共查询到20条相似文献，搜索用时 15 毫秒
1.
Laurent Bartholdi 《Israel Journal of Mathematics》2006,154(1):93-139
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted. 相似文献
| – | • is finitely generated and infinite-dimensional, but has only finitedimensional quotients; |
| – | • has a subalgebra of finite codimension, isomorphic toM 2(k); |
| – | • is prime; |
| – | • has quadratic growth, and therefore Gelfand-Kirillov dimension 2; |
| – | • is recursively presented; |
| – | • satisfies no identity; |
| – | • contains a transcendental, invertible element; |
| – | • is semiprimitive if % MathType!End!2!1! has characteristic ≠2; |
| – | • is graded if % MathType!End!2!1! has characteristic 2; |
| – | • is primitive if % MathType!End!2!1! is a non-algebraic extension of % MathType!End!2!1!; |
| – | • is graded nil and Jacobson radical if % MathType!End!2!1! is an algebraic extension of % MathType!End!2!1!. |
2.
Marie-Claude Arnaud 《Annales Henri Poincare》2008,9(5):881-926
In this article, we prove different results concerning the regularity of the C
0-Lagrangian invariant graphs of the Tonelli flows. For example :
Submitted: July 23, 2007. Accepted: February 14, 2008. 相似文献
| • | in dimension 2 and in the autonomous generic case, we prove that such a graph is in fact C 1 on some set with (Lebesgue) full measure; |
| • | under certain dynamical additional hypothesis, we prove that these graphs are C 1. |
Résumé. Dans cet article, on démontre différents résultats concernant la régularité des graphes C 0-lagrangiens invariants par des flots de Tonelli. Par exemple :
• en dimension 2, dans le cas autonome et générique, on montre que ces graphes sont de classe C 1 sur un ensemble de mesure (de Lebesque) pleine; • sous certaines hypothèses concernant la dynamique restreinte, on montre que ces graphes sont de classe C 1.
Submitted: July 23, 2007. Accepted: February 14, 2008. 相似文献
3.
A. S. Sivatski 《Journal of Mathematical Sciences》2007,145(1):4823-4830
The main purpose of the paper is to strengthen previous author’s results. Let k be a field of characteristic ≠ 2, n ≥ 2. Suppose
that elements
are linearly independent over ℤ/2ℤ. We construct a field extension K/k and a quaternion algebra D = (u, v) over K such that
In particular, the algebra A provides an example of an indecomposable algebra of index 2n+1 over a field, the u-invariant and the 2-cohomological dimension of which equal 2n+3 and n + 3, respectively. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 338, 2006, pp. 227–241. 相似文献
| (1) | the field K has no proper extension of odd degree |
| (2) | the u-invariant of K equals 4 |
| (3) | the multiquadratic extension is not 4-excellent, and the quadratic form 〈uv,-u,-v, a〉 provides a relevant counterexample |
| (4) | the central division algebra A = D ⊗E (a, t0) ⊗E (b1, t1) ⋯ ⊗E (bn, tn) does not decompose into a tensor product of two nontrivial central simple algebras over E, where E = K ((t0))((t1)) … ((tn)) is the Laurent series field in the variables t0, t1, …, tn |
| (5) | ind A = 2n+1. |
4.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by
X
α,p
. We show
相似文献
| (i) | The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented. |
| (ii) | The identity operator from X α,p to X α,p when p > q is unbounded. |
| (iii) | Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then |
| (iv) | duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0. |
| (v) | We investigate the properties of the operators from X α,p spaces to their predual. |
5.
John W. Snow 《Algebra Universalis》2005,54(1):65-71
A congruence lattice L of an algebra A is called power-hereditary if every 0-1 sublattice of Ln is the congruence lattice of an algebra on An for all positive integers n. Let A and B be finite algebras. We prove
Received November 11, 2004; accepted in final form November 23, 2004. 相似文献
| • | If ConA is distributive, then every subdirect product of ConA and ConB is a congruence lattice on A × B. |
| • | If ConA is distributive and ConB is power-hereditary, then (ConA) × (ConB) is powerhereditary. |
| • | If ConA ≅ N5 and ConB is modular, then every subdirect product of ConA and ConB is a congruence lattice. |
| • | Every congruence lattice representation of N5 is power-hereditary. |
6.
