Judul: Evaluation of Water Availability Using  Supply and Demand Balance Index (SDBI) for Yogyakarta Province, Evaluation of Water Availability Using Supply and Demand Balance Index (SDBI) for Yogyakarta Province
Abstrak: Jumlah air yang tersedia di suatu wilayah, secara umum dipengaruhi oleh aktivitas manusia. Salah satu indikasinya adalah pemakaian air yang kurang efisien. Cepatnya pertumbuhan jumlah penduduk, jumlah industri, dan urbanisasi yang sejalan dengan kebutuhan air yang terus meningkat menyebabkan sumberdaya air tersebut belum bisa dimanfaatkan secara maksimal. Sehingga kondisi hidrologi suatu wilayah perlu dievaluasi untuk menentukan langkah-langkah pengembangan sumberdaya air wilayah tersebut. Penelitian ini bertujuan untuk mengevaluassi kondisi hidrologi wilayah menggunakan Supply and Demand Balance Index (SDBI) di Provinsi DI Yogyakarta. Dalam penelitian ini, supply air dihitung dengan menggunakan data curah hujan dan evapotranspirasi, sedangkan nilai demand air dihitung berdasarkan nilai dari jumlah penduduk, jumlah industri, dan luas lahan pertanian. Hasil analisis menunjukkan kategori SDBI wilayah di Provinsi DI Yogyakarta selama tiga tahun cukup bervariasi. Hasil perhitungan pada tahun 2005 menunjukkan bahwa kategori SDBI di Provinsi DI Yogyakarta secara umum tidak mengalami kekurangan air dan hanya beberapa kecamatan berada pada kategori “Sedang”, “Moderat”, dan “Akut”. Pada tahun 2010 kategori SDBI di Provinsi DI Yogyakarta berindeks aman, artinya tidak mengalami kekurangan air. Namun, pada tahun 2015 Provinsi DI Yogyakarta mengalami peningkatan dalam kekurangan air terutama di Kabupaten Gunung Kidul dimana dari tiap kecamatan banyak yang memiliki indeks “Moderat” hingga “Ekstrem”. Penelitian ini menyimpulkan bahwa perhitungan supply and demand balance index mampu digunakan dalam menentukan status kondisi hidrologi wilayah., The amount of water available in an area is generally influenced by human activities. One indication is the use of water that is less efficient. The rapid growth of population, number of industries, and urbanization in line with the increasing demand for water causes these water resources to not be utilized optimally. So that the hydrological conditions of an area need to be evaluated to determine the steps for developing the area's water resources. This study aims to evaluate the hydrological conditions of the region using the Supply and Demand Balance Index (SDBI) in Yogyakarta Province. In this study, water supply is calculated using data on rainfall and evapotranspiration, while the value of water demand is calculated based on the value of population, number of industries, and area of agricultural land. The results of the analysis show that the regional SDBI categories in Yogyakarta Province for three years are quite varied. The results of calculations in 2005 showed that the SDBI category in Yogyakarta Province in general did not experience water shortages and only a few sub-districts were in the “Slight”, “Moderate”, and “Acute” categories. In 2010 the SDBI category in Yogyakarta Province had a safe index, meaning that it did not experience water shortages. However, in 2015 Yogyakarta Province experienced an increase in water shortages, especially in Gunung Kidul Regency where from each sub-district many had an index of "Moderate" to "Extreme". This study concludes that the calculation of supply and demand balance index can be used in determining the status of the hydrological conditions of the region.
Keyword: Agriculture, Industry, Population, Rainfall, Water Supply Index

Judul: Bogor City Water Adequacy Status 2009-2019
Abstrak: Curah hujan merupakan faktor iklim yang sangat berpengaruh terhadap ketersediaan air, hal ini menyebabkan kecukupan air menjadi salah satu aspek yang sangat terdampak oleh perubahan iklim yang terjadi saat ini dan di masa mendatang. Penelitian ini bertujuan mengetahui ketersediaan air, kebutuhan air, serta kondisi kecukupan air meteorologis Kota Bogor dari tahun 2009 hingga tahun 2019. Nilai kecukupan air Kota Bogor dapat diketahui dengan perhitungan kebutuhan air dan ketersediaan air. kebutuhan air dapat dibagi menjadi kebutuhan air domestik, kebutuhan air industri dan kebutuhan air pertanian. Kebutuhan air domestik dipengaruhi oleh jumlah penduduk, Kebutuhan air industri dipengaruhi oleh jumlah industri dan Kebutuhan air pertanian dipengaruhi oleh luas lahan pertanian serta kebutuhan air tanaman. Tren ketersediaan air meteorologis Kota Bogor menunjukkan tren menurun sebanyak 0.6% per tahun, di sisi lain kebutuhan air Kota Bogor cenderung meningkat setiap tahunnya sebesar 1.7%, dengan kebutuhan air yang berkontribusi terbesar adalah kebutuhan air domestik yaitu sekitar 48%. Status kecukupan air meteorologis Kota Bogor menunjukkan hasil persentase neraca air tertinggi bernilai 44% dan terendah bernilai -23%, yang menunjukkan bahwa selama satu dekade terakhir air meteorologis yang tersedia di Kota Bogor tidak selalu dapat memenuhi kebutuhan airnya. Berdasarkan indeks penggunaan air Kota Bogor, terlihat bahwa penggunaan air Kota Bogor bernilai tinggi sementara indeks ketersediaan air per kapita menunjukkan nilai yang sangat rendah dengan kondisi kelangkaan mutlak. Ketersediaan air meteorologis yang cenderung menurun menjadi suatu masalah dalam penyediaan air bagi masyarakat. Oleh karena itu pemeliharaan sumber daya air harus diprioritaskan untuk menjaga kelestarian sumber daya air di masa mendatang., Climate factor that have a big influence on water supply is rainfall which make water adequacy to become one of the aspects that is strongly affected by climate change. The aim of this research are to know about Bogor city water supply, water demand and water adequacy from year 2009 until 2019. Analysis of Bogor City water adequacy on year 2009 until 2019 can be known by calculating the water demand that can be divided into domestic water demand, industrial water demand and agricultural water demand. The value of domestic water demand is influenced by the number of population, the value of industrial water demand is influenced by the number of industries and the value of agricultural water demand is influenced by the area of agricultural land and crop water needs. Bogor City water supply tends to decrease with a decrease in value of around 0.6% per year, while Bogor City water demand tend to increase of 1.7% per year with water demand category that contribute the most is domestic water demand with around of 48%. Bogor City water adequacy status for most of the years betwen 2009 and 2019 are surplus with highest surplus value is 44% and the lowest deficit value is -23%, which mean that in the last decade meteorological water supply in Bogor City has not always been available to meet its water demand. The result of Bogor City water index showed high and very high on the most years, while water supply per capita index is absolute scarcity for all the years. Meteorological water supply that tend decrease
Keyword: Adequacy, Demand, Rainfall, Supply, Water

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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