Judul: Super Edge Magic Strength Pada Graf Fire Crackers Dan Graf Banana Trees
Abstrak: Karya ilmiah ini menjelaskan pembuktian teorema-teorema yang menyatakan bahwa graf Fire Crackers dan graf Banana Trees memiliki super edge magic strength. Suatu graf disebut super edge magic jika terdapat pemetaan satu-satu dari himpunan verteks ke himpunan bilangan bulat , dengan adalah banyaknya verteks dan pemetaan satu-satu dari himpunan edge ke himpunan bilangan bulat dengan adalah banyaknya edge sedemikian sehingga untuk setiap edge pada graf, jumlah label edge dan verteks yang incident dengan edge tersebut memiliki nilai yang sama dan disebut konstanta magic. Super edge magic strength adalah nilai minimum dari konstanta magic yang diperoleh dari semua pelabelan super edge magic pada graf tersebut.
Keyword: graf Banana Trees, graf Fire Crackers, konstanta magic, super edge magic

Judul: Pelabelan Super Edge Magic pada Graf Banana Tree 𝐵𝑇(𝑛1, 𝑛2, … , 𝑛𝑘 ), 𝑚𝐵𝑇(𝑛, 𝑛), dan 2𝐵𝑇(𝑛1, 𝑛2, … , 𝑛𝑘 )
Abstrak: Pelabelan super edge magic pada suatu graf dengan banyaknya verteks �������� dan banyaknya sisi �������� adalah fungsi bijektif dari himpunan verteks yang dipasangkan ke himpunan bilangan bulat terurut dimulai dari 1 sampai �������� , sedemikian sehingga himpunan bilangan dari penjumlahan label dua verteks yang adjacent terdiri dari �������� bilangan asli yang berurutan dan diperoleh nilai minimum dari himpunan tersebut yang dinotasikan dengan ��������. Nilai penjumlahan dari ��������, ��������, dan �������� akan sama dengan ℎ, dengan ℎ adalah konstanta magic. Karya ilmiah ini menunjukkan bahwa graf Banana Tree ����������������(��������1, ��������2, … , ���������������� ), ������������������������(��������, ��������), dan 2����������������(��������1, ��������2, … , ���������������� ) memiliki pelabelan super edge magic.
Keyword: Graf Banana Tree, pelabelan super edge magic

Judul: Extracellular Expression of thermostable Geobacillus stearothermophilus T1.2RQ Lipase for Biodiesel Production
Abstrak: The extracellular expression of enzymes in an excellent secretion host such as Bacillus subtilis is a useful strategy for making enzymes of industrial significance more affordable by lowering the cost of its downstream processing. Lipases are a category of hydrolases that catalyze the hydrolysis of triglycerides to glycerol and free fatty acids. Also, lipases catalyze the hydrolysis and transesterification of other esters as well as the synthesis of esters. They can perform very specific biotransformation reactions and are widely used in food, organic synthesis, detergents, cosmetic, and pharmaceutical industries. Geobacillus stearothermophilus T1.2RQ lipase is an industrially-desired thermostable lipolytic enzyme with an excellent hydrolytic and transesterification activity. This study aimed to express T1.2RQ lipase, in B. subtilis WB800 and ensure its secretion into the extracellular medium. Three signal peptides (AmyQ, Epr, LipA) and two promoters (Pgrac01 and Pgrac100) were used in the secretory-expression of T1.2RQ lipase, based on five constructed expression vectors constructed by restriction cloning and PCR mutagenesis. Sangers sequencing was used to verify constructs to ensure they are in the correct reading frame. Recombinants vectors, pHT43 (plasmid control), pHT43-T1.2RQ, pHT43- T1.2RQ_AmyQ, pHT43-T1.2RQ_Epr, and pHT43-T1.2RQ_LipA, were transformed by electroporation into Bacillus subtilis WB800. The electroporation was successful with the optimum condition of 2500V, 200 ohms, 25µF, and 5milliseconds. Recombinant B. subtilis pHT43 (negative control) and pHT43-T1.2RQlip + signal peptides were streaked on the lipidic agar, LA+TBN. All four recombinants, including the negative control (B. subtilis WB800-pHT43), produced clear zones on the TBN agar plate after overnight incubation (fig 2), indicating the presence of a lipolytic enzyme in all of the recombinant B. subtilis cells. pHT43-T1.2RQlip + signal peptides (AmyQ, Epr, and LipA) have clear zones with significantly higher diameters than B. subtilis WB800-pHT43 (negative control). This phenomenon suggests that the recombinant thermostable lipase T1.2RQ introduced into these cells was successfully expressed, thereby increasing the lipolytic capability of its host cells T1.2RQ lipase was expressed in 50ml terrific broth medium (TB) and the expression induced with 1mM IPTG. Lipase activity assay using p-nitrophenyl esters showed that all three signal peptides directed the secretion of T1.2RQ lipase into the extracellular medium. Signal peptide, LipA, resulted in the highest extracellular activity of 5.6 U/mL, which corresponds to a 6-fold increase over the parent B. subtilis WB800 strain. Meanwhile, signal peptides, AmyQ and Epr produced 4.2 U/mL and 3.4 U/mL activity respectively. SDS-Zymogram analysis confirmed that T1.2RQ lipase was correctly processed and secreted in its original size of 44 kDa. An attempt to further increase lipase expression level by promoter optimization showed that, contrary to expectation, promoter Pgrac100 exhibited similar expression levels as the original Pgrac01. Nevertheless, the demonstration of the successful secretion of T1.2RQ lipase in this work confirms the latter as a promising approach for the industrial production of the enzyme
Keyword: Bacillus subtilis, Expression, Extracellular, Heterologous, Lipase, Thermostable