Following our approach to metric Lie algebras developed in a previous paper we propose a way of understanding pseudo-Riemannian
symmetric spaces which are not semisimple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal
modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric
space M to a triple consisting of:
That leads to a classification scheme of indecomposable nonsimple pseudo-Riemannian symmetric spaces. In addition, we obtain
a full classification of symmetric spaces of index 2 (thereby completing and correcting in part earlier classification results
due to Cahen and Parker and to Neukirchner). 相似文献
| (i) a Lie algebra with involution (of dimension much smaller than the dimension of the transvection group of M); | |
| (ii) a semisimple orthogonal module of the Lie algebra with involution; and | |
| (iii) a quadratic cohomology class of this module. |
7.
E. G. Kwon 《Integral Equations and Operator Theory》2009,64(2):251-260
We characterize the composition operators mapping Blochs boundedly into the weighted Bergman spaces of logarithmic weight.
For 0 < p < ∞, 1 < α < ∞, let Ap, log α denote the space of holomorphic functions F in the unit disc D for which
and let Ap, log ασ denote the class of holomorphic self maps f of D for which
Then for the Bloch pullback operator Cf, the following are equivalent:
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion
Fund) (KRF-2007-313-C00026). 相似文献
| (1) | Cf maps Bloch space boundedly into A2p, log α |
| (2) | |
| (3) | . |
8.
Eric Schmutz 《Central European Journal of Mathematics》2008,6(3):482-487
It is known that the unit sphere, centered at the origin in ℝ
n
, has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds
on the complexity of the coordinates: for every point ν on the unit sphere in ℝ
n
, and every ν > 0; there is a point r = (r
1; r
2;…;r
n) such that:
One consequence of this result is a relatively simple and quantitative proof of the fact that the rational orthogonal group
O(n;ℚ) is dense in O(n;ℝ) with the topology induced by Frobenius’ matrix norm. Unitary matrices in U(n;ℂ) can likewise be approximated by matrices in U(n;ℚ(i))
相似文献
| – | ⊎ ‖r-v‖∞ < ε. |
| – | ⊎ r is also a point on the unit sphere; Σ r i 2 = 1. |
| – | ⊎ r has rational coordinates; for some integers a i , b i . |
| – | ⊎ for all . |
9.
Joseph Corneli Neil Hoffman Paul Holt George Lee Nicholas Leger Stephen Moseley Eric Schoenfeld 《Journal of Geometric Analysis》2007,17(2):189-212
We prove the double bubble conjecture in the three-sphereS
3 and hyperbolic three-spaceH
3 in the cases where we can apply Hutchings theory:
A balancing argument and asymptotic analysis reduce the problem inS
3 andH
3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces. 相似文献
| – | • InS 3, when each enclosed volume and the complement occupy at least 10% of the volume ofS 3. |
| – | • inH 3, when the smaller volume is at least 85% that of the larger. |
10.
Let G be a 2-edge-connected simple graph with girth g, independence number α(G), and if one of the following two conditions holds
then G is upper embeddable and the lower bound v − 3g + 7 is best possible. Similarly the result for 3-edge-connected simple graph with girth g and independence number α(G) is also obtained.
Huang Yuanqiu: Partially supported by National Science Foundation of China (No. 10771062) and Program for New Century Excellent
Talents in University (No. NCET-07-0276). 相似文献
| (1) | α(G) ≤ 2; | |
| (2) | α(G) ≥ 3, and for any three nonadjacent vertices v
i
(i = 1,2,3), it has
|
11.
12.
A. I. Pavlov 《Mathematical Notes》2000,68(3):370-377
The main result of this paper is the following theorem. Suppose thatτ(n) = ∑
d|n
l and the arithmetical functionF satisfies the following conditions:
Then there exist constantsA
1,A
2, andA
3 such that for any fixed \g3\s>0 the following relation holds:
. Moreover, if for any primep the inequality \vbf(p)\vb\s<1 holds and the functionF is strongly multiplicative, thenA
1\s>0.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 429–438, September, 2000. 相似文献
| 1) | the functionF is multiplicative; |
| 2) | ifF(n) = ∑ d|n f(d), then there exists an α>0 such that the relationf(n)=O(n −α) holds asn→∞. |
13.
14.
We investigate the large time behavior of positive solutions with finite mass for the viscous Hamilton-Jacobi equationu
t
= Δu + |Δu|
p
,t>0,x ∈ ℝ
N
, wherep≥1 andu(0,.)=u
0≥0,u
0≢0,u
0∈L
1. DenotingI
∞=lim
t→∞‖u(t)‖1≤∞, we show that the asymptotic behavior of the mass can be classified along three cases as follows:
We also consider a similar question for the equationu
t=Δu+u
p
. 相似文献
| – | • ifp≤(N+2)/(N+1), thenI ∞=∞ for allu 0; |
| – | • if (N+2)/(N+1)<p<2, then bothI ∞=∞ andI ∞<∞ occur; |
| – | • ifp≥2, thenI ∞<∞ for allu 0. |
15.
