Judul: Determinan dan Invers Matriks Left Circulant dengan Entri  Barisan Bilangan Geometri
Abstrak: Matriks left circulant yang dinotasikan dengan LCirc merupakan matriks berukuran n x n yang setiap entri pada baris selanjutnya mengalami pergeseran satu satuan ke arah kiri secara berurutan sehingga membentuk sirkular. Entri pada baris matriks tersebut dapat diisi dengan berbagai pola barisan bilangan yang salah satunya adalah barisan geometri. Penelitian ini bertujuan untuk menentukan formula dari determinan dan invers menggunakan metode operasi baris dasar dan operasi kolom dasar. Pada karya tulis ini, matriks LCircn (g) diubah secara ekuivalen menjadi matriks diagonal dengan serangkaian operasi baris dasar dan operasi kolom dasar. Determinan matriks LCircn (g) ditentukan melalui hasil perkalian diagonal utama pada matriks diagonal. Invers matriks LCircn (g) ditentukan melalui persamaan LCircn-1 = QD-1P dengan Q dan P adalah matriks tak singular yang didapatkan dari matriks identitas I yang dikenakan operasi baris dasar dan operasi kolom dasar yang sama pada matriks LCircn (g)., The left circulant matrix denoted by LCirc is an nxn matrix in which each entry in the next row shifts one unit to the left sequentially to form a circle. The entries in the matrix row can be filled with various patterns of sequence of number, one of which is a geometric sequence. This research aims to determine the formula of determinant and inverse using elementary row operation and elementary column operation methods. In this paper, the matrix LCiren (g) is transformed equivalently into a diagonal matrix by a series of elementary row operations and elementary column operations. The determinant of the LCircn (g) matrix is determined by multiplying the main diagonal of the diagonal matrix. The inverse of the LCircn (g) matrix is determined through the equation [LCiren] ^(- 1)=QD^(-1) P with Q and P are non-singular matrices obtained from the identity matrix I subjected to the same elementary row operation and elementary column operation on the LCircn (g) matrix.
Keyword: invers, determinant, geometric sequence, left circulant matrix

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: Effetcs of Pretreatment and Drying Temperature on Quality of Dried Bamboo Shoots (Dendrocalamus membranaceus Munro)
Abstrak: Whole bamboo shoots (Dendrocalamus membranaceus Munro) freshly harvested in Doi Tung were blanched at 90-100 ⁰C in various concentrations of sodium metabisulfite solution (0, 0.5%, 1.0%, and 1.5%) for ten minutes, as pretreatment, and then dried at various temperatures (50 ⁰C, 60 ⁰C, and 70 ⁰C) using a laboratory scale hot air drier. Effects of both pretreatment and drying temperature on quality of dried bamboo shoots were evaluated. There were seven parameters observed: drying time, aw, color, rehydration ratio, shrinkage, firmness, and total residual sulfites. Results showed that drying time decreased with increase in the drying temperature (p<0.01) while both pretreatment and drying temperature had no significant effect (p>0.05) on aw and shrinkage of dried bamboo shoots. Moreover, L* value, b* value, and rehydration ratio increased with increase in concentration of sodium metabisulfite and decrease in drying temperature, whereas a* value increased. The higher b* value and rehydration ratio (p<0.01) were found in samples blanched in 1.5% Na2S2O5 solution and dried at 50 ⁰C and samples blanched in 1.0% Na2S2O5 solution and dried at 60 ⁰C. It was also observed that total residual sulfites in dried-sulfited sample was quite high, ranged from 1250 to 3378 ppm SO2 while the sample blanched in 1.5% Na2S2O5 solution had higher residual sulfites than the other concentrations. Based on the parameters, sample blanched in 1.0% Na2S2O5 solution and then dried at 60 ⁰C was chosen to be the best sample. Results of rating hedonic test confirmed that the rehydrated of the best sample was more preferrable than the rehydrated-commercial dried bamboo shoots. It is suggested that blanching in 1.0% Na2S2O5 solution and then drying at 60 ⁰C is a better drying condition to produce dried bamboo shoots with a desired quality and applicable in Doi Tung.
Keyword: