Judul: Determinan dan Invers Matriks Circulant dengan entri Jacobsthal Numbers.
Abstrak: Matriks circulant adalah matriks yang entrinya bergeser satu kolom ke kanan secara berurutan, sehingga untuk mengetahui entri dari matriks circulant dapat dilihat dari satu kolom ataupun satu baris dari matriks tersebut. Salah satu sifat yang dimiliki matriks circulant, yaitu inversnya juga berupa circulant. Entrientri dari matriks circulant dapat diisi dengan berbagai entri, salah satunya adalah bilangan-bilangan yang membentuk suatu barisan bilangan. Salah satu barisan bilangan adalah Jacobsthal Number. Pada karya ilmiah ini ditentukan determinan matriks circulant dengan entri Jacobsthal Number menggunakan sifat determinan ketika matriks tersebut sudah dibentuk menjadi matriks segitiga atas dan mencari invers matriks tersebut cukup dengan mencari entri-entri pada baris terakhir dari matriks invers tersebut dengan memanfaatkan teorema invers dari matriks direct sum.
Keyword: bilangan Jacobsthal, determinan, inverse, matriks circulant

Judul: Perhitungan Determinan dan Invers Matriks Circulant dengan Entri Jacobsthal Numbers Menggunakan Operasi Baris atau Kolom Dasar
Abstrak: Matriks circulant merupakan matriks segi berukuran n × n dengan setiap diagonal mempunyai elemen yang sama serta elemen matriks pada baris sebelumnya digeser satu posisi ke kanan pada baris berikutnya. Salah satu sifat yang dimiliki matriks circulant, yaitu inversnya juga berupa circulant. Entri-entri dari matriks circulant dapat menggunakan entri dengan berbagai bilangan, salah satunya adalah Jacobsthal Number. Pada karya ilmiah ini ditentukan perhitungan determinan dan invers matriks circulant dengan entri Jacobsthal Numbers. Pembuktian formulasi determinan matriks circulant dengan entri Jacobsthal Numbers didapatkan dari serangkaian operasi baris dasar sehingga terbentuk matriks segitiga atas, sedangkan formulasi invers matriks didapatkan berdasarkan sifat-sifat ekuivalensi matriks dari hasil serangkaian operasi baris dan kolom dasar sehingga terbentuk matriks diagonal. Matrix circulant is a n × n triangular matrix with the identical elements on each diagonal and the elements from the previous row relocated one place to the right in the next row. The circulant's entries can contain a variety of numbers, one of which is the Jacobsthal numbers. In this scientific work, it is determined the calculation of the determinant and the inverse of the circulant with the entry of Jacobsthal Numbers. The determinant formulation is obtained from a series of elementary row operations to get an upper triangular matrix, and the inverse formulation is based on the matrix equivalence properties of a series of elementary row and column operations to get a diagonal matrix.
Keyword: elementary row or column operation, circulant matrices, determinant, invers, jacobsthal numbers

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.
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