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1.
Hans Peter Schlickewei 《Monatshefte für Mathematik》1997,123(2):171-178
LetG be a finitely generated subgroup of rankr of the multiplicative groupK
* of a number field. We construct a basis 1,...,
r
ofG such that for G, writing
where is a root of unity and where thex
i are integers, we get a lower bound for the absolute heighth() in terms ofr and max
. 相似文献
2.
Let
be the set of all coloured permutations on the symbols 1, 2, . . . , n
with colours 1, 2, . . . , r, which is the analogous of the
symmetric group when r = 1, and the hyperoctahedral
group when r = 2. Let
be a subset of d colours; we define
to be the set of all coloured permutations
.
We prove that the number of
-avoiding coloured permutations in
.
We then prove that for any
,
the number of coloured permutations in
which avoid all patterns in
except for and contain exactly once equals
.
Finally, for any
,
this number equals
.
These results generalize recent results due to Mansour, Mansour and West, and Simion.AMS Subject Classification: 05A05, 05A15. 相似文献
3.
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
4.
Let p be a prime number.
Let G be a finite
p-group and
. Denote by
the complex conjugate of
. Assume that
. We show that the number of
distinct irreducible constituents of the product
is at least
.
Received: 17 March 2003 相似文献
5.
Let {\bold x}[] be a stationary Gaussian process with zero mean and spectral density f, let
be the -algebra induced by the random variables {\bold x}[], D(R1), and let
t, t > 0, be the -algebra induced by the random variables x[],supp [-t,t]. Denote by
(f) the Gaussian measure on
generated by {\bold x}. Let
t(f) be the restriction of
(f) to
t. Let f and g be nonnegative functions such that the measures
t(f) and
t(g) are absolutely continuous. Put
For a fixed g(u) and for f(u)= ft(u) close to g(u) in some sense, the asymptotic normality of
t(f,g) is proved under some regularity conditions. Bibliography: 14 titles. 相似文献
6.
Suppose that k and l are integers such that
and
, M
k is a set of numbers without kth powers, and
. In this paper, we obtain asymptotic estimates of the sums
over
相似文献
7.
P. Cubiotti 《Journal of Optimization Theory and Applications》1997,92(3):477-495
Given a nonempty set
and two multifunctions
, we consider the following generalized quasi-variational inequality problem associated with X, : Find
such that
. We prove several existence results in which the multifunction is not supposed to have any continuity property. Among others, we extend the results obtained in Ref. 1 for the case (x(X. 相似文献
8.
Given a unital associative commutative ring containing
, we consider a homotope of a Novikov algebra, i.e., an algebra
that is obtained from a Novikov algebra A by means of the derived operation
on the -module A, where the mapping satisfies the equality
. We find conditions for a homotope of a Novikov algebra to be again a Novikov algebra. 相似文献
9.
E. S. Dubtsov 《Journal of Mathematical Sciences》2001,107(4):4002-4021
Let K be a compact space, let X be a closed subspace of C(K), and let
be a positive measure on K. The triple
is said to be regular if, for any positive function
and for any
, there exists a function
such that
on K and
. The case where K is the unit sphere in
and the subspace X is invariant with respect to the unitary group is investigated. Sufficient spectral conditions and a necessary condition for the regularity of a triple are obtained. Connections with compactness of certain Hankel operators and applications to interpolation problems are presented. Bibliography: 16 titles. 相似文献
10.
Todor Gramchev 《Monatshefte für Mathematik》1991,112(2):99-113
We study the weak limits
(t, .)of solutions to semilinear strictly hyperbolic systems and wave equations with initial datau
(0, .) approximating a distribution, 0 <
1. We propose an optimal link between the singularity of and the growth of the nonlinear term in order that
exists. In this way we extend some of the results in [3], [10], [13]. 相似文献
11.
In this work the authors study the conditions for the existence of diffusion equations
in the cylinder Q = 3D ×
+,
n
, satisfying the homogeneous Dirichlet or Neumann conditions on the side boundary of the cylinder Q and decreasing with respect to t as a power for t . 相似文献
12.
13.
Let
be the j-fold iterated function of
. Let
and > 0 be fixed, Q be a prime, and let N
k(Q|x) denote the number of those nx for which Q
. We give the asymptotics of N
k(Q|x) in the range
. 相似文献
14.
