Judul: Review of Runoff in the Context of  Construction of the Baranangsiang Retention Pool in Bogor City
Abstrak: Beberapa faktor penyebab banjir, seperti berkurangnya daerah tangkapan air akibat peralihan fungsi lahan dan curah hujan tinggi menjadi dasar dalam perencanaan kolam retensi. Pengkajian ulang limpasan untuk pembangunan kolam retensi Baranangsiang dilakukan seiring dengan perubahan landuse dan curah hujan. Penelitian ini bertujuan menganalisis volume limpasan serta merekomendasikan kapasitas dan dimensi kolam retensi yang sesuai dengan volume limpasan. Digunakan metode Hidrograf Satuan Sintetik Nakayasu dan diperoleh debit puncak runoff dengan kala ulang 5 tahun sebesar 7,26 m3/detik dan volume kumulatif limpasan sebesar 69.187,13 m3 sedangkan kapasitas tamping kolam hasil kaji awal hanya 38.573,48 m3. Efektivitas tampungan kolam retensi hasil kaji awal terhadap volume limpasan diperoleh sebesar 55,75 % sehingga perlu dilakukan perubahan dimensi tampungan kolam dari 9.643,37 m3 menjadi 11.531,19 m3 untuk luas kolam dan kedalaman kolam retensi diubah dari 4 m menjadi 6 m sehingga efektivitas kolam retensi menjadi 100%. Dinding kolam retensi menggunakan tipe kantilever di inlet kolam. Beda tinggi antara inlet dan outlet sekitar 7 m sehingga pada titik keluar (outlet) dibangun konstruksi tubuh bendungan dengan tinggi 7 m dan lebar bentang pondasi 9,61 m., Several factors that cause flooding, such as reduced water catchment areas due to landuse changes and high rainfall, are the basis for planning retention ponds. The review of runoff for the construction of the Baranangsiang retention pond was carried out in line with changes in landuse and rainfall. This research aims to analyze runoff volume and recommend the capacity and dimensions of retention ponds that are appropriate to the runoff volume. The Nakayasu Synthetic Unit Hydrograph method was used and the peak runoff discharge with a return period of 5 years was 7.26 m3 /second and the cumulative runoff volume was 69,187.13 m3 , while the tamping capacity of the pond from the initial study was only 38,573.48 m3 . The effectiveness of the retention pond storage from the initial study on runoff volume was found to be 55.75% so it was necessary to change the dimensions of the retention pond from 9,643.37 m3 to 11,531.19 m3 for the area of the pond and the depth of the retention pond to be changed from 4 m to 6 m so that the effectiveness of the pond retention to 100%. The retention pool wall uses a cantilever type at the pool inlet. The height difference between the inlet and outlet is around 7 m so that at the outlet point a dam body construction is built with a height of 7 m and a foundation span width of 9.61 m.
Keyword: discharge, runoff volume, retention pond, effectiveness, dimensions

Judul: Perencanaan Sumur Resapan dan Kolam Retensi di Bogor Barat Agrohills Kabupaten Bogor
Abstrak: Bogor Barat Agrohills adalah proyek kaveling berkonsep eduwisata di Kecamatan Leuwisadeng Kabupaten Bogor. Saat ini pemerintah berupaya untuk menyimpan air sebanyak mungkin ke dalam tanah dan berusaha untuk mencapai zero runoff. Sejalan dengan itu maka penelitian bertujuan merencanakan sumur resapan dan kolam retensi di Bogor Barat Agrohills. Dari hasil analisis diperoleh nilai permeabilitas tanah di lokasi tidak memenuhi syarat SNI 03-2453-2002 sehingga direncanakan hanya pembuatan kolam retensi. Dari analisis curah hujan dengan metode Gumbel, diperoleh curah hujan rencana sebesar 147,9 mm untuk periode ulang 5 tahun. Dari hasil pengamatan diperoleh 4 daerah tangkapan air (DTA) dan nilai koefisien limpasan gabungan sebesar 0,32. Kolam retensi direncanakan memiliki 3 tipe dan berjumlah satu buah di tiap DTA. Tipe 1 memiliki panjang 10,0 m dan lebar 6,7 m. Tipe 2 memiliki panjang 8,6 m dan lebar 5,8 m. Tipe 3 memiliki panjang 6,4 m dan lebar 4,3 m. Ketiga tipe kolam memilki kedalaman 4 m. Lokasi kolam retensi direncanakan di dekat outlet setiap DTA. Kolam tipe 1 berjumlah dua buah sedangkan kolam tipe 2 dan tipe 3 masing - masing satu buah. Biaya pembuatan kolam retensi tipe 1 (2 buah kolam) sebesar Rp159.620.000,00, tipe 2 sebesar Rp68.310.000,00, dan tipe 3 sebesar Rp52.150.000,00., Bogor Barat Agrohills is a land plot project with an edutourism concept in Leuwisadeng District, Bogor Regency. Currently the government is trying to store as much water as possible into the ground and to achieve zero runoff. Accordingly, this study aims to plan infiltration wells and retention ponds in Bogor Barat Agrohills. From the results of the analysis, the permeability value of the soil at the location does not meet the SNI 03-2453-2002 requirements, so only retention ponds were planned. From the rainfall analysis using the Gumbel method, a design rainfall was 147.9 mm for the 5-year return period. From the observations were obtained 4 water catchment areas and a combined runoff coefficient value of 0,32. Three types of retention ponds were planned and one pond in each catchment area. Type 1 had dimention of 10,0 m long and 6,7 m wide and type 2 had 8,6 m long and 5,8 m wide, while type 3 had 6,4 m long and 4,3 m wide. The three types of ponds had a depth of 4 m. The location of the retention ponds were planned near the outlet of each DTA. There were two ponds of type 1 pond and one each of type 2 and type 3 ponds. The construstion cost of retention pond type 1 (2 ponds) was IDR159.620.000.00, type 2 was ID68.310.000.00, and type 3 was IDR52.150.000.00.
Keyword: permeability, runoff coefficient, runoff volume

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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