Judul: Kajian Daya Dukung Lingkungan Aspek Sumber Daya Air di Kabupaten Lebak
Abstrak: Development activities have affected many aspects that need to be considered , namely the physical, economic , social, cultural and environmental aspect. Environmental impacts happen, such as changes in the proportion of land cover, the increasing number of critical areas, watershed damage, changes in water storage capacity, changes in ecosystems and biodiversity. The purpose of this study was to analyze the environmental carrying capacity based on water resources, including the determination of the status of environmental carrying capacity, water supply potential analysis, climate resources for agriculture (agro-climatic) and assessment of water resource degradation indicators and to compare the results of the analysis to the environmental contents in RTRW Lebak Regency 2013-2033. Annual environmental capacity of Lebak is in a sustain condition, and discharge of Ciujung watershed can supply the water needs. Based on Oldeman method for agro-climatic, Lebak Regency is in C1 , C2 , D2 Zone, means Lebak can be planted with rice and corps. Based on the analysis on water balance, surplus rainfall is 217 mm and the deficit is 232 mm that occurred in May – November. Runoff and groundwater recharging are 102 mm and 115 mm. By simulating of the land composition, minimum area for forest is 30 %. Degradation of water quality in Lebak occured by flood. Recommended water resources conservation for flood and erosion prevention is terrace which is equipped with 1050 rorak that built in the plantation area.
Keyword: water resources, water balance, spatial planning document, environmental carrying capacity, agro-climatic

Judul: Kajian Daya Dukung Lingkungan Berbasis Neraca Air di Kabupaten Serang, Banten
Abstrak: In the Spatial Planning Document (RTRW), environmental sustainability is one of the important principles. The assessment of environmental carrying capacity in Kabupaten Serang conducted to describe the condition of the environment, especially on water resources. The analysis of environmental carrying capacity of water resource aspectsconducted through four hierarchy includes the status of environmental carrying capacity based on water balance, agroclimate resources assessment, water supply potential analysis, and assessment of water resource degradation indicators. The purpose of this research is analyzing the four hierarchical of environmental carrying capacity based on water balance in Serang and to assess the environmental charges in Serang spatial planning documents based on water balance analysis. Supply-demand ratio obtained that the status of Serang environmental carrying capacity is on conditional sustain with the rate ratio is 1.15. Serang classified to the type of agro-climatic Oldeman B2. The results of the water balance analysis showed that in July-September there are rainfall deficits, wich is 11 mm/month, 64 mm/month, and 35 mm/month and rainfall surpluses occur from November to June. The runoff and recharging groundwater contained in the span of October to June. The minimum proportion of forest area is 30 %, and ideal is 45%. The availability of surface water from Ciujung river can still meet the total requirement of water per month in Serang.
Keyword: water balance, recharging groundwater, runoff, environmental carrying capacity

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
Keyword: