共查询到20条相似文献,搜索用时 453 毫秒
1.
Kyriakos Keremedis 《Mathematical Logic Quarterly》2012,58(3):130-138
Given a set X, $\mathsf {AC}^{\mathrm{fin}(X)}$ denotes the statement: “$[X]^{<\omega }\backslash \lbrace \varnothing \rbrace$ has a choice set” and $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )$ denotes the family of all closed subsets of the topological space $\mathbf {2}^{X}$ whose definition depends on a finite subset of X. We study the interrelations between the statements $\mathsf {AC}^{\mathrm{fin}(X)},$ $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega })},$ $\mathsf {AC}^{\mathrm{fin} (F_{n}(X,2))},$ $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ and “$\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set”. We show:
- (i) $\mathsf {AC}^{\mathrm{fin}(X)}$ iff $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega } )}$ iff $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set iff $\mathsf {AC}^{\mathrm{fin}(F_{n}(X,2))}$.
- (ii) $\mathsf {AC}_{\mathrm{fin}}$ ($\mathsf {AC}$ restricted to families of finite sets) iff for every set X, $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set.
- (iii) $\mathsf {AC}_{\mathrm{fin}}$ does not imply “$\mathcal {K}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set($\mathcal {K}(\mathbf {X})$ is the family of all closed subsets of the space $\mathbf {X}$)
- (iv) $\mathcal {K}(\mathbf {2}^{X})\backslash \lbrace \varnothing \rbrace$ implies $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ but $\mathsf {AC}^{\mathrm{fin}(X)}$ does not imply $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$.
2.
We construct a global solution with $\mathcal {C}^{k}$‐estimates for the $\bar{\partial }$‐equation on q‐convex intersections. 相似文献
3.
Wei Wang 《Mathematische Nachrichten》2013,286(13):1353-1376
On quadratic hypersurfaces in $\mathbb {H}^2$, we find the explicit forms of tangential Cauchy‐Fueter operators and associated tangential Laplacians □b. Then by using the Fourier transformation on the associated nilpotent Lie groups of step two, we construct the relative fundamental solutions to the tangential Laplacians and Szegö kernels on the nondegenerate quadratic hypersurfaces. It is different from the complex case that the quaternionic tangential structures on the nondegenerate quadratic hypersurfaces in $\mathbb {H}^2$ cannot be reduced to one standard model and the non‐homogeneous tangential Cauchy‐Fueter equations are solvable even in many convex cases. 相似文献
4.
In this paper, the irreducible p, q‐representations of the Lie algebras $\mathcal {G}(0,1)$ and $\mathcal {G}(0,0)$ are discussed. We prove two theorems that classify certain irreducible p, q‐representations of these Lie algebras and construct their one variable models in terms of p, q‐derivative and dilation operators. As an application, we derive a p, q‐special function identity based on one such model. 相似文献
5.
We prove several dichotomy theorems which extend some known results on σ‐bounded and σ‐compact pointsets. In particular we show that, given a finite number of $\Delta ^{1}_{1}$ equivalence relations $\mathrel {\mathsf {F}}_1,\dots ,\mathrel {\mathsf {F}}_n$, any $\Sigma ^{1}_{1}$ set A of the Baire space either is covered by compact $\Delta ^{1}_{1}$ sets and lightface $\Delta ^{1}_{1}$ equivalence classes of the relations $\mathrel {\mathsf {F}}_i$, or A contains a superperfect subset which is pairwise $\mathrel {\mathsf {F}}_i$‐inequivalent for all i = 1, …, n. Further generalizations to $\Sigma ^{1}_{2}$ sets A are obtained. 相似文献
6.
Eduard A. Nigsch 《Mathematische Nachrichten》2013,286(10):1007-1021
We present a point value characterization for elements of the elementary full Colombeau algebra ${\mathcal {G}}^e(\Omega )$ and the diffeomorphism invariant full Colombeau algebra $\mathcal {G}^d(\Omega )$. Moreover, several results from the special algebra ${\mathcal {G}}^s(\Omega )$ about generalized numbers and invertibility are extended to the elementary full algebra. 相似文献
7.
Let R be the ring $ {\mathbb Z}[x]/\left({{x^p-1}\over{x-1}}\right) = {\mathbb Z}[\bar{x}] $ and let $ \mathfrak {a} $ be the ideal of R generated by $ (\bar{x}-1) $ . In this paper, we discuss the structure of the $ {\mathbb Z}[C_p] $‐module $ (R/\mathfrak {a}^{n-1}) \wedge (R/\mathfrak {a}^{n-1}) $, which plays an important role in the theory of p‐groups of maximal class (see 2 - 5 ). The generators of this module allow us to obtain the defining relations of some important examples of p‐groups of maximal class with Y1 of class two. In particular we obtain the best possible estimates for the degree of commutativity of p‐groups of maximal class with Y1 of class two. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
8.
