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: Kajian Daya Dukung Lingkungan Berbasis Neraca Air di Kabupaten Cianjur, Jawa Barat
Abstrak: To realize sustainable development, preparation of spatial planning (RTRW) should consider the environmental carrying capacity. This research aims to analyze the four hierarchical environmental capacity assessment of water resources and to compare the results of this analysis to the charge contained in the environment of the spatial planning documents. Status of environmental carrying capacity is obtained by comparing the availability of water and water footprint area, the type of agricultural climate resources is obtained by Oldeman classification, potential water supply can be assessed from the data of surface water, ground water and water balance analysis of Tornthwaite. Cianjur is located in a safe condition. The Citarum River is one of potential surface water to sufficient the needs of actual water. Type of agriculture that can be developed are B1 and B2 with a continuous rice. Existing forest area is 23.71% less than the minimum area 32% and ideal area 36%. Indicators of water resource degradation that occurs as floods, landslides, drougth. For that conservation can be done is to construct reservoir, recharge wells about 1.25 million in residential areas.
Keyword: water balance, Spatial Planning Document (RTRW ), run off management, 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
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