Judul: On Determinant, Inverse, and Eigenvalues of  Circulant Matrix with Geometric Progression
Abstrak: Matriks Circulant adalah matriks segi yang disusun oleh operasi pergeseran sirkular kanan, yaitu pergeseran entri terakhir ke posisi utama disertai pergeseran semua entri lainnya ke posisi berikutnya. Entri dari matriks circulant dapat diisi dengan barisan bilangan apapun, salah satunya barisan bilangan geometri yang mana digunakan sebagai objek utama dari penelitian ini. Karya ilmiah ini bertujuan menurunkan formulasi sederhana dari nilai eigen, determinan, dan invers. Formulasi determinan diperoleh sebagai hasil kali semua elemen dari diagonal utama matriks diagonal setelah melakukan serangkaian operasi baris dasar dan kolom dasar. Sementara itu, formulasi invers diperoleh dari mengadaptasi langkah pada metode sebelumnya, dan kita peroleh C_(a,r,n)^(-1)=QD^(-1) P dengan P dan Q berturut-turut merupakan matriks yang diperoleh dari serangkaian operasi baris dasar dan kolom dasar tersebut yang dikenakan pada matriks indentitas I_n. Formulasi nilai eigen diperoleh dengan pendekatan konsep subgrup siklik dan geometri dari akar kesatuan ke-n., Circulant matrix is a square matrix composed by a right circular shift operation, namely the shift of the last entry to the first position followed by the shift of all other entries to the next position. The entry of a circulant matrix can be filled in any sequence of numbers, such as a geometric progression sequence which we use as the main object of this research. The goal of this research is to derive simple formulations for the eigenvalues, determinant, and inverse. The determinant formulation obtained as the product of all elements in the main diagonal matrix after applying a series of elementary row operations and elementary column operations. Meanwhile, the inverse formulation is obtained from adapted the previous method, and we get C_(a,r,n)^(-1)=QD^(-1) P where P and Q are matrices of a series of elementary row and column operations performed previously applied to identity matrix I_n, respectively. Formulation of eigenvalues is obtained from approaching the concept of cyclic subgroup and geometry representation of n^throot of unity.
Keyword: circulant matrix, eigenvalues, determinant, inverse, geometric progression

Judul: Determinan dan Invers Matriks Circulant dengan Entri Barisan Aritmetika
Abstrak: Matriks circulant adalah matriks segi yang entrinya bergeser satu kolom ke kanan secara berurutan. Sehingga entri matriks circulant dapat dilihat dari satu kolom atau satu baris matriks tersebut. Salah satu sifat yang dimiliki matriks circulant, adalah bahwa inversnya juga bersifat circulant. Entri baris pertama suatu matriks circulant dapat diisi dengan berbagai bentuk barisan bilangan yang salah satunya adalah barisan aritmetika. Pada karya ilmiah ini diformulasikan secara eksplisit determinan dan invers matriks ... dst, Circulant matrix is a square matrix whose entry are shifted one column to the right sequentially. So the entry of a circulant matrix can be seen as one column or one row of the matrix. One of the property of a circulant matrix is the inverse also in the form of circulant. The first row of a circulant matrix can be filled in various type of sequence of numbers such as arithmetic sequence. In this research, the determinant and the inverse of a circulant matrix ... dst
Keyword: arithmetic sequence, circulant matrix, determinant, inverse

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.
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