Judul: Kajian intrusi air asin pada sistem akuifer Jakarta
Abstrak: Saltwater intrusion in the aquifer system of Jakarta area, is a study of ground-water in conjunction with hydrostatic equilibrium between freshwater and saltwater flows in aquifer system at border of coastal. There are two main objectives of this study, namely: (i). To analyze the rate of saltwater instrusion in Jakarta aquifer system and (ii) To analyze the impact of recharge of rainwater to control the rate of saltwater intrusion in Jakarta aquifer system. To achieve that objectives, research methodology and material use are as follows: (i). Method use are descriptive, analysis and modelling; (ii) System and technique of data required use secondary and primary data which are grouped in three area of transected zones. (iii). Material use are: Salinity data (EC, Cl- and TDS) were collected over period of 1995 - 2010 with inverval per 3 km at zone transected, hydrogeology, water consumption and recharge; and (iv) Mathematic model use is SHARP model with block-centered finite-difference grid at scale 3 km x 3 km area. Conclusion of this study are: (1). The average rate of saltwater instrusion during period of 1982 – 2010 at transection zone I was 0,1 km/year, at transection zone II was 0,06 km/year and at transection zone III was 0,11km/year. (2). Based on prediction in 2025 ground water consumption amount of 8,02 m3/second will impacted saltwater intrusion at transection zone I at distance of 9 km, at transection zone II at distance of 9 km and at transection zone III at distance of 13,5 km from coastal border. (3). Based on prediction for 2025, increase of ground-water recharge with amount of 3,95 m3/second by applied 100% artificial-recharge based on requirement government regulations, will decrease the saltwater instrusion at all transection zones which are transection zone I will decrease with amount of 1,5 km, transection zone II will decrease with amount of 3 km and at transection zone III will decrease with amount of 4,5 km compare with without artificial recharge, or decrease of saltwater intrusion as of conclusion item (2) above and (4). Based on prediction for 2025, increase of ground water recharge with amount of 0,99 m3/second by applied 25% artificial recharge based on requirement of government regulations, will decrease the saltwater instrusion at 2 transection zones which are transection zone II will decrease with amount of 1,5 km and at transection zone III will decrease with amount of 1,5 km compare with without artificial recharge, or decrease of saltwater intrusion as of conclusion item (2) above.
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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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