Judul: Extending the Shelf Life of Mandarins (Citrus  nobilis Lour) with Palm Oil Coating.
Abstrak: Jeruk siam (Citrus nobilis Lour) memiliki karakteristik yang khas, yakni kulit berwarna hijau meskipun telah matang dan daging buahnya lunak dengan rasa manis dan harum. Edible coating merupakan lapisan tipis yang terbuat dari bahan yang dapat dikonsumsi, dibentuk untuk melapisi makanan atau produk. Tujuan dari penelitian ini mengetahui pengaruh konsentrasi emulsi minyak kelapa sawit dalam memperpanjang umur simpan buah jeruk siam. Penelitian dilaksanakan di Laboratorium pascapanen Agonomi dan Hortikultura IPB. Jeruk Siam yang digunakan berasal dari mitra yang berada di Sumatera Utara. Penelitian ini menggunakan rancangan percobaan Rancangan Kelompok Lengkap Teracak (RKLT) faktor tunggal, yaitu konsentrasi bahan pelapisan. Perlakuan konsentrasi minyak kelapa sawit yang diuji adalah 0% (kontrol), 3, 6, 9, dan 12%. Hasil penelitian perlakuan emulsi minyak kelapa sawit berpengaruh nyata terhadap nilai citrus color index, dapat mengurangi susut bobot, kilap warna. Emulsi minyak kelapa sawit berpengaruh nyata terhadap PTT, namun perlakuan emulsi minyak kelapa sawit tidak mempengaruhi kekerasan buah dan kualitas internal buah seperti, asam total, dan vitamin C. Perlakuan pelapisan dengan emulsi minyak kelapa sawit konsentrasi 3% merupakan perlakuan paling efektif dalam masa simpan dibandingkan perlakuan yang lainnya selama penyimpanan 21 hari pada suhu ruang., Mandarins (Citrus nobilis Lour) have distinctive characteristics, namely green skin even when ripe and soft flesh with a sweet and fragrant taste. Edible coatings are thin layers made of edible materials, formed to coat food or products. The purpose of this study is to determine the effect of palm oil emulsion concentration on extending the shelf life of mandarins fruit. The research was conducted at the Agronomy and Horticulture IPB postharvest laboratory. The mandarins used are originated from partners in North Sumatra. This study used a single-factor namely the concentration of coating material. Completely randomized group design experimental design is used. The palm oil concentration treatments tested were 0% (control), 3, 6, 9, and 12%. The results of palm oil emulsion treatment significantly affect the citrus color index, can reduce weight loss, color glossyness. Palm oil emulsion had a significant effect on total soluble solid, but did not affect fruit firmness and internal fruit quality such as total acid and vitamin C. Coating treatment with 3% of palm oil emulsion was the best treatment in terms of shelf life compared to the other treatments during 21 days of storage at room temperature.
Keyword: Edible coating, susut bobot, Citrus color index, Warna kulit

Judul: The Effect of Ethephon and Beeswax Concentrations on Degreening and Shelf Life of Medan Honey Siamese Mandarin (Citrus nobilis L.)
Abstrak: Jeruk Siam Madu Medan (Citrus nobilis L.) merupakan jeruk yang berpotensi tinggi karena manis, segar, dan mengandung vitamin C yang tinggi. Umumnya jeruk ini memiliki warna hijau dan kuning yang tidak merata meskipun sudah matang dibandingkan dengan jeruk impor yang jingga penuh sehingga menyebabkan tingginya volume impor. Degreening adalah proses menghasilkan pigmen karotenoid dan menurunkan pigmen klorofil yang dapat memperbaiki kualitas warna kulit buah jeruk. Penelitian ini bertujuan mengetahui pengaruh konsentrasi ethephon terhadap perubahan sifat fisik dan konsentrasi lilin lebah dalam memperpanjang umur simpan buah jeruk. Degreening dilakukan menggunakan konsentrasi ethephon 0, 500, dan 1000 ppm. Pelilinan dilakukan menggunakan konsentrasi lilin lebah 0% dan 4%. Hasil analisis penelitian menunjukkan selama penyimpanan 27 hari pada suhu ruangan 26.5-28.0 oC dan RH 52.7-61.0% tidak terdapat interaksi antara ethephon dan lilin lebah. Perlakuan ethephon berpengaruh nyata terhadap degreening dengan konsentrasi ethephon 500 ppm menghasilkan warna jingga tertinggi dengan nilai CCI 7.51 dan ohue 70.12 pada 14 HSP. Pelapisan lilin lebah konsentrasi 4% efektif mencegah pengurangan ukuran diameter buah sebesar 0.60 cm dari 6 hingga 14 HSP, namun hanya berpengaruh nyata dalam menekan susut bobot pada 2 HSP. Degreening hanya mempengaruhi kualitas eksternal, namun tidak dengan internal buah jeruk Siam Madu Medan., Medan Honey Siamese mandarin (Citrus nobilis L.) is high potential fruits because its sweet, fresh, and high of vitamin C. Visually, these mandarins have uneven green and yellow color even though already ripe compared to the imported mandarins with fully orange color that causing Indonesia has high import volume. Degreening is a process of producing carotenoid and degrading the chlorophyll chemically to improve the quality of citrus peel color. The study aims to observe the effects of ethephon and beeswax concentrations on changes the physical properties and extending the shelf life of citrus fruits. Degreening was conducted using ethephon at concentrations of 0, 500, and 1000 ppm and beeswax coating at concentrations of 0% and 4%. The analysis showed that during 27 days of storage at room temperature of 26.5-28.0 oC and RH 52.7-61.0%, degreening with 500 ppm ethephon produced the highest orange colour with Citrus Color Index (CCI) value of 7.51 and ohue 70.12. The treatment of 4% beeswax effectively suppressed the diameter shrinkage by 0.6 cm at day 6 to 14, but only effected on reducing weight loss at second day after treatment. Postharvest degreening treatment only affected the external quality but not the internal quality of Medan Honey Siamese mandarins.
Keyword: carotenoid, coating, exogenous, peel color, rutaceae

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: