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1.
Some Processes Associated with Fractional Bessel Processes 总被引:1,自引:0,他引:1
Let
be a d-dimensional fractional Brownian motion with Hurst parameter H and let
be the fractional Bessel process. Itôs formula for the fractional Brownian motion leads to the equation
. In the Brownian motion case
is a Brownian motion. In this paper it is shown that Xt is not an
-fractional Brownian motion if H 1/2. We will study some other properties of this stochastic process as well. 相似文献
2.
Let X1, X2,... be, i.i.d. random variables, and put
. We find necessary and sufficient moment conditions for
, where δ≥ 0 and q>0, and
with an>0 and bn is either
or
The series f(x) we deal with are classical series studied by Hsu and Robbins, Erdős, Spitzer, Baum and Katz, Davis, Lai, Gut, etc 相似文献
3.
For pairing based cryptography we need elliptic curves defined over finite fields
whose group order is divisible by some prime
with
where k is relatively small. In Barreto et al. and Dupont et al. [Proceedings of the Third Workshop on Security in Communication Networks (SCN 2002), LNCS, 2576, 2003; Building curves with arbitrary small Mov degree over finite fields, Preprint, 2002], algorithms for the construction of ordinary elliptic curves over prime fields
with arbitrary embedding degree k are given. Unfortunately, p is of size
.We give a method to generate ordinary elliptic curves over prime fields with p significantly less than
which also works for arbitrary k. For a fixed embedding degree k, the new algorithm yields curves with
where
or
depending on k. For special values of k even better results are obtained.We present several examples. In particular, we found some curves where
is a prime of small Hamming weight resp. with a small addition chain.AMS classification: 14H52, 14G50 相似文献
4.
We prove that for any continuous piecewise monotone or smooth interval map f and any subset
of the set of periods of periodic trajectories of f, there is another map
such that the set of periods of periodic trajectories common for f and
, which is denoted by
, coincides with
. At the same time, for each integer
, there exists a continuous map f such that
for any map
if
is an infinite set.
Dedicated to Vladimir Igorevich Arnold 相似文献
5.
Let
be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian
and we prove that the limit of
when
is 2/d(M), where d(M) is the diameter of M. Moreover, if
is an oriented compact hypersurface of the Euclidean space
or
, we prove an upper bound of
in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of
then:
.
Mathematics Subject Classifications (2000): 53A07, 53C21. 相似文献
6.
Lutz Strüngmann 《Archiv der Mathematik》2006,86(3):193-204
Let R be a unital associative ring and
two classes of left R-modules. In this paper we introduce the notion of a
In analogy to classical cotorsion pairs as defined by Salce [10], a pair
of subclasses
and
is called a
if it is maximal with respect to the classes
and the condition
for all
and
Basic properties of
are stated and several examples in the category of abelian groups are studied.
Received: 17 March 2005 相似文献
7.
Let
be a continuous semimartingale and let
be a continuous function of bounded variation. Setting
and
suppose that a continuous function
is given such that F is C1,2 on
and F is
on
. Then the following change-of-variable formula holds:
where
is the local time of X at the curve b given by
and
refers to the integration with respect to
. A version of the same formula derived for an Itô diffusion X under weaker conditions on F has found applications in free-boundary problems of optimal stopping. 相似文献
8.
Let M be a right R-module,
the class of all M-small modules, and P a projective cover of M in
[M]. We consider the torsion theories
= (
),
= (
), and
= (
) in
[M], where
is the torsion theory generated by
is the torsion theory cogenerated by
, and
is the dual Lambek torsion theory. We study some conditions for
to be cohereditary, stable, or split, and prove that Rej(M,
) = M
=
(=
=
)
=
GenM(P)
.2000 Mathematics Subject Classification: 16S90 相似文献
9.
If E is a separable symmetric sequence space with trivial Boyd indices and
is the corresponding ideal of compact operators, then there exists a C1-function fE, a self-adjoint element
and a densely defined closed symmetric derivation δ on
such that
, but
相似文献
10.
We determine conditions under which a subordinated random walk of the form
tends to infinity almost surely (a.s), or
tends to infinity a.s., where {N(n)} is a (not necessarily integer valued) renewal process,
denotes the integer part of N(n), and Sn is a random walk independent of {N(n)}. Thus we obtain versions of the Alternatives, for drift to infinity, or for divergence to infinity in the strong law, for
. A complication is that
is not, in general, itself, a random walk. We can apply the results, for example, to the case when N(n)= n, > 0, giving conditions for lim
, a.s., and lim sup
, a.s., etc. For some but not all of our results, N(1) is assumed to have finite expectation. Examples show that this is necessary for the kind of behaviour we consider. The results are also shown to hold in the same degree of generality for subordinated Lévy processes. 相似文献
11.
