共查询到20条相似文献,搜索用时 625 毫秒
1.
2.
S. Yu. Orevkov 《Mathematical Notes》2000,68(5-6):588-593
Dehornoy constructed a right invariant order on the braid group B
n uniquely defined by the condition
1{\text{ if }}\beta _0 ,\beta _1$$
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are words in
. A braid is called strongly positive if
1$$
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for any
. In the present paper it is proved that the braid
is strongly positive if the word
does not contain
. We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity. 相似文献
3.
We study Banach spaces of the form
We call such a space a p-space, p[1,), if for every k the space
is isomorphic to pk and the sequence (pk) strictly decreases to p. We examine the finite block representability of the spaces r in a p-space proving that it depends not only on p but also on the sequences (pk) and (nk). Assuming that i ni
1/q decreases to 0, where q is the conjugate exponent of p, we prove the existence of an asymptotic biorthogonal system in X and also that c
0 is finitely representable in X. Moreover we investigate the modified versions of p-spaces proving that, if nkm1/pkm-1/pkm-1 increases to infinity for a subsequence (nkm) , then 1 embeds into X. We also investigate complemented minimality for the class of spaces
where
is either a subsequence of the sequence of Schreier classes (
n)n N or a subsequence of (
n)n N. 相似文献
4.
Let
be i.i.d. random variables and let, for each
and
. It is shown that
a.s. whenever the sequence of self-normalized sums S
n
/V
n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if
相似文献
5.
Vidmantas Bentkus 《Journal of Theoretical Probability》1994,7(2):211-224
LetF be the distribution function of a sumS
n ofn independent centered random variables, denote the standard normal distribution function and its density. It follows from our results that
相似文献
6.
A renormalization group transformation R
1 has a single stable point
in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number
(the golden mean). Let a homeomorphism T be the C
1-conjugate of
. We let
denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any
, the sequence
has a finite limiting distribution function
, which is continuous in
, and singular on the interval [0,1]. We also study the sequence
for k>1. 相似文献
7.
8.
Let be a field and q be a nonzero element of that is not a root of unity. We give a criterion for 〈0〉 to be a primitive ideal of the algebra of quantum matrices. Next, we describe all height one primes of ; these two problems are actually interlinked since it turns out that 〈0〉 is a primitive ideal of whenever has only finitely many height one primes. Finally, we compute the automorphism group of in the case where m ≠ n. In order to do this, we first study the action of this group on the prime spectrum of . Then, by using the preferred basis of and PBW bases, we prove that the automorphism group of is isomorphic to the torus when m ≠ n and (m,n) ≠ (1, 3),(3, 1).
This research was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme
and by Leverhulme Research Interchange Grant F/00158/X. 相似文献
9.
Peter Hellekalek 《Monatshefte für Mathematik》1980,90(4):291-295
Ifp2 is an integer, then every nonnegative integerk is represented by an expression of the form
with integersa
i
(k), 0a
i
(k)p–1,i=0.1,...,s. The radical-inverse function to the basep,
p
(k), is defined by
. The sequence
is uniformly distributed modulo 1 (it may be called a one-dimensional Halton sequence). In the casep=2 it is the van der Corput sequence. The set of all numbers (0, 1] such that the local discrepancy
is bounded inn is determined. 相似文献
10.
N. L. Zmatrakov 《Mathematical Notes》1976,19(2):100-107
Let the sequence of nets n be such that
, where hi
(n) are the lengths of the segments of a net. The bound
is necessary in order that interpolating parabolic and cubic splines converge for any function in C ( = 0) or C(0 < < 1), where C is the class of functions satisfying a Lipschitz condition of order. It is also shown that this bound cannot essentially be weakened.Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 165–178, February, 1976.The author thanks Yu. N. Subbotin for a useful discussion of the results obtained. 相似文献
11.
12.
E. G. Emel'yanov 《Journal of Mathematical Sciences》1987,38(4):2081-2090
Let A={a1,...,an} and B={b1,...,bm} be systems of distinct points in
, let be a family of homotopic classes Hi,i=1,..., j+m, of closed Jordan curves on, where the classes Hj+l, l=1,...,m, consist of curves that are homotopic to a point curve in b. Let =1,..., j+m be a system of positive numbers and letU be the modulus of the extremal-metric problem for the family and the system . In this paper we investigate the dependence of the modulusU=U(,A,B) on the parameters i and on the disposition of the points ak and b. One shows thatU is a smooth function of the indicated arguments and one obtains expressions for the derivatives
U,
U, and
U. One gives some applications of these results.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 72–82, 1985. 相似文献
13.
