共查询到20条相似文献,搜索用时 31 毫秒
1.
Andrea Bonfiglioli 《Archiv der Mathematik》2009,93(3):277-286
Let ${\mathbb{G}}Let
\mathbbG{\mathbb{G}} be a Carnot group of step r and m generators and homogeneous dimension Q. Let
\mathbbFm,r{\mathbb{F}_{m,r}} denote the free Lie group of step r and m generators. Let also
p:\mathbbFm,r?\mathbbG{\pi:\mathbb{F}_{m,r}\to\mathbb{G}} be a lifting map. We show that any horizontally convex function u on
\mathbbG{\mathbb{G}} lifts to a horizontally convex function u°p{u\circ \pi} on
\mathbbFm,r{\mathbb{F}_{m,r}} (with respect to a suitable horizontal frame on
\mathbbFm,r{\mathbb{F}_{m,r}}). One of the main aims of the paper is to exhibit an example of a sub-Laplacian L=?j=1m Xj2{\mathcal{L}=\sum_{j=1}^m X_j^2} on a Carnot group of step two such that the relevant L{\mathcal{L}}-gauge function d (i.e., d
2-Q
is the fundamental solution for L{\mathcal{L}}) is not h-convex with respect to the horizontal frame {X
1, . . . , X
m
}. This gives a negative answer to a question posed in Danielli et al. (Commun. Anal. Geom. 11 (2003), 263–341). 相似文献
2.
A variety ${\mathbb{V}}${\mathbb{V}} is var-relatively universal if it contains a subvariety
\mathbbW{\mathbb{W}} such that the class of all homomorphisms that do not factorize through any algebra in
\mathbbW{\mathbb{W}} is algebraically universal. And
\mathbbV{\mathbb{V}} has an algebraically universal α-expansion
a\mathbbV{\alpha\mathbb{V}} if adding α nullary operations to all algebras in
\mathbbV{\mathbb{V}} gives rise to a class
a\mathbbV{\alpha\mathbb{V}} of algebras that is algebraically universal. The first two authors have conjectured that any varrelative universal variety
\mathbbV{\mathbb{V}} has an algebraically universal α-expansion
a\mathbbV{\alpha\mathbb{V}} . This note contains a more general result that proves this conjecture. 相似文献
3.
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
4.
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
5.
David Fried 《Journal of Fixed Point Theory and Applications》2009,6(1):87-92
When X is a finite complex and p1X\pi_{1}X acts on
\mathbbR2{\mathbb{R}}^2 by translations we give criteria involving H2X for an equivariant map
F : [(X)\tilde] ? \mathbbR2F : \tilde{X} \rightarrow {\mathbb{R}}^2 to be onto. Following work of Manning and Shub, this leads to entropy bounds related to Shub’s entropy conjecture. 相似文献
6.
We study hypersurfaces in the Lorentz-Minkowski space
\mathbbLn+1{\mathbb{L}^{n+1}} whose position vector ψ satisfies the condition L
k
ψ = Aψ + b, where L
k
is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed k = 0, . . . , n − 1,
A ? \mathbbR(n+1)×(n+1){A\in\mathbb{R}^{(n+1)\times(n+1)}} is a constant matrix and
b ? \mathbbLn+1{b\in\mathbb{L}^{n+1}} is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature, open pieces of totally umbilical hypersurfaces
\mathbbSn1(r){\mathbb{S}^n_1(r)} or
\mathbbHn(-r){\mathbb{H}^n(-r)}, and open pieces of generalized cylinders
\mathbbSm1(r)×\mathbbRn-m{\mathbb{S}^m_1(r)\times\mathbb{R}^{n-m}},
\mathbbHm(-r)×\mathbbRn-m{\mathbb{H}^m(-r)\times\mathbb{R}^{n-m}}, with k + 1 ≤ m ≤ n − 1, or
\mathbbLm×\mathbbSn-m(r){\mathbb{L}^m\times\mathbb{S}^{n-m}(r)}, with k + 1 ≤ n − m ≤ n − 1. This completely extends to the Lorentz-Minkowski space a previous classification for hypersurfaces in
\mathbbRn+1{\mathbb{R}^{n+1}} given by Alías and Gürbüz (Geom. Dedicata 121:113–127, 2006). 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.
Let j{\varphi} be an analytic self-map of the unit disk
\mathbbD{\mathbb{D}},
H(\mathbbD){H(\mathbb{D})} the space of analytic functions on
\mathbbD{\mathbb{D}} and
g ? H(\mathbbD){g \in H(\mathbb{D})}. The boundedness and compactness of the operator DCj : H¥ ? Z{DC_\varphi : H^\infty \rightarrow { \mathcal Z}} are investigated in this paper. 相似文献
9.
Paul D. Nelson 《The Ramanujan Journal》2012,27(2):235-284
Let
\mathbbF\mathbb{F} be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on
\operatornameGL2/\mathbbF\operatorname{GL}_{2}/\mathbb{F} of weight
(k1,?,k[\mathbbF:\mathbbQ])(k_{1},\ldots,k_{[\mathbb{F}:\mathbb{Q}]}), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as
max(k1,?,k[\mathbbF:\mathbbQ]) ? ¥\max(k_{1},\ldots,k_{[\mathbb{F}:\mathbb{Q}]}) \rightarrow \infty. 相似文献
10.
