共查询到20条相似文献,搜索用时 31 毫秒
1.
Commutative congruence-simple semirings have already been characterized with the exception of the subsemirings of ℝ+. Even the class
CongSimp(\mathbb Q+)\mathit{\mathcal{C}ong\mathcal{S}imp}(\mathbb {Q}^{+}) of all congruence-simple subsemirings of ℚ+ has not been classified yet. We introduce a new large class of the congruence-simple saturated subsemirings of ℚ+. We classify all the maximal elements of
CongSimp(\mathbbQ+)\mathit{\mathcal{C}ong\mathcal {S}imp}(\mathbb{Q}^{+}) and show that every element of
CongSimp(\mathbbQ+)\{\mathbbQ+}\mathit{\mathcal{C}ong\mathcal{S}imp}(\mathbb{Q}^{+})\setminus\{\mathbb{Q}^{+}\} is contained in at least one of them. 相似文献
2.
John R. Akeroyd 《Arkiv f?r Matematik》2011,49(1):1-16
It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that
G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\}
and with the property that the analytic polynomials are dense in the Bergman space
\mathbbAt(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)
. It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous
real-valued function on [0,1], where the polynomials are dense in
Ht(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma)
; improving upon a result in an earlier paper. 相似文献
3.
We give a characterization of the class Co(F)\mathbf{Co}(\mathcal{F}) [Co(Fn)\mathrm{\mathbf{Co}}(\mathcal{F}_n), n < ω, respectively] of lattices isomorphic to convexity lattices of posets which are forests [forests of length at most n, respectively], as well as of the class Co(L)\mathbf{Co}(\mathcal{L}) of lattices isomorphic to convexity lattices of linearly ordered posets. This characterization yields that the class of finite
members from Co(F)\mathbf{Co}(\mathcal{F}) [from Co(Fn)\mathbf{Co}(\mathcal{F}_n), n < ω, or from Co(L)\mathbf{Co}(\mathcal{L})] is finitely axiomatizable within the class of finite lattices. 相似文献
4.
Let ${s,\,\tau\in\mathbb{R}}Let
s, t ? \mathbbR{s,\,\tau\in\mathbb{R}} and q ? (0,¥]{q\in(0,\infty]} . We introduce Besov-type spaces
[(B)\dot]s, tp, q(\mathbbRn){{{{\dot B}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}} for p ? (0, ¥]{p\in(0,\,\infty]} and Triebel–Lizorkin-type spaces
[(F)\dot]s, tp, q(\mathbbRn) for p ? (0, ¥){{{{\dot F}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}\,{\rm for}\, p\in(0,\,\infty)} , which unify and generalize the Besov spaces, Triebel–Lizorkin spaces and Q spaces. We then establish the j{\varphi} -transform characterization of these new spaces in the sense of Frazier and Jawerth. Using the j{\varphi} -transform characterization of
[(B)\dot]s, tp, q(\mathbbRn) and [(F)\dot]s, tp, q(\mathbbRn){{{{\dot B}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}\, {\rm and}\, {{\dot F}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}} , we obtain their embedding and lifting properties; moreover, for appropriate τ, we also establish the smooth atomic and
molecular decomposition characterizations of
[(B)\dot]s, tp, q(\mathbbRn) and [(F)\dot]s, tp, q(\mathbbRn){{{{\dot B}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}\,{\rm and}\, {{\dot F}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}} . For
s ? \mathbbR{s\in\mathbb{R}} , p ? (1, ¥), q ? [1, ¥){p\in(1,\,\infty), q\in[1,\,\infty)} and
t ? [0, \frac1(max{p, q})¢]{\tau\in[0,\,\frac{1}{(\max\{p,\,q\})'}]} , via the Hausdorff capacity, we introduce certain Hardy–Hausdorff spaces
B[(H)\dot]s, tp, q(\mathbbRn){{{{B\dot{H}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}}} and prove that the dual space of
B[(H)\dot]s, tp, q(\mathbbRn){{{{B\dot{H}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}}} is just
[(B)\dot]-s, tp¢, q¢(\mathbbRn){\dot{B}^{-s,\,\tau}_{p',\,q'}(\mathbb{R}^{n})} , where t′ denotes the conjugate index of t ? (1,¥){t\in (1,\infty)} . 相似文献
5.
