supported on the minimal dimension double coset has the property that ${\mu _{a}^{n-1}}$ is singular to the Haar measure. 相似文献
2.
Let n ≥ 2 be a fixed integer, let q and c be two integers with q > n and (n, q) = (c, q) = 1. For every positive integer a which is coprime with q we denote by [`(a)]c{\overline{a}_{c}} the unique integer satisfying 1 £ [`(a)]c £ q{1\leq\overline{a}_{c} \leq{q}} and a[`(a)]c o c(mod q){a\overline{a}_{c} \equiv{c}({\rm mod}\, q)}. Put
L(q)={a ? Z+: (a,q)=1, n \not| a+[`(a)]c }.L(q)=\{a\in{Z^{+}}: (a,q)=1, n {\not\hskip0.1mm|} a+\overline{a}_{c} \}. 相似文献
3.
Jean B. Lasserre 《Optimization Letters》2011,5(4):549-556
We consider the convex optimization problem P:minx {f(x) : x ? K}{{\rm {\bf P}}:{\rm min}_{\rm {\bf x}} \{f({\rm {\bf x}})\,:\,{\rm {\bf x}}\in{\rm {\bf K}}\}} where f is convex continuously differentiable, and
K ì \mathbb Rn{{\rm {\bf K}}\subset{\mathbb R}^n} is a compact convex set with representation
{x ? \mathbb Rn : gj(x) 3 0, j = 1,?,m}{\{{\rm {\bf x}}\in{\mathbb R}^n\,:\,g_j({\rm {\bf x}})\geq0, j = 1,\ldots,m\}} for some continuously differentiable functions (g
j
). We discuss the case where the g
j
’s are not all concave (in contrast with convex programming where they all are). In particular, even if the g
j
are not concave, we consider the log-barrier function fm{\phi_\mu} with parameter μ, associated with P, usually defined for concave functions (g
j
). We then show that any limit point of any sequence (xm) ì K{({\rm {\bf x}}_\mu)\subset{\rm {\bf K}}} of stationary points of fm, m? 0{\phi_\mu, \mu \to 0} , is a Karush–Kuhn–Tucker point of problem P and a global minimizer of f on K. 相似文献
4.
Recently, Girstmair and Schoissengeier studied the asymptotic behavior of the arithmetic mean of Dedekind sums
\frac1j(N) ? 0 £ m < Ngcd(m,N)=1 |S(m,N)|\frac{1}{\varphi(N)} \sum_{\mathop{\mathop{ 0 \le m< N}}\limits_{\gcd(m,N)=1}} \vert S(m,N)\vert
, as N → ∞. In this paper we consider the arithmetic mean of weighted differences of Dedekind sums in the form
Ah(Q)=\frac1?\fracaq ? FQh(\fracaq) ×?\fracaq ? FQh(\fracaq) |s(a¢,q¢)-s(a,q)|A_{h}(Q)=\frac{1}{\sum_{\frac{a}{q} \in {\cal F}_{Q}}h\left(\frac{a}{q}\right)} \times \sum_{\frac{a}{q} \in {\cal F}_{\!Q}}h\left(\frac{a}{q}\right) \vert s(a^{\prime},q^{\prime})-s(a,q)\vert
, where
h:[0,1] ? \Bbb Ch:[0,1] \rightarrow {\Bbb C}
is a continuous function with
ò01 h(t) d t 1 0\int_0^1 h(t) \, {\rm d} t \ne 0
,
\fracaq{\frac{a}{q}}
runs over
FQ{\cal F}_{\!Q}
, the set of Farey fractions of order Q in the unit interval [0,1] and
\fracaq < \fraca¢q¢{\frac{a}{q}}<\frac{a^{\prime}}{q^{\prime}}
are consecutive elements of
FQ{\cal F}_{\!Q}
. We show that the limit lim
Q→∞
A
h
(Q) exists and is independent of h. 相似文献
5.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}
6.
Lin-Feng Wang 《Annals of Global Analysis and Geometry》2010,37(4):393-402
Let M be an n-dimensional complete non-compact Riemannian manifold, dμ = e
h
(x)dV(x) be the weighted measure and
\trianglem{\triangle_{\mu}} be the weighted Laplacian. In this article, we prove that when the m-dimensional Bakry–émery curvature is bounded from below by Ric
m
≥ −(m − 1)K, K ≥ 0, then the bottom of the Lm2{{\rm L}_{\mu}^2} spectrum λ1(M) is bounded by
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