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1.
In this paper, we establish several decidability results for pseudovariety joins of the form
, where
is a subpseudovariety of
or the pseudovariety
. Here,
(resp.
) denotes the pseudovariety of all
-trivial (resp.
-trivial) semigroups. In particular, we show that the pseudovariety
is (completely) κ-tame when
is a subpseudovariety of
with decidable κ-word problem and
is (completely) κ-tame. Moreover, if
is a κ-tame pseudovariety which satisfies the pseudoidentity x1 ⋯ xryω+1ztω = x1 ⋯ xryztω, then we prove that
is also κ-tame. In particular the joins
,
,
, and
are decidable.
Partial support by FCT, through the Centro de Matemática da Universidade do Porto, is also gratefully acknowledged.
Partial support by FCT, through the Centro de Matemática da Universidade do Minho, is also gratefully acknowledged. 相似文献
2.
Given a finite subset
A{\cal A}
of an additive group
\Bbb G{\Bbb G}
such as
\Bbb Zn{\Bbb Z}^n
or
\Bbb Rn{\Bbb R}^n
, we are interested in efficient covering of
\Bbb G{\Bbb G}
by translates of
A{\cal A}
, and efficient packing of translates of
A{\cal A}
in
\Bbb G{\Bbb G}
. A set
S ì \Bbb G{\cal S} \subset {\Bbb G}
provides a covering if the translates
A + s{\cal A} + s
with
s ? Ss \in {\cal S}
cover
\Bbb G{\Bbb G}
(i.e., their union is
\Bbb G{\Bbb G}
), and the covering will be efficient if
S{\cal S}
has small density in
\Bbb G{\Bbb G}
. On the other hand, a set
S ì \Bbb G{\cal S} \subset {\Bbb G}
will provide a packing if the translated sets
A + s{\cal A} + s
with
s ? Ss \in {\cal S}
are mutually disjoint, and the packing is efficient if
S{\cal S}
has large density.
In the present part (I) we will derive some facts on these concepts when
\Bbb G = \Bbb Zn{\Bbb G} = {\Bbb Z}^n
, and give estimates for the minimal covering densities and maximal packing densities of finite sets
A ì \Bbb Zn{\cal A} \subset {\Bbb Z}^n
. In part (II) we will again deal with
\Bbb G = \Bbb Zn{\Bbb G} = {\Bbb Z}^n
, and study the behaviour of such densities under linear transformations. In part (III) we will turn to
\Bbb G = \Bbb Rn{\Bbb G} = {\Bbb R}^n
. 相似文献
3.
The algebra Bp(\Bbb R){\cal B}_p({\Bbb R}), p ? (1,¥)\{2}p\in (1,\infty )\setminus \{2\}, consisting of all measurable sets in \Bbb R{\Bbb R} whose characteristic function is a Fourier p-multiplier, forms an algebra of sets containing many interesting and non-trivial elements (e.g. all intervals and their finite unions, certain periodic sets, arbitrary countable unions of dyadic intervals, etc.). However, Bp(\Bbb R){\cal B}_p({\Bbb R}) fails to be a s\sigma -algebra. It has been shown by V. Lebedev and A. Olevskii [4] that if E ? Bp(\Bbb R)E\in {\cal B}_p({\Bbb R}), then E must coincide a.e. with an open set, a remarkable topological constraint on E. In this note we show if $2 < p < \infty $2 < p < \infty , then there exists E ? Bp(\Bbb R)E\in {\cal B}_p({\Bbb R}) which is not in Bq(\Bbb R){\cal B}_q({\Bbb R}) for any q > pq>p. 相似文献
4.
Fukun Zhao Leiga Zhao Yanheng Ding 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,15(6):495-511
This paper is concerned with the following periodic Hamiltonian elliptic system
{l-Du+V(x)u=g(x,v) in \mathbbRN,-Dv+V(x)v=f(x,u) in \mathbbRN,u(x)? 0 and v(x)?0 as |x|?¥,\left \{\begin{array}{l}-\Delta u+V(x)u=g(x,v)\, {\rm in }\,\mathbb{R}^N,\\-\Delta v+V(x)v=f(x,u)\, {\rm in }\, \mathbb{R}^N,\\ u(x)\to 0\, {\rm and}\,v(x)\to0\, {\rm as }\,|x|\to\infty,\end{array}\right. 相似文献
5.
