Judul: The effect of pipe perforation on the productivity  of pine oleoresin using the drill method
Abstrak: Metode bor merupakan metode tertutup sehingga udara yang berada di dalam wadah penampung tidak terhubung dengan udara luar. Ketika oleoresin keluar dari saluran getah maka akan menekan udara yang ada di dalam wadah penampung dan terjadi tekanan udara balik yang menghambat keluarnya getah. Penelitian ini menggunakan 5 perlakuan berbeda yaitu perlakuan A dengan metode bor dan penampung getah berupa mangkok plastik tertutup, perlakuan B dengan metode bor menggunakan pipa yang tidak dilubangi, perlakuan C berupa metode bor tanpa pipa, perlakuan D berupa metode bor menggunakan pipa yang telah dibuat 1 lubang, dan perlakuan E berupa metode bor menggunakan pipa yang telah dibuat 2 lubang. Hasil penelitian menunjukkan metode bor dengan pipa yang telah dibuat 2 lubang memberikan hasil yang paling tinggi. Sehingga penggunaan pipa yang dibuat 2 lubang dapat dijadikan solusi dalam penyadapan oleoresin pinus agar menghasilkan getah yang lebih banyak dibandingkan metode bor dengan pipa yang tidak dilubangi., The drill method is a method of closing the air that is in the container not connected to the outside air. When oleoresin comes out of the sap channel, it will press on the container and air pressure will occur which inhibits the release of sap. This study used 5 different treatments, namely treatment A with a drill method and a sap reservoir in the form of a closed plastic bowl, B with a drill method using a pipe that is not perforated, treatment C in the form of a drill method without a pipe, treatment D in the form of a drill method using a pipe that has been made 1 hole, and treatment E in the form of a drill method using a pipe that has been made 2 holes. The results showed that the drill method with a pipe that had 2 holes made gave the highest results. So that the use of pipes made of 2 holes can be used as a solution in tapping pine oleoresin to produce more sap compared to the drill method with pipes that are not perforated.
Keyword: air, drill method, pipe perforation, presussure, productivity

Judul: Produktivitas Penyadapan Getah Pinus dengan Metode Bor tanpa Pipa
Abstrak: Drill method is a method of tapping that gives many advantages but also has many deficiency, such as the use of pipes is not efficient and add more costs, it also difficult to move the resin from the receptacle into a drum, and it can’t accommodate the resin which came after the tapping period. This research uses five different treatments. Treatment A by using the quarre method without stimulansia as a control, treatment B by using the quarre method with stimulansia, treatment C by using the drilling method with a pipe, treatment D by using drilling method without a pipe, and treatment E by using the drill method with a pipe and resin shelters not on a pipe. The tree sample used in every treatment is 10. The research shows that the treatment D by using drill method without a pipe gives the highest resin productivity however it has more water content and higher levels of impurities than the other drill method designed. Thus, drill methods without a pipe, is a tapping solution that capable of producing qualified resin also has not destructive to trees compared to the quarre method. It also can produce more resin with an economical and practical surplus than the drill method by using a pipe.
Keyword: quality, productivity, pine resin, drill method

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
Keyword: