Judul: Batas bawah nilai eigen terkecil dari matriks simetrik real
Abstrak: Dalam perkembangan ilmu dan teknologi di kehidupan sehari-hari, banyak diterapkan penggunaan nilai eigen (eigenvalues) dan vektor eigen (eigenvectors) seperti dalam bidang ilmu matematika, mekanika, sistem dinamika, dan sebagainya. Nilai eigen dari suatu matriks sangat dipengaruhi oleh entri-entri matriksnya. Oleh karena itu, mengetahui batas bawah nilai eigen terkecil dari suatu matriks akibat perubahan entrinya menjadi sangat penting. Matriks yang dibahas pada karya ilmiah ini merupakan matriks simetrik real yang entri-entrinya terletak pada suatu selang tertentu. Penentuan batas bawah nilai eigen terkecil dari matriks simetrik real tersebut ditinjau berdasarkan ukuran matriks dan nilai titik-titik ujung selang serta digunakan metode Faddeev-Leverrier untuk menentukan polinomial karakteristik dari matriks simetrik real tersebut.
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Judul: Perhitungan Nilai Eigen Terkecil dari Matriks Toeplitz Simetrik Real dan Definit-Positif dengan Metode Single Newton
Abstrak: Suatu metode yang paling luas digunakan untuk mencari hampiran akar dari suatu fungsi adalah metode Newton. Tujuan dari karya ilmiah ini adalah menghitung nilai eigen terkecil dari matriks Toeplitz simetrik real dan definit-positif dengan menggunakan metode single Newton. Polinomial karakteristik dan turunan polinomial karakteristik sangat dibutuhkan dalam melakukan iterasi pada metode ini. Untuk menunjukkan kebenaran dari rumus-rumus yang digunakan dalam metode Newton seperti nilai eigen, polinomial karakteristik, dan turunan polinomial karakteristik, maka diberikan ilustrasi serta metode analitik untuk matriks yang berorde 2 dan 3. Hasil perhitungan nilai eigen terkecil dari suatu matriks, dalam hal ini matriks Toeplitz simetrik real dan definit-positif, yang ditentukan dengan menggunakan metode single Newton sesuai dengan metode analitik.
Keyword: matriks definit-positif Toeplitz, metode Newton, nilai eigen

Judul: Development of DNA Vaccine Encoding Glycoprotein of Koi Herpes Virus Using Local Isolate.
Abstrak: The aim of this research was to develop DNA vaccine of Koi Herpesvirus in carp. Glycoprotein gene originated from ORF 25 KHV virus that is 1.8 kbp in size, is a potential gene in DNA vaccine construction. The sequencing and similarity analysis of the gene using BLAST software showed that this gene is a GP25 gene and was found to be very similar (99%) to GP25 of KHV virus from the USA and Israel. When this GP25 gene was ligated with pGEMT Easy (pT, 3 kbp in size) vector, plasmid size was increasing up to 5 kb. Following this, a digestion of pT-GP25 plasmid using Sal I enzyme was applied resulted in a GP25 fragment (1.8 kbp). Subsequently, pAct-D6 with a size of 8.5 kbp was also cut using the same enzyme to eleminate a D6 gene with a size of 1.6 kbp. GP25 gene was then ligated with pAct resulted a pAct-GP25 plasmid with a size of 8.8 kbp. As there was only one restriction site applied, ligation can be occurred in two different directions. Thus, in order to determine the plasmid with the desired direction PCR analysis was carried out, and plasmid with the right direction was the one that sized approximately 2.1 kbp (no. 6, 17 and 20). High level of GFP gene expression was detected in all tissues analyzed, i.e. kidney, gil, spleen, and muscle 24 hours after injection which indicated that β-actin promoter of Japanese medaka could be active in common carp. Although not as high as on 24 hours, expression was still detected until day 7 and disappeared after day 28 post injection indicating that pAct-GFP can be remained and β-actin promoter of Japanese medaka can be active in muscle, gills and kidney at least a week after injection. The result of RT-PCR analysis on pAct-GP25 injected common carp showed that GP25 gene expression can be detected 14 days after injection in all tissues observed. The expression level differences between GFP and GP25 genes possibly related to the primer sensitivity on annealing process to cDNA template and the size of PCR targeted DNA fragment, as smaller PCR targeted product will be easier to be amplified than a bigger one. The length of PCR targeted DNA with GP25 primer was 1.8 kbp whereas GFP gene was 0.6 kbp.The challenge test on common carp results showed that all unvaccinated and negative control (not infected with KHV) was alive until the end of the experiment. Whereas, the survival of fish vaccinated with a dose of 12.5 was ranged from 60.9 and 96.7%. In relation to the activity of β-actin promoter that was used in this DNA vaccine, gene expression was occured 24 hours after vaccination and remained until 2 weeks. The control fish that was not injected by GP25 showed no GP25 expression either in the observed tissues or organs and resulted in a lower survival, i.e. 23.3%. The challenge test results has indicated that the fish vaccinated with GP25 at doses of 7.5 and 12.5 μg/100μL were able to produce KHV glycoprotein in their body which would be
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