Continuum Limit of the Volterra Model, Separation of Variables and Non-Standard Realizations of the Virasoro Poisson Bracket

The classical Volterra model, equipped with the Faddeev-Takhtajan Poisson bracket provides a lattice version of the Virasoro algebra. The Volterra model being integrable, we can express the dynamical variables in terms of the so-called separated variables. Taking the continuum limit of these formulae, we obtain the Virasoro generators written as determinants of infinite matrices, the elements of which are constructed with a set of points lying on an infinite genus Riemann surface. The coordinates of these points are separated variables for an infinite set of Poisson commuting quantities including L ₀. The scaling limit of the eigenvector can also be calculated explicitly, so that the associated Schroedinger equation is in fact exactly solvable.     

Students’ conceptual understanding of a function and its derivative in an experimental calculus course

Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its derivative as viewed by students of a reformed Calculus 1 course offered in two experimental sections at the Lebanese American University in Beirut, Lebanon. Results have shown that the general approach adopted in the course proved to be unpopular for a great majority of the students, but rewarding for others. Interviews conducted with some students and a study of their performance on very specific exam questions reveal that for most students, the algebraic representation of a function still dominated their thinking; however, these students showed an almost complete understanding of the derivative, particularly the idea of the instantaneous rate of change and/or the slope of a curve at a given point. Furthermore, very few of these students referred to the mechanical methods for finding derivatives.     

Reaction of methyl bromopropiolate with diamines as a method of synthesis of imidazolidine derivatives

A convenient method of synthesis of 2-(methoxycarbonylmethylene)-substituted imidazolidines and imidazolidinium bromides, and also of bicyclic diazo compounds has been developed starting from methyl bromopropiolate and ethylenediamine and its derivatives.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1205–1208, September, 1991.     

The effect of Erbium concentration on the optical spectrum of Erbium-doped fiber laser

We report an experimental observation of the influence of concentration of Er³⁺ ions in an Erbiumdoped silica fiber on the spectral characteristics of an erbium fiber laser. Our basic conclusion is that an increase of erbium concentration in the fiber results in the laser optical spectrum narrowing. We also discuss possible mechanisms responsible for this effect.     

Measurement of the Seperation between Atoms beyond Diffraction Limit

We propose a scheme to obtain the distance of two identical atoms placed inside the standing wave field by monitoring the collective resonance fluorescence spectrum emitted by the two particles. We find three different parameter ranges, depending on the distance of the atoms as compared to the transition wavelength. For large interparticle distances, dipole-dipole coupling is negligible, and the main system evolution arises from the interaction with the standing wave field. In the small-distance limit, the dynamics is dominated by the dipole-dipole interaction. Finally, in the intermediate region, a rich interplay of the various couplings arises, which however is lifted for strong driving laser fields. The present measurement procedure allows us to distinguish the three cases. In each of the cases, we show how to determine the distance of the two particles and their respective positions relative to the nodes of the standing wave field with fractional-wavelength precision.     

Noiselike magnetic resonance fine structure for ferromagnetic powders: Dipole-dipole interaction effects

A noiselike fine structure of ferromagnetic resonance spectra in magnetic powders was investigated after ultrasonic treatment. Magnetic interactions between particles are proved to have an influence upon the fine structure formation. After decreasing dipole-dipole magnetic interactions in dilute suspension a special order appears in fine-structure spectra, which is generally the same for different systems.     

Magnetic-field-induced valence transition in EuNi2(Si1−x Gex)2 in fields up to 500 T

The critical fields of the valence transition induced by a magnetic field in the EuNi₂(Si_1?x Ge_x)₂ (x=0.5–0.75) compound in an intermediate valence state are measured. The magnetic-field-induced valence transition is observed in the low-concentration range down to x=0.5. It is demonstrated that the critical field increases linearly with a decrease in the germanium concentration.     

The influence of interatomic distances on magnetic ordering in RMnSi compounds (R=La, Y, Sm, and Gd)

Magnetic ordering in the RMnSi (R=La, Y, Sm, and Gd) compounds is investigated. It is found that the type of magnetic ordering depends on the d _Mn-Mn distance between manganese atoms inside the magnetic layers located in the planes perpendicular to the c axis. This inference is based on the results of studies performed with SmMnSi and GdMnSi compounds in which the distances between manganese atoms are close to the critical value d _Mn-Mn that corresponds to the crossover between ferromagnetic and antiferromagnetic ordering in RMnSi compounds. The introduction of lanthanum and yttrium atoms into the rare-earth sublattice leads to an increase and a decrease in the unit cell size, respectively, and brings about magnetic phase transitions in the compounds under investigation.     

Effect of gamma irradiation on photoconversion characteristics of metal/gallium arsenide barrier structures with textured interface

The effect of ⁶⁰Co gamma irradiation at doses of 10³-2×10⁵ Gy on the photoconversion and dark I-V characteristics of Au/GaAs surface-barrier solar cells (SCs) is studied. The morphology of the interface microrelief is varied to reach the highest photoconversion efficiency. Of the two types of microrelief morphology (dendritic and quasi-grating) obtained by the chemical anisotropic etching of n-(100)GaAs, the latter is more promising, particularly for SCs designed for space application, since the associated SCs offer higher efficiency and radiation resistance.