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: Reformulation of Dairy Cattle Ration Based on RDP/RUP Balance and Energy Adeqquacy: In Vitro Study
Abstrak: Rumen degradable protein (RDP) diperlukan untuk pertumbuhan mikroba yang optimal dan proses fermentasi, tetapi RDP harus diimbangi dengan energi. Penelitian ini bertujuan untuk mengetahui keseimbangan optimal antara RDP: RUP dan tingkat energi dalam ransum sapi perah dengan metode in vitro. Sumber inokulum rumen diambil dari dua fistula sapi perah Holstein Friesian. Perlakuan terdiri dari imbangan RDP: RUP yaitu 45:55, 50:50, 55:45 dan 60:40, dengan perlakuan TDN yaitu rendah, sedang dan tinggi. Rancangan penelitian menggunakan rancangan acak kelompok berpola faktorial. Data dianalisis menggunakan uji ANOVA, jika terdapat perbedaan berbeda nyata di uji lanjut dengan Duncan dan di uji lanjut dengan Tukey jika terdapat interaksi antar kedua faktor. Hasil penelitian menunjukkan bahwa peningkatan imbangan RDP:RUP dengan level TDN dapat meningkatkan konsentrasi NH3, konsentrasi VFA total, kecernaan bahan kering, kecernaan bahan organi. Ransum dengan imbangan RDP:RUP dengan level high TDN dapat meningkatkan kecernaan nutrisi. Peningkatan ditunjukkan dengan manfaat dari ransum yang berbasis imbangan RDP:RUP dapat meningkatkan kecernaan nutrisi dan fermentabilitas sapi perah. Kata kunci: degradasi protein, fermentasi dan kecernaan., Rumen degradable protein (RDP) is required for optimal microbial growth and fermentation process, however RDP requirement must be balanced with energy. This study aims to find out the optimal balance between RDP:RUP and energy levels in dairy rations by in vitro method. The source of the inoculum was taken from two Friesian Holstein male rumen fistulas. Treatments consisted of RDP:RUP balance which were 45:55, 50:50, 55:45 and 60:40, while TDN treatments were low TDN, medium TDN and high TDN. The experimental design used a randomized block design of factorial groups. The data was analyzed using ANOVA and Duncan's test if it differs markedly and Tukey test if there is interaction between the two factors. The results showed that ratio of RDP:RUP with TDN levels affected NH3, VFA’s, DMD and OMD. RDP:RUP balances with high TDN levels can improve nutritional digestability. The increase shown by the benefits of rations based on RDP:RUP balance can improve nutritional digestibility and fermentability of dairy cows. Keywords: degestibility, rumen degradable protein, rumen fermentation
Keyword: Degradasi protein, Fermentasi, Kecernaan

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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