Varieties generated by modular lattices of width four

A variety (equational class) of lattices is said to be finitely based if there exists a finite set of identities defining the variety. Let M^∞_n denote the lattice variety generated by all modular lattices of width not exceeding n. M^∞₁ and M^∞₂ are both the class of all distributive lattices and consequently finitely based. B. Jónsson has shown that M^∞₃ is also finitely based. On the other hand, K. Baker has shown that M^∞_n is not finitely based for 5 ≤ n ˂ ω. This thesis settles the finite basis problem for M^∞₄. M^∞₄ is shown to be finitely based by proving the stronger result that there exist ten varieties which properly contain M^∞₄ and such that any variety which properly contains M^∞₄ contains one of these ten varieties.

The methods developed also yield a characterization of sub-directly irreducible width four modular lattices. From this characterization further results are derived. It is shown that the free M^∞₄ lattice with n generators is finite. A variety with exactly k covers is exhibited for all k ≥ 15. It is further shown that there are 2^Ӄo sub- varieties of M^∞₄.

Propriedades ópticas, magnéticas e estruturais de monocristais Cs2NaAlF6 dopados com cromo trivalente

Este trabalho teve por objetivo a realização do estudo das propriedades ópticas, magnéticas e estruturais do cristal elpasolita Cs2NaAlF6 dopado com as concentrações de 0,1%, 1,0%, 3,0%, 10,0%, 30,0% e 50,0% de Cr3+. O interesse no estudo deste sistema reside na existência de uma larga e intensa banda de luminescência na temperatura ambiente, que se estende do visível ao infravermelho próximo, podendo então ser utilizado como fonte de radiação sintonizável em dispositivos ópticos, optoeletrônicos e detectores, entre outros. Para a investigação das propriedades ópticas foram feitas medidas de luminescência, excitação e luminescência resolvida no tempo, na temperatura ambiente e a baixas temperaturas. Os resultados obtidos mostram largas bandas de luminescência atribuídas aos íons de Cr3+, ocupando dois sítios octaédricos não equivalentes. Os resultados também mostram que a intensidade integrada da luminescência, o baricentro da banda de emissão e o tempo de vida do estado luminescente variam com a concentração de impureza residente no sistema. Foram realizadas medidas de calor específico em função do campo magnético em uma larga faixa de temperatura, cujos resultados mostram o aparecimento do efeito Schottky a baixas temperaturas. Medidas de susceptibilidade magnética em funcão da temperatura também foram realizadas, e mostram um comportamento paramagnético, típico do íon impureza Cr3+, com um ordenamento magnético de curto alcance. Para a determinação das propriedades estruturais foram realizadas medidas de difração de nêutrons na temperatura ambiente.

A Q-swicthed all-solid-state single-longitudinal-mode laser with adjustable pulse-width and high repetition rate

A single-longitudinal-mode (SLM) laser-diode pumped Nd: YAG laser with adjustable pulse width is developed by using the techniques of pre-lasing and changing polarization of birefingent crystal. The Q-switching voltage is triggered by the peak of the pre-lasing pulse to achieve the higher stability of output pulse energy. The output energy of more than 1 mJ is obtained with output energy stability of 3% (rms) at 100 Hz. The pulse-width can be adjusted from 30 ns to 300 ns by changing the Q-switching voltage. The probability of putting out single-longitudinal-mode pulses is almost 100%. The laser can be run over four hours continually without mode hopping.

纳米ZnO粉末中随机激光现象

实验采用三倍频Nd：YAG（波长355nm，脉宽8ns，频率30Hz）脉冲激光器作为抽运光源，在ZnO纳米粉末（直径～100nm）中发现了类似激光现象．并用环形腔理论模拟了ZnO的颗粒密度对平均自由程的影响，从理论上证明在纳秒级激光器的抽运下，ZnO纳米粉末也可以发射激光．

Line-width reduction of a laser diode array using an external cavity with two feedback mirrors

A novel Littman-Metcalf external cavity laser diode array with two feedback mirrors is introduced. The line-width broadening effect caused by smile can be reduced by the novel external cavity. At the drive current of 16A, the line-width is narrowed to 0.1nm from free-running width of 1.6nm with output efficiency of 84%.

Generation of 1.5-12 ns width-tunable 532 nm pulses by adopting laser-induced plasma shutter technique

The pulse-shaping technique has found widespread applications in nonlinear optics and material processing. Experimental research on laser-induced plasma shutter to control the 532 nm pulse width is conducted. The impacts of the total pulse output energy on pulse compression are investigated, and a useful conclusion can be drawn that there exists an optimal value of pulse energy at which the shortest output pulse of 3.23 ns can be obtained without a device for delay-time. Once the device for delay-time is employed to change the optical differences between two laser paths, the pulse width can be further shortened to 1.51 ns. In short, the 1.5-12 ns width-tunable 532 nm laser pulses have been obtained by adopting the laser-induced plasma shutter technique. (C) 2007 Elsevier GmbH. All rights reserved.