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1.
An extension of a classical theorem of Rellich to the exterior of a closed proper convex cone is proved: Let Γ be a closed
convex proper cone inR
n and −Γ′ be the antipodes of the dual cone of Γ. Let
be a partial differential operator with constant coefficients inR
n, whereQ(ζ)≠0 onR
n−iΓ′ andP
i is an irreducible polynomial with real coefficients. Assume that the closure of each connected component of the set {ζ∈R
n−iΓ′;P
j(ζ)=0, gradP
j(ζ)≠0} contains some real point on which gradP
j≠0 and gradP
j∉Γ∪(−Γ). LetC be an open cone inR
n−Γ containing both normal directions at some such point, and intersecting each normal plane of every manifold contained in
{ξ∈R
n;P(ξ)=0}. Ifu∈ℒ′∩L
loc
2
(R
n−Γ) and the support ofP(−i∂/∂x)u is contained in Γ, then the condition
implies that the support ofu is contained in Γ. 相似文献
2.
Let I≥1 be an integer, ω
0=0<ω
1<⋯<ω
I
≤π, and for j=0,…,I, a
j
∈ℂ, a-j=[`(aj)]a_{-j}={\overline{{a_{j}}}}, ω
−j
=−ω
j
, and aj 1 0a_{j}\not=0 if j 1 0j\not=0. We consider the following problem: Given finitely many noisy samples of an exponential sum of the form
[(x)\tilde](k) = ?j=-II ajexp(-iwjk) +e(k), k=-2N,?,2N,\tilde{x}(k)= \sum_{j=-I}^I a_j\exp(-i\omega _jk) +\epsilon (k), \quad k=-2N,\ldots,2N, 相似文献
3.
A note on nil power serieswise Armendariz rings 总被引:1,自引:0,他引:1
Sana Hizem 《Rendiconti del Circolo Matematico di Palermo》2010,59(1):87-99
A ring R is called nil power serieswise Armendariz if $
\forall f = \sum\limits_{i = 0}^\infty {a_i X^i }
$
\forall f = \sum\limits_{i = 0}^\infty {a_i X^i }
and $
g = \sum\limits_{i = 0}^\infty {b_i X^i }
$
g = \sum\limits_{i = 0}^\infty {b_i X^i }
in R[[X]] such that f g ∈ Nil(R)[[X]], then a
i
b
j
∈ Nil(R) for all i and j. In this note we characterize completely nil power serieswise Armendariz rings with their nilradical Nil(R) (where the nilradical is the set of nilpotent elements). We prove that a ring is nil power serieswise Armendariz if and
only if Nil(R) is an ideal of R. We prove that each power serieswise Armendariz ring is nil power serieswise Armendariz and we give examples of nil power
serieswise Armendariz rings. 相似文献
4.
Let F ì PG \mathcal{F} \subset {\mathcal{P}_G} be a left-invariant lower family of subsets of a group G. A subset A ⊂ G is called F \mathcal{F} -thin if xA ?yA ? F xA \cap yA \in \mathcal{F} for any distinct elements x, y ∈ G. The family of all F \mathcal{F} -thin subsets of G is denoted by t( F ) \tau \left( \mathcal{F} \right) . If t( F ) = F \tau \left( \mathcal{F} \right) = \mathcal{F} , then F \mathcal{F} is called thin-complete. The thin-completion t*( F ) {\tau^*}\left( \mathcal{F} \right) of F \mathcal{F} is the smallest thin-complete subfamily of PG {\mathcal{P}_G} that contains F \mathcal{F} . Answering questions of Lutsenko and Protasov, we prove that a set A ⊂ G belongs to τ*(G) if and only if, for any sequence (g
n
)
n∈ω
of nonzero elements of G, there is n ∈ ω such that
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