On nonimmersibility of compact hypersurfaces into a ball of a simply connected space form

We give a nonimmersibility theorem of a compact manifold with nonnegative scalar curvature bounded from above into a geodesic ball of a simply connected space form.

Encriptación óptica empleando llaves Weierstrass-Mandelbrot

[EN] This paper presents the generation of encryption keys using the local oscillating properties of the partial sums of Weierstrass-Mandelbrot fractal function. In this way, the security key can be replicated if the parameters used to obtain it are known. Therefore, these parameters can be sent instead of sending the key. This procedure reduces the amount of information to be sent and prevents possible interception of the key. Moreover, the key can not be affected by data loss or pollution. The effectiveness of the Weierstrass-Mandelbrot keys were demonstrated by computer simulation in a 4f optical encryption system and the double random phase encoding technique. These keys allow us to enc…

Devil’s vortex-lenses

In this paper we present a new kind of vortex lenses in which the radial phase distribution is characterized by the "devil's staircase" function. The focusing properties of these fractal DOEs coined Devil's vortex-lenses are analytically studied and the influence of the topological charge is investigated. It is shown that under monochromatic illumination a vortex devil's lens give rise a focal volume containing a delimited chain of vortices that are axially distributed according to the self-similarity of the lens.

A virtual laboratory designed for teaching diffractive lenses

[EN] We present a virtual laboratory generated in Matlab GuiQc (Graphical User Interface) for its use in Optics courses as an informatic tool for teaching the focusing properties of a diffractive lens. This Gui allows the students to learn easily and rapidly about the influence on the focal volume of the lens construction parameters. As an example in this work we analyze fractal diffractive lenses because we found that fractal geometry is a highly motivating topic for students since it is related to a wide range of scientific and technological phenomena.

Devil's lenses.

In this paper we present a new kind of kinoform lenses in which the phase distribution is characterized by the “devil’s staircase” function. The focusing properties of these fractal DOEs coined devil’s lenses (DLs) are analytically studied and compared with conventional Fresnel kinoform lenses. It is shown that under monochromatic illumination a DL give rise a single fractal focus that axially replicates the self-similarity of the lens. Under broadband illumination the superposition of the different monochromatic foci produces an increase in the depth of focus and also a strong reduction in the chromaticity variation along the optical axis.

WAVEFRONT TESTER: Un nuevo laboratorio virtual para el estudio de los sensores frente de onda.

[EN] We present a new virtual laboratory developed with MatlabcGUI (Graphical User Interface) used toteach di erent aberration eff ects in the "Tecnologi a de Sensores Optoelectr onicos" at "Escuela T ecnicaSuperior de Ingenier a del Diseño" of the Universitat Polit ecnica de Val encia. The objective of this lab is to provide a computer tool to study the working principle of a Shack Hartman sensor and the parameters that determine the dynamic range of the same. Some examples made with di fferent aberrations (defocus,astigmatism, coma) and for diff erent sensor con gurations are presented.

Difract: Un nuevo laboratorio virtual para la modelización matemática de las propiedades de difracción de redes fractales

[EN] This work presents a new virtual laboratory, Difract, developed with Easy Java Simulations, for using in Optics courses as a computer tool for the mathematical modelling of the diffraction properties of 1D and 2D fractal gratings. This virtual laboratory enables students to quickly and easily analyze the influence on the Fraunhofer diffraction pattern of the different construction parameters of the fractal grating. As an application example, the Cantor fractal set has been considered.

Multifractal zone plates

We present multifractal zone plates (MFZPs) as what is to our knowledge a new family of diffractive lenses whose structure is based on the combination of fractal zone plates (FZPs) of different orders. The typical result is a composite of two FZPs with the central one having a first-order focal length f surrounded by outer zones with a third-order focal length f. The focusing properties of different members of this family are examined and compared with conventional composite Fresnel zone plates. It is shown that MFZPs improve the axial resolution and also give better performance under polychromatic illumination.

Cantor Dust Zone Plates

In this paper we use the Cantor Dust to design zone plates based on a two-dimensional fractal for the first time. The pupil function that defines the coined Cantor Dust Zone Plates (CDZPs) can be written as a combination of rectangle functions. Thus CDZPs can be considered as photon sieves with rectangular holes. The axial irradiances produced by CDZPs of different fractal orders are obtained analitically and experimentally, analyzing the influence of the fractality. The transverse irradiance patterns generated by this kind of zone plates has been also investigated.

Lacunar fractal photon sieves

We present a new family of diffractive lenses whose structure is based on the combination of two concepts: photon sieve and fractal zone plates with variable lacunarity. The focusing properties of different members of this family are examined. It is shown that the sieves provide a smoothing effect on the higher order foci of a conventional lacunar fractal zone plate. However, the characteristic self-similar axial response of the fractal zone plates is always preserved.

Volume estimate for a cone with a submanifold as vertex

We give some estimates for the volume of a cone with vertex a submanifold P of a Riemannian or Kaehler manifold M. The estimates are functions of bounds of the mean curvature of P and the sectional curvature of M. They are sharp on cones having a basis which is contained in a tubular hypersurface about P in a space form or in a complex space form.

A generalized finite difference method using Coatmèlec lattices

Generalized finite difference methods require that a properly posed set of nodes exists around each node in the mesh, so that the solution for the corresponding multivariate interpolation problem be unique. In this paper we first show that the construction of these meshes can be computerized using a relatively simple algorithm based on the concept of a Coatmelec lattice. Then, we present a generalized finite difference method which provides a numerical solution of a partial differential equation over an arbitrary domain, using the generated meshes. The accuracy and mesh adaptivity of the method is evaluated using elliptical equations in several domains.

