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121.
Let T = T(A, D) be a self-affine attractor in
defined by an integral expanding matrix A and
a digit set D. In the
first part of this paper, in connection with canonical number systems,
we study connectedness of T when
D corresponds to the set of
consecutive integers
. It is shown that in
and
, for any integral expanding matrix A, T(A, D) is connected.
In the second part, we study connectedness of Pisot dual tiles, which
play an important role in the study of
-expansions, substitutions and
symbolic dynamical systems. It is shown that each tile of the dual
tiling generated by a Pisot unit of degree 3 is arcwise connected. This
is naturally expected since the digit set consists of consecutive
integers as above. However surprisingly, we found families of
disconnected Pisot dual tiles of degree 4. We even give a simple
necessary and sufficient condition of connectedness of the Pisot dual
tiles of degree 4. Detailed proofs will be given in [4].
Received: 2 March 2003 相似文献
122.
123.
Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and ?p for 1?p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E?(⊕?2n)c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ?21,?22,…,?2n,… . 相似文献
124.
We prove the well-posedness of the transmission problem for the Laplacian across a Lipschitz interface, with optimal non-tangential maximal function estimates, for data in Lebesgue and Hardy spaces on the boundary. As a corollary, we show that the spectral radius of the (adjoint) harmonic double layer potential K∗ in is less than , whenever is a bounded convex domain and 1<p?2. 相似文献
125.
Graziano Guerra 《Journal of Differential Equations》2004,206(2):438-469
We consider the Cauchy problem for the 2×2 strictly hyperbolic system
126.
4-Phenyl-3,4-dihydro--carboline was prepared using the Bischler—Napieralski reaction on -phenyltryptamine.Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 486–487, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date. 相似文献
127.
In earlier papers the authors studied finite pseudorandom binary sequences, and they constructed sequences with strong pseudorandom properties. In these earlier constructions multiplicative characters were used. In this paper a new construction is presented which utilizes properties of additive characters. These new sequences can be computed fast, they are well-distributed relative to arithmetic progressions and their correlations of small order are small, but the price paid for the fast computation is that the correlations of large order can be large. 相似文献
128.
We examine the operator algebra
behind the boundary integral equation method for solving transmission problems. A new type of boundary integral operator, the rotation operator, is introduced, which is more appropriate than operators of double layer type for solving transmission problems for first order elliptic partial differential equations. We give a general invertibility criteria for operators in
by defining a Clifford algebra valued Gelfand transform on
. The general theory is applied to transmission problems with strongly Lipschitz interfaces for the two classical elliptic operators
and . We here use Rellich techniques in a new way to estimate the full complex spectrum of the boundary integral operators. For
we use the associated rotation operator to solve the Hilbert boundary value problem and a Riemann type transmission problem. For the Helmholtz equation, we demonstrate how Rellich estimates give an angular spectral estimate on the rotation operator, which with the general spectral mapping properties in
translates to a hyperbolic spectral estimate for the double layer potential operator. 相似文献
129.
Jaros?aw K?dra 《Differential Geometry and its Applications》2004,21(1):93-112
Moduli spaces of stable pseudoholomorphic curves can be defined parametrically, i.e., over total spaces of symplectic fibrations. This imposes several restrictions on the spectral sequence of a symplectic fibration. We prove, among others, that under certain assumptions the spectral sequence collapses at E2. In the appendix, we prove nontriviality of certain Gromov-Witten invariant for blow-ups. As an application we obtain that any Hamiltonian fibration with the blow-up of along four dimensional submanifold as a fibre c-splits. That is its spectral sequence collapses. 相似文献
130.
Pavol?QuittnerEmail author 《NoDEA : Nonlinear Differential Equations and Applications》2004,11(2):237-258
Consider the Dirichlet problem for the parabolic equation
in
, where
$\Omega$ is a bounded domain in
and f has superlinear subcritical growth in u.
If f is independent of t and satisfies some
additional conditions then using a dynamical method we find multiple (three, six or infinitely many) nontrivial
stationary solutions. If f has the form
where m is periodic, positive and m,g satisfy some technical
conditions then we prove the existence of a positive periodic solution and
we provide a locally uniform bound for all global solutions. 相似文献