Showing papers by "National Autonomous University of Mexico published in 1976"

Symmetry and separation of variables for the Helmholtz and Laplace equations

Abstract: This paper is one of a series relating the symmetry groups of the principal linear partial differential equations of mathematical physics and the coordinate systems in which variables separate for these equations. In particular, we mention [1] and paper [2] which is a survey of and introduction to the series. Here we apply group-theoretic methods to study the separable coordinate systems for the Helmholtz equation.

U(5) ⊆O(5) ⊆O(3) and the exact solution for the problem of quadrupole vibrations of the nucleus

Abstract: Over twenty years ago A. Bohr discussed the quantum mechanical problem of the quadrupole vibrations in the liquid drop model of the nucleus. States of definite angular momentum L could not be obtained exactly except when L=0,3. In the present paper we indicate how we can determine states for arbitrary angular momentum L and definite number of quanta ν in terms of polynomials of the creation operators characterized by irreducible representation (IR) of the chain of groups U(5) ⊆O(3). We furthermore characterize the states by a definite IR λ of O(5) by replacing the creation operators by traceless ones. These states are fully determined by an extra label μ that gives the number of triplets of traceless creation operators coupled to angular momentum zero. We show then how all the wavefunctions of the problem discussed by Bohr can be obtained in a recursive fashion and briefly discuss some of their applications.

Modal Analysis for Building-Soil Interaction

Abstract: An approximate method of modal analysis is presented for the earthquake response of linear building-foundation systems. Modal damping is obtained as a formal extension of the classical method of modal analysis and is shown to be equivalent to the energy ratio criterion proposed by Jacobsen. By making use of the modal shapes of the fixed-base superstructure, modal damping in the system is expressed as a weighted sum of the critical damping ratios of the superstructure plus an additional term representing the energy dissipated by the soil. To estimate the accuracy of the suggested method, both analytical and numerical studies are performed. Several examples are included to illustrate the effect of hysteretic soil damping on the system response.

Non linear canonical transformations and their representations in quantum mechanics

Abstract: In the present paper we analyze the representations in quantum mechanics of classical canonical transformations that are non-bijective, i.e. not one to one onto. We take as the central example the canonical transformation that changes the Hamiltonian of a one-dimensional oscillator of frequency K−1 into one of frequency k−1 where k, K are relatively prime integers. For the particular case k = 1, the mapping of the original phase space (x,p) onto the new one \((\bar x,\bar p)\)is K to 1 and the equivalent points in (x,p) are related by a cyclic group CK of linear canonical transformations. When formulating this problem in Bargmann Hilbert space the canonical transformation can be related with the conformal transformation w = zK which again is K to 1 and where a group CK also appears. This cyclic group proves fundamental for the determination of representations of the conformal transformation in Bargmann Hilbert space. To begin with it suggests that while we can take in the original Bargmann Hilbert space a single component function, in the new Bargmann Hilbert space we must take a K component one. In this way we can map in a one to one fashion the states and operators in the old and new Bargmann Hilbert spaces. When translating these results to ordinary Hilbert space we get in an ambiguous way the quantization of the observables appearing in the equations that determine the representation of the classical canonical transformation relating oscillators of frequencies K−1 and k−1. Furthermore we also get the solutions of these equations, and the resulting representation is unitary.

Towards Optimum Design Through Building Codes

Abstract: The main purpose of codes should be producing optimum structures. Within one plausible system of ethics one should optimize for all of society, including future generations, taking into account protection of property, not only of life. Wide uncertainties demand use of probability theory, particularly Baysian statistics. Limit-states design, split factors, characteristic values, semiprobabilistic codes, and second-moment formats approximate reliability levels design. This familiarizes engineers with probability theory but overemphasizes influence of uncertainties and of statistical correlation and does not reflect the economic framework. Intuitive adjustments of reliability levels are unsatisfactory. Advent of optimization codes should be accelerated. A strategy for code evolution comprises education, production of design aids, flexibility in format, and research into statistics of human error and workings of intuition.

Possible rip current origin for bottom ripple zones, to 30-m depth

Abstract: Side-scan sonar records along the moderate- to high-energy Pacific Coast of Mexico show ripple-marked bands normal to the surf. These bands have been traced as far seaward as 1,500 m from the beach in water as deep as 30 m. There is strong evidence that these ripple bands are produced by rip currents. Earlier studies suggested that rip currents do not extend to the bottom beyond the breaker zone. Our interpretations indicate that rip currents—probably those that develop under severe wave conditions—transport sediment, shape the bottom, and produce internal sedimentary structures much farther seaward than was previously believed.

An approach to the problem of meaning: Semantic networks

Abstract: An approach to the problem of meaning through the postulation of semantic networks is presented. Subjects generated them for ten concrete and ten abstract nouns with two different procedures. Comparisons were made between the semantic network and the set of associations given to each concept. Finally, both the concrete concepts' and the abstract concepts' networks were compared. It was suggested that a form of meaning is given by the semantic network of the concept, by a reconstructive memory process.

