A semi-automatic method for measuring interferometry fringes: prototype design and first results

A device for automatically obtaining the information contained in holographic interferometry fringes is proposed. The method may be applied to any kind of interferometric fringes. Accuracy has been demonstrated by contrasting the results obtained with our prototype system and those with the single-beam speckle interferometry technique for the measurement of displacements in a plane. The results show good correlation between the two series of measurements.     

New results on restriction of Fourier multipliers

We develop an extension of the Transference methods introduced by R. Coifman and G. Weiss and apply it to study the problem of the restriction of Fourier multipliers between rearrangement invariant spaces, obtaining natural extensions of the classical de Leeuw’s result and its further extension to maximal Fourier multipliers due to C. Kenig and P. Tomas.     

Influence of the differentiation system on the analytical parameters for the spectrophotometric determination of clonazepam in urine

Electronic and mathematical differentiation of the ultraviolet visible spectra were compared from the study of the analytical parameters of the direct determination of clonazepam in urine samples. Third-order derivative spectra were used. The mathematical differentiation provides higher sensitivity, a lower limit of detection, and better accuracy and precision than the electronic one. The use of a diode array instrument provides lower sensitivity than that found using a conventional spectrometer; however, the limit of detection obtained in both cases is of the same order.     

Banach Spaces of Solutions of the Helmholtz Equation in the Plane

The purpose of this article is to study the Hilbert space W²\mathcal{ W}^2 consisting of all solutions of the Helmholtz equation Du+u=0\Delta u+u=0 in \BbbR²\Bbb{R}^2 that are the image under the Fourier transform of L²L^2 densities in the unit circle. We characterize this space as a close subspace of the Hilbert space H²\mathcal{ H}^2 of all functions belonging to L²( | x | ^-3dx) L^2( | x | ^{-3}dx) jointly with their angular and radial derivatives, in the complement of the unit disk in \BbbR²\Bbb{R}^2. We calculate the reproducing kernel of W²\mathcal{ W}^2 and study its reproducing properties in the corresponding spaces H^p\mathcal{H}^p, for $p>1$p>1.     

Homeomorphisms of the annulus with a transitive lift

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift ${\tilde{f}}$ to the infinite strip à which is transitive. We show that, if the rotation numbers of both boundary components of A are strictly positive, then there exists a closed nonempty unbounded set ${B^{-} \subset \tilde{A}}$ such that B ^? is bounded to the right, the projection of B ^? to A is dense, ${B^{-}-(1, 0) \subset B^{-}}$ and ${\tilde{f}(B^{-}) \subset B^{-}}$ . Moreover, if p ₁ is the projection on the first coordinate of Ã, then there exists d > 0 such that, for any ${\tilde z \in B^{-}}$ , $$\limsup_{n\to\infty}\frac{p_1(\tilde f^n(\tilde z))-p_1(\tilde z)}{n}<-d.$$ In particular, using a result of Franks, we show that the rotation set of any homeomorphism of the annulus that preserves orientation, boundary components, which has a transitive lift without fixed points in the boundary is an interval with 0 in its interior.     

Fixed point theorems for generalized contractions on partial metric spaces

We obtain two fixed point theorems for complete partial metric space that, by one hand, clarify and improve some results that have been recently published in Topology and its Applications, and, on the other hand, generalize in several directions the celebrated Boyd and Wong fixed point theorem and Matkowski fixed point theorem, respectively.     

The Dirichlet problem associated to the relativistic heat equation

We prove existence and uniqueness of entropy solutions for the nonhomogeneous Dirichlet problem associated to the relativistic heat equation.     

Totally Bounded Quasi-Uniformities and Pseudocompactness of Bispaces

 We characterize pairwise Tychonoff bispaces that admit only totally bounded quasi-uniformities in terms of a suitable notion of bitopological pseudocompactness. We also show that a pairwise Tychonoff bispace has a unique (up to equivalence) bicompactification if and only if it admits a unique totally bounded quasi-unifomity. These results extend classical theorems of R. Doss for uniform spaces to the quasi-uniform (bitopological) setting, and are applied to the study of T ₀ topological spaces that admit a unique quasi-uniformity and a unique bicompactification, respectively. Finally, we discuss the problem of extending the classical Glicksberg theorem on product of pseudocompact spaces to bispaces and a partial solution is obtained. Supported by the Spanish Ministry of Science and Technology, grant BFM2000-1111. Supported by a grant from Generalitat Valenciana. Received November 7, 2001; in revised form August 14, 2002