Judul: Isoterm Adsorpsi pada Filter Karbon Aktif dengan Pengaruh Model Multimedia Filter pada Recirculating Aquaculture System (RAS)
Abstrak: Teknik pengolahan air yang dapat digunakan untuk menghasilkan kualitas air yang baik bagi budidaya ikan koi salah satunya adalah dengan penerapan Recirculating Aquaculture System (RAS). Penelitian ini bertujuan untuk menganalisis kesesuaian adsorpsi dari multimedia filter dan karbon aktif yang digunakan dengan model isoterm adsorpsi. Penelitian dilakukan dengan mengukur konsentrasi parameter amonia, nitrit, TSS, alkalinitas, suhu, pH, dan DO pada kualitas air dengan menerapkan beberapa variasi pada ketebalan dan debit multimedia filter. Variasi debit yang digunakan antara lain 45 L/menit dan 22,5 L/menit, serta variasi ketebalan media zeolite yang digunakan antara lain 30 cm, 60 cm, dan 90 cm. Kemudian melakukan analisis isoterm adsorpsi dengan menggunakan model isoterm adsorpsi langmuir, freundlich, temkin, halsey, dan khan. Kualitas air influen dan efluen pada unit filter karbon aktif menunjukan penurunan konsentrasi amonia, nitrit, dan TSS. Dari beberapa variasi yang digunakan, variasi ke-5 (ketebalan zeolite 90 cm dan debi 45 L/menit) merupakan variasi yang terbaik. Model isoterm adsorpsi khan merupakan model yang paling sesuai dikarenakan memiliki tingkat kesesuaian regresi yang paling tinggi., One of the water treatment techniques that can be used to produce good water quality for koi fish farming is the application of the Recirculating Aquaculture System (RAS). This study aims to analyze the adsorption suitability of the multimedia filter and activated carbon used with the adsorption isotherm model. The research was conducted by measuring the concentration of ammonia, nitrite, TSS, alkalinity, temperature, pH, and DO parameters on water quality by applying several variations on the thickness and discharge of the multimedia filter. Variations in the discharge used included 45 L/min and 22.5 L/min, and variations in the thickness of the zeolite media used were 30 cm, 60 cm, and 90 cm. Then analyze the adsorption isotherm using the Langmuir, Freundlich, Temkin, Halsey, and Khan adsorption isotherm models. The quality of the influent and effluent water in the activated carbon filter unit showed a decrease in the concentration of ammonia, nitrite, and TSS. Of the several variations used, the fifth variation (zeolite thickness 90 cm and debi 45 L/min) is the best variation. Khan adsorption isotherm model is the most suitable model because it has the highest level of regression suitability.
Keyword: Budidaya, karbon aktif, RAS, variasi

Judul: Optimization of Effluent Water Quality in Recirculating Aquaculture System Based on Variations in Pre-Treatment Configurations of Nanofiltration Membrane Technology
Abstrak: Teknologi membran nanofiltrasi (NF) yang diterapkan pada sistem resirkulasi akuakultur (RAS) memiliki kekurangan berupa terjadinya fouling. Fouling dapat direduksi dengan adanya unit pra-pengolahan seperti unit filter multimedia (FMM) serta filter karbon aktif (FK). Oleh karena itu, penelitian ini dilakukan pengaturan konfigurasi pada RAS menggunakan FMM, FK, dan membran NF90-4040 agar diketahuinya pengaturan sistem pengolahan terbaik dalam mereduksi kontaminan pada air limbah akuakultur. V1 (FMM-FK-NF) merupakan konfigurasi dengan nilai total efisiensi tertinggi dalam menurunkan konsentrasi kontaminan amonia sebesar 97,5% dan nitrit sebesar 100%. Unit FMM pada V1 dapat mereduksi amonia 36,25% dan nitrit 35,48% serta unit FK dapat mereduksi amonia dan nitrit sebesar 86,27% dan 10%. Selain itu, unit NF dapat mereduksi amonia sebesar 71,43% dan nitrit sebesar 100%. Reaktor RAS optimal dalam bekerja mereduksi nitrat dan TSS pada V1 sebesar 100%. V1 memiliki fenomena penurunan nilai fluks dan peningkatan resistensi yang lebih kecil daripada kondisi V2 (FMM-NF) dan V3 (FK-NF). Pengembangan model konsentrasi permeate memiliki kemampuan yang sangat baik dalam menggambarkan dan memprediksi proses filtrasi menggunakan membran NF dengan nilai Aw, Bs, dan X berbeda-beda pada setiap variasi., The nanofiltration (NF) membrane technology implemented in the recirculating aquaculture system (RAS) suffers from fouling issues. Fouling can be reduction by incorporating pre-treatment units such as the multimedia filter unit (FMM) and activated carbon filter (FK). Therefore, this study aims to investigate the configuration optimization of the RAS using FMM, FK, and NF90-4040 membrane to determine the most effective treatment system for reducing contaminants in aquaculture wastewater. Configuration V1 (FMM-FK-NF) demonstrated the highest overall efficiency in reducing ammonia concentration by 97.5% and nitrite by 100%. The FMM unit in V1 reduced ammonia and nitrite levels by 36.25% and 35.48% respectively, while the FK unit reduced ammonia and nitrite levels by 86.27% and 10% respectively. Additionally, the NF unit reduced ammonia by 71.43% and nitrite by 100%. The optimized RAS reactor achieved 100% reduction in nitrate and TSS in V1. Furthermore, V1 exhibited a smaller decline in flux value and resistance increase compared to V2 (FMM-NF) and V3 (FK-NF) conditions. The developed permeate concentration model showed excellent ability to describe and predict the filtration process using NF membranes with varying values of Aw, Bs, and X for each variation.
Keyword: flux, pre-treatment configuration, nanofiltration membrane, RAS

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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