Mahmoud Baroun Lahcen Maniar Roland Schnaubelt 《Integral Equations and Operator Theory》2009,65(2):169-193
We show the existence and uniqueness of the (asymptotically) almost periodic solution to parabolic evolution equations with
inhomogeneous boundary values on
\mathbbR{\mathbb{R}} and
\mathbbR±\mathbb{R}_{\pm}, if the data are (asymptotically) almost periodic. We assume that the underlying homogeneous problem satisfies the ‘Acquistapace–Terreni’
conditions and has an exponential dichotomy. If there is an exponential dichotomy only on half intervals ( − ∞, − T] and [T, ∞), then we obtain a Fredholm alternative of the equation on
\mathbbR{\mathbb{R}} in the space of functions being asymptotically almost periodic on
\mathbbR+{\mathbb{R}}_{+} and
\mathbbR-\mathbb{R}_{-}. 相似文献
11.
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
12.
Esteban Andruchow Jorge Antezana Gustavo Corach 《Integral Equations and Operator Theory》2010,67(4):451-466
Given a closed subspace ${\mathcal{S}}Given a closed subspace S{\mathcal{S}} of a Hilbert space H{\mathcal{H}}, we study the sets FS{\mathcal{F}_\mathcal{S}} of pseudo-frames, CFS{\mathcal{C}\mathcal{F}_\mathcal{S}} of commutative pseudo-frames and
\mathfrakXS{\tiny{\mathfrak{X}}_{\mathcal{S}}} of dual frames for S{\mathcal{S}}, via the (well known) one to one correspondence which assigns a pair of operators (F, H) to a frame pair
({fn}n ? \mathbbN,{hn}n ? \mathbbN){(\{f_n\}_{n\in\mathbb{N}},\{h_n\}_{n\in\mathbb{N}})},
F:l2? H, F({cn}n ? \mathbbN )=?n cn fn,F:\ell^2\to\,\mathcal{H}, \quad F\left(\{c_n\}_{n\in\mathbb{N}} \right)=\sum_n c_n f_n, 相似文献
13.
In Finsler geometry, minimal surfaces with respect to the Busemann-Hausdorff measure and the Holmes-Thompson measure are called
BH-minimal and HT-minimal surfaces, respectively. In this paper, we give the explicit expressions of BH-minimal and HT-minimal
rotational hypersurfaces generated by plane curves rotating around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski (α, β)-space
(\mathbbVn+1,[(Fb)\tilde]){(\mathbb{V}^{n+1},\tilde{F_b})} , where
\mathbbVn+1{\mathbb{V}^{n+1}} is an (n+1)-dimensional real vector space, [(Fb)\tilde]=[(a)\tilde]f([(b)\tilde]/[(a)\tilde]), [(a)\tilde]{\tilde{F_b}=\tilde{\alpha}\phi(\tilde{\beta}/\tilde{\alpha}), \tilde{\alpha}} is the Euclidean metric, [(b)\tilde]{\tilde{\beta}} is a one form of constant length
b:=||[(b)\tilde]||[(a)\tilde], [(b)\tilde]\sharp{b:=\|\tilde{\beta}\|_{\tilde{\alpha}}, \tilde{\beta}^{\sharp}} is the dual vector of [(b)\tilde]{\tilde{\beta}} with respect to [(a)\tilde]{\tilde{\alpha}} . As an application, we first give the explicit expressions of the forward complete BH-minimal rotational surfaces generated
around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski Randers 3-space
(\mathbbV3,[(a)\tilde]+[(b)\tilde]){(\mathbb{V}^{3},\tilde{\alpha}+\tilde{\beta})} . 相似文献
14.
Alexander Premet 《Inventiones Mathematicae》2010,181(2):395-420
Let ${\mathfrak{g}}
15.
Juan A. Aledo Victorino Lozano José A. Pastor 《Mediterranean Journal of Mathematics》2010,7(3):263-270
We prove that the only compact surfaces of positive constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} (resp. positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}}) whose boundary Γ is contained in a slice of the ambient space and such that the surface intersects this slice at a constant
angle along Γ, are the pieces of a rotational complete surface. We also obtain some area estimates for surfaces of positive
constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} and positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}} whose boundary is contained in a slice of the ambient space. These estimates are optimal in the sense that if the bounds
are attained, the surface is again a piece of a rotational complete surface. 相似文献
16.
Amol Sasane 《Complex Analysis and Operator Theory》2012,6(2):465-475
Let
\mathbb Dn:={z=(z1,?, zn) ? \mathbb Cn:|zj| < 1, j=1,?, n}{\mathbb {D}^n:=\{z=(z_1,\ldots, z_n)\in \mathbb {C}^n:|z_j| < 1, \;j=1,\ldots, n\}}, and let
[`(\mathbbD)]n{\overline{\mathbb{D}}^n} denote its closure in
\mathbb Cn{\mathbb {C}^n}. Consider the ring
|