Erik Talvila 《Journal of Fourier Analysis and Applications》2012,18(1):27-44
Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional
derivative of a continuous function. This space of distributions is denoted
Ac(\mathbbT){\mathcal{A}}_{c}(\mathbb{T}) and is a Banach space under the Alexiewicz norm,
||f||\mathbbT=sup|I| £ 2p|òI f|\|f\|_{\mathbb{T}}=\sup_{|I|\leq2\pi}|\int_{I} f|, the supremum being taken over intervals of length not exceeding 2π. It contains the periodic functions integrable in the sense of Lebesgue and Henstock–Kurzweil. Many of the properties of
L
1 Fourier series continue to hold for this larger space, with the L
1 norm replaced by the Alexiewicz norm. The Riemann–Lebesgue lemma takes the form [^(f)](n)=o(n)\hat{f}(n)=o(n) as |n|→∞. The convolution is defined for
f ? Ac(\mathbbT)f\in{\mathcal{A}}_{c}(\mathbb{T}) and g a periodic function of bounded variation. The convolution commutes with translations and is commutative and associative.
There is the estimate
||f*g||¥ £ ||f||\mathbbT ||g||BV\|f\ast g\|_{\infty}\leq\|f\|_{\mathbb{T}} \|g\|_{\mathcal{BV}}. For
g ? L1(\mathbbT)g\in L^{1}(\mathbb{T}),
||f*g||\mathbbT £ ||f||\mathbb T ||g||1\|f\ast g\|_{\mathbb{T}}\leq\|f\|_{\mathbb {T}} \|g\|_{1}. As well, [^(f*g)](n)=[^(f)](n) [^(g)](n)\widehat{f\ast g}(n)=\hat{f}(n) \hat{g}(n). There are versions of the Salem–Zygmund–Rudin–Cohen factorization theorem, Fejér’s lemma and the Parseval equality. The
trigonometric polynomials are dense in
Ac(\mathbbT){\mathcal{A}}_{c}(\mathbb{T}). The convolution of f with a sequence of summability kernels converges to f in the Alexiewicz norm. Let D
n
be the Dirichlet kernel and let
f ? L1(\mathbbT)f\in L^{1}(\mathbb{T}). Then
||Dn*f-f||\mathbbT?0\|D_{n}\ast f-f\|_{\mathbb{T}}\to0 as n→∞. Fourier coefficients of functions of bounded variation are characterized. The Appendix contains a type of Fubini theorem. 相似文献
6.
For 3-codimensional, smooth subvarieties X of
\mathbbPr(\mathbbC){\mathbb{P}^{r}(\mathbb{C})} we prove a new Castelnuovo bound depending only on r and the degree of X. 相似文献
7.
We show that if A is a closed analytic subset of
\mathbbPn{\mathbb{P}^n} of pure codimension q then
Hi(\mathbbPn\ A,F){H^i(\mathbb{P}^n{\setminus} A,{\mathcal F})} are finite dimensional for every coherent algebraic sheaf F{{\mathcal F}} and every
i 3 n-[\fracn-1q]{i\geq n-\left[\frac{n-1}{q}\right]} . If
n-1 3 2q we show that Hn-2(\mathbbPn\ A,F)=0{n-1\geq 2q\,{\rm we show that}\, H^{n-2}(\mathbb{P}^n{\setminus} A,{\mathcal F})=0} . 相似文献
8.
Dong Yang 《Algebras and Representation Theory》2007,10(6):619-629
Let A be a finitary algebra over a finite field k, and A-
\textmod\text{mod} the category of finite dimensional left A-modules. Let H(A)\mathcal{H}(A) be the corresponding Hall algebra, and for a positive integer r let D
r
(A) be the subspace of H(A)\mathcal{H}(A) which has a basis consisting of isomorphism classes of modules in A-
\textmod\text{mod} with at least r + 1 indecomposable direct summands. If A is the path algebra of the quiver of type A
n
with linear orientation, then D
r
(A) is known to be the kernel of the map from the twisted Hall algebra to the quantized Schur algebra indexed by n + 1 and r. For any A, we determine necessary and sufficient conditions for D
r
(A) to be an ideal and some conditions for D
r
(A) to be a subring of H(A)\mathcal{H}(A). For A the path algebra of a quiver, we also determine necessary and sufficient conditions for D
r
(A) to be a subring of H(A)\mathcal{H}(A). 相似文献
9.
Christopher Kennedy 《Algebras and Representation Theory》2011,14(2):317-339
A deep matrix algebra,
DM(X,\mathbbK)\mathcal{DM}(X,\mathbb{K}), is a unital associative algebra over a field
\mathbbK\mathbb{K} with basis all deep matrix units,
\mathfrake(h,k)\mathfrak{e}(h,k), indexed by pairs of elements h and k taken from a free monoid generated by a set X. After briefly describing the construction of
DM(X,\mathbbK)\mathcal{DM}(X,\mathbb{K}), we determine necessary and sufficient conditions for constructing representations for
DM(X,\mathbbK)\mathcal{DM}(X,\mathbb{K}). With these conditions in place, we define null modules and give three canonical examples of such. A classification of general
null modules is then given in terms of the canonical examples along with their submodules and quotients. In the final section,
additional examples of natural actions for
DM(X,\mathbbK)\mathcal{DM}(X,\mathbb{K}) are given and their submodules determined depending on the cardinality of the set X. 相似文献
10.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
11.
