896 resultados para Unique factorisation Rings
Resumo:
I have been asked by administration, how much of our collection could go into storage. They optimistically hoping for a room or two for faculty/staff offices, as some buildings need renovation or need to be closed due to safety issues. Clearly, much of the population believes that all/most library materials are available on-line – free. I will present the results of our survey’s of material held and available on-line and space “freed” thanks to archiving. How little space is freed.
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If R is a ring with identity, let N(R) denote the Jacobson radical of R. R is local if R/N(R) is an artinian simple ring and ∩N(R)i = 0. It is known that if R is complete in the N(R)-adic topology then R is equal to (B)n, the full n by n matrix ring over B where E/N(E) is a division ring. The main results of the thesis deal with the structure of such rings B. In fact we have the following.
If B is a complete local algebra over F where B/N(B) is a finite dimensional normal extension of F and N(B) is finitely generated as a left ideal by k elements, then there exist automorphisms gi,...,gk of B/N(B) over F such that B is a homomorphic image of B/N[[x1,…,xk;g1,…,gk]] the power series ring over B/N(B) in noncommuting indeterminates xi, where xib = gi(b)xi for all b ϵ B/N.
Another theorem generalizes this result to complete local rings which have suitable commutative subrings. As a corollary of this we have the following. Let B be a complete local ring with B/N(B) a finite field. If N(B) is finitely generated as a left ideal by k elements then there exist automorphisms g1,…,gk of a v-ring V such that B is a homomorphic image of V [[x1,…,xk;g1,…,gk]].
In both these results it is essential to know the structure of N(B) as a two sided module over a suitable subring of B.
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176 p.
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The characteristics of the cladding band structure of air-core photonic crystal fibers with silica rings in triangular lattice are investigated by using a standard plane wave method. The numerical results show that light can be localized in the air core by the photonic band gaps of the fiber. By increasing the air-filling fraction, the band gap edges of the low frequency photonic band gaps shift to shorter wavelength.. whereas the band gap width decreases linearly. In order to make a specified light fall in the low frequency band gaps of the fiber, the interplay of the silica ring spacing and the air-filling fraction is also analyzed. It shows that the silica ring spacing increases monotonously when the air-filling fraction is increased, and the spacing range increases exponentially. This type fiber might have potential in infrared light transmission. (c) 2006 Elsevier B.V. All rights reserved.
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The sagittal otoliths of Lates niloticus, Haplochromis obesus, and Oreochromis niloticus from Lake Victoria were examined for daily growth rings using scanning electron microscopy. In the three species the increments were clear and thick enough to allow future studies with light microscopy. The daily nature of the increments seems supported by the rhythmic growth that were found.
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A fish aggregating device made of aquatic weeds and grass (Phoom) is used in Loktak lake in the northeastern region of India. It has been used successfully in this very productive fishery for centuries. Today, the fishery itself is under pressure from overexploitation, soil erosion leading to siltation and a hydroelectric project that has blocked the migratory route of the fish that used the lake as a breeding ground.
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Bush park fishing / padal fishing is an indigenous fishing method widely employed in the Ashtamudi estuary of Kerala (south India). An artificial reef made from twigs and leaves of trees is planted in the shallow areas of the estuary. The aim is to harvest fish that find shelter in these structures for the purpose of feeding and breeding. Though the State Department of Fisheries has banned this method of fishing in the inland waters of Kerala, 400 padals are operating in this estuary. About 300 of them are anchored in the western parts of the estuary (west Kayal). Fish are harvested in the padals at monthly intervals almost round the year and this results in the destruction of a sizeable quantity of juveniles and sub-adults of the commercially important fishes, such as Pearl spot and mullets, from the estuary. These padals pose a major threat to the sustainability of the fishery resources of this estuary and, therefore, need to be phased out by providing alternative occupations for the fishermen who are dependant on the padals.