Judul: Modifikasi Biohidrogenasi Rumen dan Suplementasi Asam Lemak Tidak Jenuh untuk Meningkatkan Asam Linoleat Terkonjugasi dalam Susu
Abstrak: Recently, people have become increasingly aware of their health by consuming bioactive compounds such as Conjugated Linoleic Acid (CLA) found in CLA-rich milk. Various factors, such as the type of feed, environmental conditions, fatty acid content, and biohydrogenation processes in the rumen, influence the synthesis of CLA in milk. To date, there has been limited research on optimizing feed selection, environmental conditions, fatty acid (FA) content in the feed, and protection against biohydrogenation in the rumen to produce CLA-rich milk. In general, this research aims to produce CLA-rich milk through a series of studies with specific objectives: (1) Selecting the type of forage, its environmental origin, and in vitro fermentation biohydrogenation processes that have the potential to provide precursors and the best conditions for CLA synthesis, (2) Choosing the supplementation of high unsaturated fatty acid (UFA) oils and their inclusion levels in the diet that do not disrupt rumen fermentation and digestion, and (3) Testing the diet with the best forage type and protected oil supplements to achieve the highest milk production and CLA content. This research's first phase was to select the type of grass, its origin, and harvest age that contains the best FAs for healthy milk fat synthesis. Forage was the primary and most cost-effective source of FAs, including CLA, which influences milk FAs. The first phase of the research aims to analyze fermentation, digestibility, biohydrogenation, nutritional composition, and FAs of diets consisting of elephant grass (EG) and king grass (KG). The forage was obtained from highland (Pangalengan Regency) and lowland (Dramaga Regency) areas, with three different harvest ages (1, 1.5, and 2 months). The diets were then analyzed for their nutrition and FAs. In vitro research was conducted to analyze in vitro fermentation, biohydrogenation, and digestibility. The treatments showed significant differences in NH3 levels, ranging from 5.31 to 8.86 mM. The highest NH3 levels were found in diets containing highland EG harvested at 1.5 months. Dry matter digestibility (DMD) values ranged from 58.27 – 64.39 %, and organic matter digestibility (OMD) values ranged from 61.07 – 67.18 %. Different digestibility values were found for different harvest ages, with an interaction between elevation and harvest age. This aligns with the content of cellulose, neutral detergent fiber (NDF), and lignin in the grass. The highest digestibility was found in EG at 1.5 months. Diets containing KG significantly produced higher C18:0 and trans C18:1 than diets containing EG. The lower content of C18:0 and trans C18:1 in EG diets was likely due to partial biohydrogenation processes. Inhibition of the biohydrogenation process was suspected to be caused by the phenolic content in EG grass. Thus, it can be concluded that highland EG at 1.5 months was a potential diet to support healthier FA production in milk. The study's second stage was to choose the high UFA oil supplementation used. High UFA supplementation oil is believed to improve milk FA, including CLA. The study aimed to analyze the effect of oil high in UFA supplementation on the fermentation and digestibility of the ration. The ration contains 40 % EG and 60 % commercial
Keyword: biohydrogenation products, calcium soap, digestibility, fatty acid, lemuru oil

Judul: Effect of Vegetable Oils Supplementation in Dairy Cow Ration
on Rumen Fermentation and In Vitro Digestibility.
Abstrak: Pemberian suplemen minyak nabati kaya asam lemak tidak jenuh dalam ransum sapi perah memiliki banyak fungsi, salah satunya meningkatkan kualitas susu khususnya kandungan CLA (Conjugated Linoleic Acid). Minyak kanola dan minyak kedelai mengandung lebih banyak asam lemak tidak jenuh namun ketersediaannya tidak sebanyak minyak sawit yang cukup mudah dijumpai di Indonesia. Suplementasi minyak dalam ransum sapi perah dapat menyebabkan dampak negatif karena gangguan proses fermentasi dalam rumen. Suplementasi lemak yang tepat diperlukan untuk menghasilkan manfaat yang diinginkan. Penelitian ini bertujuan mencari jenis minyak dan taraf suplementasi terbaik yang tidak mengganggu proses fermentasi rumen dan kecernaan in vitro. Faktor yang diuji pada penelitian ini adalah Jenis Minyak (M) yang terdiri dari M1 = minyak kanola, M2 = minyak kedelai, M3 = minyak sawit dan faktor taraf penggunaan minyak (T) yang terdiri dari T0 – T3 berturut-turut 0%, 1%, 2%, dan 3% suplementasi dalam ransum. Ransum yang digunakan terdiri dari rumput gajah, konsentrat dan ampas tahu dengan imbangan BK 58.28 : 33.62 : 8.10 dengan kandungan TDN 57.17%, PK 12.03%, lemak 2.54%, SK 22.47%, Ca 0.667% dan P 0.481% . Pengujian dilakukan secara in vitro. Peubah yang diamati diantaranya pH, NH3, VFA, KCBK, KCBO, KNDF dan KADF. Penelitian ini menggunakan rancangan acak kelompok faktorial dengan cairan rumen yang berbeda sebagai kelompok. Data yang diperoleh dianalisis ragam dan dilanjutkan dengan uji lanjut Tukey. Hasil penelitian menunjukkan bahwa jenis minyak tidak berpengaruh nyata terhadap fermentabilitas dan kecernaan ransum, namun taraf pemberian menurunkan parameter fermentabilitas protein dan kecernaan BK, BO, NDF dan ADF. Tidak terdapat interaksi antara jenis minyak dan taraf pemberian. Suplementasi minyak hingga taraf 1% menghasilkan kecernaan BK dan BO yang tidak berbeda nyata dibandingkan tanpa suplementasi. Dari penelitian ini disimpulkan bahwa suplementasi minyak hanya dapat dilakukan hingga 1%.
Keyword: canola oil, CLA, diet, level, soybean oil

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
Keyword: