Abstract. Based on an extensive site survey conducted during [1980][1981][1982][1983][1984][1985][1986][1987][1988][1989][1990] in the Shivalik Hills of the Central Himalayan range, a promising site Devasthal has been identified. The longitude and latitude of Devasthal Peak are 79• 41 E and 29• 23 N. It is situated at an altitude of 2540 m and about 50 km by road from Nainital towards East. The surroundings of Devasthal are thinly populated and it is logistically well suited for establishing modern optical observational facilities. The prevailing wind direction at Devasthal is NW. For a large fraction of the night time, variation in the ambient temperature was less than a degree and wind speed was less than 10 m/s. During spectroscopic nights (> 200 in a year) relative humidity is less than 80% for about 70% of the time. During 1997 and 1998 seeing measurements using differential image motion techniques have been carried out close to ground at two locations namely Site 1 and Site 2 in Devasthal. Our observations for Site 1 carried over 88 nights yield a median seeing value of 1. 4. For Devasthal Site 2 observations carried over 37 nights yield a median seeing value of 1. 1. Devasthal Site 2 has therefore been selected for locating a modern 3 m optical telescope.

Leti?(/<) denote the associated Lie ring of an associative ring R with identity 1^0 under the Lie multiplication [x, y] = xv-vx with x, y e R. Further, suppose that the Lie ringi?(R) is solvable of length n. It has been proved that if 3 is invertible in R, then the ideal J of R generated by all elements [[[*,, jc2],[x3, x4]], xs], x¡, x2, x3, x4, x¡ e R, is nilpotent of index at most I (19 ■ 10"~3-1) for n > 3. Also, if 2 and 3 are both invertible in R, then the ideal I of R generated by all elements [x, y), x, y s R, is a nil ideal of R. Some applications to Lie solvable group rings are also given.

A complete characterization is given for the unit group U (F S 4 ) of the group algebra F S4 of the symmetric group S4 of degree 4 over a nite eld F .

No abstract

No abstract