Judul: Induksi Pembelahan Sporofitik pada Kultur Antera Kelapa Sawit (Elaeis guineensis Jacq.) dengan Perlakuan Cekaman Suhu dan Media Starvasi.
Abstrak: Haploid culture via androgenesis is a rapid technique to produce pure lines as parental candidates in producing superior hybrid varieties. This technique has not been reported successful in oil palm plant. Cold shock pretreatment followed by combination of starvation medium and temperature treatment, is expected to induce sporophytic division for androgenesis induction in oil palm. The flower buds of oil palm, used in this experiment were derived from the upper part of spikelet located at the middle part of the inflorescence with a half part of spatha was opened. The anthers from this buds contained population of microspores mostly in late uninucleate. Spikelet immersion pretreatment on starvation medium (B medium) in cold temperature (4-9°C) for 1 day then continued by culturing the anthers in double-layer Y3 medium, was able to induce sporophytic division of microspore with 4-5 cells as much as 0.9% after 2 weeks of culture. The percentage of multicellular microspores could be increased up to 2.1%, when after 1 day of pretreatment at cold temperature the anthers were cultured in double-layer B medium at 25-28°C for 7 days, then were subcultured in double-layer Y3 medium at 25-28°C for 1 week after culture. The results of this research could be used as the first step for induction of androgenesis in developing haploid technology in oil palm.
Keyword: oil palm, microspore, sporophytic, pretreatment, starvation

Judul: Viabilitas dan Perkembangan Mikrospora dalam Kultur Antera Kelapa Sawit (Elaeis guineensis Jacq.) dengan Perlakuan Suhu Rendah dan Konsentrasi Maltosa
Abstrak: Haploid technology through anther culture is an alternative means to accelerate genetic stability of crops. Development and application of this technology in oil palm (Elaeis guineensis Jacq.) will enhance the establishment of haploid and double haploid plants in only one generation. The objective of this study was to determine the effect of low temperature stress and carbon source of maltose concentration on the viability and development of microspore to induce sporophytic division in anther culture of oil palm in a double layer medium system. The treatment was a combination of incubation period of cold stress (4-9°C) and concentration of maltose as carbon source. Anthers used containing microspores mostly at late uninucleate phase (30-41%) and early binucleate (42-59%) were obtained from male flowers from half open spatha at middle spikelet position. Microspores cultured in all concentrations of maltose and low temperature stress in general continued to grow gametophyitically then gradually die. However, the viability of microspores on the medium with carbon source 20 g/l maltose and incubation period of low temperature stress for one day was approximately 52% at 5 weeks after culture. From this treatment, there was indications that the induction has been initiated shown by the finding of sporophytic division of microspores with two relatively symmetrical nuclei, although in a very low percentage.
Keyword: maltose, microspore, temperature, palm oil, Sporophytic division

Judul: Monotonicity Properties of Trapezoid Sum Sequence on Class of Nonconvex and Nonconcave Function
Abstrak: Bernhard Riemann mendefinisikan integral tentu sebagai luas daerah di bawah kurva dari suatu fungsi real taknegatif pada sebuah interval yang tertutup dan terbatas. Beberapa alternatif yang dapat digunakan untuk menghampiri luas tersebut adalah Darboux sums melalui penjumlahan beberapa luas persegi panjang dan trapezoid sum melalui penjumlahan luas trapesium. Trapezoid sum lebih baik dalam menghampiri nilai integral untuk fungsi-fungsi yang well-behaved daripada Darboux sums. Untuk fungsi f yang bernilai real dan kontinu pada interval [a,b], f terintegral Riemann jika dan hanya jika f terintegral Darboux. Pada tesis ini ditunjukkan bahwa f terintegral Riemann jika dan hanya jika f terintegral secara trapesium. Misalkan f adalah suatu fungsi bernilai real yang kontinu pada interval [a,b]. Untuk setiap partisi P_n yang membagi [a,b] menjadi n subinterval dengan jarak yang sama, dibentuk trapezoid sum T_n (f) yang merupakan jumlah luas n trapesium sebagai pendekatan dari nilai integral f pada [a,b]. Jika f adalah fungsi konveks maka barisan trapezoid sum {T_n (f)} bersifat monoton turun dan akan bersifat monoton naik jika f fungsi konkaf. Fokus tesis ini adalah sifat kemonotonan barisan {T_n (f)} untuk fungsi f yang nonkonkaf dan fungsi f yang nonkonveks. Pada tesis ini dibuktikan sifat monoton turun dari {T_n (f)} secara generik tidak terjadi pada kelas fungsi nonkonkaf f, serta secara generik, barisan itu juga tidak monoton naik pada kelas fungsi nonkonveks. Meskipun demikian, sifat generik mengakibatkan bahwa untuk sebarang fungsi f baik di kelas fungsi nonkonkaf maupun nonkonveks, terdapat fungsi g yang menghampiri f sedemikian sehingga ekor barisan {T_n (g)} bersifat monoton. Ditunjukkan pula bahwa himpunan fungsi naik nonkonkaf dengan {T_n (f)} yang tidak monoton turun dense terhadap kelas fungsi naik nonkonkaf f. Hal tersebut juga ditunjukkan untuk himpunan fungsi turun nonkonkaf terhadap kelas fungsi turun nonkonkaf. Lalu, dibuktikan bahwa himpunan fungsi naik nonkonveks dan himpunan fungsi turun nonkonveks dengan {T_n (f)} yang tidak monoton naik, berturut-turut dense terhadap kelas fungsi naik nonkonveks dan turun nonkonveks. Himpunan-himpunan yang dense tersebut mengartikan bahwa setiap fungsi f pada kelas-kelas tersebut, dapat dihampiri oleh suatu fungsi g yang bersesuaian dengan kelas-kelas tersebut sedemikiam sehingga barisan {T_n (g)} tidak monoton., Bernhard Riemann defined definite integral as an area under the curve of a real nonnegative function on a closed bounded interval. The alternatives that can be used to estimate the area are Darboux sum which is sum of rectangular areas and trapezoid sum which is sum of trapezium areas. Trapezoid sum is better than Darboux sum as approximations toward the integral of well-behaved functions. Let f be a real valued continuous function on interval [a,b], f is Riemann integrable if and only if it is Darboux integrable. In this master’s thesis, it showed that f is Riemann integrable if and only if it is trapezium integrable. Let f be a real valued continuous function on interval [a,b]. For each partition P_n that divides the interval [a,b] into n equal length subintervals, defined trapezoid sum T_n (f) which is the total of n trapezium areas as an approach of integral value f on [a,b]. If f is a convex function then the trapezoid sum sequence {T_n (f)} is decreasing
Keyword: monotonicity, nonconcave, nonconvex, trapezoid sum