The main purpose of this paper is to prove the following result. Let R be a 2-torsion free semiprime ring with symmetric Martindale ring of quotients Q
s
and let q{\theta} and f{\phi} be automorphisms of R. Suppose T:R? R{T:R\rightarrow R} is an additive mapping satisfying the relation T(xyx)=T(x)q(y)q(x)-f(x)T(y)q(x)+f(x)f(y)T(x){T(xyx)=T(x)\theta (y)\theta (x)-\phi (x)T(y)\theta (x)+\phi (x)\phi (y)T(x)}, for all pairs x,y ? R{x,y\in R}. In this case T is of the form 2T(x)=qq(x)+f(x)q{2T(x)=q\theta (x)+\phi (x)q}, for all x ? R{x\in R} and some fixed element q ? Qs{q\in Q_{s}}. 相似文献
6.
By a totally regular parallelism of the real projective 3-space
P3:=PG(3, \mathbb R){\Pi_3:={{\rm PG}}(3, \mathbb {R})} we mean a family T of regular spreads such that each line of Π
3 is contained in exactly one spread of T. For the investigation of totally regular parallelisms the authors mainly employ Klein’s correspondence λ of line geometry and the polarity π
5 associated with the Klein quadric H
5 (for details see Chaps. 1 and 3). The λ-image of a totally regular parallelism T is a hyperflock of H
5, i.e., a family H of elliptic subquadrics of H
5 such that each point of H
5 is on exactly one subquadric of H. Moreover, {p5(span l(X))|X ? T}=:HT{\{\pi_5({{\rm span}} \,\lambda(\mathcal {X}))\vert\mathcal {X}\in\bf{T}\}=:\mathcal {H}_{\bf{T}}} is a hyperflock determining line set, i.e., a set Z{\mathcal {Z}} of 0-secants of H
5 such that each tangential hyperplane of H
5 contains exactly one line of Z{\mathcal {Z}} . We say that dim(span HT)=:dT{{{\rm dim}}({{\rm span}}\,\mathcal {H}_{\bf{T}})=:d_{\bf{T}}} is the dimension of
T and that T is a d
T
- parallelism. Clifford parallelisms and 2-parallelisms coincide. The examples of non-Clifford parallelisms exhibited in Betten
and Riesinger [Result Math 47:226–241, 2004; Adv Geom 8:11–32, 2008; J Geom (to appear)] are totally regular and of dimension
3. If G{\mathcal{G}} is a hyperflock determining line set, then {l-1 (p5(X) ?H5) | X ? G}{\{\lambda^{-1}\,{\rm (}\pi_5(X){\,\cap H_5)\,|\, X\in\mathcal{G}\}}} is a totally regular parallelism. In the present paper the authors construct examples of topological (see Definition 1.1)
4- and 5-parallelisms via hyperflock determining line sets. 相似文献
7.
Bernhard Burgstaller 《Monatshefte für Mathematik》2009,265(4):1-11
There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x
1, x
2, ... we have
limn ? ¥\mathbb P(C*(x1,?,xn) is nuclear)=0{\rm {lim}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra O2{\mathcal {O}_2} such that for an independent sequence x
1, x
2, ... of μ-distributed random elements x
i
we have
lim infn ? ¥\mathbb P(C*(x1,?,xn) is nuclear)=0{\rm {lim\, inf}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1]
d
) is d. 相似文献
8.
Franki Dillen Johan Fastenakels Joeri Van der Veken Luc Vrancken 《Monatshefte für Mathematik》2007,40(1):89-96
In this article we study surfaces in
\Bbb S2×\Bbb R {\Bbb S}^2\times {\Bbb R}
for which the unit normal makes a constant angle with the
\Bbb R {\Bbb R}
-direction. We give a complete classification for surfaces satisfying this simple geometric condition. 相似文献
9.
Jiabao Su 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,21(2):51-62
We study the existence and multiplicity of nontrivial radial solutions of the quasilinear equation
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