Judul: Masalah spektrum matrik simetri taknegatif
Abstrak: Karya ilmiah ini membahas tentang syarat cukup bagi pasangan bilangan real sehingga himpunan bilangan real tersebut menjadi spektrum dari suatu matriks simetri taknegatif berukuran nxn. Sistematika penulisan karya ilmiah ini adalah sebagai berikut. Pada bab dua diberikan landasan teori sebagai dasar analisis masalah. Pada bab tiga diberikan deskripsi mengenai syarat cukup bagi pasangan bilangan real sehingga himpunan bilangan real tersebut menjadi spektrum dari suatu matriks taknegatif berukuran nxn. Pada bab empat akan ditunjukkan bahwa syarat cukup pada bab tiga juga merupakan syarat cukup bagi pasangan bilangan real sehingga himpunan bilangan real tersebut menjadi spektrum dari suatu matriks simetri taknegatif berukuran nxn...
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Judul: Nilai Eigen, Spektral Norm, dan Determinan dari Matriks Circulant dengan Entri Bilangan Generalized.
Abstrak: Pada karya ilmiah ini akan dibahas tentang matriks circulant yaitu matriks yang memiliki urutan bilangan sesuai dengan baris pertama. Matriks circulant memiliki nilai eigen, spektral norm, dan determinan. Karya ilmiah ini bertujuan mengkaji secara teoritis tentang mencari nilai eigen, spektral norm, dan determinan dari matriks circulant. Dari hasil pembuktian diperoleh bahwa spektral norm adalah nilai maximum dari nilai eigen. Sedangkan determinan dipengaruhi oleh perkalian nilai eigen pada matriks circulant. Selanjutntya diberikan contoh – contoh aplikasi dengan entri bilangan Generalized Tribonacci dan Generalized Pell untuk menunjukkan bahwa teorema berlaku.
Keyword: Bilangan Generalized Tribonacci, Bilangan Generalized Pell contoh aplikasi, determinan, matriks circulant, nilai eigen, spektral norm

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