共查询到20条相似文献,搜索用时 15 毫秒
1.
We study certain groupoids generating Abelian, strongly Abelian, and Hamiltonian varieties. An algebra is Abelian if t( a,[`(c)] ) = t( a,[`(d)] ) ? t( b,[`(c)] ) = t( b,[`(d)] ) t\left( {a,\bar{c}} \right) = t\left( {a,\bar{d}} \right) \to t\left( {b,\bar{c}} \right) = t\left( {b,\bar{d}} \right) for any polynomial operation on the algebra and for all elements a, b, [`(c)] \bar{c} , [`(d)] \bar{d} . An algebra is strongly Abelian if t( a,[`(c)] ) = t( b,[`(d)] ) ? t( e,[`(c)] ) = t( e,[`(d)] ) t\left( {a,\bar{c}} \right) = t\left( {b,\bar{d}} \right) \to t\left( {e,\bar{c}} \right) = t\left( {e,\bar{d}} \right) for any polynomial operation on the algebra and for arbitrary elements a, b, e, [`(c)] \bar{c} , [`(d)] \bar{d} . An algebra is Hamiltonian if any subalgebra of the algebra is a congruence class. A variety is Abelian (strongly Abelian,
Hamiltonian) if all algebras in a respective class are Abelian (strongly Abelian, Hamiltonian). We describe semigroups, groupoids
with unity, and quasigroups generating Abelian, strongly Abelian, and Hamiltonian varieties. 相似文献
2.
Markus Haase 《Integral Equations and Operator Theory》2006,56(2):197-228
We generalize a Hilbert space result by Auscher, McIntosh and Nahmod to arbitrary Banach spaces X and to not densely defined injective sectorial operators A. A convenient tool proves to be a certain universal extrapolation space associated with A. We characterize the real interpolation space
( X,D( Aa ) ?R( Aa ) )q,p{\left( {X,\mathcal{D}{\left( {A^{\alpha } } \right)} \cap \mathcal{R}{\left( {A^{\alpha } } \right)}} \right)}_{{\theta ,p}}
as
{ x ? X|t - q\textRea y1 ( tA )x, t - q\textRea y2 ( tA )x ? L*p ( ( 0,¥ );X ) } {\left\{ {x\, \in \,X|t^{{ - \theta {\text{Re}}\alpha }} \psi _{1} {\left( {tA} \right)}x,\,t^{{ - \theta {\text{Re}}\alpha }} \psi _{2} {\left( {tA} \right)}x \in L_{*}^{p} {\left( {{\left( {0,\infty } \right)};X} \right)}} \right\}} 相似文献
3.
A. I. Podvysotskaya 《Ukrainian Mathematical Journal》2009,61(5):847-853
We prove that max |p′(x)|, where p runs over the set of all algebraic polynomials of degree not higher than n ≥ 3 bounded in modulus by 1 on [−1, 1], is not lower than
( n - 1 ) \mathord | / | \vphantom ( n - 1 ) ?{1 - x2} ?{1 - x2} {{\left( {n - 1} \right)} \mathord{\left/{\vphantom {{\left( {n - 1} \right)} {\sqrt {1 - {x^2}} }}} \right.} {\sqrt {1 - {x^2}} }} for all x ∈ (−1, 1) such that | x | ? èk = 0[ n \mathord | / |
\vphantom n 2 2 ] [ cos\frac2k + 12( n - 1 )p, cos\frac2k + 12np ] \left| x \right| \in \bigcup\nolimits_{k = 0}^{\left[ {{n \mathord{\left/{\vphantom {n 2}} \right.} 2}} \right]} {\left[ {\cos \frac{{2k + 1}}{{2\left( {n - 1} \right)}}\pi, \cos \frac{{2k + 1}}{{2n}}\pi } \right]} . 相似文献
4.
Let
G ì \mathbb C G \subset {\mathbb C} be a finite region bounded by a Jordan curve L: = ?G L: = \partial G , let
W: = \textext[`(G)] \Omega : = {\text{ext}}\bar{G} (with respect to
[`(\mathbb C)] {\overline {\mathbb C}} ), $ \Delta : = \left\{ {z:\left| z \right| > 1} \right\} $ \Delta : = \left\{ {z:\left| z \right| > 1} \right\} , and let w = F(z) w = \Phi (z) be a univalent conformal mapping of Ω onto Δ normalized by $ \Phi \left( \infty \right) = \infty, \;\Phi '\left( \infty \right) > 0 $ \Phi \left( \infty \right) = \infty, \;\Phi '\left( \infty \right) > 0 . By A
p
(G); p > 0; we denote a class of functions f analytic in G and satisfying the condition
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