Judul: Formulasi dan Kestabilan Minuman Fungsional Berbasis Rumput Laut Cokelat (Sargassum sp.), Bunga Telang, dan Kayu Secang
Abstrak: Minuman rumput laut yang banyak diteliti sebelumnya hanya mengandung satu unsur rumput laut dan belum menggunakan tambahan rempah lokal. Manfaat kesehatan dan senyawa bioaktif pada Sargassum sp., bunga telang dan kayu secang berpotensi untuk dijadikan sebagai minuman fungsional ready to drink. Penelitian bertujuan untuk mendapatkan formula minuman fungsional berbasis Sargassum sp., bunga telang, dan kayu secang, sehingga didapatkan formula minuman yang mengandung antioksidan dan memiliki penerimaan sensori yang baik, serta memprediksi stabilitas minuman selama penyimpanan. Tahapan penelitian terdiri dari formulasi minuman fungsional dan pengujian kestabilan mutu. Hasil uji hedonik menunjukkan perlakuan komposisi Sargassum sp. berpengaruh nyata terhadap kesukaan panelis pada parameter rasa dan aroma. Formula F1 (jahe) memiliki tingkat penerimaan tertinggi dari panelis. Formula F1 memiliki nilai aktivitas antioksidan sebesar 9,93 ppm. Penyimpanan pada suhu ruang dan suhu chilling serta penambahan natrium benzoat dan natrium metabisulfit berpengaruh terhadap kestabilan mutu minuman fungsional selama penyimpanan., The seaweed drink that has been studied previously only possesses one element of seaweed and has not used additional local spices. The health benefits and bioactive compounds in Sargassum sp., butterfly pea flower, and secang wood have the potential to be mixed as ready-to-drink functional drinks. The study aimed to develop a mix-functional drink formula based on Sargassum sp., butterfly pea flower, and sappan wood, to obtain a drink formula that contains antioxidants and has good sensory acceptance, and evaluate the stability of the drink during storage. The stages of the research consisted of making functional drink formulations and analyzing quality stability. The hedonic test results showed that the composition of Sargassum sp. had a significant effect on the preference of panelists on the parameters of taste and aroma. F1 Formula (ginger) has the highest acceptance rate from the panelists. F1 formula had an antioxidant activity value of 9.93 ppm. Storage condition at room temperature and chilling temperature and the addition of sodium benzoate and sodium metabisulfite affected the stability of the quality of functional drinks during storage.
Keyword: antioxidant, formula, functional drink, Sargassum sp.

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
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