Alexey V. Petukhov 《Transformation Groups》2011,16(4):1173-1182
Let
\mathfrakg \mathfrak{g} be a reductive Lie algebra and
\mathfrakk ì \mathfrakg \mathfrak{k} \subset \mathfrak{g} be a reductive in
\mathfrakg \mathfrak{g} subalgebra. A (
\mathfrakg,\mathfrakk \mathfrak{g},\mathfrak{k} )-module M is a
\mathfrakg \mathfrak{g} -module for which any element m ∈ M is contained in a finite-dimensional
\mathfrakk \mathfrak{k} -submodule of M. We say that a (
\mathfrakg,\mathfrakk \mathfrak{g},\mathfrak{k} )-module M is bounded if there exists a constant C
M
such that the Jordan-H?lder multiplicities of any simple finite-dimensional
\mathfrakk \mathfrak{k} -module in every finite-dimensional
\mathfrakk \mathfrak{k} -submodule of M are bounded by C
M
. In the present paper we describe explicitly all reductive in
\mathfraks\mathfrakln \mathfrak{s}{\mathfrak{l}_n} subalgebras
\mathfrakk \mathfrak{k} which admit a bounded simple infinite-dimensional (
\mathfraks\mathfrakln,\mathfrakk \mathfrak{s}{\mathfrak{l}_n},\mathfrak{k} )-module. Our technique is based on symplectic geometry and the notion of spherical variety. We also characterize the irreducible
components of the associated varieties of simple bounded (
\mathfrakg,\mathfrakk \mathfrak{g},\mathfrak{k} )-modules. 相似文献
9.
设 $p\geq 7$ 为任意奇素数. 证明了当 $3\leq s
相似文献
10.
Hiroaki Minami 《Archive for Mathematical Logic》2010,49(4):501-518
We investigate splitting number and reaping number for the structure (ω)
ω
of infinite partitions of ω. We prove that
\mathfrakrd £ non(M),non(N),\mathfrakd{\mathfrak{r}_{d}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N}),\mathfrak{d}} and
\mathfraksd 3 \mathfrakb{\mathfrak{s}_{d}\geq\mathfrak{b}} . We also show the consistency results ${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and ${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})}${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})} . To prove the consistency
\mathfrakrd < add(M){\mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and
\mathfraksd < cof(M){\mathfrak{s}_{d} < \mathsf{cof}(\mathcal{M})} we introduce new cardinal invariants
\mathfrakrpair{\mathfrak{r}_{pair}} and
\mathfrakspair{\mathfrak{s}_{pair}} . We also study the relation between
\mathfrakrpair, \mathfrakspair{\mathfrak{r}_{pair}, \mathfrak{s}_{pair}} and other cardinal invariants. We show that
cov(M),cov(N) £ \mathfrakrpair £ \mathfraksd,\mathfrakr{\mathsf{cov}(\mathcal{M}),\mathsf{cov}(\mathcal{N})\leq\mathfrak{r}_{pair}\leq\mathfrak{s}_{d},\mathfrak{r}} and
\mathfraks £ \mathfrakspair £ non(M),non(N){\mathfrak{s}\leq\mathfrak{s}_{pair}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N})} . 相似文献
11.
A. V. Petukhov 《Journal of Mathematical Sciences》2012,186(4):655-666
Let $ \mathfrak{g} $ be a reductive Lie algebra over $ \mathbb{C} $ and $ \mathfrak{k} \subset \mathfrak{g} $ be a reductive in $ \mathfrak{g} $ subalgebra. We call a $ \mathfrak{g} $ -module M a $ \left( {\mathfrak{g}{\hbox{,}}\;\mathfrak{k}} \right) $ -module whenever M is a direct sum of finite-dimensional $ \mathfrak{k} $ -modules. We call a $ \left( {\mathfrak{g}{\hbox{,}}\;\mathfrak{k}} \right) $ -module M bounded if there exists $ {C_M} \in {\mathbb{Z}_{{ \geqslant 0}}} $ such that for any simple finite-dimensional $ \mathfrak{k} $ -module E the dimension of the E-isotypic component is not greater than C M dim E. Bounded $ \left( {\mathfrak{g}{\hbox{,}}\;\mathfrak{k}} \right) $ -modules form a subcategory of the category of $ \mathfrak{g} $ -modules. Let V be a finite-dimensional vector space. We prove that the categories of bounded $ \left( {\mathfrak{sp}\left( {{{\mathrm{S}}^2}V \oplus {{\mathrm{S}}^2}{V^{*}}} \right),\;\mathfrak{gl}(V)} \right) $ - and $ \left( {\mathfrak{sp}\left( {{\varLambda^2}V \oplus {\varLambda^2}{V^{*}}} \right),\;\mathfrak{gl}(V)} \right) $ -modules are isomorphic to the direct sum of countably many copies of the category of representations of some explicitly described quiver with relations under some mild assumptions on the dimension of V . 相似文献
12.
13.
Christopher Manon 《Transformation Groups》2013,18(4):1165-1187
We construct and study a family of toric degenerations of the Cox ring of the moduli of quasi-parabolic principal SL3( $ \mathbb{C} $ ) bundles on a smooth, marked curve (C, $ \vec{p} $ ): Elements of this algebra have a well known interpretation as conformal blocks, from the Wess-Zumino-Witten model of conformal field theory. For the genus 0; 1 cases we find the level of conformal blocks necessary to generate the algebra. In the genus 0 case we also find bounds on the degrees of relations required to present the algebra. As a consequence we obtain a toric degeneration for the projective coordinate ring of an effective divisor on the moduli $ {{\mathcal{M}}_{{C,\vec{p}}}}\left( {\mathrm{S}{{\mathrm{L}}_3}\left( \mathbb{C} \right)} \right) $ of quasi-parabolic principal SL3( $ \mathbb{C} $ ) bundles on (C, $ \vec{p} $ ). Along the way we recover positive polyhedral rules for counting conformal blocks. 相似文献
14.
Let G be a finite soluble group and
F\mathfrakX(G) {\Phi_\mathfrak{X}}(G) an intersection of all those maximal subgroups M of G for which
G