Two generalizations of the PRV conjecture

Let G be a complex connected reductive group. The PRV conjecture, which was proved independently by S. Kumar and O. Mathieu in 1989, gives explicit irreducible submodules of the tensor product of two irreducible G-modules. This paper has three aims. First, we simplify the proof of the PRV conjecture, then we generalize it to other branching problems. Finally, we find other irreducible components of the tensor product of two irreducible G-modules that appear for "the same reason" as the PRV ones

Dielectric anomalies and spiral magnetic order in CoCr2O4

We have investigated the structural, magnetic, thermodynamic, and dielectric properties of polycrystalline CoCr$_2$O$_4$, an insulating spinel exhibiting both ferrimagnetic and spiral magnetic structures. Below $T_c$ = 94 K the sample develops long-range ferrimagnetic order, and we attribute a sharp phase transition at $T_N$ $\approx$ 25 K with the onset of long-range spiral magnetic order. Neutron measurements confirm that while the structure remains cubic at 80 K and at 11 K; there is complex magnetic ordering by 11 K. Density functional theory supports the view of a ferrimagnetic semiconductor with magnetic interactions consistent with non-collinear ordering. Capacitance measurements on CoCr$_2$O$_4$, show a sharp decrease in the dielectric constant at $T_N$, but also an anomaly showing thermal hysteresis falling between approximately $T$ = 50 K and $T$ = 57 K. We tentatively attribute the appearance of this higher temperature dielectric anomaly to the development of \textit{short-range} spiral magnetic order, and discuss these results in the context of utilizing dielectric spectroscopy to investigate non-collinear short-range magnetic structures.Comment: & Figure

Predicting morphotropic phase boundary locations and transition temperatures in Pb- and Bi-based perovskite solid solutions from crystal chemical data and first-principles calculations

Using data obtained from first-principles calculations, we show that the position of the morphotropic phase boundary (MPB) and transition temperature at MPB in ferroelectric perovskite solutions can be predicted with quantitative accuracy from the properties of the constituent cations. We find that the mole fraction of PbTiO$_3$ at MPB in Pb(B$'$B$''$)O$_3$-PbTiO$_3$, BiBO$_3$-PbTiO$_3$ and Bi(B$'$B$''$)O$_3$-PbTiO$_3$ exhibits a linear dependence on the ionic size (tolerance factor) and the ionic displacements of the B-cations as found by density functional theory calculations. This dependence is due to competition between the local repulsion and A-cation displacement alignment interactions. Inclusion of first-principles displacement data also allows accurate prediction of transiton temperatures at the MPB. The obtained structure-property correlations are used to predict morphotropic phase boundaries and transition temperatures in as yet unsynthesized solid solutions.Comment: Accepted for publication in J. Appl. Phy

The effect of calcium channel blockers against scopolamine induced cognitive impairment and oxidative stress

Background: the present work has been planned to find out the effect of calcium channel blockers on learning and memory. there are numerous reports indicating that calcium channel blockers (CCBS) impair memory and learning and on the other side there are reports indicating that CCBS improve memory and learning .This contradictory reports led us to investigate the effect of CCBS on memory and learning by taking three different types of calcium channel blockers verapamil, nimodipine and diltiazem.Methods: The methods used were elevated plus maze and novel recognition object tests. Ten groups of animals were treated with CCBS and scopolamine. Both prophylactic and curative studies were carried out.Results: It was evident from our studies that the CCBS effectively antagonized the scopolamine induced cognitive impairment in the paradiagms studied. The inflex ratio and novel object discrimination index also increased indicating decrease in the trancefer latencies. CCBS showed good protection against scopolamine induced cognitive.Conclusions: In our Studies we observed that verapamil was good in prophylactic studies and diltiazem in curative studies

Nuevo puente, en Ceilán

Sobre el río Kelani Ganga, situado al norte de la ciudad de Colombo, capital de Ceilán, se ha construido un nuevo puente de hormigón armado, de diez tramos, 275 m de longitud total, 24 m de anchura de tablero y calzada de 18 m de ancho, que se ha subdivido en seis bandas de circulación, tres para cada una de las dos direcciones de tráfico

Warragamba. Sydney, Australia

El pantano de Warragamba, cuyo objeto es el de producir energía hidroeléctrica en su primera fase de explotación y solamente agua potable cuando las necesidades de ésta así lo requieran, se haya situado en las proximidades de Sydney (Australia). Su extensa cuenca está constituida por una serie de ríos en cuyas cabeceras se han construido diques de retención, que no solamente almacenan grandes cantidades de agua, sino que sirven parcialmente para la regularización de caudales, función de gran interés en esta zona donde las avenidas, seguidas de extensas inundaciones, se hacen sentir con relativa frecuencia

Reactor atómico, Trombay

El reactor de Trombay, denominado reactor Canadá-India, e instalado en las proximidades de Bombay (India), constituye el proyecto de mayor amplitud construido con la colaboración internacional y dedicado al empleo de la energía atómica para usos de carácter puramente pacíficos