BIRD, BCAM's Institutional Repository Data
http://bird.bcamath.org:80
The BIRD digital repository system captures, stores, indexes, preserves, and distributes digital research material.2018-09-20T22:40:26ZProof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates
http://hdl.handle.net/20.500.11824/856
Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates
Li K.; Ombrosi S.; Pérez C.
We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that
$$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, \|f\|_{L^1(uv)},$$
where $T$ can be the Hardy-Littlewood maximal function or any Calder\'on-Zygmund operator. This result was conjectured in [IMRN, (30)2005, 1849--1871] and constitutes the most singular case of some extensions of several problems proposed by E. Sawyer and Muckenhoupt and Wheeden. We also improve and extends several quantitative estimates.
2018-09-01T00:00:00ZOn the geometry of strongly flat semigroups and their generalizations
http://hdl.handle.net/20.500.11824/855
On the geometry of strongly flat semigroups and their generalizations
László T.; Némethi A.
Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and numerical semigroups. More precisely, we prove that the strongly flat semigroups, which satisfy the maximality property with respect to the Diophantine Frobenius problem, are exactly the numerical semigroups associated with negative de nite Seifert homology spheres via the possible `weights' of the generic $S^1$-orbit. Furthermore, we consider their generalization to the Seifert rational homology sphere case and prove an explicit (up to a Laufer computation sequence) formula for their Frobenius number. The singularities behind are
the weighted homogeneous ones, whose several topological and analytical properties are exploited.
2018-09-18T00:00:00ZA Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
http://hdl.handle.net/20.500.11824/854
A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
Shahriari M.; Rojas S.; Pardo D.; Rodríguez-Rozas A.; Bakr S.A.; Calo V.M.; Muga I.
In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a Hankel transform. The resulting formulation is often solved via a semi-analytic method, mainly due to its high performance. However, semi-analytic methods have important limitations such as, for example, their inability to model piecewise linear variations on the resistivity. Herein, we develop a multi-scale finite element method (FEM) to solve the secondary field formulation. This numerical scheme overcomes the limitations of semi-analytic methods while still delivering high performance. We illustrate the performance of the method with numerical synthetic examples based on two symmetric logging-while-drilling (LWD) induction devices operating at 2 MHz and 500 KHz, respectively.
2018-06-14T00:00:00ZOn the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids
http://hdl.handle.net/20.500.11824/853
On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids
Scrobogna S.
We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are globally defined if the initial data is in $ H^k\pare{\bR^2}, k\geqslant 1 $.
2018-09-01T00:00:00Z