Giuseppe Pellegrino 《Rendiconti del Circolo Matematico di Palermo》1998,47(1):141-168
| 1. | Letm be the greatest integer such that . ThenPG(3,q) contains complete caps of sizek=(m+1)(q+1)+ω, with ω=0, 1, 2. | |
| 2. |
PG(3,q),q≥5, contains complete caps of size |
|
| 3. | InPG(3,q) complete caps different from ovaloids have some external planes. |
16.
LetG be a finite nonsolvable group andH a proper subgroup ofG. In this paper we determine the structure ofG ifG satisfies one of the following conditions:
相似文献
| (1) | Every solvable subgroupK(K⊉H) is eitherp-decomposable or a Schmidt group,p being the smallest odd prime factor of |G|. |
| (2) | |G∶H| is divisible by an odd prime and every solvable subgroupK(K⊉H) is either 2′-closed or a Schmidt group. |
| (3) | |G∶H| is even and every solvable subgroupK(K⊉H) is either 2-closed or a Schmidt group. |
17.
The star unfolding of a convex polytope with respect to a pointx on its surface is obtained by cutting the surface along the shortest paths fromx to every vertex, and flattening the surface on the plane. We establish two main properties of the star unfolding:
These two properties permit conceptual simplification of several algorithms concerned with shortest paths on polytopes, and
sometimes a worst-case complexity improvement as well:
相似文献
| 1. | It does not self-overlap: it is a simple polygon. |
| 2. | The ridge tree in the unfolding, which is the locus of points with more than one shortest path fromx, is precisely the Voronoi diagram of the images ofx, restricted to the unfolding. |
| • | The construction of the ridge tree (in preparation for shortest-path queries, for instance) can be achieved by an especially simpleO(n 2) algorithm. This is no worst-case complexity improvement, but a considerable simplification nonetheless. |
| • | The exact set of all shortest-path “edge sequences” on a polytope can be found by an algorithm considerably simpler than was known previously, with a time improvement of roughly a factor ofn over the old bound ofO(n 7 logn). |
| • | The geodesic diameter of a polygon can be found inO(n 9 logn) time, an improvement of the previous bestO(n 10) algorithm. |
18.
Abstract This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF
(the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here is a language with a distinguished linear order <, and REF
consists of formulas of the form
where φ is an -formula, φ
<x
is the -formula obtained by restricting all the quantifiers of φ to the initial segment determined by x, and x is a variable that does not appear in φ. Our results include:
Theorem
The following five conditions are equivalent for a complete first order theory T in a countable language
with a distinguished linear order:
Moreover, if κ is a regular cardinal satisfying κ = κ
<κ
, then each of the above conditions is equivalent to:
相似文献
| (1) | Some model of T has an elementary end extension with a first new element. |
| (2) | T ⊢ REF . |
| (3) | T has an ω 1-like model that continuously embeds ω 1. |
| (4) | For some regular uncountable cardinal κ, T has a κ-like model that continuously embeds a stationary subset of κ. |
| (5) | For some regular uncountable cardinal κ, T has a κ-like model that has an elementary extension in which the supremum of M exists. |
| (6) | T has a κ + -like model that continuously embeds a stationary subset of κ. |
19.
Non-singular solutions to the normalized Ricci flow equation 总被引：2，自引：0，他引：2
In this paper, we study non-singular solutions to Ricci flow on a closed manifold of dimension at least 4. Amongst other things
we prove that, if M is a closed 4-manifold on which the normalized Ricci flow exists for all time t > 0 with uniformly bounded sectional curvature, then the Euler characteristic . Moreover, the 4-manifold satisfies one of the followings
where (resp. ) is the Euler characteristic (resp. signature) of M.
The first author was supported by a NSF Grant of China and the Capital Normal University. 相似文献
| (i) | M is a shrinking Ricci soliton; |
| (ii) | M admits a positive rank F-structure; |
| (iii) | the Hitchin–Thorpe type inequality holds |
20.
Belmesnaoui Aqzzouz 《Rendiconti del Circolo Matematico di Palermo》2006,55(2):147-162
We show that if (K,L) is a semi-abelian category, there exists an abelian categoryK
x with the followings properties:
相似文献
| 1 | The categoryK is a full subcategory ofK x. |
| 2 | The free objects ofK are projectives inK x. |
| 3 | A sequence ofK-morphismes isK-exact if, and only if, it isK x-exact. |
| 4 | To each objectU ofK x we can associate a surjections:X→U whereX is an object ofK. |