Judul: Anti-Aging Activities of Cream Formulated with Nanophytosome of Jernang Waste and Gotu Kola Leaf
Abstrak: Krim anti penuaan kulit (antiaging) berbahan aktif (BA) sintetis impor dan berefek samping sehingga krim antiaging BA dari limbah jernang/LJ (Daemonorops acehensis Rustami) dan daun pegagan/DP (Cantella asiatica Linn) dikembangkan. Penelitian bertujuan menentukan rendemen dan fitokimia ekstrak DP dan LJ, karakterisasi nanofitosom kombinasi ekstrak (KE) dan uji aktivitas antioksidan dan tabir surya, dan menguji efektivitas formula krim (in vivo). Ekstraksi LJ dan DP dengan etanol. KE 1:1 dibuat menjadi nanofitosom (NF), diuji antioksidan dan tabir surya (in vitro). Krim F1 (KE 4%), F2 (KE 8%), F3 (NFKE 4%), dan F4 (NFKE 8%), krim tanpa BA (KN), dan krim komersial (KP) diolesi ke kulit mencit jantan (14 hari). Rendemen ekstrak LJ dan DP adalah 18,35% dan 30,39%. LJ mengandung dracohorbin perchlorate dan 2’,5- Dimethoxyflavonei. DP mengandung asiatikosida dan kaempferol. Terjadi ikatan P=O lesitin dengan OH KE. Ukuran partikel NFKE masuk ke Large Unilamelar Vesicle. Antioksidan dan SPF in vitro menurun namun meningkat secara in vivo. Formula krim NFKE 8% (F4) memiliki aktivitas anti penuaan kulit terbaik karena alergenitas, persen kolagen, kecerahan (GVU 177,94), dan kerutan tidak berbeda nyata dengan KP.
Keyword: alergenitas, fisikokimia, in vivo, kecerahan, kolagen/allergenicity, brightness, collagen, in vivo, physicochemistry

Judul: Physicochemical Stability of Anti-aging Cream Formulas with Active Ingredients of Nanoemulsion and Nanophytosome of Merbau Wood  Extracts and Pegagan Leaf Extracts Combination
Abstrak: Penuaan kulit dapat dicegah dengan menggunakan krim anti-aging, tetapi umumnya berbahan aktif sintetik yang berbahaya dan impor. Nanofitosom dan nanoemulsi kombinasi ekstrak kayu merbau dan daun pegagan (KE) menjadi subsitusinya. Penelitian ini bertujuan menentukan stabilitas sifat fisikokimia empat belas formula krim berbahan aktif KE1:2 (F1:1,2%; F2:2,4%), KE2:1 (F3:4%; F4:8%), nanoemulsi KE1:2 (F5:4%; F6:8%), nanoemulsi KE2:1 (F7:4%; F8:8%), nanofitosom KE1:2 (F9:4%; F10:8%), nanofitosom KE2:1 (F11:4%; F12:8%), kontrol negatif (KN), dan kontrol positif (KP) yang disimpan pada suhu ruang selama 21 hari. Hasil penelitian menunjukkan homogenitas, warna, dan aroma semua formula krim stabil. Kecuali F2 dan F12, kedua belas formula krim memenuhi standar SNI 16-4399- 1996 untuk nilai pH, viskositas, dan daya sebar. Formula krim KP, F3, F4, F5, F6, F7, dan F8 termasuk krim terbaik untuk diaplikasikan pada wajah karena memiliki pH sekitar 4,5-6,5. Penyimpanan selama 21 hari mempengaruhi nilai pH, viskositas, dan daya sebar formula krim tersebut, tetapi masih memenuhi standar SNI 16-4399- 1996., Skin aging can be prevented by using anti-aging creams, but generally using synthetic active ingredients that are dangerous and imported. The combination of merbau woods extract and pegagan leaves (KE) became the substitute. To improve its bioavailability, KE was made into nanophytosome and nanoemulsion. This study aim to determine the stability of the physicochemical properties of fourteen cream formulas with active ingredients KE1:2 (F1:1,2%; F2:2,4%), KE2:1 (F3:4%; F4:8%), KE1 nanoemulsion: 2 (F5:4%; F6:8%), KE2:1 nanoemulsion (F7:4%; F8:8%), KE1:2 nanophytosome (F9:4%; F10:8%), KE2:1 nanophytosome (F11:4%; F12:8%), negative control (KN), and positive control (KP). The creams were stored at room temperature for 21 days. The results showed that all cream formulas' homogeneity, color, and aroma were stable. Except for F2 and F12, the twelve cream formulas met the standards of SNI 16-4399-1996 for the value of pH, viscosity, and spreadability. KP, F3, F4, F5, F6, F7, and F8 cream formulas are among the best creams to be applied to the face because they have a pH value of around 4.5-6.5. The storage for 21 days affected the pH value, viscosity, and spreadability, but they still met the standard of SNI 16-4399-1996.
Keyword: spreadability, homogeneity, organoleptic, pH, viscosity

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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