共查询到20条相似文献,搜索用时 46 毫秒
1.
2.
By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra L(A) generated by indecomposable constructible sets in the varieties of modules for any finite- dimensional C-algebra A. We obtain a geometric realization of the universal enveloping algebra R(A) of L(A), this generalizes the main result of Riedtmann. We also obtain Green's formula in a geometric form for any finite-dimensional C-algebra A and use it to give the comultiplication formula in R(A). 相似文献
3.
LU Qikeng 《中国科学A辑(英文版)》2001,44(4):445-451
In the compactized Minkowski space, which is equivalent to the conformal spaceM 4, we introduced a Lorentz metric d σ2 and a Yang-Mills field θ. Later, we proved that dσ2 and θ together satisfy the EYM (Einstein-Yang-Mills) equation. In this paper, it is proved that θ onM 4 (which is the boundary of the anti-de-Sitter space AdS5) can be extended to be a Yang-Mills field [^(q)]\hat \theta on AdS5 such that Hua’s metric ds2 on AdS5, together with [^(q)]\hat \theta satisfies the EYM equation on AdS5. 相似文献
4.
Stein’s higher Riesz transforms are translation invariant operators on L
2(R
n
) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this
article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete
series representations for hyperboloids associated to the indefinite quadratic form of signature (p,q). We prove that these operators extend to L
r
-bounded operators for 1<r<∞ if the parameter of the discrete series representations is generic. 相似文献
5.
L. D. Faddeev 《Theoretical and Mathematical Physics》2011,166(3):279-290
We describe an alternative formalism for Einstein’s theory of gravity. The role of dynamical variables is played by a collection
of ten vector fields f
μ
A
, A = 1,..., 10. The metric is a composite variable, g
μν = f
μ
A
f
ν
A
. The proposed scheme may lead to further progress in a theory of gravity where Einstein’s theory is to play the role of an
effective theory, with Newton’s constant appearing by introducing an anomalous Green’s function. 相似文献
6.
Gellerstedt and Laplace–Beltrami operators relative to a certain mixed signature metric share among themselves an interesting
and important property: under suitable change of coordinates they can be represented, up to a multiplying factor, in terms
of Q
α and R
α singular first order perturbations of the Laplace and D’Alembertian operators. Knowledge of fundamental solutions for Q
α and R
α leads us to finding explicit formulas for fundamental solutions to those operators.
J. Barros-Neto’s research partially supported by NSF, Grant # INT 0124940. F. Cardoso’s research partially supported by CNPq
(Brazil). 相似文献
7.
8.
If ψ ∈ L2(R), Λ is a discrete subset of the affine groupA =R
+ ×R, and w: Λ →R
+ is a weight function, then the weighted wavelet system generated by ψ, Λ, and w is
. In this article we define lower and upper weighted densities D
w
−
(Λ) and D
w
+
(Λ) of Λ with respect to the geometry of the affine group, and prove that there exist necessary conditions on a weighted wavelet
system in order that it possesses frame bounds. Specifically, we prove that if W(ψ, Λ, w) possesses an upper frame bound,
then the upper weighted density is finite. Furthermore, for the unweighted case w = 1, we prove that if W(ψ, Λ, 1) possesses
a lower frame bound and D
w
+
(Λ−1) < ∞, then the lower density is strictly positive. We apply these results to oversampled affine systems (which include the
classical affine and the quasi-affine systems as special cases), to co-affine wavelet systems, and to systems consisting only
of dilations, obtaining some new results relating density to the frame properties of these systems. 相似文献
9.
F. Carbonell K. J. Worsley L. Galan 《Annals of the Institute of Statistical Mathematics》2011,63(1):1-27
The statistical problem addressed in this paper is to approximate the P value of the maximum of a smooth random field of Wilks’s Λ statistics. So far results are only available for the usual univariate
statistics (Z, t, χ2, F) and a few multivariate statistics (Hotelling’s T
2, maximum canonical correlation, Roy’s maximum root). We derive results for any differentiable scalar function of two independent
Wishart random fields, such as Wilks’s Λ random field. We apply our results to a problem in brain shape analysis. 相似文献
10.
Shing-Tung Yau 《Milan Journal of Mathematics》2006,74(1):339-356
This is the Leonardo da Vinci Lecture given in Milan in March 2006. It is a survey on the concept of space-time over the last 3000 years: it starts with Euclidean
geometry, discusses the contributions of Gauss and Riemannian geometry, presents the dynamic concept of space-time in Einstein’s
general relativity, describes the importance of symmetries, and ends with Calabi-Yau manifolds and their importance in today’s
string theories in the attempt for a unified theory of physics.
Leonardo da Vinci Lecture held on March 28, 2006 相似文献
11.
We study ring homeomorphisms and, on this basis, obtain a series of theorems on the existence of the so-called ring solutions
for degenerate Beltrami equations. A general statement on the existence of solutions for the Beltrami equations that extends
earlier results is formulated. In particular, we give new existence criteria for homeomorphic solutions f of the class W
loc
1,1
with f
−1 ∈ W
loc
1,2
in terms of tangential dilatations and functions of finite mean oscillation. The ring solutions also satisfy additional capacity
inequalities.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 11, pp. 1571–1583, November, 2006. 相似文献
12.
