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
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Judul: Optimasi kapasitas antioksidan dan penerimaan sensori pada minuman fungsional jahe merah (Zingiber Officinale. Rosc) dengan penambahan rempah-rempah
Abstrak: Minuman fungsional mempunyai manfaat positif bagi kesehatan. Minuman berbasis jahe banyak dikonsumsi karena rasa menyenangkan dan efek trigeminal yang bisa memberikan efek hangat bagi tubuh. Penelitian tentang minuman jahe merah dikombinasikan dengan pandan dan sereh telah dilaporkan, tetapi penerimaan konsumen terhadap minuman ini dari segi cita rasa masih rendah. Kombinasi dengan rempah lain, yaitu kunyit dan daun pandan, dilakukan pada penelitian ini untuk meningkatkan penerimaan. Response Surface Methodology (RSM) digunakan untuk mengoptimalkan formulasi dan menganalisis pengaruh konsentrasi jahe merah, kunyit dan daun pandan terhadap karakteristik sensori dan kapasitas antioksidan. Karakteristik sensori meliputi atribut aroma, rasa dan overall. Optimasi formula minuman fungsional jahe merah-pandan-kunyit menggunakan disain campuran menghasilkan formula yang optimum yaitu kombinasi jahe merah sebesar 2.65%(w/v), kunyit 1.45%(w/v), dan pandan sebesar 3.90%(w/v). Formula optimum dapat meningkatkan atribut sensori minuman fungsional dibandingkan formula penelitian terdahulu dan produk komersial. Formula optimasi memiliki kapasitas antioksidan sebesar 0.17 mgAEq/ml sedangkan sebelumnya 0.16 mgAEq/ml. Nilai uji rating hedonik dari formula optimasi adalah 6.4 (suka) untuk aroma, 5.9 (mendekati suka) untuk rasa, dan 6.1 (suka) untuk keseluruhan, sedangkan formula sebelumnya adalah 5.5 (agak suka) untuk aroma, 5.2 (agak suka) untuk rasa dan 5.6 (agak suka) untuk keseluruhan. Formula optimasi memiliki kapasitas antioksidan sebesar 0.17 mgAEq/ml sedangkan sebelumnya 0.16 mgAEq/ml.
Keyword: Red Ginger, Turmeric, Pandan, Functional Drink, Response Surface Methodology (RSM)

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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