Judul: Semak Daun Island Aquatic Management Based On The Carrying Capacity in Conservation Coral Reef Ecosystem (Case Study: Water Semak Daun Island Administrative District Thousand Islands)
Abstrak: The existing floating cage culture activities in Semak Daun Island waters has enriched organic load to coral reefs ecosystem. The organic load came from food waste that enter the waters. Along with organic waste from various activities on land if not properly controlled lead to eutrophication, causing degradation of coral reefs through increased growth of macroalgae (overgrowth). Coral reef health in Semak Daun Island waters is indispensable for the success of sea ranching activities. It is necessary to study the condition coral reef ecosystems and assess the carrying capacity based on the optimal number of floating cages development activities, there for coral reefs ecosystem in Semak Daun Island waters remain sustain. This study was conducted from May to July 2013. The method used in this study is a survey method. Data collected included primary and secondary data. Analysis was done for percentage of coral and macroalgae coverage, herbivorous fish, aquatic productivity, estimation of organic waste and aquatic carrying capacity. Results showed that percentage of live coral coverage at Semak Daun Island waters are categorized moderate by the average percentage coverage of 44.95% and the average percentage cover of macroalgae was 42.24%. Herbivorous abundance is dominated by family Pomacentridae 32,140 individuals/ha. Chemical parameters for nitrate concentrations in the category mesotrofik, with a range of 0.136 mg/l - 0.364 mg/l. Waste loads estimation of net aquaculture that enter the waters was 1,178.1 Kg/ton/6 months of fish production (N 243.9 Kg/ton/6 months of fish and P 54.1 Kg/ton/6 months of fish). Estimated of anthropogenic waste load around the Semak Daun Island was 4,167 Kg N/6 months and 1,738.8 Kg P/6 months. Based on N load, the optimal - maximum carrying capacity of Semak Daun Island for grouper floating cages was 45 − 151 units (270 − 906 plot cages) or 2.8 – 9.4 ha of 9.99 ha area that appropriate for floating cage activities. In addition, based on dissolved oxygen, the optimal - maximum carrying capacity was 37 − 55 units (222 − 330 plot cages) or 2.3 – 3.4 ha of 9.99 ha area that appropriate for floating cage activities.
Keyword: Coral Reef, Organic Waste, Carrying Capacity, Semak Daun Island

Judul: Semak Daun Island Aquatic Management Based On The Carrying Capacity in Conservation Coral Reef Ecosystem (Case Study: Water Semak Daun Island Administrative District Thousand Islands).
Abstrak: The existing floating cage culture activities in Semak Daun Island waters has enriched organic load to coral reefs ecosystem. The organic load came from food waste that enter the waters. Along with organic waste from various activities on land if not properly controlled lead to eutrophication, causing degradation of coral reefs through increased growth of macroalgae (overgrowth). Coral reef health in Semak Daun Island waters is indispensable for the success of sea ranching activities. It is necessary to study the condition coral reef ecosystems and assess the carrying capacity based on the optimal number of floating cages development activities, there for coral reefs ecosystem in Semak Daun Island waters remain sustain. This study was conducted from May to July 2013. The method used in this study is a survey method. Data collected included primary and secondary data. Analysis was done for percentage of coral and macroalgae coverage, herbivorous fish, aquatic productivity, estimation of organic waste and aquatic carrying capacity. Results showed that percentage of live coral coverage at Semak Daun Island waters are categorized moderate by the average percentage coverage of 44.95% and the average percentage cover of macroalgae was 42.24%. Herbivorous abundance is dominated by family Pomacentridae 32,140 individuals/ha. Chemical parameters for nitrate concentrations in the category mesotrofik, with a range of 0.136 mg/l - 0.364 mg/l. Waste loads estimation of net aquaculture that enter the waters was 1,178.1 Kg/ton/6 months of fish production (N 243.9 Kg/ton/6 months of fish and P 54.1 Kg/ton/6 months of fish). Estimated of anthropogenic waste load around the Semak Daun Island was 4,167 Kg N/6 months and 1,738.8 Kg P/6 months. Based on N load, the optimal - maximum carrying capacity of Semak Daun Island for grouper floating cages was 45 − 151 units (270 − 906 plot cages) or 2.8 – 9.4 ha of 9.99 ha area that appropriate for floating cage activities. In addition, based on dissolved oxygen, the optimal - maximum carrying capacity was 37 − 55 units (222 − 330 plot cages) or 2.3 – 3.4 ha of 9.99 ha area that appropriate for floating cage activities.
Keyword: Coral Reef, Organic Waste, Carrying Capacity, Semak Daun Island

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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