Judul: Penyelesaian Masalah Rotasi Aliran Fluida Kental Von Karman Menggunakan Metode Spektral Homotopi
Abstrak: Masalah rotasi aliran fluida kental Von Karman sering muncul pada masalah rotasi bahan bakar pesawat ruang angkasa yang diluncurkan oleh NASA. Pengendalian besaran kecepatan rotasi pada aliran Von Karman penting dilakukan. Persamaan yang menjelaskan rotasi aliran pada fluida kental yang disebabkan oleh cakram yang berputar terus-menerus adalah persamaan Von Karman. Pada karya ilmiah ini, pendekatan analitik untuk menyelesaikan persamaan Von Karman dilakukan dengan metode spektral homotopi. Dalam metode ini, dikombinasikan metode spektral dan metode homotopi. Sebagaimana metode homotopi, diperlukan parameter bantu untuk mengontrol daerah kekonvergenan penyelesaian. Penyelesaian yang dihasilkan merupakan suatu rumus rekursif dengan suatu hampiran awal yang diberikan. Menggunakan perangkat lunak berbasis fungsional, diperoleh penyelesaian berupa besaran komponen kecepatan yang konvergen ke suatu nilai.
Keyword: persamaan Von Karman, metode spektral homotopi, masalah taklinear

Judul: Penyelesaian Masalah Rotasi Aliran Fluida Kental Von Karman Menggunakan Metode Homotopi
Abstrak: Von Karman equation is an equation that describes fluid viscous flow induced by infinite disk rotation. By assuming steady flow and laminar, viscous incompressible fluid flow is represented in Von Karman equation by an angular velocity and the vertical direction velocity as the independent variables. Von Karman equation is a nonlinear problem that is solved using the homotopy method. The use of homotopy method is done by defining an homotopy function that requires auxiliary parameters to control the convergent region of the solution. The solution is a recursive formula with given initial conditions. Using software based-functional shows that velocity components converge to a value.
Keyword: 

Judul: Lejeuneaceae Subfamily Ptychanthoideae (Hepaticae) in  West Java
Abstrak: Subfamily Ptychanthoideae of the family Lejeuneaceae (Hepaticae) in West Java is still poorly known. Publications on this subfamily are out of dated and written in the 19th or early of 20th century. The last taxonomic treatment of Ptychanthoideae of West Java was in 1933, many species names have changed since then. Studies on Ptychanthoideae of West Java are urgently needed. Studies on the Ptychanthoideae were based on the specimens collected from West Java. A total number of 361 of specimens deposited in the Herbarium Bogoriense (BO), Herbarium Biotrop (BIOT), Gottingen Herbarium (GOET) and Bangi Herbarium (UKMB) were examined, those are old and several recent specimens collected in West Java. Recent collections were made from Telaga Warna, Ciater, Gunung Halimun Salak National Park, Cibodas Botanical Garden, Bodogol Education Center and Conservation (Gunung Gede Pangrango National Park), University of Indonesia Campus Depok, including several collections from Banten Province. Twenty four species of Lejeuneaceae subfamily Ptychanthoideae are known from West Java, belonging to 8 genera namely Acrolejeunea (Spruce) Schiffn. (2 species), Archilejeunea (Spruce) Schiffn. (1 species), Lopholejeunea (Spruce) Schiffn. (10 species), Mastigolejeunea (Spruce) Schiffn. (3 species), Ptychanthus Nees (1 species), Schiffneriolejeunea Verd. (1 species), Spruceanthus Verd. (2 species) and Thysananthus Lindenb. (4 species). Two new records of Ptychanthoideae: Mastigolejeunea indica Steph. and Thysananthus minor Verdoorn are reported for Java. A determination key to the species is presented including their descriptions and illustrations.
Keyword: