Judul: Sifat Kemonotonan pada Darboux Sums
Abstrak: Darboux sums untuk fungsi di , - terbagi menjadi dua yaitu, upper Darboux sum dan lower Darboux sum. Untuk setiap partisi yang membagi interval , - menjadi subinterval dengan jarak yang sama, dibentuk suatu pendekatan dari nilai integral atau luas di bawah kurva yakni, upper Darboux sum ( ) yang mendekati dari atas kurva dan lower Darboux sum ( ) yang mendekati dari bawah kurva Tujuan penelitian ini adalah menunjukkan kemonotonan pada barisan { ( )} dan { ( )} tidak umum terjadi di , -. Setiap di , - dapat dihampiri oleh fungsi linear sesepenggal di , - sehingga barisan lower Darboux sum { ( )} dan upper Darboux sum { ( )} dari secara umum, berturut-turut tidak monoton turun dan naik. Tetapi, ekor barisan { ( )} dan { ( )} dari berturut-turut bersifat monoton turun dan naik. Kemudian, untuk kasus monoton naik di , -, sifat di atas juga berlaku untuk yang juga monoton naik. Demikian pula halnya bila monoton turun yang dihampiri oleh yang juga monoton turun.
Keyword: Darboux sums, kategori Baire, kemonotonan

Judul: Pemrograman semidefinit
Abstrak: Pemrograman Semidefinit adalah suatu cara mengoptimalkan suatu fungsi linear terhadap suatu batasan yang merupakan kombinasi linear dari matriks simetri semidefinit positif. Untuk suatu bilangan asli n didefinisikan himpunan S={ Anx A matriks simetri}. Pemrograman Semidefinit didefinisikan sebagai berikut: Minimumkan tr (CX) terhadap A(X) =B X 0, dengan X,CES, BES (mn), tr (.) menyatakan operator teras, dan A adalah operator linear. Dalam tulisan ini ditunjukkan bahwa S adalah ruang Hilbert. Kemudian ditunjukkan pula bahwa Pemrograman Semidefinit yang menggunakan operator linear A(X) = MXM, dengan M sebarang matriks berukuran mxn, mempunyai solusi optimal.
Keyword: 

Judul: Embryo rescue secara in vitro dan produksi bibit aren (Arenga pinnata (Wurmb) Merr.).
Abstrak: Sugar palm is a member of Arecaceae (palmaceae) originated from Indo- Malayan archipelago. Sugar palm may have important position as biofuel producing crop. Hence, research and development of sugar palm need to be done. Availability of planting material is one of significant constraints to develop sugar palm for cultivation and breeding program. The main constraints of planting material (sugar palm seedlings) in Indonesia are the seed dormancy and the use of physiologically mature seed as planting material. Embryo rescue technique can be applied as a breakthrough to obtain sugar palm seedlings in a relatively short time. The objectives of the experiment were to evaluate: 1) the effect of zygotic embryo age and basal medium composition on germination and development of rescued zygotic embryo of sugar palm, 2) the effect of pre-treatment and cytokinins and 3) the effect of PGR combination (auxin with or without cytokinin) in vitro embryo culture and seedlings production of sugar palm. In exp. 1, zygotic embryos isolated from immature and mature sugar palm fruit were cultured on Y3 or WPM medium without of plant growth regulators. In exp. 2. sub-unit 1, immature zygotic embryos with or without pre-treatment were cultured onto Y3 medium containing cytokinin in the form of coconut water (100, 150 and 200 ml/l) or BAP (5 ppm). In exp. 2. sub-unit 2, addition of NAA (1 or 5 ppm), kinetin (5 ppm), BAP (5 ppm), a combination of NAA (1 or 5 ppm)+kinetin (5 ppm), or NAA (1 or 5 ppm)+BAP (5 ppm) in Y3 medium for plantlet regeneration. The result showed that the viability and germination of immature zygotic embryo (92%) was better than the mature one (72%). On the other hand, the composition of the basal medium (Y3 or WPM) did not significantly affect embryo germination. Some of the culture zygotic embryo developed abnormal development of haustorium and cotyledonary petiole, at 32% and 26%, respectively. The percentage of planlets from zygotic embryo in this experiment range from 6%-25%. The results showed that cytokinin (coconut water or BAP) did not affect growth of the rescued zygotic embryo, whereas immature embryo with pretreatment led to the highest shoot and root formations, respectively. On the other hand, addition of PGR (auxin with or without cytokinin) showed positive effects on length of root from the zygotic embryos. A combination of NAA (5 ppm)+BAP (5 ppm) gave the highest number planlets. The plantlet of sugar palm were successfully regenerated from rescued embryos and transferred into soil.
Keyword: auxin, coconut water, cytokinin, embryo rescue and sugar palm