Judul: The Sabo Dam Design as an Evaluation of the Water Quality of the Nadya Krenceng Reservoir
Abstrak: Waduk Nadra Krenceng dibuat untuk menampung air Sungai Kapudenok dan sungai Brambang. Seiring jalanya waktu, penggunaan lahan yang menyebabkan perubahan tutupan lahan yang menyebabkan erosi pada DAS Krenceng dan pembuangan limbah industri menyebabkan adanya penurunan kualitas air waduk Nadra Krenceng Waduk Nadra Krenceng mengalami laju erosi mencapai 36.946 ton/tahun atau setara 984 m3/tahun yang membuat terjadinya pencemaran air yang dilihat dari parameter warna, Padatan tersuspensi total (TSS), Padatan terlarut total (TDS), dan Warna. Sabo Dam dibangun untuk mengurangi sedimen yang masuk. Rancangan Sabo dam sebagai pengendali sedimen didapat sedimen yang dapat ditampung dalam sabo dam sebesar 41378.66 m3 dengan debit banjir debit rencana 50 tahun 95.91 m3/det). panjang lantai apron (L) sebesar 22 m. Tinggi efektif dari sabo dam didapat 8 m dan besar, The Nadra Krenceng Reservoir was made to accommodate the water of the Kapudenok and Brambang rivers. Over time, land use causes changes in land cover which causes erosion in the Krenceng watershed and industrial waste disposal causes a decrease in the water quality of the Nadra Krenceng reservoir. water as seen from the color parameters, total suspended solids (TSS), total dissolved solids (TDS), and color. Sabo Dam was built to reduce incoming sediment. The design of the sabo dam as a sediment controller obtained sediment that can be accommodated in the sabo dam of 41378.66 m3 with a planned 50 year flood discharge discharge of 95.91 m3/s). apron floor length (L) of 22 m. The effective height of the sabo dam is 8 m and the width of the base of the spillway is 39.17 m, the width of the top of the spillway is 40.57 m..
Keyword: DAS Krenceng, Sabo Dam, Waduk Nadra Krenceng, Krenceng Watershed, Sabo Dam, Nadra Krenceng Reservoir

Judul: Kajian Dimensi Bangunan Spillway
Abstrak: Bangunan spillway merupakan bangunan hidrolika dari suatu bendungan yang berfungsi pada saat keadaan darurat (emergency), yaitu keadaan muka air pada saat volume tampungan banjir maksimum. Penelitian ini bertujuan untuk melakukan kaji ulang bangunan spillway pada Bendungan Randugunting berdasarkan kajian terhadap desain existing bangunan spillway, debit rencana bangunan spillway, kedalaman aliran kritis, dan profil muka air bangunan spillway. Tipe bangunan spillway yang direncanakan adalah tipe side spillway dengan tipe mercu Ogee. Hasil analisis luas catchment area Sungai Banyuasin adalah 17.39 km2 dengan panjang sungai 8.52 km. Nilai curah hujan rencana dengan periode ulang 1000 tahun adalah sebesar 180.40 mm. Hasil analisis debit rencana metode rasional sebesar 124.07 m3/det, sedangkan dengan metode HSS Nakayasu distribusi hujan 2 jam sebesar 207.40 m3 /det. Kedalaman aliran kritis di atas mercu bendung bangunan spillway diperkirakan setinggi 1.39 m. Elevasi muka air pada saat banjir maksimum adalah 95.66 mdpl di atas mercu bendung spillway, 88.78 - 90.11 mdpl di segmen saluran samping, 88.23 - 88.78 mdpl di segmen saluran transisi, 61.34 - 88.62 mdpl di segmen saluran peluncur, dan 66.28 mdpl di segmen akhir peredam energi., Spillway is a hydraulics building of a dam that functions during an emergency, when the water level of the maximum flood storage volume. This study aims to review the spillway building on the Randugunting Dam based on a study of the existing design of the spillway building, the design discharge of the spillway building, the critical flow depth, and the water level profile of the spillway building. The planned type of spillway building is a side spillway type with an Ogee crest type. The analysis of Banyuasin River catchment area are 17.39 km2 with the river length of 8.52 km. The result of the planned rainfall with a return period of 1000 years is 180.40 mm. The result of discharge with rational method is 124.07 m3/s, while with the Nakayasu HSS method the 2-hour rain distribution is 207.40 m3/s. The critical depth above the weir crest is estimated to be 1.39 m. The maximum water level during flooding is 95.66 masl above the spillway weir crest, 88.78 - 90.11 masl in the side channel segment, 88.23 - 88.78 masl in the transition channel segment, 61.34 - 88.62 masl in the drop channel segment, and 66.28 masl in the stilling basin segment.
Keyword: Critical flow depth, design discharge, water surface profile

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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