Zhen-long Chen San-yang Liu 《应用数学学报(英文版)》2005,21(4):623-636
Let φ be a Hausdorff measure function and A be an infinite increasing sequence of positive integers. The Hausdorff-type measure φ - mA associated to φ and A is studied. Let X(t)(t ∈ R^N) be certain Gaussian random fields in R^d. We give the exact Hausdorff measure of the graph set GrX([0, 1]N), and evaluate the exact φ - mA measure of the image and graph set of X(t). A necessary and sufficient condition on the sequence A is given so that the usual Hausdorff measure function for X([0, 1] ^N) and GrX([0, 1]^N) are still the correct measure functions. If the sequence A increases faster, then some smaller measure functions will give positive and finite ( φ A)-Hausdorff measure for X([0, 1]^N) and GrX([0, 1]N). 相似文献
13.
Following Jacobi's geometrization of Lagrange's least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor (U + h), where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^*≌S^2 (1/2).
In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve (which only records the change of shape) in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems. 相似文献
In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve (which only records the change of shape) in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems. 相似文献
14.
The total curvature of a compact C∞-immersed surface in Euclidean 3-space
3 can be interpreted as the average number of critical points for a linear ‘height’ function. The Morse inequalities provide
an intrinsic topological lower bound for the total curvature and ‘tight’ surfaces, which realize equality, have been an active
topic of research. The objective of this paper is to describe the natural notion of total curvature for C∞-singular surfaces which fail to immerse on C∞-embedded closed curves, but which have a
C∞-globally defined unit normal (e.g. caustics, or critical images for mappings of 3-manifolds into Euclidean 3-space). For
such surfaces total curvature consists of a sum of two-dimensional and one-dimensional integrals, which have various lower
bounds. Large sets of LT-surfaces which realize equality are then constructed. As an application, the orthogonal projection
of an immersed tight hypersurface in Euclidean 4-space is shown to have LT-tight critical image, and several related inequalities
are given.
Mathematics Subject Classifications (2000): 57N65, 14P99, 53C21, 53B25, 53B20. 相似文献
15.
Let Θ be a point in R
n
. We are concerned with the approximation to Θ by rational linear subvarieties of dimension d for 0 ≤ d ≤ n−1. To that purpose, we introduce various convex bodies in the Grassmann algebra Λ(R
n+1). It turns out that our convex bodies in degree d are the dth compound, in the sense of Mahler, of convex bodies in degree one. A dual formulation is also given. This approach enables
us both to split and to refine the classical Khintchine transference principle. 相似文献
16.
For a regular semigroup with an inverse transversal, we have Saito’s structureW(I,S
o, Λ, *, {α, β}). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist
of congruences on the structure component partsI,S
o and Λ. The structure of images of this type of semigroups is also presented.
This work is supported by Natural Science Foundation of Guangdong Province 相似文献
17.
Zbigniew Slodkowski 《Mathematische Annalen》1997,308(1):47-63
We use holomorphic motions and Beltrami equation to study a class of polynomially convex hulls in ℂ
2
with Jordan fibers over the disc D. It is shown that every such hull is biholomorphically equivalent to a unique (up to suitable normalisation) canonical model.
These models are the hulls whose complements in D×ℂmacr; are biholomorphic to a bidisc and are further characterized in terms of capacity of the fibers, Green’s function, pseudoconcavity
and approximability by (very) special analytic polyhedra.
Received: 11 September 1995 / Revised version: 11 March 1996 相似文献
18.
19.
M. S. Ratinsky 《Journal of Mathematical Sciences》2007,141(1):1071-1074
Problems on reciprocal transformation of solutions to equations of Λ2-class (equations related to special coordinate nets on the Lobachevsky plane Λ2) are discussed. A method of construction of solutions to one analytic differential equation of Λ2-class by a given solution of another analytic differential equation of this class is proposed. The reciprocal transformation
of one-soliton solutions of the sine-Gordon equation and one-soliton solutions of the modified Korteweg-de Vries equation
(MKdV) is obtained. This result confirms the possibility of construction of such transition.
__________
Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry,
2005. 相似文献
20.
Deguang Han 《Journal of Fourier Analysis and Applications》2009,15(2):201-217
Let
be a full rank time-frequency lattice in ℝ
d
×ℝ
d
. In this note we first prove that any dual Gabor frame pair for a Λ-shift invariant subspace M can be dilated to a dual Gabor frame pair for the whole space L
2(ℝ
d
) when the volume v(Λ) of the lattice Λ satisfies the condition v(Λ)≤1, and to a dual Gabor Riesz basis pair for a Λ-shift
invariant subspace containing M when v(Λ)>1. This generalizes the dilation result in Gabardo and Han (J. Fourier Anal. Appl. 7:419–433, [2001]) to both higher dimensions and dual subspace Gabor frame pairs. Secondly, for any fixed positive integer N, we investigate the problem whether any Bessel–Gabor family G(g,Λ) can be completed to a tight Gabor (multi-)frame G(g,Λ)∪(∪
j=1
N
G(g
j
,Λ)) for L
2(ℝ
d
). We show that this is true whenever v(Λ)≤N. In particular, when v(Λ)≤1, any Bessel–Gabor system is a subset of a tight Gabor frame G(g,Λ)∪G(h,Λ) for L
2(ℝ
d
). Related results for affine systems are also discussed.
Communicated by Chris Heil. 相似文献