Judul: Penurunan Bahan Polutan Air Baku Biofiltrasi dengan Media Pengisi Pasir dan Plastik Sarang Tawon
Abstrak: Biofiltration is a biological treatment process utilizing the biofilm activity of certain microorganisms. The microorganism is utilized to degrade contaminants in the raw water. River water is widely used for drinking water supply, although it sometimes does not meet the standard of raw water. This research was aimed to determine the effectivity of biofiltration to pre-treat raw water and to evaluate the capability of biofiltration in equalizing a quality fluctuation. Honeycomb plastic and sand were used as media in this study. Continuous air supply was done so that an aerobic condition was created. This study was conducted to determine the effectiveness of biofilters for the treatment of raw water and to determine the capability of the biofilters in equalizing of a quality fluctuations. The research consisted of three stages, namely characterization of the raw water, the acclimatization for 4 weeks and loading test. The biofiltration with sand as media could reduce organic pollutants (COD) approx. 80%, that was higher than the COD reduction approx. 69% by biofiltration using honeycomb plastic has. Sand media biofiltration with detergent loading rate of 0.1-32 mg/L resulted in detergent reduction of approx. 55%, whereas the biofilter with honeycomb plastic resulted in detergent reduction of approx. 45%. Generally, increased loading rate would resulted in reducing of pollutant, both media. The absolut pollutants removal increased with increasing of load.
Keyword: contaminated raw water, biofilm, Biofiltration

Judul: Peningkatan Kualitas Air Menggunakan Biofiltrasi dengan Media Pasir Kuarsa dan Botol AMDK
Abstrak: Biofiltration is a process that can be used to improve the quality of the raw water biologically. This study aimed to determine the effectiveness of biofiltration using media of quartz sand and drinking water bottles, as well as to evaluate the effect of ammonium loading on the ability of biofilters to reduce ammonium, nitrate, phosphate, organic compounds, pH changes, color and turbidity. Based on testing characterization raw water and according to PP. No. 82 / 2001 that raw water quality belong to the groups II. Acclimatization is a process of microorganisms in the press biofiltrasi. . Biofiltration using sand medium test reduced ammonium from 60,48 into 25,45 mg/L, nitrate from 1,8 to 1,74 mg/L, phosphate from 0,36 to 0,29 mg/L, organic compounds from 9,79 to 6,36 mg/L, the color from 30 to 24 PtCo, TSS from 17 to 8 mg/L and turbidity from 17 to 13 FTU. Whereas, biofiltration using drinking water bottles media reduced ammonium from 60,48 into 35,56 mg/L, increasing nitrate from 1,8 to 2,4 mg/L, reduce phosphate from 0,36 to 0,34 mg / L, reduce organic compounds 9,79 to 5,72 mg/L , the color of 30 to 18 PtCo, TSS from 17 to 6 mg/L, and turbidity from 17 to 8 FTU. Biofiltration process could lower the water quality fluctuation and save coagulant material costs. The application of the medium sand biofiltration reactor capable of coagulant material savings of Rp 1.588.673.986 per year, while media Rp 1.418.311.317 bottles of drinking water per year. The use of the medium sand biofiltration reactor is recommended for use in water treatment plants IPB Dramaga, Bogor
Keyword: raw water, quartz sand, drinking water bottled, biofiltration

Judul: igenvalues and Eigenvectors of Tridiagonal Matrix with Non Constant and Recurrent Diagonal Entries.
Abstrak: Matriks tridiagonal adalah suatu matriks yang mempunyai entri-entri bernilai nol kecuali pada diagonal utama, di bawah diagonal utama (subdiagonal) dan di atas diagonal utama (superdiagonal). Entri pada diagonal utama tidak konstan dan berulang. Setiap entri pada matriks tridiagonal ini adalah bilangan kompleks. Dalam karya ilmiah ini, akan dibuktikan 3 teorema untuk menentukan nilai eigen dengan 2 kasus dan 1 teorema untuk menentukan vektor eigen. Teorema pertama menentukan polinomial karakteristik dari matriks tridiagonal. Polinomial karakteristik dari matriks tridiagonal tersebut digunakan untuk menentukan nilai eigen pada teorema kedua dan ketiga serta menentukan vektor eigen pada teorema keempat
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