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1.
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
2.
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
3.
Let A be a Banach algebra which does not contain any nonzero idempotent element, let γ > 0, and let
. We show that if
then
. We also show, assuming a suitable spectral condition on x, that if
, then
Received: 12 July 2006 Revised: 31 January 2007 相似文献
4.
Birkhoff coordinates for KdV on phase spaces of distributions 总被引:1,自引:0,他引:1
The purpose of this paper is to extend the construction of Birkhoff coordinates for the KdV equation from the phase space
of square integrable 1-periodic functions with mean value zero to the phase space
of mean value zero distributions from the Sobolev space
endowed with the symplectic structure
More precisely, we construct a globally defined real-analytic symplectomorphism
where
is a weighted Hilbert space of sequences
supplied with the canonical Poisson structure so that the KdV Hamiltonian for potentials in
is a function of the actions
alone. 相似文献
5.
Frank Müller 《Calculus of Variations and Partial Differential Equations》2005,24(3):283-288
Let $P={\rm \Gamma}\cap{\cal S}Let
be the point of non-tangential intersection of a closed Jordan arc
and an embedded, regular support surface
. Let
be a conformally parametrized solution of
with partially free boundaries
. It is proved, that
is H?lder continuous up to
with
, whenever
meets
orthogonally along its free trace. This provides a regularity result for stationary minimal surfaces and is applicable also
to surfaces of prescribed bounded mean curvature.
Mathematics Subject Classification (2000) 53 A 10, 35 J 65, 35 R 35, 49 Q 05 相似文献
6.
Let n
i
,m
j
> 1. In [5], the sperical noncommutative torus
was defined by twisting
in
by a totally skew multiplier p on
for T
pd
a pd-homogeneous C*-algebra over
. It is shown that
is strongly Morita equivalent to
.
This work is supported by Grant No. 1999-2-102-001-3 from the interdisciplinary research program year of the KOSEF 相似文献
7.
M. A. Bastos C. A. Fernandes Yu. I. Karlovich 《Integral Equations and Operator Theory》2006,55(1):19-67
We establish a symbol calculus for the C*-subalgebra
of
generated by the operators of multiplication by slowly oscillating and piecewise continuous functions and the operators
where
is the Cauchy singular integral operator and
The C*-algebra
is invariant under the transformations
where Uz is the rotation operator
Using the localtrajectory method, which is a natural generalization of the Allan-Douglas local principle to nonlocal type
operators, we construct symbol calculi and establish Fredholm criteria for the C*-algebra
generated by the operators
and
for the C*-algebra
generated by the operators
and
and for the C*-algebra
generated by the algebras
and
The C*-algebra
can be considered as an algebra of convolution type operators with piecewise slowly oscillating coefficients and shifts acting
freely. 相似文献
8.
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
9.
For an arbitrary set E and a given closure operator
, we want to construct a symmetric closure operator
via some – possibly infinite – iteration process. If E is finite, the corresponding symmetric closure operator .
defines a matroid. If
and
is the convex closure operator,
turns out to be the affine closure operator. Moreover, we apply the symmetrization process to closure operators induced by
visibility.
Received March 9, 2005 相似文献
10.
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
11.
Daoxing Xia 《Integral Equations and Operator Theory》2006,55(3):439-452
This paper studies pure subnormal k-tuples of operators
with finite rank of self-commutators. It determines the substantial part of the conjugate of the joint point spectrum of
which is the union of domains in Riemann surfaces in some algebraic varieties in
The concrete form of the principal current [4] related to
is also determined. Besides, some operator identities are found for
相似文献
12.
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
13.
M. Rovinsky 《Selecta Mathematica, New Series》2005,11(3-4):491-522
Let L be the function field of a projective space
over an algebraically closed field k of characteristic zero, and H be the group of projective transformations. An H-sheaf
on
is a collection of isomorphisms
for each g ∈ H satisfying the chain rule.
We construct, for any n > 1, a fully faithful functor from the category of finite-dimensional L-semilinear representations of H extendable to the semigroup End(L/k) to the category of coherent H-sheaves on
The paper is motivated by a study of admissible representations of the automorphism group G of an algebraically closed extension of k of countable transcendence degree undertaken in [4]. The semigroup End(L/k) is considered as a subquotient of G, hence the condition on extendability.
In the appendix it is shown that, if
is either H, or a bigger subgroup in the Cremona group (generated by H and a certain pair of involutions), then any semilinear
of degree one is an integral L-tensor power of
It is also shown that this bigger subgroup has no non-trivial representations of finite degree if n > 1. 相似文献
14.
Mouez Dimassi 《Annales Henri Poincare》2006,7(3):513-525
In the large-coupling constant limit we obtain an asymptotic expansion in powers of
of the derivative of the spectral shift function corresponding to
. Here the potential W(x) is positive and
near infinity for some δ> n and ω0 ∈C∞ (Sn-1).
submitted 18/05/05, accepted 19/10/05 相似文献
15.
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
16.
Let M be a four-holed sphere and Γ the mapping class group of M fixing the boundary ∂M. The group Γ acts on
which is the space of completely reducible SL (2,
-gauge equivalence classes of flat SL
-connections on M with fixed holonomy
on ∂M. Let
and
be the compact component of the real points of
. These points correspond to SU(2)-representations or SL(2,
-representations. The Γ-action preserves
and we study the topological dynamics of the Γ-action on
and show that for a dense set of holonomy
, the Γ-orbits are dense in
. We also produce a class of representations
such that the Γ-orbit of [ρ] is finite in the compact component of
, but
is dense in SL(2,
.Mathematics Subject Classiffications (2000). 57M05, 54H20, 11D99 相似文献
17.
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
19.
In this paper, we continue our investigation on “Extremal problems under dimension constraints” introduced [1]. The general problem we deal with in this paper can be formulated as follows. Let
be an affine plane of dimension k in
. Given
determine or estimate
.Here we consider and solve the problem in the special case where
is a hyperplane in
and the “forbidden set”
. The same problem is considered for the case, where
is a hyperplane passing through the origin, which surprisingly turns out to be more difficult. For this case we have only partial results.AMS Classification: 05C35, 05B30, 52C99 相似文献
20.
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