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"ABSTRAKDalam analisis multivariate klasik dalam suatu uji hipotesa sering digunakananalisis nilai eigen dalam penetuan statistik ujinya. Dibawah kondisi H0, nilaistatistik uji yang diperoleh akan digunakan untuk bentuk distribusi yang berkaitandengan statistik uji. Daerah kritis penolakan suatu uji uji hipotesa ditentukanberdasarkan bentuk distribusi yang diperoleh. Nilai eigen yang diperoleh untukanalisi multivariat ini untuk pembentukan statistik ujinya bisa menggunakanfungsi yang melibatkan keseluruhan nilai eigen atau dengan menggunakan nilaiyang ekstrem. Untuk nilai eigen yang maksimum statistik uji yang digunakanberdasar Roy test maksimum. Cara lain yang digunakan adalah denganpendekatan distribusi Tracy-Widom. Disamping daerah kritis yang diperoleh jugadibutuhkan p-value berdasar nilai statistik uji yang sebenarnya.

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ABSTRACTClasical multivariate analysis in test hipothesa H0 most used eigen analysis indetermined their test statistics . Under H0 test statistics which founded wiil beused to make distribution concerning with test statistics. Critical area H0determined their distributions. Eigenvalue which founded will be used to buildtest statistics may included entilrely or eigen value maximum. Roy maximum testhad used maximum eigen value for inference by Tracy-Widom distribution.Besides founded critical area, for also wanted p-value for their test statisticswhich had found"

"Hotspot adalah daerah yang memiliki intensitas yang paling tinggi pada suatu lokasi tertentu. Salah satu metode yang digunakan dalam mendeteksi hotspot adalah Upper Level Set (ULS) scan statistics. ULS scan statistics adalah suatu metode yang digunakan untuk mendeteksi dan mengevaluasi kelompok daerah yang memiliki intensitas paling tinggi dari suatu kejadian yang diperhatikan. Dalam tulisan ini, kejadian diasumsikan berdistribusi Gamma. Pada ULS scan statistics, calon - calon hotspot di ditentukan oleh suatu rate atau level g. Daerah - daerah yang memiliki rate lebih besar dari g membentuk suatu scanning window yang merupakan kumpulan daerah calon hotspot. Pembentukan hotspot pada metode ini dapat dinyatakan dengan ULS Scan Tree. Tiap node pada tree merupakan anggota scanning window. Statistik likelihood yang sesuai dan metode Monte Carlo digunakan untuk menentukan signifikansi scanning window sebagai hotspot. Dalam skripsi ini, ULS scan statistics dengan model respon Gamma digunakan untuk mendeteksi daerah dengan curah hujan tertinggi di wilayah Daerah Aliran Sungai (DAS) Citarum, Bandung, Jawa Barat."

"This update of the 1987 title of the same name is an examination of what is currently known about the probabilistic method, written by one of its principal developers. Based on the notes from Spencer's 1986 series of ten lectures, this new edition contains an additional lecture: The Janson Inequalities. These inequalities allow accurate approximation of extremely small probabilities. A new algorithmic approach to the Lovasz Local Lemma, attributed to Jozsef Beck, has been added to Lecture 8, as well. Throughout the monograph, Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favor of clearer exposition. The book is not encyclopedic--it contains only those examples that clearly display the methodology. The probabilistic method is a powerful tool in graph theory, combinatorics, and theoretical computer science. It allows one to prove the existence of objects with certain properties (e.g., colorings) by showing that an appropriately defined random object has positive probability of having those properties."

"This volume constitutes the refereed proceedings of the 15th International Workshop on Combinatorial Image Analysis, IWCIA 2012, held in Austin, TX, USA in November 2012. The 23 revised full papers presented were carefully reviewed and selected from numerous submissions. The topics covered include digital geometry, combinatorics in digital spaces, digital curves and surfaces; digital topologyl grammars, transformation, applications; grammars and models in image analysis; picture transformations, morphologic operations, image segmentation; and discrete tomography, applications"

"Probability theory is a rapidly expanding field and is used in many areas of science and technology. Beginning from a basis of abstract analysis, this mathematics book develops the knowledge needed for advanced students to develop a complex understanding of probability. The first part of the book systematically presents concepts and results from analysis before embarking on the study of probability theory. The initial section will also be useful for those interested in topology, measure theory, real analysis and functional analysis. The second part of the book presents the concepts, methodology and fundamental results of probability theory. Exercises are included throughout the text, not just at the end, to teach each concept fully as it is explained, including presentations of interesting extensions of the theory. "

"This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface geometry in higher-dimensional Euclidean spaces, in particular the differential equations of Gauss-Weingarten together with various integrability conditions and corresponding surface curvatures. It includes a chapter on curvature estimates for such surfaces, and, using results from potential theory and harmonic analysis, it addresses geometric and analytic methods to establish the existence and regularity of Coulomb frames in their normal bundles, which arise as critical points for a functional of total torsion."

"This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings. Still, there are several nongeometric optimization problems that receive full treatment, and these include the problems of the longest common subsequence and the longest increasing subsequence. The philosophy that guides the exposition is that analysis of concrete problems is the most effective way to explain even the most general methods or abstract principles."