Judul: Kaji Ulang Neraca  Air pada Daerah Irigasi Sempor Kabupaten Kebumen
Abstrak: Daerah Irigasi Sempor terletak di Kecamatan Sempor, Kabupaten Kebumen, Provinsi Jawa Tengah. Daerah Irigasi Sempor memiliki luas sebesar 6.478 ha. Daerah Tangkapan Air (DTA) Waduk Sempor memiliki luas 4.231 ha. Perubahan tata guna lahan dari lahan hijau menjadi lahan permukiman yang terjadi di DTA Waduk Sempor dapat mengakibatkan terjadinya erosi. Erosi yang terjadi akan menyebabkan sedimen di dasar waduk dan mengakibatkan berkurangnya kapasitas tampungan waduk. Penelitian ini bertujuan untuk melakukan kaji ulang besaran kebutuhan, ketersediaan, dan neraca air yang ada di Daerah Irigasi Sempor. Ketersediaan air DTA Waduk Sempor dihitung menggunakan metode F.J. Mock. Ketersediaan air tertinggi terjadi pada bulan Januari periode I sebesar 5,20 Juta m3 dan terkecil terjadi pada bulan Oktober periode I sebesar 0,01 Juta m3. Sedangkan kebutuhan air Daerah Irigasi Sempor terbesar terjadi pada bulan Mei periode I sebesar 6,97 Juta m3 dan yang terkecil pada bulan September periode II sebesar 0,70 Juta m3. Secara keseluruhan, neraca air DI Sempor mengalami defisit sebesar 38 Juta m3. Ketersediaan air DTA Waduk Sempor hanya dapat memenuhi 60% dari kebutuhan air Daerah Irigasi Sempor., The Sempor Irrigation Area is located in Sempor District, Kebumen Regency, Central Java Province. The Sempor Irrigation Area has an area of 6,478 ha. The Sempor Reservoir Water Catchment Area (DTA) has an area of 4,231 ha. The change in land use from green land to residential land that occurs in the Sempor Reservoir catchment can result in erosion. The erosion that occurs will cause sediment at the bottom of the reservoir and result in a reduction in the reservoir's storage capacity. This research aims to review the amount of demand, availability and balance of water in the Sempor Irrigation Area. The water availability of the Sempor Reservoir DTA was calculated using the F.J. Mock. The highest water availability occurred in January period I is 5.20 million m3 and the smallest occurred in October period I is 0.01 million m3. Meanwhile, the largest water demand for the Sempor Irrigation Area occurred in May period I is 6.97 million m3 and the smallest in September period II is 0.70 million m3. Overall, DI Sempor's water balance experienced a deficit of 38 million m3. Water availability in the Sempor Reservoir DTA can only meet 60% of the water needs of the Sempor Irrigation Area.
Keyword: F.J. Mock, Water Requirement, Water Availability, Water Balance

Judul: Kaji Ulang Neraca Air Daerah Irigasi  Waduk Cengklik Kabupaten Boyolali
Abstrak: Waduk Cengklik memiliki luas daerah tangkapan air 25,016 km2 dengan Daerah Irigasi sebesar 1957 Ha. Terjadi penurunan kapasitas volume waduk sebesar 43,57% akibat adanya sedimentasi. Perubahan tata guna lahan di daerah tangkapan air waduk berdampak terhadap ketersediaan air. Oleh karena itu, perhitungan neraca air diperlukan sebagai upaya dalam mengetahui kesanggupan waduk memenuhi kebutuhan air irigasi. Metode yang digunakan dalam penentuan ketersediaan air adalah F.J.Mock dan kebutuhan air digunakan metode berdasarkan kriteria perencanaan irigasi (KP-01). Nilai rata-rata evapotranspirasi potensial pada tahun 2013-2022 berada pada interval 40,97 mm/bulan – 66,11 mm/bulan. Debit ketersediaan air berada pada interval 0,003 m³/dt – 1,550 m³/dt, dengan debit terendah pada bulan Oktober periode 2 dan tertinggi pada bulan Februari periode 1. Curah hujan andalan setengah bulanan untuk kebutuhan air berada pada interval 1,25-139,19 mm. Kebutuhan air irigasi tertinggi sebesar 1,41 l/dt/Ha dan terendah sebesar 0 l/dt/Ha. Secara keseluruhan neraca air tahunan di Daerah Irigasi Waduk Cengklik mengalami defisit sebesar 11,41 juta m3. Beberapa tindakan dapat dilakukan untuk mengantisipasi defisit tersebut antara lain penjadwalan ulang, pengerukan sedimen, dan pengelolaan DTA., Cengklik Reservoir has a catchment area of 25,016 km2 with an Irrigation Area of 1957 Ha. There was a decrease in reservoir volume capacity of 43.57% due to sedimentation. Changes in land use in the reservoir catchment area have an impact on water availability. Therefore, water balance calculations are needed as an effort to determine the ability of the reservoir to meet irrigation water needs. The method used in determining water availability is F.J.Mock and water requirements use a method based on irrigation planning criteria (KP-01). The average value of potential evapotranspiration in 2013-2022 is in the interval 40.97 mm/month – 66.11 mm/month. The water availability discharge is in the interval 0.003 m³/s – 1,550 m³/s, with the lowest discharge in October period 2 and the highest in February period 1. The semi-monthly reliable rainfall for water needs is in the interval 1,25-139,19 mmm. The highest irrigation water requirement is 1,41 l/s/Ha and the lowest is 0 l/s/Ha. Overall, the annual water balance in the Cengklik Reservoir Irrigation Area experienced a deficit of 11,41 million m3. Several actions can be taken to anticipate this deficit, including rescheduling, sediment dredging, and DTA management.
Keyword: F.J. Mock, Water Requirement, Water Availability, Water Balance

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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