Marko Huhtanen 《BIT Numerical Mathematics》2003,43(3):563-570
In this note it is shown that any square matrix AC
n×n
can be represented as the sum A=
, where
is complex symmetric and rank
. The corresponding persymmetric result can be used in finding the terms of a small rank perturbed Toeplitz matrix via an O(n
2) computation. This allows one to perform fast matrix–vector products in case n is large. 相似文献
14.
Some Groups Having Only Elementary Actions on Metric Spaces with Hyperbolic Boundaries 总被引:1,自引:0,他引:1
We study isometric actions of certain groups on metric spaces with hyperbolic-type bordifications. The class of groups considered includes SL
n
(), Artin braid groups and mapping class groups of surfaces (except the lower rank ones). We prove that in various ways such actions must be elementary. Most of our results hold for non-locally compact spaces and extend what is known for actions on proper CAT(-1) and Gromov hyperbolic spaces. We also show that SL
n
() for n 3 cannot act on a visibility space X without fixing a point in
. Corollaries concern Floyd's group completion, linear actions on strictly convex cones, and metrics on the moduli spaces of compact Riemann surfaces. Some remarks on bounded generation are also included. 相似文献
15.
P. McMullen 《Archiv der Mathematik》1978,31(1):509-516
Let be a lattice ind-dimensional euclidean space
, and
the rational vector space it generates. If is a valuation invariant under, andP is a polytope with vertices in
, then for non-negative integersn there is an expression
, where the coefficient(P, n) depends only on the congruence class ofn modulo the smallest positive integerk such that the affine hull of eachr-face ofk P is spanned by points of. Moreover,
r satisfies the Euler-type relation
where the sum extends over all non-empty facesF ofP. The proof involves a specific representation of simple such valuations, analogous to Hadwiger's representation of weakly continuous valuations on alld-polytopes. An example of particular interest is the lattice-point enumeratorG, whereG(P) = card(P); the results of this paper confirm conjectures of Ehrhart concerningG. 相似文献
16.
The complement of the hyperplane arrangement associated to
the (complexified) action of a finite, real reflection group on
n
is known to be a K(,1) space
for the corresponding Artin group
$\Cal A$. A long-standing conjecture states that an analogous statement
should hold for infinite reflection groups. In this paper we
consider the case of a Euclidean reflection group of type
Ã
n
and its associated Artin group, the affine braid group $\tilde{\Cal A}$.
Using the fact that $\tilde{\Cal A}$ can be embedded as a
subgroup of a finite type Artin group, we prove a number of
conjectures about this group. In particular, we construct a finite,
$n$-dimensional K(,1)-space
for $\tilde{\Cal A}$, and use it to prove the
K(,1) conjecture for the associated hyperlane complement.
In addition, we show that the affine braid groups are biautomatic and
give an explicit biautomatic structure. 相似文献
17.
18.
Yu. Yu. Bagderina 《Siberian Mathematical Journal》2005,46(2):226-232
19.
The Asymptotic Distributions of Sums of Records 总被引:3,自引:0,他引:3
LetX
1,X
2... be a sequence of i.i.d. random variables and let
be the associated (upper) record sequence. Resnick (1973) identified the class of all possible limit distributions for
. Here we focus on sums of records,
. We describe three cases in which T
n can be normalized to have a non-trivial limiting distribution. The problem of identifying all possible limit laws for normalized sums of records remains open. 相似文献
20.
We define a statistic, called weight, on involutions and consider two applications in which this statistic arises. Let I(n) denote the set of all involutions on [n](={1,2,..., n}) and let F(2n) denote the set of all fixed point free involutions on [2n]. For an involution , let || denote the number of 2-cycles in . Let[ n]
q
=1+q++qn-1 and let
denote the q-binomial coefficient. There is a statistic wt on I(n) such that the following results are true.(i) We have the expansion
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