Judul: Silver Nanoparticle Biosynthesis Using Kaffir Lime  Peel Waste (Citrus hystrix) with Bioreductor Volume Variations
Abstrak: Jeruk purut (Citrus hystrix) merupakan tanaman yang telah dikenal masyarakat yang memiliki banyak kegunaan. Kandungan dalam kulit jeruk purut berpotensi dijadikan bahan bioreduktor dalam sintesis nanopartikel. Nanopartikel perak sebagai salah satu jenis nanopartikel logam memiliki sifat antibakteri serta proses sintesisnya sudah banyak dilakukan. Sintesis nanopartikel perak dilakukan dengan mereaksikan ekstrak kulit jeruk purut sebagai bioreduktor dan AgNO3 dengan konsentrasi 1 mM untuk meninjau kondisi optimal pengaruh volume bioreduktor dan suhu terhadap biosintesis nanopartikel perak. Rancangan percobaan dibuat menggunakan Response Surface Methodology dengan bentuk Central Composite Design (CCD). Nilai absorbansi maksimum 0.41-2.52 yang tercapai pada panjang gelombang 267-289 nm. Ukuran partikel yang diperoleh berkisar pada 84-503 nm yang masih dalam ukuran toleransi nanopartikel. Hasil penelitian ini menunjukkan bahwa nanopartikel perak berdiameter kurang dari 100 nm tercapai pada variasi volume 1.5 ml dengan suhu 70⁰C., Kaffir lime (Citrus hystrix) is a plant that has been known to the public that has many uses. The content in kaffir lime peel has the potential to be used as a bioreductant in the synthesis of nanoparticles. Silver nanoparticles as a type of metal nanoparticles have antibacterial properties and many synthesis processes have been carried out. The synthesis of silver nanoparticles was carried out by reacting kaffir lime peel extract as a bioreductant and AgNO3 with a concentration of 1 mM to examine the optimal conditions for the effect of bioreductant volume and temperature on the biosynthesis of silver nanoparticles. The experimental design was made using Response Surface Methodology in the form of Central Composite Design (CCD). The maximum absorbance value is 0.41-2.52 which is achieved at a wavelength of 267-289 nm. The particle size obtained is in the range of 84-503 nm which is still within the tolerance of nanoparticles. The results of this study indicate that silver nanoparticles with a diameter of less than 100 nm are achieved at a volume variation of 1.5 ml at a temperature of 70⁰C.
Keyword: AgNO3, biosynthesis, Citrus hystrix, RSM, silver nanoparticles

Judul: Green Synthesis Nanopartikel Perak Menggunakan Limbah Jeruk Purut (Citrus hystrix dc) dengan Variasi Konsentrasi AgNO3
Abstrak: Jeruk purut (Citrus hystrix) merupakan tumbuhan perdu yang kaya manfaat. Kandungan dalam kulit jeruk purut berpotensi dijadikan bahan bioreduktor dalam sintesis nanopartikel. Nanopartikel dengan sifat fisis dan kimiawinya yang unik diharapkan mampu meningkatkan nilai jual serta efektivitas pemanfaatannya. Nanopartikel perak sebagai salah satu jenis nanopartikel logam secara alami memiliki kemampuan antibakteri yang baik serta proses sintesisnya sudah banyak dilakukan. Pada penelitian ini, kulit jeruk purut dipilih sebagai bioreduktor dengan meninjau kondisi optimal pengaruh variasi konsentrasi AgNO3 dan waktu penyimpanan terhadap green synthesis nanopartikel perak. Rancangan percobaan dibuat menggunakan Response Surface Methodology dengan bentuk Central Composite Design. Ukuran partikel yang dihasilkan berkisar pada 86-236 nm yang masih dalam ukuran toleransi nanopartikel. Nilai absorbansi maksimum 0,241-0,506 yang tercapai pada panjang gelombang 268-279 nm. Hasil penelitian ini menunjukkan bahwa nanopartikel perak berdiameter kurang dari 100 nm tercapai pada variasi konsentrasi 1 mM dengan waktu simpan 1 dan 29 jam., Kaffir lime (Citrus hystrix) is a herbaceous plant that is rich in benefits. The content in kaffir lime peel has the potential to be used as a bioreductant in the synthesis of nanoparticles. Nanoparticles with unique physical and chemical properties are expected to increase the selling value and effectiveness of their utilization. Silver nanoparticles as a type of metal nanoparticles naturally have good antibacterial abilities and many synthesis processes have been carried out. In this study, kaffir lime peel was chosen as a bioreductant by reviewing the optimal conditions for the effect of variations in AgNO3 concentration and storage time on the green synthesis of silver nanoparticles. The experimental design was made using the Response Surface Methodology in the form of a Central Composite Design. The resulting particle size ranges from 86-236 nm which is still within the tolerance of nanoparticles. The maximum absorbance value of 0.241-0.506 is achieved at a wavelength of 267-279 nm. The results of this study showed that silver nanoparticles with a diameter of less than 100 nm were achieved at a concentration variation of 1 mM with a shelf life of 1 and 29 hours.
Keyword: AgNO3, Kulit jeruk purut, Nanopartikel, RSM, Sintesis hijau

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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