Temperature dependence of second order Raman spectra of rubidium iodide crystal

The temperature variation of the second order Raman spectra of RbI has been theoretically studied in three basic symmetries on the basis of the modified Born and Bradburn theory. The phonon frequencies and corresponding eigenvectors have been determined at the room temperature by employing a three body force shell model. It has been assumed that the major factor which governs the temperature dependence of Raman intensity is the occupation number and the changes in the phonon eigen data and the polarizability parameters with temperature have been ignored. Calculations have been made at three temperatures namely, 300,90 and 23 K and the theoretical results have been compared to the experimental Raman spectra.     

Analysis of τ-mesons

We describe in this paper measurements made on the decay products of 11 τ-mesons observed in large nuclear emulsion block detectors. Out of the 33 charged decay products; 27 have been arrested in the block, and were identified as π-mesons. The charge of the τ-meson was found to be positive in 6 cases. In one case the charge of the τ-meson is possibly negative and in 4 cases it could not be determined. Omitting one τ-meson in which a high energy γ-ray is emitted and which has been reported earlier¹ the weighted mean Q-value of the remaining 10 τ-mesons is:

$$Q_\tau = 76 \cdot 3 \pm 0 \cdot 3 MeV$$     

Absence of biologically related Raman lines in cultures of Bacillus megaterium

Cultures of Bacillus megaterium have been examined with laser-Raman spectroscopy in the 20–300 and 800–1800 cm^?1 ranges. No lines were detected in the 20–300 cm^?1 range, and evidence is presented that sporadic lines observed in the other range can be ascribed to experimental artifacts.     

Hydroxy(tosyloxy)iodo]benzene mediated alpha-azidation of ketones

Reaction of various ketones with [hydroxy(tosyloxy)iodo]benzene (HTIB) followed by treatment of the alpha-tosyloxy ketones thus generated in situ with NaN3 offers a one-pot procedure for the synthesis of alpha-azido ketones. The HTIB used in this conversion may also be generated in situ by using iodosobenzene in combination with p-toluene-sulphonic acid.     

A Fractional Schrödinger Equation and Its Solution

This paper presents a fractional Schrödinger equation and its solution. The fractional Schrödinger equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrödinger equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Schrödinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function.     

A generalization of sumset and its applications

Let A be a nonempty finite subset of an additive abelian group G and let r and h be positive integers. The generalized h-fold sumset of A, denoted by \(h^{(r)}A\), is the set of all sums of h elements of A, where each element appears in a sum at most r times. The direct problem for \(h^{(r)}A\) is to find a lower bound for \(|h^{(r)}A|\) in terms of |A|. The inverse problem for \(h^{(r)}A\) is to determine the structure of the finite set A for which \(|h^{(r)}A|\) is minimal with respect to some fixed value of |A|. If \(G = \mathbb {Z}\), the direct and inverse problems are well studied. In case of \(G = \mathbb {Z}/p\mathbb {Z}\), p a prime, the direct problem has been studied very recently by Monopoli (J. Number Theory, 157 (2015) 271–279). In this paper, we express the generalized sumset \(h^{(r)}A\) in terms of the regular and restricted sumsets. As an application of this result, we give a new proof of the theorem of Monopoli and as the second application, we present new proofs of direct and inverse theorems for the case \(G = \mathbb {Z}\).     

PHOTOACOUSTIC SPECTROSCOPIC STUDIES OF POLYCYCLIC AROMATIC HYDROCARBONS: NAPHTHALENE CATION

The photoacoustic (PA) spectrum of naphthalene cation in boric acid glass, in the region 250–400 nm is reported for the first tune and compared with its optical absorption spectrum. The energy levels for the ions are calculated using open shell Wasilewski method with limited configuration interaction and used to interpret the observed PA spectrum.     

Studies on electrical conduction behavior of La1‐3xCaxBaxSrxMnO3 synthesized by chemical route

In the manganite La_1‐xM_xMnO₃ (M = Ca, Ba, Sr) the doping concentration introduces a mixed valency (Mn³⁺, Mn⁴⁺) which governs the magnetic and electrical properties of the compound. The perovskite oxides La_1‐3xCa_xBa_xSr_xMnO₃ (x = 0.00, 0.05, 0.10) were prepared by chemical method. Single‐phase formation is confirmed by XRD studies. The electrical behavior of compositions with x = 0.00, 0.05 and 0.10 in the system La_1‐3xCa_xBa_xSr_xMnO₃ was studied in the temperature range 300‐420 K. It is observed that conductivity decreases with increasing temperature as well as dopants concentration. Metallic behavior of these compositions decreases with increasing dopants concentration (x). The microstructures of these samples have been characterized using scanning electron microscopy (SEM). (© 2007 WILEY ‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Metal-free synthesis of pyridin-2-yl ureas from 2-aminopyridinium salts

An unprecedented base promoted domino approach has been developed for the synthesis of pyridin-2-yl urea derivatives via the reaction of 2-aminopyridinium salts and arylamines. The developed strategy tolerated a wide range of functional groups and afforded pyridin-2-yl ureas in moderate to good yields. The reaction was postulated to involve tandem cyclization, intermolecular nucleophilic addition, ring opening, and demethylation.