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51.
A transversely homogeneous foliation is a foliation whose transverse model is a homogeneous space G/H. In this paper we consider the class of transversely homogeneous foliations
on a manifold M which can be defined by a family of 1-forms on M fulfilling the Maurer–Cartan equation of the Lie group G. This class includes as particular cases Lie foliations and certain homogeneous spaces foliated by points. We develop, for the foliations belonging to this class, a deformation theory for which both the foliation
and the model homogeneous space G/H are allowed to change. As the main result we show that, under some cohomological assumptions, there exist a versal space of deformations of finite dimension for the foliations of the class and when the manifold M is compact. Some concrete examples are discussed. 相似文献
52.
53.
54.
Ricardo S. Leite Nicolau C. Saldanha Carlos Tomei 《Foundations of Computational Mathematics》2010,10(1):15-36
One of the most widely used methods for eigenvalue computation is the QR iteration with Wilkinson’s shift: Here, the shift s is the eigenvalue of the bottom 2×2 principal minor closest to the corner entry. It has been a long-standing question whether the rate of convergence of the algorithm is always cubic. In contrast, we show that there exist matrices for which the rate of convergence is strictly quadratic. More precisely, let $T_{ {\mathcal {X}}}One of the most widely used methods for eigenvalue computation is the QR iteration with Wilkinson’s shift: Here, the shift s is the eigenvalue of the bottom 2×2 principal minor closest to the corner entry. It has been a long-standing question whether
the rate of convergence of the algorithm is always cubic. In contrast, we show that there exist matrices for which the rate
of convergence is strictly quadratic. More precisely, let
T XT_{ {\mathcal {X}}}
be the 3×3 matrix having only two nonzero entries
(T X)12=(T X)21=1(T_{ {\mathcal {X}}})_{12}=(T_{ {\mathcal {X}}})_{21}=1
and let
T\varLambda {\mathcal {T}}_{\varLambda }
be the set of real, symmetric tridiagonal matrices with the same spectrum as
T XT_{ {\mathcal {X}}}
. There exists a neighborhood
U ì T\varLambda \boldsymbol {{\mathcal {U}}}\subset {\mathcal {T}}_{\varLambda }
of
T XT_{ {\mathcal {X}}}
which is invariant under Wilkinson’s shift strategy with the following properties. For
T0 ? UT_{0}\in \boldsymbol {{\mathcal {U}}}
, the sequence of iterates (T
k
) exhibits either strictly quadratic or strictly cubic convergence to zero of the entry (T
k
)23. In fact, quadratic convergence occurs exactly when
limTk=T X\lim T_{k}=T_{ {\mathcal {X}}}
. Let
X\boldsymbol {{\mathcal {X}}}
be the union of such quadratically convergent sequences (T
k
): The set
X\boldsymbol {{\mathcal {X}}}
has Hausdorff dimension 1 and is a union of disjoint arcs
Xs\boldsymbol {{\mathcal {X}}}^{\sigma}
meeting at
T XT_{ {\mathcal {X}}}
, where σ ranges over a Cantor set. 相似文献
55.
We define cut-and-paste, a construction which, given a quadriculated disk obtains a disjoint union of quadriculated disks of smaller total area. We provide two examples of the use of this procedure as a recursive step. Tilings of a disk Δ receive a parity: we construct a perfect or near-perfect matching of tilings of opposite parities. Let BΔ be the black-to-white adjacency matrix: we factor , where L and U are lower and upper triangular matrices, is obtained from a larger identity matrix by removing rows and columns and all entries of L, and U are equal to 0, 1 or -1. 相似文献
56.
Claudio Palomo Nicolau 《Angewandte Chemie (International ed. in English)》2011,50(28):6207-6208
57.
58.
Let be a holomorphic function in the unit disk omitting a set of values of the complex plane. If has positive logarithmic capacity, R. Nevanlinna proved that has a radial limit at almost every point of the unit circle. If is any infinite set, we show that has a radial limit at every point of a set of Hausdorff dimension 1. A localization technique reduces this result to the
following theorem on inner functions. If is an inner function omitting a set of values in the unit disk, then for any accumulation point of in the disk, there exists a set of Hausdorff dimension 1 of points in the circle where has radial limit .
Received: 13 February 1997 相似文献
59.
In this paper we study the classM of all inner functions whose non-zero Frostman shifts are Carleson-Newman Blaschke products. We present several geometric,
measure theoretic and analytic characterizations ofM in terms of level sets, distribution of zeros, and behaviour of pseudohyperbolic derivatives and observe thatM is the set of all functions inH
∞ whose range on the set of trivial points in the maximal ideal space is ∂D∪{0}
The second author thanks the University of Metz for its support during a one-month research visit and acknowledges partial
support by DGYCIT and CIRIT grants. Also both authors were partially supported by the European network HPRN-CT-2000-00116. 相似文献
60.
Konstantin Dyakonov Artur Nicolau 《Transactions of the American Mathematical Society》2007,359(9):4449-4465
We are concerned with interpolation problems in where the values prescribed and the function to be found are both zero-free. More precisely, given a sequence in the unit disk, we ask whether there exists a nontrivial minorant (i.e., a sequence of positive numbers bounded by 1 and tending to 0) such that every interpolation problem has a nonvanishing solution whenever for all . The sequences with this property are completely characterized. Namely, we identify them as `` thin" sequences, a class that arose earlier in Wolff's work on free interpolation in VMO.