共查询到20条相似文献,搜索用时 31 毫秒
1.
Jochen Heinloth 《Mathematische Annalen》2010,347(3):499-528
We show some of the conjectures of Pappas and Rapoport concerning the moduli stack BunG{{\rm Bun}_\mathcal {G}} of G{\mathcal {G}}-torsors on a curve C, where G{\mathcal {G}} is a semisimple Bruhat-Tits group scheme on C. In particular we prove the analog of the uniformization theorem of Drinfeld-Simpson in this setting. Furthermore we apply
this to compute the connected components of these moduli stacks and to calculate the Picard group of BunG{{\rm Bun}_\mathcal {G}} in case G{\mathcal {G}} is simply connected. 相似文献
2.
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
3.
Wenbin Guo 《manuscripta mathematica》2008,127(2):139-150
Let G be a finite group and a formation of finite groups. We say that a subgroup H of G is -supplemented in G if there exists a subgroup T of G such that G = TH and is contained in the -hypercenter of G/H
G
. In this paper, we use -supplemented subgroups to study the structure of finite groups. A series of previously known results are unified and generalized.
Research of the author is supported by a NNSF grant of China (Grant #10771180). 相似文献
4.
A class Uk1 (J){\mathcal{U}}_{\kappa 1} (J) of generalized J-inner mvf’s (matrix valued functions) W(λ) which appear as resolvent matrices for bitangential interpolation problems in the generalized Schur class of p ×q mvf¢s Skp ×qp \times q \, {\rm mvf's}\, {\mathcal{S}}_{\kappa}^{p \times q} and some associated reproducing kernel Pontryagin spaces are studied. These spaces are used to describe the range of the
linear fractional transformation TW based on W and applied to Sk2p ×q{\mathcal{S}}_{\kappa 2}^{p \times q}. Factorization formulas for mvf’s W in a subclass U°k1 (J) of Uk1(J){\mathcal{U}^{\circ}_{\kappa 1}} (J)\, {\rm of}\, {\mathcal{U}}_{\kappa 1}(J) found and then used to parametrize the set Sk1+k2p ×q ?TW [ Sk2p ×q ]{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} \cap T_{W} \left[ {\mathcal{S}}_{\kappa 2}^{p \times q} \right]. Applications to bitangential interpolation problems in the class Sk1+k2p ×q{\mathcal{S}}_{{\kappa 1}+{\kappa 2}}^{p \times q} will be presented elsewhere. 相似文献
5.
Margarida Melo 《Mathematische Zeitschrift》2009,263(4):939-957
We study algebraic (Artin) stacks over [`(M)]g{\overline{\mathcal M}_{g}} giving a functorial way of compactifying the relative degree d Picard variety for families of stable curves. We also describe for every d the locus of genus g stable curves over which we get Deligne–Mumford stacks strongly representable over[`(M)]g{\overline{\mathcal M}_{g}} . 相似文献
6.
An integral coefficient matrix determines an integral arrangement of hyperplanes in
\mathbbRm{\mathbb{R}^m} . After modulo q reduction ${(q \in {\mathbb{Z}_{ >0 }})}${(q \in {\mathbb{Z}_{ >0 }})} , the same matrix determines an arrangement Aq{\mathcal{A}_q} of “hyperplanes” in
\mathbbZmq{\mathbb{Z}^m_q} . In the special case of central arrangements, Kamiya, Takemura, and Terao [J. Algebraic Combin. 27(3), 317–330 (2008)] showed that the cardinality of the complement of Aq{\mathcal{A}_q} in
\mathbbZmq{\mathbb{Z}^m_q} is a quasi-polynomial in ${q \in {\mathbb{Z}_{ >0 }}}${q \in {\mathbb{Z}_{ >0 }}} . Moreover, they proved in the central case that the intersection lattice of Aq{\mathcal{A}_q} is periodic from some q on. The present paper generalizes these results to the case of non-central arrangements. The paper also studies the arrangement
[^(B)]m[0,a]{\hat{\mathcal{B}}_m^{[0,a]}} of Athanasiadis [J. Algebraic Combin. 10(3), 207–225 (1999)] to illustrate our results. 相似文献
7.
