Judul: Feed Formulation of Transition Dairy Cattle based on  Dietary Cation Anion Difference and NDF using Local Feed Ingredients.
Abstrak: Manipulasi pakan melalui perbedaan keseimbangan kation anion pada ternak ruminansia perlu dilakukan untuk memperbaiki kondisi fisiologis ternak yang akan melahirkan demi mencegah kekurangan mineral seperti milk fever. Kecernaan NDF (Neutral Detergent Fiber) merupakan salah satu faktor yang menentukan kualitas pakan ruminansia. Tujuan penelitian ini adalah membuat ransum sapi perah transisi dengan menggunakan program solver berbasis bahan baku pakan lokal dengan constraint berupa DCAD dan NDF. Metode penelitian yang digunakan yaitu inventarisasi bahan baku pakan lokal yang memiliki komposisi mineral sesuai rumus DCAD dan NDF, menghitung DCAD untuk semua bahan baku pakan, menyusun formula ransum sapi perah periode transisi menggunakan program solver. Data sekunder diperoleh dari berbagai literatur. Ransum yang diformulasikan yaitu ransum dengan menggunakan contraint DCAD dan tanpa menggunakan constraint DCAD. Hasil penelitian dianalisis secara deskriptif. Hasil penelitian, ransum 1 diperoleh nilai DCAD dan NDF yaitu 7.63mEqKg-1 dan 33%, sedangkan pada ransum 2 nilai DCAD dan NDF yang dihasilkan yaitu 24mEqKg-1 dan 33%. Ransum 1 menghasilkan penggunaan hijauan sebanyak 60%, sedangkan ransum 2 menghasilkan penggunaan hijauan sebanyak 50%. Hasil formulasi menunjukkan bahwa ransum dengan penambahan constraint DCAD menghasilkan harga yang lebih mahal dan penggunaan rasio hijauan yang lebih besar. Simpulan penelitian yaitu penambahan constraint DCAD dan NDF dalam formulasi ransum dengan menggunakan bahan baku lokal dapat diterapkan karena mampu menghasilkan ransum dengan keseimbangan nutrien yang lebih teliti, namun kekurangannya terjadi peningkatan biaya pakan dan penggunaan hijauan di dalam ransum. Kata kunci : DCAD, formulasi ransum, NDF, program solver, sapi perah, Feed manipulation through differences in anion cation balance in ruminants needs to be done to improve the physiological condition of cattle that will give birth in order to prevent mineral deficiencies such as milk fever. Digestibility of NDF (Neutral Detergent Fiber) is one of the factors that determine the quality of ruminant feed. The purpose of this study was to make transitional dairy cattle rations using a solver program based on local feed raw materials with limitations in the form of DCAD and NDF. The research method used is an inventory of local feed raw materials that have a mineral composition according to the DCAD and NDF formulas, calculating DCAD for all feed raw materials, compiling the transition period dairy cow ration formula using the solver program. Secondary data were obtained from various literatures. The formulated ration is a ration using DCAD constraint and without DCAD constraint. The research results were analyzed descriptively. The results showed that in ration 1 the DCAD and NDF values were 7.63mEqKg-1 and 33%, while in ration 2 the DCAD and NDF values were 24mEqKg-1 and 33%. Ration 1 resulted in 60% forage use, while Ration 2 resulted in 50% forage use. The results of the formulation show that the ration with the addition of the DCAD constraint results in a higher price and the use of a higher forage ratio. The conclusion of the study is that the addition of DCAD and NDF constraints in the formulation of rations using local raw materials can be applied because they are able to produce rations with a more precise balance of nutrients, but the drawback is that there
Keyword: dairy cattle, DCAD, feed formulation, NDF, Solver program

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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