Judul: Effect of Addition of Probiotic Bacillus NP5 in  Biofloc System on Growth and Health Status of Catfish Juvenile Clarias sp.
Abstrak: Teknologi bioflok telah diketahui dapat menurunkan kadar amonia pada media pemeliharaan budidaya sistem intensif dan probiotik Bacillus NP5R telah diketahui dapat meningkatkan pertumbuhan dan tingkat kelangsungan hidup melalui peningkatan efisiensi pencernaan dan kesehatan ikan. Penelitian bertujuan mengevaluasi penambahan probiotik Bacillus NP5R pada sistem bioflok dalam meningkatkan kinerja pertumbuhan dan status kesehatan benih lele Clarias sp.. Penelitian menggunakan rancangan acak lengkap (RAL) dengan tiga perlakuan dan tiga ulangan, yaitu ikan dipelihara tanpa aplikasi bioflok dan penambahan probiotik Bacillus NP5R (K), ikan dipelihara dengan sistem bioflok (BF), dan ikan dipelihara dalam sistem bioflok dengan penambahan probiotik Bacillus NP5R (BFP). Larva lele dengan panjang rata-rata 0,83±0,00 cm dan bobot rata-rata 0,02±0,01 g dipelihara dengan padat tebar 300 ekor/akuarium selama 30 hari. Parameter yang diamati meliputi pertumbuhan panjang mutlak, laju pertumbuhan harian, rasio konversi pakan, koefisien keragaman, kelimpahan bakteri Bacillus NP5R , total eritrosit, total leukosit, kadar hemoglobin, kadar hematokrit, dan tingkat kelangsungan hidup. Hasil penelitian menunjukkan bahwa penambahan probiotik Bacillus NP5R dalam sistem bioflok dapat meningkatkan laju pertumbuhan 5%, tingkat kelangsungan hidup 15%, dan status kesehatan benih lele yang menunjukkan hasil terbaik dibandingkan perlakuan lainnya. Penerapan sistem bioflok dengan penambahan Bacillus NP5R diharapkan menjadi alternatif solusi untuk mengurangi limbah amonia pada budidaya ikan lele., Biofloc technology has been known to reduce ammonia levels in aquaculture’s intensive system maintenance media and the probiotic Bacillus NP5R has been known to increase growth and survival rates through improved digestive efficiency and fish health. This study aimed to evaluate the addition of probiotic Bacillus NP5R in the biofloc system in improving growth and health status of catfish juvenile Clarias sp.. This study used a complete randomized design (RAL) of three treatments and three replications, namely fish reared without biofloc system and without addition of probiotic Bacillus NP5R (K), fish reared in a biofloc system (BF), and fish reared in a biofloc system with the addition of probiotic Bacillus NP5R (BFP) within 30 days of treatment. The larvae that used had an average length of 0,83±0,00 cm and an average weight of 0,02±0,01 g with a stocking density of 300 individuals per aquarium. Parameters observed during the study included absolute length growth, daily growth rate, feed conversion ratio, coefficient of diversity, abundance of Bacillus NP5R bacteria, total erythrocytes, total leukocytes, hemoglobin levels, hematocrit levels, and survival rates. The results showed that the addition of the probiotic Bacillus NP5R in the biofloc system can increase the growth rate by 5%, survival rate by 15%, and the health status of catfish juvenile which showed the best results compared to other treatments. The application of the biofloc system with the addition of Bacillus NP5R is expected to be an alternative solution to reduce ammonia waste in catfish farming.
Keyword: Bacillus NP5R, biofloc, Clarias sp., growth, health status

Judul: Penambahan Probiotik dan Prebiotik Komersial pada Sistem Bioflok terhadap Status Kesehatan dan Kinerja Pertumbuhan Benih Ikan Lele (Clarias sp.)
Abstrak: Penambahan probiotik dan prebiotik pada sistem budidaya ikan diketahui dapat meningkatkan pertumbuhan, respons imun, serta menurunkan FCR. Penelitian ini bertujuan menganalisis pengaruh penambahan probiotik komersial dan prebiotik MOS pada sistem bioflok dalam meningkatkan status kesehatan dan kinerja pertumbuhan benih ikan lele (Clarias sp.). Penelitian menggunakan tiga perlakuan dan tiga ulangan, yaitu BF (ikan dipelihara dalam sistem bioflok), BFPro (ikan dipelihara dalam sistem bioflok dengan penambahan probiotik komersial 0,6 mL m-2 (tiga hari sekali), BFPre (ikan dipelihara dalam sistem bioflok dengan penambahan prebiotik MOS dengan dosis 0,6%). Larva lele dengan panjang rata-rata 0,85±0,03 cm dan bobot rata-rata 0,007±0,00 g dipelihara dengan padat tebar 2.500 ekor m-2 selama 21 hari. Parameter yang diamati yaitu kelimpahan bakteri total, eritrosit total, leukosit total, kadar hemoglobin, kadar hematokrit, laju pertumbuhan panjang mutlak, laju pertumbuhan panjang spesifik, laju pertumbuhan bobot mutlak, laju pertumbuhan bobot spesifik, rasio konversi pakan, koefisien keragaman, dan tingkat kelangsungan hidup. Penambahan probiotik komersial dan prebiotik MOS dalam sistem bioflok dapat meningkatkan kinerja pertumbuhan dan status kesehatan benih ikan lele. Hasil terbaik diperoleh pada perlakuan dengan penambahan probiotik komersial dengan nilai tingkat kelangsungan hidup mencapai 50%, serta gambaran darah yang lebih baik dibandingkan perlakuan lainnya., The addition of probiotics and prebiotics to fish farming systems is known to increase growth, immune response, and reduce feed conversion ratio (FCR). This research aims to analyze the effect of adding commercial probiotics and MOS prebiotics to the biofloc system in improving the health status and growth performance of catfish (Clarias sp.) juveniles. The research used three treatments and three replications, namely BF (fish reared in a biofloc system), BFPro (fish reared in a biofloc system with the addition of commercial probiotics 0.6 mL m-2 every three days), BFPre (fish reared in a biofloc system with the addition of prebiotic MOS at a dose of 0.6%). Catfish larvae with an average length of 0.85±0.03 cm and an average weight of 0.007±0.00 g were reared at a stocking density of 2,500 m-2 for 21 days. The parameters observed were total bacterial abundance, total erythrocytes, total leukocytes, hemoglobin content, hematocrit content, absolute length growth rate, specific length growth rate, absolute weight growth rate,specific weight growth rate, feed conversion ratio, diversity coefficient, and survival rate. The addition of commercial probiotics and MOS prebiotics in the biofloc system can improve the growth performance and health status of catfish seeds. The best results were obtained in the treatment with the addition of commercial probiotics with a survival rate of up to 50%, as well as a better blood picture compared to other treatments.
Keyword: biofloc, Clarias sp., growth, prebiotic, probiotic

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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