El funcionamiento de los partidos políticos en los Estados Unidos: a propósito de las Elecciones Presidenciales y Legislativas de 1996

SUMARIO: 1.- Introducción. 2.- Posición de los partidos en EEUU. 3.- La organización. 4.- Los partidos a toda máquina: las elecciones presidenciales. 4.1. La selección de delegados. Primarias y caucus. 4.2. Las Convenciones. 4.3. Los elementos decisivos: dinero, grupos de interés y medios de comunicación. 5.- Los partidos en el Congreso. 6.- Recapitulación.

Comparison theorems for the volume of a complex submanifold of a Kaehler manifold

LetM be a Kaehler manifold of real dimension 2n with holomorphic sectional curvatureK H≥4λ and antiholomorphic Ricci curvatureρ A≥(2n−2)λ, andP is a complex hypersurface. We give a bound for the quotient (volume ofP)/(volume ofM) and prove that this bound is attained if and only ifP=C P n−1(λ) andM=C P n(λ). Moreover, we give some results on the volume of of tubes aboutP inM.

Volumetric multiple optical traps produced by Devil's lenses

We propose the use of a new diffractive optical element coined Devil's Vortex-Lens (DVL) to produce optical tweezers. In its more general form it results as the combination of a Devil’s lens and a helical vortex phase mask. It is shown that under monochromatic illumination a DVL generates a focal volume with several concatenated doughnut modes that are axially distributed according to the self-similarity of the lens. The orbital angular momentum associated to each link in the chain is investigated.

Fractal photon sieve

A novel focusing structure with fractal properties is presented. It is a photon sieve in which the pinholes are appropriately distributed over the zones of a fractal zone plate. The focusing properties of the fractal photon sieve are analyzed. The good performance of our proposal is demonstrated experimentally with a series of images obtained under white light illumination. It is shown that compared with a conventional photon sieve, the fractal photon sieve exhibits an extended depth of field and a reduced chromatic aberration.

Fractal square zone plates

[EN] In this paper we present a novel family of zone plates with a fractal distribution of square zones. The focusing properties of these fractal diffractive lenses coined fractal square zone plates are analytically studied and the influence of the fractality is investigated. It is shown that under monochromatic illumination a fractal square zone plate gives rise a focal volume containing a delimited sequence of two-arms-cross pattern that are axially distributed according to the self-similarity of the lens.

Bounds for the first Dirichlet eigenvalue of domains in Kaehler manifolds

Generación de fractales a partir del método de Newton

[EN] A large number of fractals known, as Julia fractals and Mandelbrot, can be generated from an iterative method. In this paper we present a virtual laboratory developed as a Graphical User Interface (GUI) of Matlab that allows us to study and visualize in real time the relationship between Newton iterative methods of two variables and the generation of fractals. The main objective is to allow Technical School students in Numerical Computation subjects to acquire the skills to generate fractals and interpret their plots in terms of the convergence or divergence speed of the sequence of iterated.

Immersions of compact riemannian manifolds into a ball of a complex space form

There are some classical theorems on non-immersibility of compact riemannian manifolds with sectional curvature bounded from above given by Tompkins, O’Neill, Chern, Kuiper and Moore (see [3], pages 221-226). More recently, attention has been paid to the case of immersions into a geodesic ball of a simply connected space form, and some conditions of non-immersibility in such a ball have been proved. In particular, estimates for the mean curvature of a complete immersion into a geodesic ball have been obtained by Jorge and Xavier [11] and a corresponding rigidity theorem for compact hypersurfaces has been proved by Markvorsen [14]. In this paper we give the Kahler analogs of the theorems of …

Bifractal focusing and imaging properties of Thue-Morse Zone Plates.

We present a new family of Zone Plates (ZPs) designed using the Thue-Morse sequence. The focusing and imaging properties of these aperiodic diffractive lenses coined Thue-Morse Zone Plates (TMZPs) are examined. It is demonstrated that TMZPs produce a pair of self-similar and equally intense foci along the optical axis. As a consequence of this property, under broadband illumination, a TMZP produces two foci with an extended depth of focus and a strong reduction of the chromatic aberration compared with conventional periodic ZPs. This distinctive optical characteristic is experimentally confirmed.

Multiple-plane image formation by Walsh zone plates.

[EN] A radial Walsh filter is a phase binary diffractive optical element characterized by a set of concentric rings that take the phase values 0 or ¿, corresponding to the values + 1 or ¿1 of a given radial Walsh function. Therefore, a Walsh filter can be re-interpreted as an aperiodic multifocal zone plate, capable to produce images of multiple planes simultaneously in a single output plane of an image forming system. In this paper, we experimentally demonstrate for the first time the focusing capabilities of these structures. Additionally, we report the first achievement of images of multiple-plane objects in a single image plane with these aperiodic diffractive lenses.

Modelización de superredes cuánticas con MathematicaQc

[EN] Quantum superlattices are composite aperiodic structures comprised of alternating layers of several semiconductors following the rules of an aperiodic sequence. From a pedagogical point of view, it is easy to obtain the electronic scattering properties of these systems by means of the Transfer Matrix Method (TMM). In this work we present a TMM code developed in Mathematica that allows modeling periodic and aperiodic superlattices for motivating students of quantum physics by using unconventional geometries such as fractals or the Fibonacci sequence.

A comparison theorem for the first Dirichlet eigenvalue of a domain in a Kaehler submanifold

AbstractWe give a sharp lower bound for the first eigenvalue of the Dirichlet eigenvalue problem on a domain of a complex submanifold of a Kaehler manifold with curvature bounded from above. The bound on the first eigenvalue is given as a function of the extrinsic outer radius and the bounds on the curvature, and it is attained only on geodesic spheres of a space of constant holomorphic sectional curvature embedded in the Kaehler manifold as a totally geodesic submanifold.