Judul: Antioxidant Activity of Ethanol Extract, Nanoparticles, and Microparticles of Red Ginger Rhizomes (Zingiber officinale var. Rubrum) from Sukabumi
Abstrak: Rimpang jahe merah telah terbukti memiliki potensi sebagai sumber antioksidan, sehingga diperlukan metode yang tepat untuk meningkatkan aktivitasnya. Penelitian ini bertujuan membandingkan aktivitas antioksidan dari ekstrak etanol, nanopartikel, dan mikropartikel rimpang jahe merah asal Sukabumi menggunakan metode DPPH. Ekstraksi dilakukan melalui metode maserasi menggunakan pelarut etanol 70%, sintesis nanopartikel menggunakan metode top down synthesis dengan Planetary Ball Mill (PBM), dan pembuatan mikropartikel melalui penyaringan simpisia jahe dengan ayakan berukuran 100 mesh. Hasil penelitian menunjukkan bahwa ekstrak etanol 70% menghasilkan kadar total fenolik tertinggi (35,012 ± 2,145 mg GAE/g) dibandingkan dengan sampel lainnya. Temuan ini sesuai dengan hasil uji aktivitas antioksidan yang menunjukkan bahwa ekstrak etanol memiliki aktivitas antioksidan terkuat dibandingkan dengan sampel lainnya, dengan nilai IC50 sebesar 185,561 ± 8,998 ppm. Metode ekstraksi terbukti lebih meningkatkan kadar total fenolik dan aktivitas antioksidan simpisia rimpang jahe merah, dibandingkan dengan hanya memperkecil ukuran partikel simpisia., Red ginger rhizome has been proven to have the potential as an antioxidant source, thus requiring an appropriate method to enhance its activity. This research aimed to compare the antioxidant activities of ethanol extract, nanoparticles, and microparticles of red ginger rhizome from Sukabumi using the DPPH method. The extraction was conducted through the maceration method using 70% ethanol solvent, nanoparticle synthesis was carried out using the top down synthesis method with Planetary Ball Mill (PBM), and microparticles were obtained through sieving the ginger simplicia using a 100-mesh sieve. The research results revealed that the 70% ethanol extract produced the highest total phenolic content (35,012 ± 2,145 mg GAE/g) compared to other samples. This finding is consistent with the antioxidant activity test results, which showed that the ethanol extract exhibited the strongest antioxidant activity compared to other samples, with an IC50 value of 185,561 ± 8,998 ppm. The extraction method proved to be more effective in increasing the total phenolic content and antioxidant activity of the red ginger rhizome simplicia compared to merely reducing the particle size of the simplicia.
Keyword: Antioxidant, extract, microparticles, nanoparticles, red ginger

Judul: α-Glucosidase Inhibition Activity and DPPH Free Radical Scavenging from Stratified Aqueous Extract of Red Ginger (Zingiber officinale Roxb. var Rubrum)
Abstrak: Jahe merah (Zingiber officinale Roxb. var. Rubrum) mengandung senyawa fenolik yang berpotensi menurunkan kadar glukosa darah (antihiperglikemik) pada pasien diabetes melitus. Penelitian ini bertujuan menentukan aktivitas inhibisi α-glukosidase, aktivitas antioksidan dalam meredam radikal bebas DPPH, dan kadar total fenolik ekstrak air jahe merah bertingkat (ekstrak ke-1, ekstrak residu ke-1, dan ekstrak residu ke-2). Metode penelitian yaitu ekstraksi jahe merah secara infundasi serta analisis dengan teknik uji spektronanometer yang meliputi analisis antidiabetes melalui aktivitas inhibisi α-glukosidase, aktivitas antioksidan metode DPPH, dan kadar total fenolik metode Folin-Ciocalteu. Aktivitas inhibisi α-glukosidase dan kadar total fenolik memiliki perbedaan nilai yang signifikan (p<0.05) dengan nilai tertinggi 97.729% (ekstrak ke-1) dan 27.624 mg GAE/g ekstrak (ekstrak residu ke-2). Aktivitas antioksidan dalam meredam radikal bebas DPPH memiliki perbedaan nilai yang tidak signifikan dengan nilai tertinggi 4.682 mg AAE/g ekstrak (ekstrak residu ke-1). Hasil analisis menunjukkan nilai aktivitas inhibisi α-glukosidase dan kadar fenolik total berbeda signifikan (p<0,05) dengan nilai tertinggi 97.729% (ekstrak ke-1) dan 27.624 mg GAE/g ekstrak (ekstrak residu ke-2). Hasil aktivitas antioksidan memiliki nilai yang tidak berbeda nyata (p>0,05) dengan nilai tertinggi 4.682 mg AAE/g ekstrak (ekstrak residu ke-1)., Red ginger (Zingiber officinale Roxb. var. Rubrum) contains phenolic compounds that have potential to reduce blood glucose levels (antihyperglycemic) in patients with diabetes mellitus. This study aimed to determine the inhibitory activity toward α-glucosidase, antioxidant activity in reducing DPPH free radicals, and total phenolic content from stratified aqueous extract of red ginger (1st extract, 1st residue extract, and 2nd residue extract). The red ginger was extracted by infundation and analyzed by spectronanometer test techniques which included analysis of antidiabetic through inhibitory activity of α-glucosidase, antioxidant activity using the DPPH method, and total phenolic content using the Folin-Ciocalteu method. The results of the analysis showed that the inhibitory activity of α-glucosidase and total phenolic content were significantly different (p<0.05) with the highest values 97.729% (1st extract) and 27.624 mg GAE/g extract (2nd residue extract). The result of antioxidant activity was not significantly different (p>0.05) with the highest value 4.682 mg AAE/g extract (1st residue extract).
Keyword: α-Glucosidase, Antioxidant, Diabetes Mellitus, Red Ginger

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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