Judul: Total Fenolik dan Kapasitas Antioksidan Tanaman Gandarusa (Justicia gendarussa Burm.f.) Terhadap Perlakuan Waktu Perebusan Daun yang Berbeda
Abstrak: Tanaman gandarusa (Justicia gendarussa Burm. f.) merupakan tumbuhan semak yang umumnya tumbuh liar dan dipelihara sebagai tanaman obat serta berpotensi sebagai antioksidan. Potensi ini dikarenakan adanya kandungan berbagai jenis metabolit sekunder pada tanaman tersebut, salah satunya fenolik. Penelitian ini bertujuan menganalisis pengaruh waktu perebusan daun gandarusa terhadap kadar total fenolik dan kapasitas antioksidan metode Ferric Reducing Antioxidant Power (FRAP) dan 1,1-diphenyl-2-picrylhydrazyl (DPPH). Sampel diekstraksi dengan metode gabungan sonikasi dan maserasi. Daun gandarusa dilakukan perlakuan pemanasan yaitu perebusan menggunakan waterbath. Kadar total fenolik diukur menggunakan metode Folin-Ciocalteu dan kapasitas antioksidan menggunakan metode FRAP dan DPPH. Hasil penelitian menunjukkan ekstrak daun gandarusa dari ketiga perlakuan memiliki kadar total fenolik tertinggi pada perlakuan 1 yaitu sampel yang tidak direbus dibandingkan dengan sampel yang direbus sebesar 4.346 (mg GAE/g BK). Begitu pula dengan hasil kapasitas antioksidan FRAP dan DPPH didapat sampel daun yang tidak rebus memiliki kapasitas antioksidan tertinggi dibandingkan dengan sampel yang rebus sebesar 31.033 (µmol TE/g BK) dan 383.851 (µmol TE/g BK)., Gandarusa plant (Justicia gendarussa Burm. f.) is a shrub that generally grows wild and is maintained as a medicinal plant and has potential as an antioxidant. This potential is due to the content of various types of secondary metabolites in these plants, one of which is phenolic. This study aims to analyze the effect of boiling time for willow leaves on total phenolic content and antioxidant capacity using the Ferric Reducing Antioxidant Power (FRAP) and 1,1-diphenyl-2-picrylhydrazyl (DPPH) methods. Samples were extracted by a combined method of sonication and maceration. Gandarusa leaves are subjected to heating treatment, namely boiling using a water bath. Total phenolic content was measured using the Folin-Ciocalteu method and antioxidant capacity using the FRAP and DPPH methods. The results showed that the gandarusa leaf extract from the three treatments had the highest Total phenolic content in treatment 1, namely the unboiled sample compared to the boiled sample, which was 4,346 (mg GAE /g DW). Likewise, with the results of the FRAP and DPPH antioxidant capacity, it was found that unboiled leaf samples had the highest antioxidant capacity compared to boiled samples, namely 31,033 (µmol TE/gDW) and 383,851 (µmol TE/g DW).
Keyword: Antioxidants, phenolics, boiling, gandarusa

Judul: Kandungan Fenolik dan Aktivitas Antioksidan Ekstrak Daun Gandarusa Hasil Optimasi Pelarut dengan Metode Sonikasi
Abstrak: Gandarusa (Justicia gendarussa Burm. f.) merupakan tanaman obat yang memiliki senyawa antioksidan untuk menangkal radikal bebas karena adanya kandungan metabolit sekunder seperti senyawa fenolik. Kandungan fenolik yang terekstrak serta nilai aktivitas antioksidan dapat dipengaruhi oleh pemakaian pelarut ekstraksi. Penelitian ini bertujuan menentukan pelarut terbaik antara air, etanol, dan asam asetat serta kombinasi ketiganya untuk ekstraksi daun tanaman gandarusa menggunakan metode sonikasi terhadap kadar total fenolik serta aktivitas antioksidan (metode DPPH dan FRAP) secara in vitro. Hasil penelitian menunjukkan bahwa nilai verifikasi yang diperoleh terhadap kadar total fenolik dan aktivitas antioksidan tidak berbeda jauh dengan nilai prediksinya dari software Design-Expert metode simplex lattice design (SLD), yaitu sebesar 3,257 mg GAE/g bobot kering pada kadar total fenolik, 0,182 µmol TE/g bobot kering pada aktivitas antioksidan metode DPPH, dan 8,117 µmol TE/g bobot kering pada aktivitas antioksidan metode FRAP dengan nilai desirability sebesar 0,621. Hal ini dilihat dari nilai signifikansi (p-value) pada kadar total fenolik dan aktivitas antioksidan yang menunjukkan lebih besar dari 0,05., Gendarussa (Justicia gendarussa Burm. f.) is a medicinal plant that has antioxidant compounds to counteract free radicals due to the content of secondary metabolites such as phenolic compounds. The extracted phenolic content and antioxidant activity value can be affected by the use of extraction solvent. This study aimed to determine the best solvent between water, ethanol, and acetic acid and their combination for extracting the leaves of the gendarussa plant using the sonication method on total phenolic content and antioxidant activity (DPPH and FRAP methods) in vitro. The results showed that the verification value obtained for total phenolic content and antioxidant activity did not differ much from the predicted values from Design-Expert software simplex lattice design (SLD) method, which was 3.257 mg GAE/g dry weight on total phenolic content, 0.182 µmol TE/g dry weight on antioxidant activity of DPPH method, and 8.117 µmol TE/g dry weight on antioxidant activity of FRAP method with a desirability value of 0.621. This can be seen from the significance value (p-value) on total phenolic content and antioxidant activity which showed greater than 0.05.
Keyword: antioxidant activity, DPPH, FRAP, gendarussa, phenolic

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: