Judul: Model penyediaan air bersih berkelanjutan di pulau kecil (studi kasus : pulau tarakan, Kalimantan Timur).
Abstrak: This research was conducted in all areas of water services of Tarakan Island that is West Tarakan, Central Tarakan, East Tarakan and North Tarakan, in October 2010 to October 2011. The main objective of this research is to build a model of sustainable water supply in the small island of Tarakan City with the scope of the study. To achieve these goals, then do some studies, that are : (1) analysis of water needs for domestic, industrial and hospitality, (2) analysis of water availability based on service taps and clean water naturally through augmentation of ground water, (3) analysis of the sustainability of water supply, (4) to design strategies for water supply, and (5) to design a model for water supply. Water demand analysis method is done by projecting development of population growth, industrial and hotel in the city of Tarakan. Analysis of services water is done by calculating the capacity of water treatment plant service taps, analysis of natural water availability is done by increasing ground water augmentation through rain water conservation with infiltration wells, reforestation and terracing. Analysis of the sustainability of water supply using the method of multidimensional scaling (MDS) called RAP-TARAKAN, Montecarlo analysis and prospective analysis. Analysis of water supply strategies performed using the method of analytical hierarchy process (AHP), SWOT analysis and the analysis of interpretative structural modeling (ISM). Water supply model using a dynamic system through software powersim constructor 2.5c. The results showed that the status of the environmental dimension of sustainability is less sustainable (31.8%), sustainable on economic dimension (88.24%), sustained enough on the legal dimensions of institutional (74.21%) and social dimensions (52.25%). While the dimensions of the infrastructure and technology are not sustainable (20.14%). In multi-dimensional, water supply of Tarakan City is sufficient sustainable (52.38%). During the period of the year 2001 - 2030, the East and West Tarakan potential water crisis whereas North and Central Tarakan no potential water crisis. But the piping water service (PDAM) in all districts do not fulfill clean water requirements in terms of quantity, so it needs to be improved with the improvement of services through the construction of water conservation and micro water treatment plant (Micro IPAB).
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Judul: Pemodelan Kebutuhan Air dan Ketersediaan Air Tanah di Pulau Tidore
Abstrak: limited catchment area and raw water sources Small island has specific characteristics limited catchment area and vulnerable to the sea water intrusion. Tidore Island is a small island that has 117,6 Km² and amount people 54 763. Annual of population growth, commercial facilities, and public facilities will increase the demand for raw water. The objectives of this study are (1) to identify the water demand and groundwater availability , (2) to build a model of water demand and groundwater availability , and (3) to formulate groundwater policies. Survey method was used to assess requared at the study area for about 71 sampling sites of will. The data result was analyzed by using the dynamic system analysis to determine the domestic water demand and non domestic demand modeling was developed using Stella version 9.0.2. The results of the analysis showed, that in 2009, the water demand of the existing population was 2 121 124.50 m3/year, the water demand of public facilities was 101 184.35 m3/year, and commercial facilities was 62 523.04 m3/year which made the total of water demand was 2 284 831.89 m3/year. While in 2033, the water demand projection on Tidore Island would be 3 181 713.17 m3/year, the water demand of public facilities would be 150 764.62 m3/year, the water demand for commercial facilities would be 400 814.17 m3/year, which made the total of water needs would become 3 735 291.97 m3/year. As for the groundwater availability in 2009 was about 2 850 000 m3/year and the projected groundwater availability in 2033 would increase into 2 856 117.14 m3/year. To increase the groundwater availability, conservation act toward every type of land use is needed. Those conservation efforts can be included reforestation, terracing and infiltration wells. The result of simulation model has obtained a scenario of an integrated policy (saving and conservation) that can reduce water consumption and increase the groundwater availability
Keyword: dynamic system, groundwater availability, groundwater, model, Tidore island, water demand

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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