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 Concentrated Based on  RDP:RUP Balance at Different Energy Level: An In Vitro Study
Abstrak: Produktivitas ternak ruminansia yang efisien membutuhkan protein, tingkat energi dan rasio RDP:RUP dalam pakan yang seimbang. Pakan harus menyediakan nitrogen yang cukup (RDP) untuk pertumbuhan mikroba rumen, serta sebagai sumber protein langsung untuk hewan inang (RUP). Penelitian ini bertujuan untuk mengetahui tingkat optimal rasio RDP:RUP dan tingkat energi ransum sapi perah dengan metode in vitro. Sumber inokulum rumen diperoleh dari rumen fistulasi sapi Friesian Holstein. Perlakuan terdiri dari 4 level rasio RDP: RUP, yaitu 45:55, 50:50, 55:45 dan 60:40, sedangkan level energi terdiri dari level TDN 65%, 70% dan 75%. Rancangan percobaan adalah rancangan acak kelompok pola faktorial. Analisis data menggunakan uji ANOVA dan Duncan multiple range test. Hasil penelitian menunjukkan rasio RDP: RUP dan variasi TDN berpengaruh terhadap KCBK, KCBO, NH3. Kandungan TDN yang lebih tinggi meningkatkan KCBK, KCBO, dan VFA total secara signifikan. Peningkatan imbangan RDP (dari 45% hingga 60%) dan level TDN (low to high) meningkatkan kecernaan nutrisi, kadar VFA total, populasi bakteri dan protozoa. Peningkatan ini menunjukkan bahwa manfaat dari pakan yang berbasis imbangan RDP:RUP dapat meningkatkan produktivitas ternak ruminansia., Efficiency of ruminant productivity requires optimal protein, energy levels, and RDP:RUP ratios in feed. Dairy feed must provide adequate of nitrogen (RDP) for the rumen microbe, as well as a direct protein source for host animals (RUP). This study aimed to determine the optimal RDP:RUP ratio at different energy level of dairy cattle rations using in vitro method. The source of rumen inoculum was obtained from rumen fistulated Friesian Holstein cattle. The treatments consisted of two factors. The factors were 4 RDP:RUP ratios (60:40; 55:45; 50:50; 45:55) and 3 TDN levels (65%; 70%; 75%). The experimental design was a factorial randomized block design. Data were analysed using ANOVA and Duncan’s multiple range test. The result showed that the ratio of RDP:RUP and level TDN had effects on DMD, OMD, NH3. Increased RDP balance (from 45% to 60%) and TDN level (low to high) improve nutrient digestibility, total VFA, bacterial population and protozoa. This increase indicates that the benefits of based feed RDP:RUP balance can increase the productivity of ruminants.
Keyword: n vitro, rumen degradable protein, rumen fermentation, total digestible nutrient

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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