The discrete snake is an arborescent structure built with the help of a conditioned Galton-Watson tree and random i.i.d. increments Y. In this paper, we show that if
and
, then the discrete snake converges weakly to the Brownian snake (this result was known under the hypothesis
). Moreover, if this condition fails, and the tails of Y are sufficiently regular, we show that the discrete snake converges weakly to an object that we name jumping snake. In both case, the limit of the occupation measure is shown to be the integrated super-Brownian excursion. The proofs rely on the convergence of the codings of discrete snake with the help of two processes, called tours. 相似文献
12.
Let
be the Poisson point process with intensity 1 in Rd and let
be
. We obtain a strong invariance principle for the total length of the nearest-neighbor graph on
. 相似文献
13.
Chong LI Genaro LOPEZ 《数学学报(英文版)》2006,22(3):741-750
Let B (resp. K, BC,KC) denote the set of all nonempty bounded (resp. compact, bounded convex, compact convex) closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B° stand for the set of all F ∈B such that the problem (F, G) is well-posed. We proved that, if X is strictly convex and Kadec, the set KC ∩ B° is a dense Gδ-subset of KC / G. Furthermore, if X is a uniformly convex Banach space, we will prove more, namely that the set B /B° (resp. K / B°, BC /B°, KC / B°) is a-porous in B (resp. K,BC, KC). Moreover, we prove that for most (in the sense of the Baire category) closed bounded subsets G of X, the set K / B° is dense and uncountable in K. 相似文献
14.
Hans-Peter Schröcker 《Journal of Geometry》2005,82(1-2):172-187
We study the projective space
of univariate rational parameterized equations of degree d or less in real projective space
The parameterized equations of degree less than d form a special algebraic variety
We investigate the subspaces on
and their relation to rational curves in
give a geometric characterization of the automorphism group of
and outline applications of the theory to projective kinematics. 相似文献
15.
Let X, Y be Banach spaces. We say that a set
is uniformly p–summing if the series
is uniformly convergent for
whenever (xn) belongs to
. We consider uniformly summing sets of operators defined on a
-space and prove, in case X does not contain a copy of c0, that
is uniformly summing iff
is, where T (φ x) = (T#φ) x for all
and x∈X. We also characterize the sets
with the property that
is uniformly summing viewed in
.
Received: 1 July 2005 相似文献
16.
Let
be a family of unit balls in
with the property that the mutual distances of the centers are at least
. If any n2 members of
have a common line transversal, then
has a line transversal too.
Received: 27 January 2005; revised: 17 October 2005 相似文献
17.
Paul Jung 《Journal of Theoretical Probability》2005,18(4):949-955
We show that the critical value for the contact process on a vertex-transitive graph
with finitely many edges added and/or removed is the same as the critical value for the contact process on
. This gives a partial answer to a conjecture of Pemantle and Stacey. 相似文献
18.
Oscar Perdomo 《Journal of Geometry》2006,84(1-2):100-105
In this paper we prove that if
is a closed minimal surface, then,
, for any homogeneous polynomial f of degree 3 with 0 a regular value of the function
. 相似文献
19.
Sébastien Dubernet 《Archiv der Mathematik》2006,86(5):430-436
A well known “zero-two law" shows that if
is a strongly continuous one-parameter group of bounded operators on a Banach space X, and if
then
Here we discuss analogous problems for general unital representations θ of a topological group G on a unital Banach algebra A. Let 1 be the unit of G, and I the unit element of A. We show that either
or
if, moreover, θ admits “continuous division by any positive integer”, then, either
or
Our argument also gives automatic continuity results for representations of abelian Baire groups on a separable Banach algebra
and representations of compact non abelian groups on a Banach algebra which are locally bounded and satisfy
Received: 8 June 2005; revised: 13 October 2005 相似文献
20.
Given a continuous linear operator T L(x) defined on a separable
-space X, we will show that T satisfies the Hypercyclicity Criterion if and only if for any strictly increasing sequence of positive integers
such that
the sequence
is hypercyclic. In contrast we will also prove that, for any hypercyclic vector x X of T, there exists a strictly increasing sequence
such that
and
is somewhere dense, but not dense in X. That is, T and
do not share the same hypercyclic vectors. 相似文献