Dielectric continuum theory of the electronic structure of interfaces

Abstract: General expressions for the density-density and potential-potential response functions, ground-state (i.e., surface) energy, and one-electron optical potential are derived for a model of planar interfaces between two media, each of which is described by a local frequency-dependent dielectric function. These expressions are utilized to evaluate the surface energies characteristic of interfaces between semiconductors (insulators) described by the uniform dielectic function ${\ensuremath{\epsilon}}_{S}(\ensuremath{\omega})=1+{\ensuremath{\omega}}_{p}^{2}{({\ensuremath{\Delta}}^{2}\ensuremath{-}{\ensuremath{\omega}}^{2}\ensuremath{-}\frac{i\ensuremath{\omega}}{\ensuremath{\tau}})}^{\ensuremath{-}1}$ metals described by ${\ensuremath{\epsilon}}_{M}(\ensuremath{\omega})=1\ensuremath{-}\frac{{\ensuremath{\omega}}_{p}^{2}}{\ensuremath{\omega}(\ensuremath{\omega}+\frac{i}{\ensuremath{\tau}})}$, and the vacuum ${\ensuremath{\epsilon}}_{V}(\ensuremath{\omega})\ensuremath{\equiv}1$. Plasmon damping (i.e., nonzero ${\ensuremath{\tau}}^{\ensuremath{-}1}$) is shown to limit the range of nonlocality of the one-electron optical potential to $\ensuremath{\lambda}\ensuremath{\sim}{(\frac{2\ensuremath{\hbar}\ensuremath{\tau}}{m})}^{\frac{1}{2}}$ and to decrease the surface energy. The surface energy of semiconductor interfaces is found to diminish monotonically with increases in the band-gap parameter ${E}_{g}=\ensuremath{\hbar}\ensuremath{\Delta}$. The conventional expressions for the surface energy of metals as a function of their density, $n=\frac{m{\ensuremath{\omega}}_{p}^{2}}{4\ensuremath{\pi}{e}^{2}}$, are recovered in the $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, although errors in some previous derivations of these expressions are displayed. Finally, the structure and limitations of local models of surface properties are examined critically, and the well-known hydrodynamic and step-density random-phase-approximation models of metal-vacuum interfaces are shown to be elementary consequences of classical electrostatics in the limit that ${\ensuremath{\epsilon}}_{M}(\ensuremath{\omega})=1\ensuremath{-}\frac{{\ensuremath{\omega}}_{p}^{2}}{{\ensuremath{\omega}}^{2}}$.

Cysteine sulphinate decarboxylase in chick and rat retina during development

Abstract: — The activity, properties and developmental pattern of cysteine sulphinate decarboxylase (CSD) were studied in chick and rat retina Retinal CSD shows properties similar to those of the enzyme in brain with respect to optimum pH, saturating substrate concentrations and stimulation by pyridoxal phosphate. CSD activity increased 3-fold from the 10th day of embryogenesis to hatching in chicks and in postnatal development in rats. The developmental pattern of CSD activity in both species is coincident with the functional maturation of visual function.

Zero-mass plane waves in nonzero gravitational backgrounds

Abstract: The mathematical definition of what is intuitively called a ''plane wave'' on the curved background of a black hole is clarified and discussed from the viewpoints of potentials and fields. Because of the long-range Newtonian part of the gravitational field the asymptotic wave fronts of an incident ''plane wave'' (describing a radiative perturbation for a scattering experiment) are distorted in a manner analogous to the wave fronts of an electron beam in the quantum-mechanical Coulomb scattering problem. In addition, the electromagnetic and gravitational fields can be described with either a potential formalism (i.e., the vector potential and the metric perturbation) or a field formalism (i.e., the electromagnetic field tensor and the Riemann tensor). In this paper we present a distorted ''plane wave'' prescription, necessary for the calculation of the scattering cross sections of electromagnetic and gravitational waves off of a black hole, which agrees with the accepted prescription for a massless scalar field and satisfies the intuitive notions of what constitutes a ''plane wave'' in terms of potentials and fields. (AIP)

Number of planetary nebulae in our galaxy

Abstract: It is found that the contribution to the ionization of the interstellar medium due to planetary nebulae is from one or two orders of magnitude smaller than that due to O stars. The mass return to the interstellar medium due to planetary nebulae is investigated, and the birth rate of white dwarfs and planetary nebulae are compared. Several arguments are given against the possibility that the infrared sources detected by Becklin and Neugebauer in the direction of the galactic center are planetary nebulae. (AIP)

Gold decoration of precipitates in doped alkali‐halide surfaces

Abstract: Sodium‐chloride crystals doped with Ca++, Fe++, and Cd++ exhibit precipitation phenomena of various phases Gold decoration of cleaved crystal surfaces has been found to be highly sensitive to the formation of these phases The study extended to other alkali halides and a wide range of other divalent impurity atoms