Judul: Formulasi dan Penentuan Umur Simpan Minuman Fungsional Campuran Sirih Merah, Jahe, Kayu Manis, dan Jeruk Nipis
Abstrak: There were many studies about potential of red betel leaves in case of diabetes prevention. One study showed the potential of red betel as antihyperglicemic either alone or in a mixture with other materials. This study aims to improve the taste of the functional beverage, analyze volatile components, and determine the shelf life of the functional beverage. This study begins with the preparation of raw materials, followed by selected functional beverage formulation, bottling, shelf life estimation, and the transformation of a shelf life into expiration time. At the beginning of the study, improvement of beverage is done by adding lime juice in 5 levels of comparison, either in the form of extracts of whole fruit or fruit juice broth, sensory testing to get 3 formula was selected, and determination of the characteristics of functional drinks. The results showed that the addition of lime juice at volume ratio of red betel, ginger, cinnamon, and lime is 5:4:3:4 with panelists approached the level of preference “rather like”. Level of preference is approximately equal to the level of preference drinks before coupled with lemon, but increased inhibition of the enzyme α-glucosidase to 79.51%, has the antioxidant capacity of 442.09 ppm AAE and 411.75 ppm for total phenols. The bottling process is done by pasteurization at a temperature of 63°C for 30 minutes and drink packaged in dark glass bottle. The beverages that have been bottled is then stored at three different temperatures (5°C, 30°C, and 50°C). Furthermore, the stability observed during 6 weeks of storage products includes pH, TAT, total phenol, TPC, and color using the Accelerated Storage Studies (ASS). Determination of the reaction rate of food deterioration by temperature differences do with the Arrhenius method. Now we know the shelf life of each of the above parameters, the two parameters are determined for the shortest shelf life, namely pH and color (value b). Improvement formula-based beverages with the addition of red betel lime juice can increase preference panelists to drink with the main volatile components are α-curcumene and zingiberene, and shelf life of beverages was 87 days
Keyword: 

Judul: Kajian Pemanfaatan dan Pengembangan Potensi Ekstrak Manggis Merah (Garcinia forbesii) sebagai Minuman Fungsional Kaya Antioksidan dan Kestabilannya
Abstrak: Red Mangosteen (Garcinia forbesii) is a fruit that comes from South Kalimantan and rarely used by people. Red mangosteen fruit has white flesh with sweet flavor and fresh red rind with strong sour taste. Red mangosteen rind has a potency to be processed into functional beverage. This study is aimed to determine the functional beverage formulas made from red mangosteen rind extract (M) and emprit ginger extract (J) with the addition of pekak extract (P) and cinnamon extract (K) and then analyzed the characterization of physicochemical properties, functional and determination of its stability at high temperatures. Raw Material M obtained in the form of extracts with 1.4 TPT oBrix while J , P and K obtained by water extraction with water and spices ratio of 1:10 for J and 1:5 for P and K. Formula drink based on M and J was made in three concentration ratio, which is 5:1 (MJ 1), 5:2 (MJ 2), and 5:3 (MJ 3) (v/v). MJ 1 formula is selected as the basic formula based on hedonic rating test and antioxidant capacity. MJ 1 formula is given each addition P extracts and K extract which is made in three different concentrations, are 5%, 10%, and 15%. Formula MJP 5% and MJK 5% is chosen as the selected formula to determine its stability. Formula MJP 5% has the antioxidant capacity 6,46 mg AEAC/mL and total phenol content 20,38 mg GAE/mL, while MJP 5% has 7,95 mg AEAC/mL antioxidant capacity and total phenol content 21,17 mg GAE/mL. Determination of stability MJP 5% and MJK 5% to 85% usable quality was conducted by using the Arrhenius method with antioxidant capacity and total phenol content as parameters. Both formulas packaged in vials dark bottles of 10 ml volume without heating treatment processes, such as pasteurization and sterilization and stored in an incubator at temperature 35°C, 45°C and 55°C. Stability of MJK 5% stored at 35°C, 45°C and 55°C are 8 days, 5 days and 4 days based on the antioxidant capacity parameter and 7 days, 6 days, and 5 days based on total phenol parameters, while the stability of MJP 5% is 9 days, 6 days, and 5 days based on antioxidant capacity parameter and 7 days, 6 days, and 5 days based on total phenol parameter. The observation results showed that the formula mixture of red mangosteen rind extract and ginger extract by the addition of pekak extract and cinnamon extract could potentially be developed as a functional drink from the utilization of rare fruit cultivation, red mangosteen fruit.
Keyword: Arrhenius, cinnamon, pekak, emprit ginger, red mangosteen rind, functional drink

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
Keyword: