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1.
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
2.
3.
The aim of this paper is to give the basic principles of hyperbolic function theory on the Clifford algebra . The structure of the theory is quite similar to the case of Clifford algebras with negative generators, but the proofs are
not obvious. The (real) Clifford algebra is generated by unit vectors with positive squares e2i = + 1. The hyperbolic Dirac operator is of the form where Q0f is represented by the composition . If is a solution of Hkf = 0, then f is called k-hypergenic in Ω, where is an open set. We introduce some basic results of hyperbolic function theory and give some representation theorems on .
Received: October, 2007. Accepted: February, 2008. 相似文献
4.
Christian Richter 《Journal of Geometry》2006,84(1-2):117-132
Let
be a group of affine transformations of the Euclidean plane
. Two topological discs D,
are called congruent by dissection with respect to
if D can be dissected into a finite number of subdiscs that can be rearranged by maps from
to a dissection of E.
Our main result says in particular that
admits congruence by dissection of any circular disc C with any square S if and only if
contains a contractive map and all orbits
,
, are dense in
. In this case any two discs D and E are congruent by dissection with respect to
and every disc D is congruent by dissection with n copies of D for every n ≥ 2.
Moreover, we give estimates on minimal numbers of pieces that are needed to realize congruences by dissection.
Dedicated to Irmtraud Stephani on the occasion of her 70th birthday 相似文献
5.
The peak algebra
is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks.
By exploiting the combinatorics of sparse subsets of [n−1] (and of certain classes of compositions of n called almost-odd and thin), we construct three new linear bases of
. We discuss two peak analogs of the first Eulerian idempotent and construct a basis of semi-idempotent elements for the peak
algebra. We use these bases to describe the Jacobson radical of
and to characterize the elements of
in terms of the canonical action of the symmetric groups on the tensor algebra of a vector space. We define a chain of ideals
of
, j = 0,...,
, such that
is the linear span of sums of permutations with a common set of interior peaks and
is the peak algebra. We extend the above results to
, generalizing results of Schocker (the case j = 0).
Aguiar supported in part by NSF grant DMS-0302423
Orellana supported in part by the Wilson Foundation 相似文献
6.
Tavan T. Trent 《Integral Equations and Operator Theory》2006,56(1):129-149
For the corona problem on the bidisk, we find analytic solutions belonging to the Orlicz-type space
In addition, for 1 ≤ p < ∞, an
corona theorem is established. Similar techniques can be used for the polydisk. 相似文献
7.
Antonio G. García Miguel A. Hernández-Medina 《Mediterranean Journal of Mathematics》2005,2(3):345-356
Let
be a symmetric operator with compact resolvent defined in a Hilbert space
For any fixed
we consider an entire
function Ka which involves the resolvent of
Associated with Ka we obtain, by duality in
a Hilbert space
of entire functions which becomes a De Branges space of entire functions. This property provides a characterization of
regardless of the anti-linear mapping which has
as its range space. There exists also a sampling formula allowing to recover any function in
from its samples at the sequence of eigenvalues of
This work has been supported by the grant BFM2003–01034 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología. 相似文献
8.
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
9.
10.
Let Ω be a bounded domain in with C2-smooth boundary, , of co-dimension 1, and let be a Schr?dinger operator on Ω with potential . We seek the weakest conditions we can find on the rate of growth of the potential V close to the boundary which guarantee essential self-adjointness of H on . As a special case of an abstract condition, we add optimal logarithmic type corrections to the known condition where . More precisely, we show that if, as x approaches ,
where the brackets contain an arbitrary finite number of logarithmic terms, then H is essentially self-adjoint on . The constant 1 in front of each logarithmic term is optimal. The proof is based on a refined Agmon exponential estimate
combined with a well-known multidimensional Hardy inequality.
Submitted: November 18, 2008.; Accepted: January 19, 2009.
We wish to thank F. Gesztesy, A. Laptev, M. Loss and B. Simon for useful comments and suggestions. I.N.’s research was partly
supported by the NSF grant DMS 0701026. 相似文献
11.
This paper deals with a class
of pseudorandom bit generators – modified alternating
–generators. This class is constructed similarly to the class
of alternating step generators. Three subclasses of
are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass
of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of
to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating
–generators, designed especially to be more secure, are presented. 相似文献
12.
The main result in Cossidente and Siciliano (J. Number Theory, Vol. 99 (2003) pp. 373–382) states that if a Singer subgroup of PGL(3,q) is an automorphism group of a projective, geometric
irreducible, non-singular plane algebraic curve
then either
or
. In the former case
is projectively equivalent to the curve
with equation Xq+1Y+Yq+1+X=0 studied by Pellikaan. Furthermore, the curve
has a very nice property from Finite Geometry point of view: apart from the three distinguished points fixed by the Singer
subgroup, the set of its
-rational points can be partitioned into finite projective planes
. In this paper, the full automorphism group of such curves is determined. It turns out that
is the normalizer of a Singer group in
. 相似文献
13.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
14.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
15.
Stefan Gille 《Archiv der Mathematik》2007,88(4):333-343
Let
be a closed subscheme of the noetherian scheme X. We show that if X has a dualizing complex
then there exists a dualizing complex
of Z such that there is an isomorphism of coherent Witt groups
for all
.
Received: 3 March 2006 相似文献
16.
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
17.
Vasily A. Prokhorov Edward B. Saff Maxim Yattselev 《Complex Analysis and Operator Theory》2009,3(2):501-524
Let be a bounded simply connected domain with boundary Γ and let be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants:
where is the supremum norm on a compact set K, is the set of all algebraic polynomials of degree at most m, and as . Subsequently, we obtain asymptotic behavior of the Kolmogorov k-widths, , of the unit ball An∞ of restricted to E in C(E), where H∞ is the Hardy space of bounded analytic functions on G and C(E) is the space of continuous functions on E.
Received: April 24, 2008. Accepted: May 15, 2008. 相似文献
18.
The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. 相似文献
19.
We establish a new 3G-Theorem for the Green’s function for the half space
We exploit this result to introduce a new class of potentials
that we characterize by means of the Gauss semigroup on
. Next, we define a subclass
of
and we study it. In particular, we prove that
properly contains the classical Kato class
. Finally, we study the existence of positive continuous solutions in
of the following nonlinear elliptic problem
where h is a Borel measurable function in
satisfying some appropriate conditions related to the class
.
Mathematics Subject Classification (1991): Primary: 34B27, 34B16, 34J65; Secondary: 35B50, 31B05 相似文献
20.
The aim of the present paper is to introduce a metric locally convex topology on the space
of δ-psh functions in the Cegrell class
. We prove that with this topology
is a non-separable and non-reflexive Fréchet space. At the same time, we extend the Monge–Ampère operator from the class
to
. 相似文献