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81.
José Ignacio Royo Prieto Martintxo Saralegi-Aranguren Robert Wolak 《manuscripta mathematica》2008,126(2):177-200
For a riemannian foliation on a closed manifold M, it is known that is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form
(relatively to a suitable riemannian metric μ) is zero (cf. álvarez in Ann Global Anal Geom 10:179–194, 1992). In the transversally
orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group , where (cf. Masa in Comment Math Helv 67:17–27, 1992). By the Poincaré Duality (cf. Kamber et and Tondeur in Astérisque 18:458–471,
1984) this last condition is equivalent to the non-vanishing of the basic twisted cohomology group , when M is oriented. When M is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results
for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation
on a compact manifold (CERF).
J. I. Royo Prieto was partially supported by EHU06/05, by a PostGrant from the Basque Government and by the MCyT of the Spanish
Government. R. Wolak was partially supported by the KBN grant 2PO3A 021 25. 相似文献
82.
According to the present state of the theory of the matroid parity problem, the existence of a good characterization to the
size of a maximum matching depends on the behavior of certain substructures, called double circuits. In this paper we prove
that if a polymatroid has no double circuits then a partition type min-max formula characterizes the size of a maximum matching.
Applications to parity constrained orientations and to a rigidity problem are given.
Research is supported by OTKA grants K60802, TS049788 and by European MCRTN Adonet, Contract Grant No. 504438. 相似文献
83.
The aim of this paper is to study, for L
1-data, the absorption problem of parabolic type : with Dirichlet boundary conditions and initial conditions. Here a satisfies the classical Leray-Lions hypotheses and β(x, ·) is the subdifferential ∂j(x, ·), where j is a convex function such that j(·, 0) = 0. Existence and uniqueness of an entropy solution is established.
相似文献
84.
The disambiguation approach to the input of formulae enables users of mathematical assistants to type correct formulae in
a terse syntax close to the usual ambiguous mathematical notation. When it comes to incorrect formulae however, far too many
typing errors are generated; among them we want to present only errors related to the formula interpretation meant by the
user, hiding errors related to other interpretations.
We study disambiguation errors and how to classify them into the spurious and genuine error classes. To this end we give a
general presentation of the classes of disambiguation algorithms and efficient disambiguation algorithms. We also quantitatively
assess the quality of the presented error classification criteria benchmarking them in the setting of a formal development
of constructive algebra.
Partially supported by the Strategic Project “DAMA: Dimostrazione Assistita per la Matematica e l’Apprendimento” of the University
of Bologna. 相似文献
85.
We consider the following Liouville equation in
For each fixed and a
j
> 0 for 1 ≤ j ≤ k, we construct a solution to the above equation with the following asymptotic behavior:
相似文献
86.
Marc Briane Juan Casado–Díaz 《Calculus of Variations and Partial Differential Equations》2008,33(4):463-492
In this paper we study the limit, in the sense of the Γ-convergence, of sequences of two-dimensional energies of the type
, where A
n
is a symmetric positive definite matrix-valued function and μ
n
is a nonnegative Borel measure (which can take infinite values on compact sets). Under the sole equicoerciveness of A
n
we prove that the limit energy belongs to the same class, i.e. its reads as , where is a diffusion independent of μ
n
and μ is a nonnegative Borel measure which does depend on . This compactness result extends in dimension two the ones of [11,23] in which A
n
is assumed to be uniformly bounded. It is also based on the compactness result of [7] obtained for sequences of two-dimensional
diffusions (without zero-order term). Our result does not hold in dimension three or greater, since nonlocal effects may appear.
However, restricting ourselves to three-dimensional diffusions with matrix-valued functions only depending on two coordinates,
the previous two-dimensional result provides a new approach of the nonlocal effects. So, in the periodic case we obtain an
explicit formula for the limit energy specifying the kernel of the nonlocal term. 相似文献
87.
Let m ≥ 1 be an integer and N > 2m. Let μ be a positive Radon measure on . We study necessary and sufficient conditions on possible distributional solutions of , that guarantee the validity of the representation formula a.e. on , where and c(2m) is a positive constant depending on m and N. Several consequences are derived. In particular we prove Liouville theorems for systems of higher order elliptic inequalities
and weighted form of Hardy-Littlewood-Sobolev systems of integral equations.
Received: March 2008 相似文献
88.
Liviu I. Ignat Julio D. Rossi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(5):918-925
In this paper we study the asymptotic behaviour as t → ∞ of solutions to a nonlocal diffusion problem on a lattice, namely, with t ≥ 0 and . We assume that J is nonnegative and verifies . We find that solutions decay to zero as t → ∞ and prove an optimal decay rate using, as our main tool, the discrete Fourier transform.
相似文献
89.
Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine
structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence between the
commutant of this structure and the fixed points of the transfer operator. We show how the covariant representation can be
realized on if the weight satisfies some low-pass condition.
相似文献
90.
Dimitra Kosta 《manuscripta mathematica》2008,127(2):151-166
We prove that for n = 8, 9, 10, 11, a nodal hypersurface of degree n in is factorial if it has at most (n − 1)2 − 1 nodes.
The author is grateful to Ivan Cheltsov for valuable comments and suggestions. 相似文献