In this paper we introduce and study the anisotropic local Hardy spaces
hAp(\mathbbRn)h_{A}^{p}(\mathbb{R}^{n}) 0<p≤1, associated with the expansive matrix A. We obtain an atomic characterization of the distributions in
hAp(\mathbbRn)h_{A}^{p}(\mathbb{R}^{n}). Also we describe the dual spaces of our local Hardy anisotropic spaces as anisotropic Campanato type spaces. 相似文献
12.
The rank of a semigroup $\mathcal{A}The rank of a semigroup A\mathcal{A} of functions from a finite set X to X is the minimum of |f(X)| over f ? Af\in \mathcal{A}. Given a finite set X and a subset Y of X, we show that if A\mathcal{A} is a semigroup of functions from X to X and ℬ a transitive semigroup of functions from Y to Y, then the rank of A\mathcal{A} divides that of ℬ provided that f(X)⊆Y for some f ? Af\in \mathcal{A} and that each function in ℬ is the restriction of a function in A\mathcal{A} to Y. To prove this, we generalize a result of Friedman which says that one can partition Y into q subsets of equal weight where q is the rank of ℬ. When one extends a transitive automaton by adding new states and letters, a similar condition guarantees
that the rank of the extension divides the original rank. 相似文献
13.
We define a generalized Li coefficient for the L-functions attached to the Rankin–Selberg convolution of two cuspidal unitary automorphic representations π and π
′ of
GLm(\mathbbAF)GL_{m}(\mathbb{A}_{F})
and
GLm¢(\mathbbAF)GL_{m^{\prime }}(\mathbb{A}_{F})
. Using the explicit formula, we obtain an arithmetic representation of the n th Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
attached to
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
. Then, we deduce a full asymptotic expansion of the archimedean contribution to
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
and investigate the contribution of the finite (non-archimedean) term. Under the generalized Riemann hypothesis (GRH) on non-trivial
zeros of
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
, the nth Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
is evaluated in a different way and it is shown that GRH implies the bound towards a generalized Ramanujan conjecture for
the archimedean Langlands parameters μ
π
(v,j) of π. Namely, we prove that under GRH for
L(s,pf×[(p)\tilde]f)L(s,\pi _{f}\times \widetilde{\pi}_{f})
one has
|Remp(v,j)| £ \frac14|\mathop {\mathrm {Re}}\mu_{\pi}(v,j)|\leq \frac{1}{4}
for all archimedean places v at which π is unramified and all j=1,…,m. 相似文献
14.
A Toeplitz operator TfT_\phi with symbol f\phi in
L¥(\mathbbD)L^{\infty}({\mathbb{D}}) on the Bergman space
A2(\mathbbD)A^{2}({\mathbb{D}}), where
\mathbbD\mathbb{D} denotes the open unit disc, is radial if f(z) = f(|z|)\phi(z) = \phi(|z|) a.e. on
\mathbbD\mathbb{D}. In this paper, we consider the numerical ranges of such operators. It is shown that all finite line segments, convex hulls
of analytic images of
\mathbbD\mathbb{D} and closed convex polygonal regions in the plane are the numerical ranges of radial Toeplitz operators. On the other hand,
Toeplitz operators TfT_\phi with f\phi harmonic on
\mathbbD\mathbb{D} and continuous on
[`(\mathbbD)]{\overline{\mathbb{D}}} and radial Toeplitz operators are convexoid, but certain compact quasinilpotent Toeplitz operators are not. 相似文献
15.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2011,63(1):84-97
For open discrete mappings
f:D\{ b } ? \mathbbR3 f:D\backslash \left\{ b \right\} \to {\mathbb{R}^3} of a domain
D ì \mathbbR3 D \subset {\mathbb{R}^3} satisfying relatively general geometric conditions in D \ {b} and having an essential singularity at a point
b ? \mathbbR3 b \in {\mathbb{R}^3} , we prove the following statement: Let a point y
0 belong to
[`(\mathbbR3)] \f( D\{ b } ) \overline {{\mathbb{R}^3}} \backslash f\left( {D\backslash \left\{ b \right\}} \right) and let the inner dilatation K
I
(x, f) and outer dilatation K
O
(x, f) of the mapping f at the point x satisfy certain conditions. Let B
f
denote the set of branch points of the mapping f. Then, for an arbitrary neighborhood V of the point y
0, the set V ∩ f(B
f
) cannot be contained in a set A such that g(A) = I, where
I = { t ? \mathbbR:| t | < 1 } I = \left\{ {t \in \mathbb{R}:\left| t \right| < 1} \right\} and
g:U ? \mathbbRn g:U \to {\mathbb{R}^n} is a quasiconformal mapping of a domain
U ì \mathbbRn U \subset {\mathbb{R}^n} such that A ⊂ U. 相似文献
16.
