GRUP QUARTENION

Konsep grup mulai dikenal setelah E. Galois, orang Perancis (1811-1832) yang dapat membuktikan suatu teori bahwa persamaan polinom dengan pangkat n > 5 tidak mungkin dapat diselesaikan dengan radikal, yang pembuktiannya memperkenalkan suatu grup permutasi tertentu. Pada perkembangannya teori grup banyak digunakan pada pengembangan geometri, analisis, dan topologi. Pada abad dua puluhan. Teori grup dipakai di berbagai bidang pada fisika seperti Kristalografi, Quantum Mekanik dan Teori Partikel. Salah satu bentuk grup yaitu grup quartenion Q dimana himpunan dan operasinya didefinisikan secara khusus yaitu : Q = {1, -1, i, -i. j, -j, k, -k} terhadap operasi V Tesis ini membahas tentang grup quartenion Q dimana himpunan dan operasinya didefiniskan secara khusus. Pada grup ini yang dicari adalah order dari unsur Q, sub grup dari Q, center dari Q, centraliser dari suatu unsur dalam Q, sub grup siklik dari Q, koset, sub grup normal dari Q, grup faktor, homomorphisma dan isomorphisma. Hasil pembahasan grup quartenion ini adalah elemen-elemennya mempunyai order 1, 2, 4, sub grup yaitu : H0, H,, H2. H3, H4, H5, center {1, -1}, centralizer setiap unsurnya H0, H|, H2, H3, sub grup siklik H,, H2, H3, koset kiri dengan koset kanan sama, semua sub grupnya merupakan sub grup normal, mempunyai grup faktor yaitu : { H„ * H2}, {H2, i * H2}, {H3, i * H3}. {R,, ' * H* j * H4, k * H4 }, { Ho }, dan terdapat pemetaan homomorphisma dari Q ke H-i dan H5 serta pemetaan isomorphisma dari Q ke H0

When is the multiaffine image of a cube a convex polygon?

We give two simple sufficient conditions under which the multiaffine image in the complex plane of an m-dimensional cube is a convex polygon. A third condition which, in some generic sense, is necessary and sufficient is then obtained. Our conditions involve checking the locations of the image of the vertices of the cube. These results help determine whether a parameterized family of polynomials th stable. © 1993.link_to_subscribed_fulltex

Fertilizing Ability of Post-Thaw of Epididymal Spermatozoa Stored for 48 H at 4derajat C Prior Cryopreservation in Domestic Cat

Many mammalian species, including felids species, are threatened or endangered. As with all animals, species within felidae provide a larger benefit to the ecosystem and to humans while pursuing their own individual purpose of survival, maintenance, and reproduction. To prevent further extinction, it is appears to be justified to bring modern reproductive techniques to assist reproduction and conservation of the genetic resources of species threatened by extinction. Much progress has been made during the last decade towards developing assisted reproductive technologies for use in captive breeding programmes for conserving or enhancing the genetic diversity of threatened and endangered felids [1,2]. Since a limited number of endangered felid female and male gametes are available, the domestic cat has served as a convenient research model species for endangered felids [3]. It has been reported that spermatozoa collected from epididymides stored at 4 C'for a few days can maintain their motility (pig [4]; horse and shika deer [5]) and that they can be frozen and retain the ability to fertilize oocytes in vitro (pig [4]; monkey [6]). Post-mortem spermatozoa recovery is an important technique for obtaining germplasm reserves from genetically valuable animals or endangered species. However, there are many factors that influence the outcome of this technique. In this research, we studied whether spermatozoa within epididymides stored at 4 °C remain their motility and are able to penetrate the feline oocytes in vitro