A tight-binding model is fitted to density-functional calculations of the electronic structure of the MoS2 monolayer. The model involves 13 atomic orbitals per unit cell: the 4d orbitals of the molybdenum atom plus the 3s and 3p orbitals of each sulfur atom. The hopping and overlap couplings of each atom with its first nearest neighbors in each crystalline sublattice are considered. Different values are allowed for the intraplane and interplane S-S hopping integrals. A closed-form expression is given for the effective-mass tensor at stationary points. The isotropy of the valence and conduction bands near the edges of the fundamental gap is proven. The role played by the orbital overlapping as well as the crystal-field splitting of the molybdenum 4d level is discussed.

It is shown that the standard sp n hybrid orbitals are orthogonal orbitals that minimize the total quadratic spread. This is done in a concise way that may improve the understanding of hybrid orbitals. The fact that maximally localized Wannier functions of crystalline materials may resemble hybrid orbitals is discussed.

Abstract The study of blue light emitting semiconductor devices has been a topic of transcendental importance since the point of view of science as well as technology. In the present paper special attention is paid to the scientific and technological development of light emitting diodes and laser diodes based on the gallium nitride technology. The principal properties of gallium nitride and two of its alloys, indium-gallium nitride and aluminum-gallium nitride are qualitatively presented. An introduction to the new sources of light based on the light emitting semiconductor devices allows a brief historical review of the researches, the developments and the innovations carried out by Isamu Akasaki, Hiroshi Amano and Shuji Nakamura. Such scientific and technological works gave as results the design, fabrication and commercialization of blue light emitting diodes and blue laser diodes. Finally, an analysis of the economical, social and environmental importance of the blue emitting devices based on gallium nitride technology is done.

Resumen El estudio de los dispositivos semiconductores emisores de luz azul ha sido un tema de trascendental importancia tanto desde el punto de vista científico como tecnológico. En el presente artículo se presta especial atención al desarrollo científico y tecnológico de los diodos emisores de luz y los diodos láser basados en la tecnología del nitruro de galio. Las principales propiedades del nitruro de galio y dos de sus aleaciones, el nitruro de indio-galio y el nitruro de aluminio-galio, se presentan cualitativamente. Una breve introducción a las nuevas fuentes de luz basadas en los dispositivos semiconductores emisores de luz sirve de base argumental para hacer una breve reseña histórica de la investigación, el desarrollo y la innovación llevadas a cabo por Isamu Akasaki, Hiroshi Amano y Shuji Nakamura que dieron como resultado el diseño, construcción y posterior comercialización de los diodos emisores de luz azul y láser de luz azul. Finalmente, se hace una valoración de la trascendencia social, económica y medioambiental del los dispositivos emisores de luz con base en la tecnología del nitruro de galio.

Estudam-se as médias temporais das densidades das energias cinética e potencial em ondas mecânicas unidimensionais. Demonstra-se que o movimento harmônico simples dos elementos do meio não é condição suficiente nem necessária para que aquelas médias sejam iguais. Isso contradiz as abordagens em textos de Halliday et al. e Nussenzveig.

The mean values (in time) of the kinetic and potential energy densities in one-dimensional mechanical waves are studied. It is shown that the simple harmonic motion of the particles is neither a sufficient nor a necessary condition for those mean values to be the same. This contrasts with the approaches in textbooks by Halliday et al. and Nussenzveig.