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"This book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed account of the theory of classical harmonic analysis together with the recent developments in spectral analysis and synthesis."

" ABSTRAKClustering adalah salah satu topik penting pada bidang Data Mining. Teori graf dapat digunakan untuk membantu clustering dengan cara membuat graf yang mewakili data-data yang akan di-cluster. Salah satu metode graf clustering adalah k-way spectral clustering yang memanfaatkan sebanyak k nilai eigen dan vektor eigen pertama dari matriks Laplacian suatu graf untuk melakukan clustering dengan k adalah banyaknya cluster yang diinginkan. Pada skripsi ini dibahas mengenai algoritma k-way spectral clustering merujuk kepada Ng, Jordan, dan Weiss (2002) dan von Luxburg (2007).

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ABSTRACT

Clustering is one of the most important topic in Data Mining. Graph can be used to do clustering by forming a representation graph data which is needed to be clustered. K-way spectral clustering is one of many methods of graph clustering. This method uses first-k eigen values and eigen vectors of a Laplacian matrix to cluster with k is the number of desired clusters. In this skripsi, it will be discussed a k-way spectral clustering algorithm by Ng, Jordan, and Weiss (2002) and von Luxburg (2007)."

"This book constitutes the refereed proceedings of the 7th International Conference on Sequences and Their Applications, SETA 2012, held in Waterloo, Canada, in June 2012. The 28 full papers presented together with 2 invited papers in this volume were carefully reviewed and selected from 48 submissions. The papers are grouped in topical sections on perfect sequences; finite fields, boolean functions, Golomb 80th birthday session, linear complexity, frequency hopping, correlation of sequences, bounds on sequences, cryptography, aperiodic correlation, and Walsh transform."

"This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters."

"Telah dilakukan inversi Elastic Impedance dan Dekomposisi Spektral pada lapangan Penobscot, untuk mengidentifikasi reservoir pada lapisan tipis. Perkembangan atribut seismik dewasa ini sangat membantu dalam menunjukkan indikasi adanya hidrokarbon pada reservoir. Atribut Dekomposisi Spektral yang didasari dari hasil komputasi CWT diharapkan dapat menjadi atribut yang berguna untuk mendeteksi adanya indikasi keberadaan hidrokarbon pada lapisan tipis. Untuk mendukung hasil metode CWT, akan dikombinasikan dengan hasil metode inversi untuk meyakinkan akan keberadaan hidrokarbon tersebut yang ditandai dengan nilai Elastic Impedance (EI) yang relatif rendah dengan sekitarnya.Dari hasil studi ini frekuensi dominan terlihat pada frekuensi 25 Hz, sedangkan pada frekuensi 10 Hz (frekuensi rendah) dan 30 Hz (frekuensi tinggi) anomali bright spot tidak terlihat di beberapa daerah prospek. Hal ini didukung dengan hasil inversi yang menunjukkan nilai EI yang rendah yaitu berkisar 13000 - 13750 ((ft/s) *(gr/cc)), 2370 - 2511((ft/s) *(gr/cc)), dan 600 - 620((ft/s) *(gr/cc)). Kombinasi metode dekomposisi spektral berbasis CWT dengan metode inversi seismik (EI) mengindikasikan adanya akumulasi gas pada beberapa daerah prospek.

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The Elastic Impedance inversion and the Spectral Decomposition process at the Penobscot field has been carried out, in order to identify the reservoir on a thin layer. The development of seismic attributes these days are very helpful in indicating any presence of Hydrocarbons in the reservoir. The Spectral Decomposition attribute, that based on the results of CWT computation is expected to become applicable in detecting and indicating any presence of Hydrocarbons in a thin layer. In order to support the results of CWT method, it will be combined with the one from the Inversion method, to assure the existence of such hydrocarbons which are characterized by the Elastic Impedance (EI) value that should be relatively low with its surroundings.

From the results of this study, the dominant frequency appears at 25 Hz, while in the frequency of 10 Hz (low frequency) and 30 Hz (high frequency), the bright spot anomaly has not been seen in some prospect areas. This result is supported by the inversion results that shows rather low EI values, ranged from 13000 to 13750 ((ft / s) * (g / cc)), from 2370 to 2511 ((ft / s) * (g / cc)), and from 600 to 620 ((ft / s) * (g / cc)). The combination of CWTbased spectral decomposition method with the seismic inversion methods (EI) indicates that there are an accumulation of gas in a some prospect areas."

"Lapangan Salemba dan Depok adalah lapangan gas yang berada di daerah Selat Madura. Pada dua sumur eksplorasi telah ditemukan akumulasi hidrokarbon gas pada Formasi Lidah yang berumur Plio-Pleistocene. Formasi Lidah didaerah studi ini diinterpretasikan sebagai sistem pengendapan channel. Permasalahan yang muncul dalam menganalisa data seismik untuk mengetahui geometri dari channel sendiri adalah adanya lapisan tipis yang tidak terdeteksi dan batas kontinuitas pelapisan yang kurang jelas. Oleh karena itu, diperlukan metode yang lebih baik untuk analisa data seismik agar masalah tersebut dapat diatasi.Dalam tesis ini, analisa data seismik metode dekomposisi spektral dengan algoritma Continuous Wavelet Transform (CWT) digunakan karena hasilnya dapat memberikan gambaran yang lebih baik dalam penyebaran ketebalan dan diskontinuitas geologi. Selain itu juga digunakan metode inversi seismik untuk mengetahui penyebaran impedansi akustik yang merupakan sifat fisis batuan.Hasil studi ini menunjukkan bahwa metode dekomposisi spektral dan inversi seismik telah berhasil membantu dalam mendeliniasi geometri channel Formasi Lidah. Penampang dekomposisi spektral merepresentasikan ketebalan dan diskontuniuitas geologi dari reservoir batupasir Formasi Lidah. Distribusi frekuensi pada reservoir direpresentasikan pada nilai frekuensi 10, 20, dan 30 Hz. Pada inversi seismik, penampang impedansi akustik merepresentasikan litologi bawah permukaan. Distribusi impedansi akustik pada reservoir mempunyai nilai rata-rata 15000 - 19700 ((ft/s)*(g/cc)), sedangkan pada non-reservoir mempunyai nilai impedansi akustik lebih dari 19700 ((ft/s)*(g/cc)).

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Salemba and Depok fields are a gas field which located in the Madura Strait. Two exploration wells have been discovered hydrocarbons accumulation of gas in the Lidah Formation aged Plio-Pleistocene. Lidah Formation in the study area was interpreted as channel depositional environment. The problem that then arises in analyzing seismic data to predict the channel geometry is undetected thin layer and unclear reservoir continuity. Therefore, the better method to analyze the seismic data is needed to solve the problem.

In this thesis, seismic data analysis spectral decomposition method with Continuous Wavelet Transform (CWT) is used because the results can provide a better map of the thickness distribution and geological discontinuities. This thesis is also used seismic inversion method to know the acoustic impedance distribution as the physical properties of rocks.

The result of this study shows that the spectral decomposition method and seismic inversion has helped to delineate the channel geometry of Lidah Formation. The section of spectral decomposition represents thickness and geological discontinuity in Lidah Formation. Frequency distribution in the reservoir has an average of 10, 20, and 30 Hz. In the seismic inversion, the section of acoustic impedance represents the subsurface lithology. Acoustic impedance distribution in the reservoir has an average of 15,000 - 19,700 ((ft/s)*(g/cc)), whereas in nonreservoir having an acoustic impedance more than 19,700 ((ft/s)*(g/cc))."

"This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated."