Judul: Antioxidant Ability and Inhibtion of  α-Glukosidase Enzyme in Samarinda (Carissa carandas L) Leaf Powder Drink
Abstrak: The samarinda plants (Carissa carandas L.) is one of the herb plants with many health benefits. However, the utilization of these plants is scarce used in Indonesia. The production of samarinda leaf-based powder drink can increase the plant utilization. This study was conducted to determine the physicochemical characteristics and examine was carried out the antioxidant potency, as well as the ability to inhibit α-glucosidase enzyme of the samarinda leaf powder drink. The powder drink was formulated using three different concentrations of tween 80: 0,1, 0,3, and 0,5%. The results showed that the samarinda leaf powder drink have the potency as an antioxidant drink (87,61-183,79 mgAEAC/100 g of powder) and able to inhibit the α-glucosidase enzyme activity (16,63-26,75%). The best formula was revealed to be the formula with 0,5% tween 80, which have the highest antioxidant potency and α-glucosidase inhibition. This formula was also in compliance with the regulated moisture and ash content stated in the current Indonesian national standard (SNI) of the traditional powder drink., Tanaman samarinda (Carissa carandas L) merupakan salah satu jenis tanaman obat yang memiliki banyak manfaat bagi kesehatan, namun pemanfaatan tanaman samarinda di Indonesia masih tergolong sedikit. Pembuatan minuman serbuk berbahan dasar daun samarinda dapat meningkatkan pemanfaatan tanaman samarinda di Indonesia. Penelitian ini dilakukan untuk mengetahui karkteristik fisikokimia dan menguji kemampuan antioksidan serta daya hambat enzim α-glukosidase yang dimiliki oleh minuman serbuk daun samarinda. Minuman serbuk daun samarinda diformulasikan menggunakan tiga buah konsentrasi tween 80: 0,1, 0,3, dan 0,5%. Hasil penelitian menunjukkan bahwa minuman serbuk daun samarinda memiliki kemampuan sebagai antioksidan (87,61-183,79 mgAEAC/100 g bubuk) dan mampu menghambat kinerja enzim α-glukosidase (16,63-26,75%). Perlakuan terbaik ditunjukkan pada konsentrasi tween 80 0,5% yang ditandai dengan tingginya kemampuan antioksidan dan daya hambat enzim α-glukosidase. Formula tersebut juga memiliki kadar air dan kadar abu yang hampir sesuai terhadap standar SNI serbuk minuman tradisional yang berlaku saat ini.
Keyword: antioksidan, inhibisi  α-glukosidase, minuman serbuk, tanaman samarinda (Carissa carandas L), tween 80, antioxidant, α-glucosidase inhibition, powder drink, samarinda plant (Carissa carandas L), tween 80

Judul: High Fiber Powder Drink Formulation based on Sargassum sp., Ipomoea batatas, and Seaweed Salt
Abstrak: Rumput laut Sargassum sp., ubi ungu dan jahe merah sudah dikombinasikan menjadi produk minuman serbuk tinggi serat. Formulasi yang digunakan masih dapat dikembangkan dan belum diuji nilai fungsionalnya. Penelitian ini bertujuan menentukan formulasi terbaik serta menganalisis pengaruh penambahan garam rumput laut terhadap serat pangan, mineral, aktivitas air, abu tidak larut asam, logam berat, dan aktivitas antioksidan. Tahapan penelitian ini yaitu pembuatan serbuk, penentuan formulasi terbaik, dan uji lanjutan. Perbedaan formula bahan baku berpengaruh terhadap warna, aroma, rasa, aftertaste, dan proksimat. Hasil uji serat pangan F1 dan F4 sebagai formulasi terbaik yaitu serat larut air 5,06–5,14%, serta serat tidak larut air 20,09–22,62%. Mineral yang terkandung yaitu kalsium 6,53–7,35 mg/g, kalium 7,41–9,075 mg/g, magnesium 3,16–3,28 mg/g, natrium 1,95–6,32 mg/g, dan besi 0,07 mg/g. Aktivitas air produk sebesar 0,29 dan abu tidak larut asam 0,15–0,20%. Senyawa fitokimia yang terkandung yaitu alkaloid, flavonoid, triterpenoid, fenol, tanin dan glikosida. Nilai aktivitas antioksidannya sebesar 86,708 μmol troloks/g (F1) dan 87,499 μmol troloks/g (F4)., Sargassum sp., purple sweet potato and red ginger have been combined into a high-fiber powder drink product. Existing formulation can still be developed and the functional value has not been tested. This research was aimed to determine the best formulation of powdered drink and analyze the effect of adding seaweed salt to dietary fiber, minerals, water activity, acid insoluble ash, heavy metals, and antioxidant activity. The phases of this research were making powder, determining the best formulation, and further testing. Differences in the formula of raw materials affect the color, aroma, taste, aftertaste, and proximate. The results of the F1 and F4 dietary fiber test as the best formulations were soluble fiber 5.06–5.14%, and insoluble fiber 20.09–22.62%. The minerals contained were calcium 6.53–7.35 mg/g, potassium 7.41–9.075 mg/g, magnesium 3.16–3.28 mg/g, sodium 1.95–6.32 mg/g, and 0.07 mg/g iron. The water activity of the product was 0.29 and the acid insoluble ash was 0.15–0.20%. Phytochemical compounds contained in the product were alkaloids, flavonoids, triterpenoids, phenols, tannins, and glycosides. The antioxidant activity values were 86,708 μmol trolox/g (F1) and 87,499 μmol trolox/g (F4).
Keyword: antioksidan, jahe merah, karbohidrat, mineral, serat pangan

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: