Judul: Invers dari Matriks Tridiagonal Jacobi
Abstrak: Suatu matriks berukuran n×n dinamakan matriks tridiagonal jika untuk . Karya ilmiah ini memberikan algoritma yang mudah untuk menemukan invers ( dari matriks tridiagonal Jacobi yang simetrik dan nonsimetrik. Setiap elemen pada matriks tridiagonal ini adalah bilangan real. Terdapat 3 lema dan 2 teorema untuk menentukan . Lema pertama menunjukkan persamaan utama dalam membuktikan lema-lema dan teorema-teorema selanjutnya. Invers dari matriks yang simetrik dibuktikan oleh lema kedua yang menunjukkan elemen-elemen baris ke- dari . Selanjutnya, lema kedua dilengkapi dengan teorema pertama yang menunjukkan elemen-elemen dengan . Invers dari matriks yang nonsimetrik dibuktikan oleh lema ketiga yang menunjukkan elemen-elemen dengan dan elemen-elemen dengan dibuktikankan oleh teorema kedua.
Keyword: symmetric, nonsymmetric, matrix

Judul: Inverse Eigenvalue Problem Untuk Matriks Tridiagonal Simetrik
Abstrak: Inverse eigenvalue problem adalah proses mengonstruksi suatu matriks yang mempertahankan struktur tertentu dari data tertentu. Biasanya Data yang digunakan dapat berupa informasi sebagian dari nilai eigen atau vektor eigen. Beberapa jenis matriks yang sering dibahas dalam inverse eigenvalue problem adalah Matriks Tridiagonal Simetrik, Matriks Jacobi, Matriks Toeplitz, dan matriks Hermitian. Dalam karya ilmiah ini, jenis matriks yang dibahas adalah Matriks Tridiagonal Simetrik beserta dua kasus khusus yaitu matriks tridiagonal simetrik dengan diagonal utama tak negatif dan matriks tridiagonal simetrik dengan diagonal utama bernilai konstan. Dalam setiap kasus tersebut masing-masing memeliki syarat perlu dan cukup yang dibahas dalam lema dan teorema.
Keyword: Inverse eigenvalue problem, Matriks Tridiagonal Simetrik, Nilai Eigen

Judul: Application of steel slag, dolomite, silica gel, and micro fertilizer in rice plant on peat soil
Abstrak: Steel slag as a by-product formed in the process of steel manufacturing consists of iron-making slag or blast furnace slag (BFS) and steel-making slag or electric furnace slag (EFS) had been used as Si fertilizer and liming materials. Steel slag containing silicate, micro elements, and bases can be used to improve chemical properties of peat soil that are poor in nutrients. Steel slag contains a lot of silicate needed by especially Si accumulator plants such as paddy rice plant. This research aimed to compare paddy rice plant’s response of IR64 and Air Tenggulang to EF slag, BF slag, dolomite, silica gel and micro fertilizer application for improving chemical properties of peat soil, to know the reason of paddy rice plant’s response on peat soil to steel slag application and to evaluate steel slag effect in content of hazardous heavy metal in brown rice. This research consisted of an incubation and a greenhouse experiments. Both of them were single factor experiment arranged in a completely randomized design. The treatments were both EFS and BFS (0%, 2%, 4%, 6%, 8% w/w of the soil), both dolomite and silica gel equivalent EFS dosage and also micro nutrients with three replications. The results showed that application of EFS on peat soil significantly improved the availability of Fe and Mn, BFS on peat soil significantly improved the availability of Si and Mg and dolomite on peat soil significantly improved soil pH and availability of Ca. Paddy rice grown on peat soil highly responded to steel slag application. Plant height, number of tillers, weight of spikilets, SiO2 of straw were significantly raised with EFS application and content of hazardous heavy metal in brown rice still within limit of food maximum pollution, but Pb and Hg were not detected. In general, the highest rice yield was achieved at dosage of EFS 8%. In conclusion, paddy rice grown responded to steel slag application was associated in increasing soil pH, the availability of Ca, Mg, Fe, Mn and Si on peat soil. Generally, Paddy rice grown on peat soil highly responded to EFS application better than the others. It meaned that not only silicate as the main factor in improving peat soil chemistry and rice yield, but also increasing soil pH, availability of Ca, Mg and micro nutrients.
Keyword: