Judul: Pengaruh Minyak Atsiri sebagai Bioaditif pada Biosolar B30 dalam Menurunkan Kadar Air dan Partikulat
Abstrak: Biodiesel is an alternative fuel that can replace the use of fossil fuels, but it has several drawbacks such as high on water, and particulate content. One way to reduce the impact of this deficiency is by adding bioadditives to improve its quality. This research aims to determine the best essential oils amongs turpentine, clove terpene oil, citronella oil, and rhodinol, to develop bioadditive formulations from the combination of the said essential oils and to get the effective concentration to reduce water, and particulates content. The research was conducted by mixing citronella oil, turpentine, clove terpene, and rhodinol, as well as a bioadditive formulas of a mixture of said essential oils, namely bioadditive A (Turpentine: Clove Terpen: Citronella Oil) with variations of A1, A2, & A3, and bioadditive B (Trepentine: Clove Terpenes: Rhodinol) with variations of B1, B2, & B3 into biosolar B30. The tests carried out were the water content test, as well as the particle count test. The results showed that the largest decrease in water content was produced by turpentine at a concentration of 1% with a percentage decrease of 19.11%, and bioadditive A1 at a concentration of 0.1% with a percentage decrease of 4.8%. The best particulate reduction was found in bioadditive B1 with the percentage reduction values for sizes 4 microns, 6 microns, and 14 microns were 93%, 95%, and 78%, respectively., Biodiesel merupakan bahan bakar alternatif yang dapat menggantikan penggunaan bahan bakar fosil, namun memiliki kekurangan seperti tingginya kadar air, dan kadar partikulat. Salah satu cara untuk mengurangi dampak dari kekurangan ini adalah dengan cara melakukan penambahan bioaditif untuk meningkatkan kualitasnya. Penelitian bertujuan untuk mengetahui minyak atsiri terbaik diantaranya minyak terpentin, clove terpen, minyak sereh wangi, dan rhodinol, lalu mengembangkan formulasi bioaditif dari kombinasi minyak atsiri yang digunakan, serta mendapatkan konsentrasi yang efektif untuk menurunkan kadar air, dan partikulat. Penelitian dilakukan dengan cara mencampurkan minyak sereh, terpentin, clove terpen, dan rhodinol, serta formula bioaditif campuran minyak atsiri yaitu bioaditif A (Terpentin: Clove Terpen: Citronella Oil) dengan variasi A1, A2, & A3, dan bioaditif B (Terpentin: Clove Terpen: Rhodinol) dengan variasi B1, B2, & B3 ke dalam biosolar B30. Pengujian yang dilakukan adalah uji kadar air, serta uji kadar partikulat (particle count). Hasil penelitian menunjukan bahwa penurunan kadar air terbesar dihasilkan oleh terpentin pada konsentrasi 1% dengan persentase penurunan sebesar 19.11%, dan bioaditif A1 pada konsentrasi 0.1% dengan persentase nilai penurunan sebesar 4.8%. Penurunan kadar partikulat terbaik didapatkan pada bioaditif B1 dengan persentase nilai penurunan untuk ukuran 4 mikron, 6 mikron, dan 14 mikron masing-masing adalah 93%, 95%, dan 78%.
Keyword: bioaditive, biosolar B30, essential oil, particulate content, water content

Judul: Bioaditive Effect of Essential Oils on Decreasing Particulate Levels and Water Content in Biosolar Fuel B30
Abstrak: One of the efforts that can be made to improve the quality of diesel fuel is the addition of additives. Natural and renewable potential alternatives as fuel additives are essential oils. The purpose of this study was to determine the effect of adding bioadditive and to obtain the best formula to reduce particulate levels and water content of diesel fuel. This research includes mixing bioadditive ingredients consisting of clove terpene, rhodinol, and turpentine oil with a concentration of 0.5%, and a mixture with a composition of 1: 1: 8; 0.33: 0.67: 8; 0.5: 1.5: 8, the addition of a bioadditive formula into the biodiesel with a concentration of 1%. Tests conducted in the form of density, viscosity, particulate content, and moisture content. The largest reduction in particulate levels was produced by the addition of 0.5% bioaditive clove terpenes. The reduction in particulate content was 38.26% at the 4 micron measurement, 62.85% at the 6 micron measurement, 91.11% at the 14 micron measurement for B30 fuel. The best reduction in water content is produced by the fuel with the addition of a single compound bioadditive in the form of turpentine oil, which reduced the water content of B30 to 282 ppm. The best additive formula to reduce particulate content was 1% bioadditive second formula (BA2) which reduced the particulate content of 4 microns by 88.37%, 6 microns by 94.34%, and 14 microns by 98.19%. The best bioadditive formula to reduce water content was 1% bioadditive third formula (BA3) which reduced water content to 218 ppm.
Keyword: : bioaditive, biosolar, essential oil, particulate, water

Judul: igenvalues and Eigenvectors of Tridiagonal Matrix with Non Constant and Recurrent Diagonal Entries.
Abstrak: Matriks tridiagonal adalah suatu matriks yang mempunyai entri-entri bernilai nol kecuali pada diagonal utama, di bawah diagonal utama (subdiagonal) dan di atas diagonal utama (superdiagonal). Entri pada diagonal utama tidak konstan dan berulang. Setiap entri pada matriks tridiagonal ini adalah bilangan kompleks. Dalam karya ilmiah ini, akan dibuktikan 3 teorema untuk menentukan nilai eigen dengan 2 kasus dan 1 teorema untuk menentukan vektor eigen. Teorema pertama menentukan polinomial karakteristik dari matriks tridiagonal. Polinomial karakteristik dari matriks tridiagonal tersebut digunakan untuk menentukan nilai eigen pada teorema kedua dan ketiga serta menentukan vektor eigen pada teorema keempat
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