Given a Lie group G with a bi-invariant metric and a compact Lie subgroup K, Bittencourt and Ripoll used the homogeneous structure of quotient spaces to define a Gauss map ${\mathcal{N}:M^{n}\rightarrow{\mathbb{S}}}$ on any hypersupersurface ${M^{n}\looparrowright G/K}$ , where ${{\mathbb{S}}}$ is the unit sphere of the Lie algebra of G. It is proved in Bittencourt and Ripoll (Pacific J Math 224:45–64, 2006) that M n having constant mean curvature (CMC) is equivalent to ${\mathcal{N}}$ being harmonic, a generalization of a Ruh–Vilms theorem for submanifolds in the Euclidean space. In particular, when n = 2, the induced quadratic differential ${\mathcal{Q}_{\mathcal{N}}:=(\mathcal{N}^{\ast}g)^{2,0}}$ is holomorphic on CMC surfaces of G/K. In this paper, we take ${G/K={\mathbb{S}}^{2}\times{\mathbb{R}}}$ and compare ${\mathcal{Q}_{\mathcal{N}}}$ with the Abresch–Rosenberg differential ${\mathcal{Q}}$ , also holomorphic for CMC surfaces. It is proved that ${\mathcal{Q}=\mathcal{Q}_{\mathcal{N}}}$ , after showing that ${\mathcal{N}}$ is the twisted normal given by (1.5) herein. Then we define the twisted normal for surfaces in ${{\mathbb{H}}^{2}\times{\mathbb{R}}}$ and prove that ${\mathcal{Q}=\mathcal{Q}_{\mathcal{N}}}$ as well. Within the unified model for the two product spaces, we compute the tension field of ${\mathcal{N}}$ and extend to surfaces in ${{\mathbb{H}}^{2}\times{\mathbb{R}}}$ the equivalence between the CMC property and the harmonicity of ${\mathcal{N}.}$ 相似文献
8.
Frédéric A. B. Edoukou 《Designs, Codes and Cryptography》2009,50(1):135-146
We study the functional codes of second order on a non-degenerate Hermitian variety as defined by G. Lachaud. We provide the best possible bounds for the number of points of quadratic sections of . We list the first five weights, describe the corresponding codewords and compute their number. The paper ends with two
conjectures. The first is about minimum distance of the functional codes of order h on a non-singular Hermitian variety . The second is about distribution of the codewords of first five weights of the functional codes of second order on a non-singular
Hermitian variety .
相似文献
9.
J. Borges C. Fernández-Córdoba J. Pujol J. Rifà M. Villanueva 《Designs, Codes and Cryptography》2010,54(2):167-179
A code C{{\mathcal C}} is
\mathbb Z2\mathbb Z4{{{\mathbb Z}_2}{{\mathbb Z}_4}} -additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C{{\mathcal C}} by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). In this paper
\mathbb Z2\mathbb Z4{{{\mathbb Z}_2}{{\mathbb Z}_4}} -additive codes are studied. Their corresponding binary images, via the Gray map, are
\mathbb Z2\mathbb Z4{{{\mathbb Z}_2}{{\mathbb Z}_4}} -linear codes, which seem to be a very distinguished class of binary group codes. As for binary and quaternary linear codes,
for these codes the fundamental parameters are found and standard forms for generator and parity-check matrices are given.
In order to do this, the appropriate concept of duality for
\mathbb Z2\mathbb Z4{{{\mathbb Z}_2}{{\mathbb Z}_4}} -additive codes is defined and the parameters of their dual codes are computed. 相似文献
10.
