Judul: Formulasi Pembuatan dan Pendugaan Umur Simpan Beras Aruk (Beras Singkong) dengan Substitusi Kacang Merah
Abstrak: Diversification program to anticipate a reduction in the consumption of rice in the future in this country need to be done include replacing the consumption of rice with other staple foods. One area that has been done diversification program is Bangka Belitung. Communities in the region have much to consume rice made from other carbohydrate sources, namely cassava rice called aruk rice. Aruk rice is rice made with cassava main raw material, the shape of small grains, and a local food community of Bangka Belitung. The addition of red beans is done to improve the nutritional value of aruk rice. This study aims to determine the best formula to make rice-based cassava with additional red beans, knowing the characteristics of the product, and determine the shelf life of the product. In this research, the selection formula is 95:5, 90:10, 85:15 (cassava : red beans). Based on the formula chosen from test sensory, the best formula of red bean aruk rice substitution is 95:5 (cassava flour : red beans). The result of this research showed addition of red beans could improve the nutritional value of aruk rice. Analysis of the characteristics of the selected formula includes 7.16% (wb) water, 0.56% (db) ash, 0.31% (db) fat, 4.29% (db) protein, 94.84% (db) carbohydrate, 2.41% dietary fiber, 1.56% crude fiber, 24.70% amylose, 76.95% in vitro digestibility of starch, and 11.28 ppm HCN. The shelf life of aruk rice selected formula packed with HDPE packaging is longer than packed with PP, LDPE and MDPE which is 988 days at 85% RH, 766 days at 90% RH, and 614 days at 95% RH.
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Judul: Determination of Shelf Life of Purple  Sweet Potato Analog Rice with Arrhenius Model Approach
Abstrak: Ubi jalar ungu yang termasuk ke dalam sumber karbohidrat mampu dimanfaatkan lebih lanjut menjadi bahan substitusi padi pada beras yang dikenal sebagai beras analog ubi jalar ungu (BAUJU). Untuk memaksimalkan potensi tersebut diperlukan informasi mengenai umur simpan. Penelitian ini bertujuan menduga umur simpannya berdasarkan metode accelerated shelf life test (ASLT) dengan model Arrhenius. Produk BAUJU disimpan pada suhu 37oC, 45oC, dan 55oC serta dianalisis secara berkala selama 35 hari. Analisis untuk sampel mentah (beras analog) dan matang (nasi analog) mencakup analisis secara objektif, yaitu pada parameter warna menggunakan instrumen Chromameter Minolta CR300 dan analisis secara subjektif meliputi parameter sensori warna, aroma grain, aroma earthy, rasa pahit, rasa BAUJU, rasa manis, dan aftertaste pahit menggunakan pengujian sensori metode quantitative descriptive analysis (QDA) oleh panelis terlatih. Perubahan mutu BAUJU selama penyimpanan ditentukan oleh perubahan parameter kritis. Selama penyimpanan, perubahan-perubahan yang terjadi juga dapat dibuktikan dengan pengolahan lanjut menggunakan metode statistika berupa One-Way ANOVA dan Post-Hoc Duncan. Hasil perhitungan dengan model Arrhenius pada penelitian ini menunjukkan masa simpan produk BAUJU adalah 3 bulan 19 hari pada suhu 25oC berdasarkan parameter warna (bahan matang) yang merupakan parameter kritis penduga umur simpan dengan nilai koefisien korelasi tertinggi., Purple sweet potato which is included in the carbohydrate source can be utilized further as a substitute for rice, known as purple sweet potato analogue rice (BAUJU). To maximize this potential, information regarding shelf life is needed. This study aims to estimate the shelf life based on the accelerated shelf life test (ASLT) method with the Arrhenius model. BAUJU products were stored at 37oC, 45oC and 55oC and analyzed periodically for 35 days. Analysis for raw and cooked analog rice samples included objective analysis, namely on color parameter using the Minolta CR300 Chromameter instrument and subjective analysis covers sensory parameters of color, grain aroma, earthy aroma, bitter taste, BAUJU taste, sweetness, and bitter aftertaste using sensory testing quantitative descriptive analysis (QDA) method by trained panelists. Changes in BAUJU quality during storage are determined by changes in critical parameters. Changes that occur during storage can also be proven by further processing using statistical methods in the form of One-Way ANOVA and Duncan's Post-Hoc. The results of calculations in this study using the Arrhenius model show that the shelf life of BAUJU products is 3 months and 19 days at 25oC with color (cooked material) being the critical significant parameter with the highest correlation coefficient value.
Keyword: ASLT, Arrhenius, purple sweet potato analog rice

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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