Rational functions associated with double infinite sequences of complex numbers

AbstractLet {μk}−∞+∞ be a given double infinite sequence of complex numbers. By defining a linear functional on the space of the Laurent polynomials, certain rational functions are first constructed and some algebraic properties studied.The hermitian case, i.e. μ−k = μk, k ∈ Z is separately considered and it is shown how the theory of polynomials orthogonal on the unit circle can be used in order to prove geometric convergence for sequences such as these rational functions

Realization of an all-optical zero to π cross-phase modulation jump

We report on the experimental demonstration of an all-optical π cross-phase modulation jump. By performing a preselection, an optically induced unitary transformation, and then a postselection on the polarization degree of freedom, the phase of the output beam acquires either a zero or π phase shift (with no other possible values). The postselection results in optical loss in the output beam. An input state may be chosen near the resulting phase singularity, yielding a pi phase shift even for weak interaction strengths. The scheme is experimentally demonstrated using a coherently prepared dark state in a warm atomic cesium vapor

La Problematica Ambiental y los Centros de Desarrolo Academico

This article is presented as the second part of the one published on Issue 10 of Poliantea: Environmental Review and Management Problem. Here, we review specific environmental management undertaken by the universities since its inception in 1950, along with its commitments and partnerships that were consolidated over time. The study shows conceptions and events of environmental culture in the different institutions of higher education, its interest in the processes of training in the subject and social responsibility as centers of generation of solutions to the problems of global environmental degradation. Finally, it includes a picture sequence of initiatives and events organized by universities since the fifties. It aims to show the importance of the various actions and accomplishments of the different university communities regarding environmental issues

Exact Random Walk Distributions using Noncommutative Geometry

Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $N$ on a two-dimensional square lattice for large $N$, taking into account finite size contributions.Comment: Latex, 3 pages, 1 figure, to be published in J. Phys. A : Math. Ge

Probalandia, un escenario de juegos de azar para la enseñanza de las técnicas de conteo y el concepto básico de probabilidad

Se asume la teoría de situaciones didácticas como forma de orientar el proceso de aprendizaje de los escolares, la cual plantea que no es posible transmitir el saber al estudiante de forma directa sino que es necesario recrear una micro-cultura del hacer matemático para que los alumnos requieran solucionar y adaptarse a problemáticas de un medio. Por ello se presenta una experiencia que consistió en recrear un escenario llamado Probalandia (centro de entretenimiento famoso por ejecutar cuatro juegos de azar que eran justos, pero que perdió credibilidad cuando se murmuró que ya no lo eran) en el cual estudiantes de 11° encontraron juegos justos e injustos y con ello aprendieron técnicas de conteo y el concepto básico de probabilidad

Entropic Barriers, Frustration and Order: Basic Ingredients in Protein Folding

We solve a model that takes into account entropic barriers, frustration, and the organization of a protein-like molecule. For a chain of size $M$, there is an effective folding transition to an ordered structure. Without frustration, this state is reached in a time that scales as $M^{\lambda}$, with $\lambda\simeq 3$. This scaling is limited by the amount of frustration which leads to the dynamical selectivity of proteins: foldable proteins are limited to $\sim 300$ monomers; and they are stable in {\it one} range of temperatures, independent of size and structure. These predictions explain generic properties of {\it in vivo} proteins.Comment: 4 pages, 4 Figures appended as postscript fil

Dimensional analysis and Rutherford Scattering

Dimensional analysis, and in particular the Buckingham $\Pi$ theorem is widely used in fluid mechanics. In this article we obtain an expression for the impact parameter from Buckingham's theorem and we compare our result with Rutherford's original discovery found in the early twentieth century

Path integral approach to no-Coriolis approximation in heavy-ion collisions

We use the two time influence functional method of the path integral approach in order to reduce the dimension of the coupled-channels equations for heavy-ion reactions based on the no-Coriolis approximation. Our method is superior to other methods in that it easily enables us to study the cases where the initial spin of the colliding particle is not zero. It can also be easily applied to the cases where the internal degrees of freedom are not necessarily collective coordinates. We also clarify the underlying assumptions in our approach.Comment: 11 pages, Latex, Phys. Rev. C in pres