Judul: Ruminant responds fed forages which fertilized with sulfuric liquid
Abstrak: This research was aimed to utilize sulfuric nutrient which is contained in sulfuric liquid, so that it could k used by forages fed to ruminant animals. The first trial used complete randomized design in factorial 2 x 5 x 2. Factor A was manure in two levels 0 tonlha or 25 tonha. Factor 8 was sulfuric liquid in 5 level concentrations 0%, 25%, 50%, 75%, or 100%. Factor C was forage species (grassedlegumes) two species each. The grasses used were P. maximum cv. Riversdale and P. maximum cv. Gatton, while the legumes were Centrmema pubescens and Macroptilium afro9upureurn. The second trial (in vifm) used b k k randomized desrgn with factorial 2 x 5 x 2. As blodr there were three sheep as different inocutant host. The third trial to investigate the respond of ruminant fed forage silage with treated and untmated. This trial used 12 sheep. Data wre analyzed with t-test. The results of the first and the second trial, the combination of manure treatment 25 tonlha and the fertilization with sulfuric liquid 50% on P. maximum cv Riversdale and C. pubescens gave the optimal result for all variables. The treated silage (P. maximum cv. Riversdale + C. pusbescens) which fertitied with manure 25 tonlha and sulfuric liquid 50% gave the positii respond on sheep performance.
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Judul: Pengaruh Keseimbangan RDP/RUP dan Suplementasi Mineral  Sulfur dalam Ransum Sapi Perah Secara In Vitro
Abstrak: Rasio Rumen Degradable Protein (RDP) dan Rumen Undegradable Protein (RUP) yang ideal diperlukan untuk meningkatkan produktivitas sapi perah. Mineral dibutuhkan dalam jumlah yang relatif sedikit namun memiliki peran yang sangat penting dalam pakan ternak, salah satunya adalah mineral sulfur. Penelitian ini bertujuan mengetahui rasio RDP/RUP dan suplementasi sulfur dalam ransum sapi perah terhadap fermentabilitas dan kecernaan ransum menggunakan metode in vitro. Cairan rumen yang digunakan diperoleh dari fistula rumen Friesian Holstein (FH). Rancangan percobaan yang digunakan adalah Rancangan Acak Kelompok 4×3 pola Faktorial terdiri atas faktor pertama adalah rasio RDP/RUP (60:40, 55:45, 50:50, 45:55), yang kedua adalah faktor suplementasi sulfur ( 0%; 0,1%; 0,2%). Data dianalisis dengan analisis varians (ANOVA) dan uji Duncan. Hasil penelitian menunjukkan bahwa rasio RDP/RUP dan suplementasi mineral sulfur dengan kadar yang berbeda dapat mempengaruhi kecernaan nutrien, konsentrasi VFA total, konsentrasi amonia, populasi bakteri dan protozoa. Namun dari data yang diperoleh dapat disimpulkan bahwa rasio RDP/RUP 60:40 dengan level sulfur 0,2% menghasilkan fermentabilitas ransum tertinggi., An ideal ratio of Rumen Degradable Protein (RDP) and Rumen Undegradable Protein (RUP) is required to increase the productivity of dairy cattle. Minerals are needed in relatively small amounts but play an essential role in animal feed, one of which is sulfur minerals. The study aimed to determine RDP to RUP ratio together with sulfur supplementation in dairy cattle rations on fermentability and digestibility of the rations using in vitro method. The rumen fluid was obtained from ruminal fistula Friesian Holstein (FH). The experimental design used was a 4×3 Factorial Randomized Block Design consisting of the first factor was the RDP to RUP ratio (60:40, 55:45, 50:50, 45:55), the second was a factor the sulfur supplementation (0%; 0.1%; 0.2%). Data were analyzed by analysis of variance (ANOVA) and Duncan test. The results showed that different levels of the RDP/RUP ratio and sulfur mineral supplementation affected nutrient digestibility, total VFA concentration, ammonia concentrations, and bacterial and protozoa populations. Based on the data obtained, it can be concluded that the ratio RDP/RUP 60:40 with sulfur level 0.2% resulted in the highest diet utilization efficiency.
Keyword: in vitro, rumen degradable protein, sulfur

Judul: igenvalues and Eigenvectors of Tridiagonal Matrix with Non Constant and Recurrent Diagonal Entries.
Abstrak: Matriks tridiagonal adalah suatu matriks yang mempunyai entri-entri bernilai nol kecuali pada diagonal utama, di bawah diagonal utama (subdiagonal) dan di atas diagonal utama (superdiagonal). Entri pada diagonal utama tidak konstan dan berulang. Setiap entri pada matriks tridiagonal ini adalah bilangan kompleks. Dalam karya ilmiah ini, akan dibuktikan 3 teorema untuk menentukan nilai eigen dengan 2 kasus dan 1 teorema untuk menentukan vektor eigen. Teorema pertama menentukan polinomial karakteristik dari matriks tridiagonal. Polinomial karakteristik dari matriks tridiagonal tersebut digunakan untuk menentukan nilai eigen pada teorema kedua dan ketiga serta menentukan vektor eigen pada teorema keempat
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