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1.
Let
and
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write
≥
if
is contained in the closure of
. This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split
real form of the simple complex Lie algebra, E
8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present
a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries
and of the intersections
. 相似文献
2.
Zhengyan Lin 《中国科学A辑(英文版)》1997,40(4):337-349
Let
be a sequence of independent Gaussian processes with (h)
Put
. The large increments forY(·) with bounded σ(p, h) are investigated. As an example the large increments of infinite-dimensional fractional Ornstein-Uhlenbeck process in IP are given. The method can also be applied to certain processes with stationary increments.
Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Zhejiang Province. 相似文献
3.
For any partial groupoid
, let Fr
be the free extension of
to a total groupoid. We show that
implies
and that the theory of Fr
is uniformly recursive in the theory of
. These results fail if “groupoid” is replaced by “semigroup”, “commutative semigroup”, “group”, “abelian group”, “semilattice”,
“K-lattice” for any nontrivial varietyK of lattices, or “Boolean algebra”.
Research supported in part by NSF Grant MCS78-01867. We thank the referee for his valuable comments.
Presented by B. Jónsson. 相似文献
4.
It is proved that (i) for
survives to E∞; (ii) for
survives to E∞.
Project supported by the Doctoral Program Foundation of China. 相似文献
5.
The asymptotic properties of the numbers of spanning trees and Eulerian trails in circulant digraphs and graphs are studied.
Let
be a directed circulant graph. Let
and
be the numbers of spanning trees and of Eulerian trails, respectively. Then
Furthermore, their line digraph and iterations are dealt with and similar results are obtained for undirected circulant graphs.
Project partially supported by the National Natural Science Foundation of China (Grant No. 69673042) and by Hong Kong CERG
(HKUST652/95E). 相似文献
6.
Furstenberg family and chaos 总被引:3,自引:0,他引:3
Jin-cheng XlONG~ Jie L Feng TAN School of Mathematical Sciences South China Normal University Guangzhou China 《中国科学A辑(英文版)》2007,50(9):1325-1333
A Furstenberg family F is a family,consisting of some subsets of the set of positive integers,which is hereditary upwards,i.e.A■B and A∈F imply B∈F.For a given system (i.e.,a pair of a complete metric space and a continuous self-map of the space) and for a Furstenberg family F, the definition of F-scrambled pairs of points in the space has been given,which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be F-scrambled pairs corresponding respectively to suitable Furstenberg family F.In the present paper we explore the basic properties of the set of F-scrambled pairs of a system.The generically F-chaotic system and the generically strongly F-chaotic system are defined.A criterion for a generically strongly F-chaotic system is showed. 相似文献
7.
8.
We introduce the notion of a generalized interval exchange
induced by a measurable k-partition
of [0,1).
can be viewed as the corresponding restriction of a nondecreasing function
on ℝ with
. A is called λ-dense if λ(A
i
∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that
. We give necessary and sufficient conditions for this equality to hold. We show that for each integer m≥2, such that 3∤2m+1, there exist 2 and 3 non λ-dense partitions A and B of [0,1), corresponding to the interval exchanges on 2m intervals, for which
and
commute. 相似文献
9.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
10.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
11.
A family of transitive modular Lie superalgebras with depth one 总被引:1,自引:0,他引:1
Wen-de LIU~ 《中国科学A辑(英文版)》2007,50(10):1451-1466
The embedding theorem is established for Z-graded transitive modular Lie superalgebras g=(?)satisfying the conditions: (i)g0(?)(g-1)and g0-module g-1 is isomorphic to the natural(?)(g-1)-module; (ii)dim g1=2/3n(2n~2 1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered. 相似文献
12.
We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks
with the form of
, where the input-output function is defined as a generalized sigmoid function, such asv
i
=2/π arctan(π/2μiμi),
and
, etc. Numerical simulations are also provided to demonstrate the theoretical results. 相似文献
13.
The asymptotic expansions are studied for the vorticity
to 2D incompressible Euler equations with-initial vorticity
, where ϕ0(x) satisfies |d ϕ0(x)|≠0 on the support of
and
is sufficiently smooth and with compact support in ℝ2 (resp. ℝ2×T) The limit,v(t,x), of the corresponding velocity fields {v
ɛ(t,x)} is obtained, which is the unique solution of (E) with initial vorticity ω0(x). Moreover,
(ℤ2)) for all 1≽p∞, where
and ϕ(t,x) satisfy some modulation equation and eikonal equation, respectively. 相似文献
14.
In this paper, we study a class of Finsler metrics in the form
, where
is a Riemannian metric, β = b
i
y
i
is a 1-form, and ε and k ≠ 0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively
flat Finsler metrics with the constant flag curvature must be locally Minkowskian. 相似文献
15.
Consider the nonparametric regression model
, whereg is an unknown function to be estimated on [0, 1],
are the fixed design points in the interval [0, 1] and
is a triangular array of row iid random variables having median zero. The nearest neighbor median estimator
is taken as the estimator of the unknown functiong(x). Median cross validation (mev) criterion is employed to select the smoothing parameterh. Leth
π
*
be the smoothing parameter chosen by mev criterion. Under mild regularity conditions, the upper and lower bounds ofh
π
*
, the rate of convergence and the weak consistency of the median cross-validated estimate
are obtained.
Project supported by the National Natural Science Foundation of China and the Doctoral Foundation of Education of China. 相似文献
16.
In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively. 相似文献
17.
Takuya Hara 《Integral Equations and Operator Theory》1992,15(4):551-567
Let
be a Hilbert space. A continuous positive operatorT on
uniquely determines a Hilbert space
which is continuously imbedded in
and for which
with the canonical imbedding
. A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space (
) which is continuously imbedded in
and for which
with the canonical imbedding
. 相似文献
18.
As an attempt to follow the direction of machine proof, a personal computer LE0386/25 is used to prove some class number formulae
for certain imaginary quadratic number fields
,q=3, 7, 11, 19, 23, 31, 43 and 47) if the real quadratic number field
has class number one for a primep = 4N
2 + 1 (N is a positive integer).
Project supported by the National Natural Science Foundation of China. 相似文献
19.
E. I. Timoshenko 《Algebra and Logic》1998,37(6):391-398
Part of any basis of a relatively free group
in the variety
is called a primitive system of elements. We provide a criterion of being primitive for
, where
is a variety of Abelian groups satisfying xm=1, and
a variety generated by a finite group. Let
be a variety of nilpotent groups of class ≤c. It is proved that, for the group
, the property of being primitive for an element g is stronger than the condition of being unimodular on a vector composed
of values of Fox derivatives in the ring
. The group
is not residually finite whenever a system of elements is primitive.
Supported by RFFR grant No. 96-01-01948.
Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 687–699, November–December, 1998. 相似文献
20.
Yasunori Fujikoshi Yoshimichi Ochi 《Annals of the Institute of Statistical Mathematics》1984,36(1):119-128
Summary In this paper we obtain an asymptotic expansion of the distribution of the maximum likelihood estimate (MLE)
based onT observations from the first order Gaussian process up to the term of orderT
−1. The expansion is used to compare
with a generalized estimate
including the least square estimate (LSE)
, based on the asymptotic probabilities around the true value of the estimates up to the terms of orderT
−1. It is shown that
(or the modified MLE
) is better than
(or the modified estimate
). Further, we note that
does not attain the bound for third order asymptotic median unbiased estimates. 相似文献