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: Inter basin management model for sustainable water supply (case study: to fulfill water supply for DKIJakarta )
Abstrak: Jakarta is capital of Indonesia and as a big city with the administrative status of a regency or province with 9.588.198 people in 2010 (BPS, July, 2010). Jakarta needs water 524.953.840 for domestic and non domestic 212.606.350 m3 and totally 737.560.145,20 m3. PAM Jaya production capacity in 2009 is about 509.431.934 m3/year, about 69,07% the total needs of DKI Jakarta. To fulfil the water, Jakarta needs water supply from the other provinces, 80% water supply for Jakarta are from Citarum (West Java) and Cisadane (Tangerang-Banten) and others. A research has been done within 13 months started from 2010 July until 2011 August. The research is aimed to identify the supply and demand of water and to structurize the role and relationship of stakeholders in the fulfilment the water supply inter basin. The methodology analysis were Interpretative Structure Modelling (ISM), Multy Dimensional Scalling (MDS) and System Dinamic. The goverment has a central role to fulfil the needs of water supply, fulfilment water needs to understand more about supply and demand of water. The problem was the flood had often occured. The sustainable of fulfillment water supply for DKI Jakarta has economy dimensional (69,17), social dimensional (56,52), dimensional of law and institution (68,24), dimensional of infrastructur and technology (61,45), but dimensional of ecology is not sustainable with the score (48,75). In the dynamic model is built, after a policy intervention program 3R, BKT, 13 rivers, desalination, reduction in leakage, PES and others, the need for clean water and adequate Jakarta in 2030 met with no water supply in the soil water uptake and shallow ground water. Jakarta water needs can be met by working together across the region with local government and local government Tangerang Banten Jabar in the utilization of water resources in the watershed that flows in the region with payments for environmental services or PES 50 billion per year.In order to achieve water security, Jakarta needs to build policy scenarios that lack of clean water to Jakarta in the future does not happen again. Both policy scenarios related to supply and demand management and water management technologies, among others, the construction of large dams which hold water from 13 rivers that flow into Jakarta. Building a pipeline project from Jatiluhur reservoir and increase flow of raw water sources other outside Jakarta to conduct inter-regional cooperation. In addition to the management of raw water in the watershed that is the method of normalization ultraviltrasi 13 coupled with the existing river / flowing in Jakarta. In 2031 the use of ground water in the capital should be discussed again with the stakeholders or the public through public consultation, needs to be rethought termination step permits the use of groundwater in the year 2031.
Keyword: Water supply, inter basin, sustainable management, supply demand, DKI Jakarta

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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