We consider the class of minimal surfaces given by the graphical strips ${{\mathcal S}}We consider the class of minimal surfaces given by the graphical strips S{{\mathcal S}} in the Heisenberg group
\mathbb H1{{\mathbb {H}}^1} and we prove that for points p along the center of
\mathbb H1{{\mathbb {H}}^1} the quantity
\fracsH(S?B(p,r))rQ-1{\frac{\sigma_H(\mathcal S\cap B(p,r))}{r^{Q-1}}} is monotone increasing. Here, Q is the homogeneous dimension of
\mathbb H1{{\mathbb {H}}^1} . We also prove that these minimal surfaces have maximum volume growth at infinity. 相似文献
11.
Charles M. Harris 《Archive for Mathematical Logic》2010,49(6):673-691
We investigate and extend the notion of a good approximation with respect to the enumeration ${({\mathcal D}_{\rm e})}We investigate and extend the notion of a good approximation with respect to the enumeration (De){({\mathcal D}_{\rm e})} and singleton (Ds){({\mathcal D}_{\rm s})} degrees. We refine two results by Griffith, on the inversion of the jump of sets with a good approximation, and we consider
the relation between the double jump and index sets, in the context of enumeration reducibility. We study partial order embeddings
is{\iota_s} and [^(i)]s{\hat{\iota}_s} of, respectively, De{{\mathcal D}_{\rm e}} and DT{{\mathcal D}_{\rm T}} (the Turing degrees) into Ds{{\mathcal D}_{\rm s}} , and we show that the image of DT{{\mathcal D}_{\rm T}} under [^(i)]s{\hat{\iota}_s} is precisely the class of retraceable singleton degrees. We define the notion of a good enumeration, or singleton, degree
to be the property of containing the set of good stages of some good approximation, and we show that is{\iota_s} preserves the latter, as also other naturally arising properties such as that of totality or of being G0n{\Gamma^0_n} , for G ? {S,P,D}{\Gamma \in \{\Sigma,\Pi,\Delta\}} and n > 0. We prove that the good enumeration and singleton degrees are immune and that the good S02{\Sigma^0_2} singleton degrees are hyperimmune. Finally we show that, for singleton degrees a
s < b
s such that b
s is good, any countable partial order can be embedded in the interval (a
s, b
s). 相似文献
12.
Ricardo Abreu Blaya Juan Bory Reyes Dixan Peña Peña Frank Sommen 《Advances in Applied Clifford Algebras》2010,20(1):1-12
The holomorphic functions of several complex variables are closely related to the continuously differentiable solutions $f
: {\mathbb{R}}^{2n} \mapsto {\mathbb{C}}_{n}$f
: {\mathbb{R}}^{2n} \mapsto {\mathbb{C}}_{n} of the so called isotonic system
?x1 + i [(f)\tilde] ?x 2 = 0\partial _{\underbar{x}_1 } + i \tilde{f} \mathop{\partial _{\underbar{x} _2 } = 0} 相似文献
13.
Let ${\Gamma < {\rm SL}(2, {\mathbb Z})}
14.
Aziz El Kacimi Alaoui 《Mathematische Annalen》2010,347(4):885-897
In (Ann Sc ENS Sér 3 4:361–380, 1887) Guichard proved that, for any holomorphic function g on ${{\mathbb C}}
15.
