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: Commercial Probiotic Supplementation on Biofloc System and Its Effects on Growth Performance and Health Status of Catfish (Clarias sp.) Fry
Abstrak: Teknologi bioflok diketahui dapat meningkatkan produktivitas budidaya dan probiotik Bacillus sp. dapat meningkatkan respons imun, menurunkan FCR, serta meningkatkan kualitas air budidaya ikan lele. Penelitian ini bertujuan mengevaluasi pengaruh suplementasi probiotik komersial pada sistem bioflok dalam meningkatkan kinerja pertumbuhan dan status kesehatan benih ikan lele (Clarias sp.). Penelitian menggunakan rancangan acak lengkap (RAL) dengan tiga perlakuan dan dua ulangan, yaitu ikan dipelihara tanpa aplikasi bioflok dan penambahan probiotik komersial (K), ikan dipelihara dengan aplikasi bioflok (BF), serta ikan dipelihara dengan aplikasi bioflok dan penambahan probiotik komersial 0,6 mL m-2 tiga hari sekali. Ikan lele yang digunakan memiliki panjang rata-rata 0,86±0,03 cm dan bobot rata-rata 0,0069±0,00 g dipelihara dengan padat tebar 2.500 ekor m-2 selama 21 hari. Parameter yang diamati yaitu laju pertumbuhan panjang harian, laju pertumbuhan bobot harian, relative percent survival, koefisien keragaman, rasio konversi pakan, kelimpahan bakteri total, eritrosit total, leukosit total, kadar hemoglobin, dan kadar hematokrit. Penambahan probiotik komersial dalam sistem bioflok mampu meningkatkan kinerja pertumbuhan dan status kesehatan benih ikan lele, ditunjukkan oleh nilai relative percent survival mencapai 52,35%, serta nilai gambaran darah yang lebih baik dibandingkan dengan dua perlakuan lainnya. Penambahan probiotik komersial pada sistem bioflok dapat diterapkan untuk meningkatkan produktivitas dan status kesehatan ikan lele., Biofloc technology is known to enhance aquaculture productivity, and the probiotic Bacillus sp. can improve immune response, reduce feed conversion ratio (FCR), and enhance water quality in catfish farming. This study aimed to evaluate the influence of commercial probiotic supplementation in a biofloc system on the growth performance and health status of catfish (Clarias sp.) juveniles. The study employed a completely randomized design (CRD) with three treatments and two replications: fish reared without biofloc and commercial probiotic supplementation (K), fish reared with biofloc application (BF), and fish reared with biofloc application and commercial probiotic supplementation at a rate of 0,6 mL m-2 every three days. The catfish used had an average length of 0,86±0,03 cm and an average weight of 0,0069±0,00 g, with a stocking density of 2.500 individuals m-2 for a duration of 21 days. The parameters observed were daily length growth rate, daily weight growth rate, relative percent survival, coefficient of variation, feed conversion ratio, total bacterial abundance, total erythrocytes, total leukocytes, hemoglobin level, and hematocrit level. The addition of commercial probiotics in the biofloc system improved the growth performance and health status of catfish juveniles, as indicated by a relative percent survival value of 52,35% and better blood profiles compared to the other two treatments. The addition of commercial probiotics in the biofloc system can be implemented to enhance the productivity and health status of catfish.
Keyword: biofloc, Clarias sp., growth, health status, 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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