Judul: Determinant and Inverse Circulant Matrix with Pell Numbers Entries
Abstrak: Matriks circulant adalah matriks yang entrinya bergeser satu kolom ke kanan secara berurutan, sehingga untuk mengetahui seluruh entrinya dapat dilihat hanya dari kolom pertama. Salah satu sifat yang dimiliki matriks circulant adalah bahwa inversnya juga berupa circulant. Entri-entri matriks circulant dapat menggunakan entri berbagai bilangan, salah satunya adalah bilangan Pell. Pada karya ilmiah ini, determinan dan invers matriks circulant dengan entri bilangan Pell diformulasikan. Pembuktian formulasi determinan matriks circulant dengan entri bilangan Pell dilakukan berdasarkan serangkaian operasi baris dasar sehingga diperoleh mariks segitiga atas. Sedangkan pembuktian formulasi inversnya berlandaskan sifat-sifat ekuivalensi dari hasil kombinasi operasi baris dasar atau operasi kolom dasar., A circulant matrix is a matrix whose entries are shifted one column to the right in sequence, so to find out all the entries can be seen only from the first column. One of the properties of a circulant matrix is that its inverse is also a circulant. Circulant matrix entries can use entries of various numbers, one of which is Pell's number. In this scientific paper, the determinant and the inverse of the circulant matrix with Pell number entries formulated. Proof of the determinant formulation matrix circulant with Pell number entries performed based on a series of base row operations so that the upper triangular matrix is obtained. While the proof of the inverse formulation based on the equivalence properties of the result combination of base row operations or base column operations.
Keyword: circulant matrices, determinant, inverse,, Pell numbers

Judul: Determinan dan Invers Matriks Skew Circulant dengan Entri Bilangan Pell
Abstrak: Matriks skew circulant adalah matriks persegi yang entrinya bergeser satu kolom ke kanan secara berurutan dengan seluruh entri sebelum diagonal utama akan bernilai negatif. Entri-entri dari matriks skew circulant dapat diisi dengan entri berbagai bilangan, salah satunya yaitu bilangan Pell. Pada karya ilmiah ini, determinan dan invers matriks skew circulant dengan entri bilangan Pell diformulasikan. Pembuktian formulasi determinan matriks skew circulant dengan entri bilangan Pell dilakukan berdasarkan serangkaian operasi baris dasar sehingga diperoleh matriks segitiga atas. Sedangkan pembuktian formulasi pada inversnya berlandaskan sifat-sifat ekuivalensi dari hasil kombinasi operasi baris dasar dan operasi kolom dasar., Skew circulant matrix is a square matrix whose entries are shifted one column to the right and all entries before the main diagonal will be negative.The entries of the circulant skew matrix can be filled in various numbers, one of which is the Pell number. In this scientific work, the determinant and inverse of skew circulant matrices with the entry of the Pell number are formulated. The substantiation of the determinant formulation of the circulant skew matrix with the entry of the Pell numbers is carried out on the basis of a series of elementary row operations so that an upper triangular matrix is obtained. Meanwhile, the proof of the formulation in the inverse is based on the equivalence proprties of the results of a combination of elementary row and column operations.
Keyword: circulant matrix, circulant skew matrix, determinant, inverse, Pell 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: