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: Total Flavonoids, Antioxidant Capacity, and Compound Identification of Red Ginger (Zingiber officinale var. rubrum) Extract from Sukabumi
Abstrak: Jahe Merah (Zingiber officinale var. rubrum) dikenal sebagai tanaman tradisional yang dimanfaatkan sebagai obat. Salah satu potensi dari jahe merah sebagai antioksidan karena adanya kandungan metabolit sekunder berupa senyawa flavonoid. Metode ekstraksi dan pelarut yang digunakan perlu diperhatikan untuk memperoleh hasil senyawa antioksidan dari ekstrak jahe merah asal Sukabumi. Penelitian ini bertujuan menentukan total flavonoid, kapasitas antioksidan, dan identifikasi senyawa dari ekstrak etanol serta ekstrak air jahe merah asal Sukabumi. Ekstraksi dilakukan dengan metode maserasi. Ekstrak dari kedua pelarut masing-masing diukur kadar total flavonoid serta kapasitas antioksidan dengan metode FRAP. Hasil penelitian menunjukkan ekstrak etanol memiliki nilai total flavonoid dan kapasitas antioksidan lebih tinggi sebesar 5,99 mg QE/g dan 473,93 µmol TE/g dibanding ekstrak air 3,73 mg QE/g dan 206,75 µmol TE/g. Uji lanjutan ekstrak etanol kemudian dianalisis menggunakan LC-MS/MS yang menghasilkan 22 senyawa aktif seperti golongan fenolik dan terpenoid. Kedua golongan tersebut memberikan kapasitas antioksidan yang tinggi di jahe merah asal Sukabumi., Red ginger (Zingiber officinale var. rubrum) is known as a traditional plant that is used as medicine. One of the potentials of red ginger as an antioxidant is that it contains secondary metabolites in the form of flavonoid compounds. The extraction method and solvent used need to be considered to obtain antioxidant compounds from red ginger extract from Sukabumi. This research aimed to determine total flavonoids, antioxidant capacity, and identify compounds from the ethanol extract and water extract of red ginger from Sukabumi. Extraction is carried out using the maceration method. Extracts from both solvents were each measured for total flavonoid content and antioxidant capacity using the FRAP method. The results showed that the ethanol extract had a higher total flavonoid and antioxidant capacity value of 5.99 mg QE/g and 473.93 µmol TE/g compared to the water extract of 3.73 mg QE/g and 206.75 µmol TE/g. Further tests of the ethanol extract were then analyzed using LC-MS/MS, which produced 22 active compounds such as phenolics and terpenoids. These two groups provide high antioxidant capacity in red ginger from Sukabumi.
Keyword: antioxidant, flavonoids, red ginger, solvent, LC-MS/MS

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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