Judul: Hubungan linear antara bilangan fibonacci, bilangan lucas dan golden section di himpunan bilangan real tak negatif
Abstrak: Leonardo of Pisa (Fibonacci), pada tahun 1202 menemukan barisan bilangan yang diperoleh dari bertambahnya jumlah pasangan kelinci tiap bulan. Kelinci tersebut diasumsikan hidup selamanya. Bilangan pada barisan tcrscbut empat abad kemudian oleh Kepler dinyatakan dalam rumus rekursif berikut: F(0) = 0, F(I) = I, F(n+2)=F(n) + F(n+I), dengan n = 0, I, 2, ..... Oleh Eduard Lucas, bilangan pada barisan tersebut diberi nama Bilangan Fibonacci. Kemudian Lucas menemukan barisan bilangan yang mirip dengan bilangan Fibonacci, yaitu : L(0) = 2, l(I) = I, l(n+2)=l(n) + l(n+I), dengan n = 0, I, 2, .... lebih dari ernpat puluh persamaan yang menyatakan hubungan linear antara bilangan Fibonacci, bilangan Lucas dan Golden Section. Sebagian besar dapat dibuktikan dengan prinsip induksi matematika dan aljabar di himpunan bilangan real.
Keyword: Fibonacci numbers, number line, mathematical induction

Judul: Nilai Eigen, Determinan dan Norm Matriks Circulant dengan Entri Bilangan k-Fibonacci
Abstrak: Matriks circulant adalah matriks yang entrinya bergeser satu kolom ke kanan secara berurutan pada baris berikutnya. Entri–entri matriks circulant dapat diisi dengan berbagai barisan bilangan, salah satunya adalah bilangan k–Fibonacci. Berdasarkan definisinya, pada karya ilmiah ini, nilai eigen, determinan dan norm matriks circulant dengan entri bilangan k–Fibonacci diformulasikan secara eksplisit. Kemudian, contoh kalkulasi berdasarkan rumusan tersebut diberikan sebagai ilustrasi., A circulant matrix is a matrix whose entries are shifted one column to the right in succession in the next row. Circulant matrix entries can be filled in various sequence of numbers, one of which is k–Fibonacci number. In this scientific paper, based on the definition, the eigenvalues, determinants and norms of the circulant matrix with the entries of k–Fibonacci numbers are formulated explicitly. Then, examples of the calculation of the obtained formulas are given as illustrations.
Keyword: circulant matrix, determinants, eigen values, matrix norms, k-Fibonacci number

Judul: Karakteristik Carboxymethyl Chitosan Dengan Variasi Konsentrasi NaOH
Abstrak: Carboxymethyl chitosan is chitosan derivative product obtained from chemical modification. CMCh were made by alkalization process and carboxymethylation process. Factors that affect CMCh characteristics were excess sodium hydroxide in alkalization process, ratio between chitosan and monochloroacetic acid, and carboxymethylation temperature. The objectives of this research were to study the NaOH effect to CMCh characteristics, to learn process of making CMCh, to set the proper concentration of NaOH, and to analyze CMCh characteristics. CMCh yields were 110.72%-114.22%. CMCh pH value were 3.74-4.31. The optimum NaOH concentration to obtain the best CHCh was 10 M. Percentage of CMCh moisture content was 10.70%-11.42%. Ash content and nitrogen content of CMCh were 0.49%-0.50% and 4.52%-4.81%. CMCh viscousity was 8.25 cps. Percentage of CMCh solubility was 61.61%-91.50%. The different functional groups from chitosan which observed in CMCh were C=O group, CH group from alkene functional group, C−O group, and C−O−C group.
Keyword: solubility., functional group, CMCh characteristics, chitosan, carboxymethyl chitosan