V. V. Lebedev 《Functional Analysis and Its Applications》2012,46(2):121-132
We consider the space
A(\mathbbT)A(\mathbb{T}) of all continuous functions f on the circle
\mathbbT\mathbb{T} such that the sequence of Fourier coefficients
[^(f)] = { [^(f)]( k ), k ? \mathbbZ }\hat f = \left\{ {\hat f\left( k \right), k \in \mathbb{Z}} \right\} belongs to l
1(ℤ). The norm on
A(\mathbbT)A(\mathbb{T}) is defined by
|| f ||A(\mathbbT) = || [^(f)] ||l1 (\mathbbZ)\left\| f \right\|_{A(\mathbb{T})} = \left\| {\hat f} \right\|_{l^1 (\mathbb{Z})}. According to the well-known Beurling-Helson theorem, if
f:\mathbbT ? \mathbbT\phi :\mathbb{T} \to \mathbb{T} is a continuous mapping such that
|| einf ||A(\mathbbT) = O(1)\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = O(1), n ∈ ℤ then φ is linear. It was conjectured by Kahane that the same conclusion about φ is true under the assumption that
|| einf ||A(\mathbbT) = o( log| n | )\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\log \left| n \right|} \right). We show that if $\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right)$\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right), then φ is linear. 相似文献
17.
We prove the maximal L
ρ regularity of the Cauchy problem of the heat equation in the Besov space
[(B)\dot]1,r0(\mathbbRn){\dot{B}_{1,\rho}^0(\mathbb{R}^n)}, 1 < ρ ≤ ∞, which is not UMD space. And as its application, we establish the time local well-posedness of the solution of two dimensional
nonlinear parabolic system with the Poisson equation in
[(B)\dot]1,20(\mathbbR2){\dot{B}_{1,2}^0(\mathbb{R}^2)} , where the equation is considered in the space invariant by a scaling and particularly the natural free energy is well defined
from the initial time. The small data global existence is also obtained in the same class. 相似文献
18.
Meirav Amram Michael Dettweiler Mina Teicher 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2010,80(1):1-8
We determine the fundamental group of the complement of the three-cuspidal quartic minus the tangent lines through the cusps.
The existence of a rigid covering of this complement whose monodromy group is isomorphic to the simple group
PSL2(\mathbbF7)\mathrm{PSL}_{2}(\mathbb{F}_{7})
is proved. 相似文献
19.
We prove a “unique crossed product decomposition” result for group measure space II1 factors L ∞(X)⋊Γ arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups Γ in a fairly large family
G\mathcal{G}, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products
over an amenable subgroup. We deduce that if T
n
denotes the group of upper triangular matrices in PSL (n,ℤ), then any free, mixing p.m.p. action of
G = \operatornamePSL(n,\mathbbZ)*Tn\operatornamePSL(n,\mathbbZ)\Gamma=\operatorname{PSL}(n,\mathbb{Z})*_{T_{n}}\operatorname{PSL}(n,\mathbb{Z}) is W∗-superrigid, i.e. any isomorphism between L ∞(X)⋊Γ and an arbitrary group measure space factor L ∞(Y)⋊Λ, comes from a conjugacy of the actions. We also prove that for many groups Γ in the family G\mathcal{G}, the Bernoulli actions of Γ are W∗-superrigid. 相似文献
20.
Dudley Stark 《Annals of Combinatorics》2011,15(3):529-539
The conjecture was made by Kahn that a spanning forest F chosen uniformly at random from all forests of any finite graph G has the edge-negative association property. If true, the conjecture would mean that given any two edges ε1 and ε2 in G, the inequality
\mathbbP(e1 ? F, e2 ? F) £ \mathbbP(e1 ? F)\mathbbP(e2 ? F){{\mathbb{P}(\varepsilon_{1} \in \mathbf{F}, \varepsilon_{2} \in \mathbf{F}) \leq \mathbb{P}(\varepsilon_{1} \in \mathbf{F})\mathbb{P}(\varepsilon_{2} \in \mathbf{F})}} would hold. We use enumerative methods to show that this conjecture is true for n large enough when G is a complete graph on n vertices. We derive explicit related results for random trees. 相似文献