Hermann Vogel 《Journal of Geometry》1994,50(1-2):159-177
In this paper at first we introduce thesystem of total polar subspaces of an arbitrary k-diniensional plane with respect to the absolute (configuration) of an arbitrary n- dimensional CAYLEY/KLEIN space
as a generalization of the total polar set of a regular k-plane of
. Using the system of total polar sets
of the intersection (n–2)-plane of two hyperplanes and we give the followingnew characterization of the angle of . and : for any straight line g with
and g=Ø the angle of and is equal to the distance of the two intersection points of g with and .
Herrn Prof. Dr.Oswald Giering zum 60. Geburtstag gewidmet 相似文献
Herrn Prof. Dr.Oswald Giering zum 60. Geburtstag gewidmet 相似文献
15.
Consider a double array
of i.i.d. random variables with mean and variance
and set
. Let
denote the empirical distribution function of Z1, n
,..., Z
N, n
and let be the standard normal distribution function. The main result establishes a functional law of the iterated logarithm for
, where n=n(N) as N. For the proof, some lemmas are derived which may be of independent interest. Some corollaries of the main result are also presented. 相似文献
16.
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
17.
V. Koubek 《Algebra Universalis》1996,35(2):296-331
Given distinct varieties
and
of the same type, we say that
is relatively
-universal if there exists an embedding :K
from a universal categoryK such that for every pairA, B ofK-objects, a homomorphismf:A B has the formf=g for someK-morphismg:A B if and only if Im(f)
. Finitely generated relatively
-universal varieties of Heyting algebras are described for the variety
of Boolean algebras, the variety generated by a three element chain, and for the variety generated by the four element Boolean algebra with an added greatest element.Dedicated to the memory of Alan DayPresented by J. Sichler.The support of the NSERC is gratefully acknowledged. 相似文献
18.
The purpose of this paper is to present the solution of time-optimal problem ofthe controlled object the dynamics of which is given by:
,
, where
and motion resistance function
if
,f(x)=-A if x > 0 where
. That model describes dynamicsof a very important class of industrial installations. As the time-optimalproblem will be understood a transfer of the initial state
to the target state
in a minimumtime
. There has been shown that in the formula defining resistancefunction f(x)there exists a value
that plays an essentialrole in time-optimal structure formation. Namely, if
then thetime-optimal control process is typical, analogous as in classical case
, i.e. there exists a switching curve formed by thetrajectories of time-optimal solutions reaching the target state and thetime-optimal process is formed by at most one switching operation. For the caseA>Abwe will examine two following singular phenomena.(a) If the target state z1=(0, 0) then there exists theswitching curve, dividing the state plane into two sets, however only one itsbranch is formed by the time-optimal solution reaching the target z1=(0, 0) and generated by the control u=-1. None of solution formsthe second branch of switching curve. It is formed by a state-locus dependingon the value of Aonly. In dependency of the starting state z0 thetime-optimal control process is generated by bang-bang control with none,one or two switching operations. This is the first singular phenomenon,because any small decrease of the value Aover A
b requires to change thestructure which would be able to generate the time-optimal process.(b) The paper shows, that if the target state z
1(x_1, 0), x1>0then there exists a set of the starting states from which there start twotrajectories reaching the target in the same minimum time. This is thesecond phenomenon.Finally, some suggestions as to practical applications have been given too. 相似文献
19.
E. Getzler 《Compositio Mathematica》2002,132(2):121-135
We calculate the Euler characteristics of the local systems S
k
S
2
on the moduli space
2 of curves of genus 2, where
is the rank 4 local system R
1 *
. 相似文献
20.
M. F. Horodnii 《Ukrainian Mathematical Journal》2003,55(7):1071-1085
For a sectorial operator A with spectrum (A) that acts in a complex Banach space B, we prove that the condition (A) i
R = Ø is sufficient for the differential equation
where is a small positive parameter, to have a unique bounded solution x
for an arbitrary bounded function f: R B that satisfies a certain Hölder condition. We also establish that bounded solutions of these equations converge uniformly on R as 0+ to the unique bounded solution of the differential equation x(t) = Ax(t) + f(t). 相似文献