Judul: Model Perubahan Kualitas Air Sungai di Daerah Aliran Sungai (DAS) Ciliwung
Abstrak: Sumber air di bumi merupakan jumlah persediaan air yang ada di bumi yang bersumber dari air samudera sebesar 97,2 %, pecahan es dan gletser sebesar 2,14%, air tanah sebesar 0,16%, air permukaan sebesar 0,009%, lapisan air sebesar 0,005% dan atmosfer sebesar 0,001%. Sungai Ciliwung merupakan salah satu sungai yang mengalir pada kota-kota yang memiliki pertumbuhan penduduk dan industri yang tinggi, telah mengalami penurunan fungsi yang cukup besar, jika diperhatikan dari kualitas air sungai dari waktu ke waktu. Oleh karena itu, dibutuhkan suatu model perubahan kualitas air sungai yang terdiri dari BOD, COD dan Fecal coli dengan adanya kelas kualitas air. Model perubahan parameter kualitas air dapat digunakan untuk memprakirakan nilai kualitas air setiap segmen dari hulu sampai hilir dengan adanya baku mutu air di Daerah Aliran Sungai (DAS) Ciliwung. Metode penelitian yang digunakan dengan mengidentifikasi karakteristik parameter kualitas air yang terdiri dari BOD, COD dan Fecal coli setiap segmen DAS Ciliwung dengan menggunakan baku mutu air menurut Peraturan Pemerintah No.82 tahun 2001 dan memprakirakan pola penyebaran BOD, COD dan Fecal coli dari analisa kualitas air dengan menggunakan persamaan regresi.
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Judul: Model Matematis Perubahan Kualitas Air di Daerah Aliran Sungai (DAS) Citarum, Jawa Barat
Abstrak: Water is vital requirement in many metabolic process of organism. Water stock which is stabil can’t meet the requirements of organism which is keeps increasing. It becomes worst by decreasing of water’s quality caused by human’s bad activity such as release waste into river. There are many watercourse in Indonesia which has been polluted and don’t worth to be consumed for many requirements. One of them is Citarum river in West Java. Citarum river has 270 km long. Its upstream is in Wayang mountain, Bandung regency. Its watercourse passing through some regions in Purwakarta regency and downstreamed in Jakarta, Bekasi and Karawang. There are three weirs in DAS Citarum (Saguling, Cirata and Jatiluhur) which functioned to controll water for irrigation (>85%) and the rest for electrical generator, drinking water and industrial requirements. Because of the important functions of Citarum river and its three weirs, thus needed a mathematic model of water quality change to estimate the value of water quality from upstream to downstream. The objectives of this research are to knowing water quality of Citarum river in BOD, COD and TSS parameters which is taken from 10 observation points from upstream to downstream, to make a model of water quality changes, and to observate the effect of three weirs in DAS Citarum to water quality changes of Citarum river. This research held by collect secondary data of water quality in 2008 and some other supporting data which is proccessed by Microsoft Office Excel 2007 Software, compared with Goverment Regulation Number 82 Year 2001 and its graphics analyzed and then made its mathematic model. The result of this research is model of water quality changes of DAS Citarum in 2008, that is in wet month (March) for BOD parameter is y = 5E-14x3 - 9E-09x2 + 0,000x + 5,902 with R2 = 0,892, COD parameter is y = 2E-14x3 - 4E-09x2 + 0,000x + 2,433 with R2 = 0,854, and TSS parameter is y = 1E-13x3 - 3E-08x2 + 0,001x + 238,5 with R² = 0,884. Model of water quality changes of DAS Citarum in dry month (July) for BOD parameter is y = 1E-09x2 - 0,000x + 26,50 with R2 = 0,673, COD parameter is y = 7E-11x2 - 0,000x + 10,14 with R2 = 0,693 and TSS parameter is y = 3E-13x3 - 5E-08x2 + 0,002x + 190,4 with R2 = 0,963. Based on result of this research, known that BOD, COD and TSS values in each observation point from upstream to downstream has a fluctuative distribution. Distance of observation point from water spring doesn’t affect the water quality changes, depend on the existence of polluter source in thet area. Distribution pattern of water quality for those three parameters show that weir could controll water quality, that is pollutan which released from weir could be decreased because the pollutant sedimented in weir base.
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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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