Judul: Karakteristik Fermentasi Rumen Domba Garut yang Diberi Pakan dengan Suplementasi Minyak BSF(Black Soldier Fly) atau Sabun Ca-BSF.
Abstrak: Penelitian ini dilakukan untuk mengevaluasi karakteristik fermentasi rumen pada domba Garut yang diberi pakan dengan suplementasi minyak BSF atau sabun Ca-BSF. Ternak yang digunakan yaitu sebanyak 8 ekor domba Garut jantan dengan rata-rata bobot badan awal 29,08 ± 3,62 kg. Perlakuan yang diterapkan yaitu P1 penambahan minyak BSF dan P2 penambahan sabun kalsium BSF. Peubah yang diamati meliputi nilai pH, konsentrasi VFA total, konsentrasi amonia, populasi bakteri, dan populasi protozoa. Data dianalisis dengan uji T menggunakan SPSS 23. Hasil analisis menunjukkan nilai pH, konsentrasi amonia, dan populasi protozoa pada rumen tidak berbeda antara perlakuan. Konsentrasi VFA total P1 (85,38 mM) sangat nyata lebih rendah (P<0,01) daripada P2 (122,51 mM). Populasi bakteri total P1(4,89 log CFU ml-1) sangat nyata lebih rendah (P<0,01) daripada P2 (6,76 log CFU ml-1). Penambahan sabun Ca-BSF efektif meningkatkan kadar VFA dan populasi bakteri total dalam rumen. Kata Kunci: fermentasi rumen, minyak BSF, sabun Ca-BSF., This study was conducted to examine the characteristics of rumen fermentation in Garut sheep fed with suplements of BSF oil or BSF Ca-soap. Eight male Garut sheep with an average initial body weight of 29.08 ± 3.62 kg were used in this experiment. The treatments applied were P1 BSF oil suplementation and P2 BSF Ca-soap suplementation. The variables measured were pH value, total VFA concentration, ammonia concentration, total population of bacteria, and protozoa. Data were analyzed using T test with statistical program of SPSS 23. The results showed that the pH value, ammonia concentration, and protozoa population in the rumen did not differ between treatments. The total VFA concentration of P1 (85.38 mM) was significantly lower (P<0.01) than that of P2 (122.51 mM). Bacteria population of P1(4.89 log CFU ml-1) was significantly lower (P<0.01) than that of P2 (6.76 log CFU ml-1) . The addition of Ca-BSF soap was effective in increasing VFA consentration and total bacteri population in rumen Keywords: BSF oil, calcium soap BSF, rumen fermentation.
Keyword: fermentasi rumen, domba garut, sabun Ca-BSF, BSF oil, calcium soap BSF, rumen fermentation

Judul: Pengaruh Pemberian Minyak Black Soldier Fly (BSF) terhadap Fermentasi Rumen pada Domba Garut
Abstrak: Penelitian ini dilakukan untuk mengkaji pengaruh pemberian minyak black soldier fly terhadap fermentasi rumen pada domba Garut. Ternak yang digunakan yaitu sebanyak delapan ekor domba Garut jantan. Perlakuan yang diterapkan yaitu P0 (ransum tanpa minyak BSF, kontrol) dan P1(P0 + 4% minyak BSF). Peubah yang diamati meliputi nilai pH, konsentrasi VFA total, kadar amonia, populasi bakteri dan populasi protozoa. Data dianalisis dengan uji T menggunakan SPSS 23. Hasil menunjukkan bahwa nilai pH, kadar amonia, VFA, dan populasi protozoa pada rumen tidak berbeda nyata antara kedua perlakuan. Jumlah bakteri pada P0 (3,84 log CFU ml-1) nyata (P<0,05) lebih rendah dari P1 (4,85 log CFU ml-1). Dapat disimpulkan bahwa pemberian minyak BSF pada level 4% dalam pakan domba tidak memberikan efek negatif terhadap fermentasi rumen bahkan meningkatkan jumlah bakteri dalam rumen., This study was conducted to examine the effect of giving black soldier fly oil on rumen fermentation in Garut sheep. The animal used were eight male Garut sheep. The treatments applied were P0 (ration without BSF oil, control) and P1 (P0 + 4% BSF oil). The variables measured included pH value, total VFA concentration, ammonia value, bacterial population, and protozoa population. Data were analyzed by T test using SPSS 23 where the results showed that the values of pH, ammonia value, VFA, and the population of protozoa in the rumen were not significantly different between treatments. The total bacteria P0 (3.84 log CFU ml-1) was significantly lower (P<0,05) than P1 (4.85 log CFU ml-1). It can be concluded that the application of BSF oil at the level of 4% in sheep feed did not have a negative effect on rumen fermentation, but it increased total bacteria in the rumen.
Keyword: BSF oil, Garut Sheep, rumen fermentation

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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