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: Xylooligosaccharide production of corncobs as prebiotic candidate by high temperature heating and enzymatic hydrolysis.
Abstrak: Corncob waste is a rich xylan source that can be utilized as raw material for xylooligosaccharides (XOS) production. XOS is a potential prebiotic and has high economic value. Two corn varieties i.e. Bisi and Pioneer were first analyzed for its hemicellulose, cellulose and lignin contents and xylan yield to choose the corn variety to be studied. Process technology for XOS production was studied using available equipment such as oven. Xylooligosaccharide (XOS) from corncob was produced in two stages i.e. xylan extraction by heating at high temperatures in oven or autoclave as comparison, followed by enzymatic hydrolysis. Analysis of two corncob varieties showed that Pioneer variety contained higher hemicellulose content (34.98%) and xylan yield (18.32%) than Bisi variety (12.28% and 10.22%, respectively), therefore Pioneer variety was chosen as raw material for XOS production. Corncob particles were soaked in dilute acid (1 g/l H2SO4) for 12 h at 60 oC, filtered and washed with tap water and then heated in oven or autoclave. Before oven heating, The corncobs were added with water at various ratios (1:1 – 1:5) and then heated in oven at various temperature (130 oC, 140 oC, 150 oC for 0.5 h) and autoclave at 121oC for 0.5, 1, 1.5 and 2 h with one and two heating cycles. During heating, the total sugar and reducing sugar were increase, while the degree of polymerization was decrease. The results showed that heating in oven to extract the xylan was affected by the ratios of corncobs and aquadest and heating temperatures. Oven heating (130-150 oC) with optimum ratio of corncobs and aquadest (1:3) successfully increased the xylan content from 3.98% up to 18.21 – 19.46% while repeated heating cycle (two cycles) did not affect the xylan content. Heating the corncobs with aquadest (at the ratio of 1:3) in oven at 130 oC for 0.5 h produced 18.98% xylan and enzymatic conversion of the xylan by xylanase significantly increased the XOS content from 19.60% up to 44.06%. Heating the corncobs in autoclave (121 oC, 0.5 h) followed by enzymatic conversion produced higher XOS content (65.67%). The corncob XOS could stimulate the growth of Lactobacillus plantarum kik and Bifidobacterium longum ATCC 15707 by 1.2 until 1.7 unit log, indicating the prebiotic properties. Cookies prebiotic produced by addition of 5% (based on wheat flour) had higher hardness texture (1256 gf) than control without XOS (1067 gf).
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