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: Determinan dan Invers Matriks Skew Left Circulant dengan Entri  Bilangan Fibonacci
Abstrak: Matriks skew left circulant adalah suatu matriks persegi dengan entri baris bergeser satu kolom secara berurutan ke kiri dan semua entri yang berada dibawah diagonal sekunder akan bernilai negatif, sehingga untuk mengetahui seluruh matriks skew left circulant dapat dilihat dari salah satu baris dari matriks tersebut. Entri-entri dari skew left circulant dapat menggunakan entri dengan berbagai barisan bilangan, salah satunya adalah dengan barisan bilangan Fibonacci. Pada karya ilmiah ini diformulasikan determinan dan invers matriks skew left circulant dengan entri bilangan Fibonacci. Pembuktian Formulasi determinan matriks skew left circulant diperoleh dari penerapan serangkaian operasi baris dasar pada matriks skew circulant sehingga diperoleh matriks segitiga atas, dilanjutkan mengalikan dengan determinan matriks Gamma. Sedangkan, formulasi inversnya diperoleh dengan membuat matriks-matriks dari matriks skew circulant representasi dari hasil serangkaian operasi baris dasar dan operasi kolom dasar, dilanjutkan dengan mengalikan dengan invers matriks Gamma., The left circulant skew matrix is a square matrix with row entries shifted one column sequentially to the left and all entries under the secondary diagonal will be negative, so to find out the entire circulant skew left matrix can be seen just from the first row of the matrix. Entries from the skew left circulant can be filled in various number sequences, one of which is the Fibonacci number sequence. In this scientific work, the determinants and inverses of the skew left circulant matrix are formulated with Fibonacci number entries. Proof The formulation of the skew left circulant matrix determinant is obtained from applying a series of basic row operations to the circulant skew matrix so that an upper triangular matrix is obtained, followed by multiplying it with the Gamma matrix determinant. Meanwhile, the inverse formulation is obtained by making matrices from a circulant skew matrix representing the results of a series of basic row or column operations, followed by multiplying by the inverse Gamma matrix.
Keyword: Fibonacci number, determinant, inverse, skew left circulant matrix

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