Judul: Aspek Komputasi Solusi Residu Kuadratik
Abstrak: Dalam menentukan apakah suatu kongruensi x2 º a (mod p) dengan a bilangan bulat dan p bilangan prima mempunyai solusi atau tidak dapat digunakan Kriteria Euler. Jika ( 1) / 2 ( ) 1 mod p a p - º maka x2 º a (mod p) mempunyai solusi. Jika x2 º a (mod p) mempunyai solusi, maka untuk mementukan solusinya dapat digunakan Algoritma RESSOL (Residue Solver). Algoritma RESSOL adalah algoritma acak (randomized algorithm) dan bukan algoritma deterministic, tetapi prosedur perhitungannya lebih praktis dan cepat. Algoritma RESSOL hanya dapat digunakan untuk mencari solusi dari x2 º a (mod p) dengan p prima ganjil. Tetapi dari Algoritma RESSOL tersebut dapat dikembangkan menjadi beberapa algoritma untuk mencari solusi dari x2 º a(mod pq) dengan p dan q prima ganjil, dan 2 (mod ) j x º a p dengan p prima ganjil dan bilangan bulat j ³ 2 .
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Judul: Kuadrat Di Z/mz
Abstrak: Misal a, m E Z, (a, m) = I, m > 3. Masalah menentukan apakah kongruensi x2= a(mod m) terselesaikan (memiliki solusi) atau tidak adalah masalah masalah klasik yang cukup terkenal dalam teori bilangan. Masalah ini dapat diselesaikan dengan apa yang disebut hukum kebalikan kuadrat (quadratic reciprocity law) yang mengatakan bahwa kongruensi x2=p(mod q) dan x2 = q(mod p) keduanya terselesaikan atau keduanya tidak terselesaikan jika dan hanya jika satu dari p atau q kongruen 1 modulo 4. Inti utama dari tulisan ini adalah membuktikan hukum kebalikan kuadrat (HKK) dan menggunakannya untuk menentukan keterselesaian dari kongruensi x2 = a(mod m). Hingga saat ini telah diketahui 193 bukti yang berbeda untuk HKK dan sebahagian besar dari bukti-bukti itu menggunakan apa yang disebut dengan Lemma Gauss. Dalam tulisan, HKK juga dibuktikan dengan menggunakan Lemma Gauss; perbedaannya terletak pada metode-metode yang digunakan untuk membuktikan Lemma Gauss itu sendiri.
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Judul: Biology and ecology of the buffalo fly, haematobia exigua de meijere (diptera:muscidae)
Abstrak: The life history of the buffalo fly was observed at room temperature of 27°-29.5°C and at a relative humidity of 48-68 percent. The eggs hatched after 17-22 hours, with an average of 18 hours. First instar larvae measured 1.25 + 0.16 mm long and 0.27 + 0.037 mm wide. reach the second larval stage. It took 6-12 hours to the second instar larvae measured 2.676 +0.187 mm long and 0.353 +0.028 mm wide. The second instar took about 12-24 hours to reach the third larval stage. The third instar measured 6.833 + 0.189 mm long and 0.919 + 0.051 mm wide. It took about 2-3 days for the third instar to become pupae. Duration of the pupal stage was about 5-7 days before the adults emerged. Under laboratory condition, the buffalo fly completed its life cycle in 9.5 to 10.5 days, whereas under field condition it took 9-14 days with an average of 10.5 days. The growth ratio which was based on the measurements of the cephalo-pharyngeal skeleton of each instar was 1.797. The preoviposition period was 8-12 days and mating usually occurred on the 6th or 7th day. The longevity of the male was 29 days, whereas it was 32 days in the female. The range of egg production under laboratory condition was between 20-139 per female fly. The belly and hind legs of the carabao were the most preferred habitat either during cloudy and cool dry or shiny and warm day. When the weather was clear and the carabao was in the shade, the flies tended to be more distributed particularly on the shoulder, dewlap, back and horns. The carabaos had relatively fewer Musca sp. and Stomoxys calcitrans than cattle; never the less carabaos had a higher infestation of buffalo fly than cattle. Oviposition occured either during the day or night but the buffalo flies were more active during the night than in the day time. The effect of various lengths of exposure time of manure in relation to the oviposition was profound. observed, the maximum number of the buffalo flies was occurred when the dung was exposed for 30 minutes. With increasing time of exposure the number and variety of insects also increase. It was evident that Sepsidae and psychodidae were the most dominant insects emerging from the dung. The number of buffalo flies also increased with increasing
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