Jean B. Lasserre 《Optimization Letters》2011,5(4):549-556
We consider the convex optimization problem P:minx {f(x) : x ? K}{{\rm {\bf P}}:{\rm min}_{\rm {\bf x}} \{f({\rm {\bf x}})\,:\,{\rm {\bf x}}\in{\rm {\bf K}}\}} where f is convex continuously differentiable, and
K ì \mathbb Rn{{\rm {\bf K}}\subset{\mathbb R}^n} is a compact convex set with representation
{x ? \mathbb Rn : gj(x) 3 0, j = 1,?,m}{\{{\rm {\bf x}}\in{\mathbb R}^n\,:\,g_j({\rm {\bf x}})\geq0, j = 1,\ldots,m\}} for some continuously differentiable functions (g
j
). We discuss the case where the g
j
’s are not all concave (in contrast with convex programming where they all are). In particular, even if the g
j
are not concave, we consider the log-barrier function fm{\phi_\mu} with parameter μ, associated with P, usually defined for concave functions (g
j
). We then show that any limit point of any sequence (xm) ì K{({\rm {\bf x}}_\mu)\subset{\rm {\bf K}}} of stationary points of fm, m? 0{\phi_\mu, \mu \to 0} , is a Karush–Kuhn–Tucker point of problem P and a global minimizer of f on K. 相似文献
16.
We study permanence properties of the classes of stable and so-called -stable -algebras, respectively. More precisely, we show that a (X)-algebra A is stable if all its fibres are, provided that the underlying compact metrizable space X has finite covering dimension or that the Cuntz semigroup of A is almost unperforated (a condition which is automatically satisfied for -algebras absorbing the Jiang–Su algebra tensorially). Furthermore, we prove that if is a K
1-injective strongly self-absorbing -algebra, then A absorbs tensorially if and only if all its fibres do, again provided that X is finite-dimensional. This latter statement generalizes results of Blanchard and Kirchberg. We also show that the condition
on the dimension of X cannot be dropped. Along the way, we obtain a useful characterization of when a -algebra with weakly unperforated Cuntz semigroup is stable, which allows us to show that stability passes to extensions of
-absorbing -algebras.
Research supported by: Deutsche Forschungsgemeinschaft (through the SFB 478), by the EU-Network Quantum Spaces - Noncommutative
Geometry (Contract No. HPRN-CT-2002-00280), and by the Center for Advanced Studies in Mathematics at Ben-Gurion University 相似文献
17.
In this paper, we mainly study polynomial generalized Vekua-type equation _boxclose)w=0{p(\mathcal{D})w=0} and polynomial generalized Bers–Vekua equation p(D)w=0{p(\mathcal{\underline{D}})w=0} defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}} where D{\mathcal{D}} and D{\mathcal{\underline{D}}} mean generalized Vekua-type operator and generalized Bers–Vekua operator, respectively. Using Clifford algebra, we obtain
the Fischer-type decomposition theorems for the solutions to these equations including
(D-l)kw=0,(D-l)kw=0(k ? \mathbbN){\left(\mathcal{D}-\lambda\right)^{k}w=0,\left(\mathcal {\underline{D}}-\lambda\right)^{k}w=0\left(k\in\mathbb{N}\right)} with complex parameter λ as special cases, which derive the Almansi-type decomposition theorems for iterated generalized
Bers–Vekua equation and polynomial generalized Cauchy–Riemann equation defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}}. Making use of the decomposition theorems we give the solutions to polynomial generalized Bers–Vekua equation defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}} under some conditions. Furthermore we discuss inhomogeneous polynomial generalized Bers–Vekua equation p(D)w=v{p(\mathcal{\underline{D}})w=v} defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}}, and develop the structure of the solutions to inhomogeneous polynomial generalized Bers–Vekua equation p(D)w=v{p(\mathcal{\underline{D}})w=v} defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}}. 相似文献
18.
19.
In this work, we focus on cyclic codes over the ring
\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} , which is not a finite chain ring. We use ideas from group rings and works of AbuAlrub et.al. in (Des Codes Crypt 42:273–287,
2007) to characterize the ring
(\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2)/(xn-1){({{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2})/(x^n-1)} and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over
\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} under two Gray maps that are defined. We also characterize the binary images of cyclic codes over
\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} in general. 相似文献
20.
Christopher Hammond 《Mathematische Zeitschrift》2010,266(2):285-288
Let Ω be a domain in ${\mathbb{C}^{2}}
|