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"This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts."

"This book builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory, Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis."

"The author?s goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric options."

"Lapangan M merupakan lapangan gas yang terletak di Cekungan Sumatera Selatan dan sudah dikembangkan dengan pemboran 5 sumur pengembangan dari reservoar paparan karbonat Formasi Baturaja, dengan rata-rata produksi sebesar 4 MMCFPD per sumur. Berdasarkan hasil interpretasi seismik dan analog dengan lapangan minyak disebelah utara lapangan M, yaitu lapangan A, masih terdapat potensi reservoar minyak (oil rim) yang terletak downdip dari reservoar gas yaitu daerah yang belum dikembangkan di antara batas kontak gas dan minyak dengan batas kontak minyak dan air. Data produksi minyak sumur-sumur di lapangan A berkisar antara 100 - 800 BOPD per sumur. Hasil studi ini diharapkan dapat mengidentifikasi zona prospek minyak tersebut dan juga untuk pengembangan lebih lanjut zona gas. Menggunakan data seismik 3D dan data sumur, dilakukan evaluasi melalui metode dekomposisi spektral Continuous Wavelet Transform (CWT) data seismogram sintetik sumur dan data tras seismik yang melewati sumur, kemudian hasilnya disebarkan ke seluruh lapangan untuk mengidentifikasi penyebaran lateral keberadaan zona anomali frekuensi rendah. Hasil analisa dekomposisi spektral CWT pada data sumur dan data tras seismik yang ditunjukkan pada crossplot antara Amplitudo CWT dengan Frekuensi memperlihatkan korelasi yang cukup bagus. Sumur gas menunjukkan nilai amplitudo CWT paling tinggi pada frekuensi 10 ? 13 hz dan sumur minyak pada frekuensi 17 - 22 hz. Nilai amplitudo menurun pada frekuensi yang lebih tinggi. Pada sumur air, nilai amplitudo CWT selalu paling rendah pada frekuensi rendah hingga tinggi, sehingga dari crossplot tersebut dapat disimpulkan bahwa cut-off amplitudo zona air adalah pada 1,0+E09. Berdasarkan hasil analisis CWT dari data sumur ini, analisa dekomposisi spektral CWT kemudian disebarkan ke seluruh lapangan untuk bisa mengidentifikasi zona prospek. Selain itu, hasil crossplot antara nilai amplitudo CWT dengan nilai Saturasi air (Sw) pada zona reservoir memperlihatkan adanya hubungan yaitu nilai amplitudo CWT yang tinggi berkorelasi dengan nilai saturasi air yang rendah, begitupun sebaliknya.

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Field M is a gas field located in the South Sumatra Basin and has been developed by the drilling of five development wells from carbonate platform reservoir of Baturaja Formation, with average production of 4 MMCFPD per well. Based on the result of seismic interpretation and its analog to the oil field located to the north of field M, namely field A, there is still potential of oil reservoir (oil rim) located downdip from the gas reservoir The potential area is limited in the area that has not been developed between gas and oil contact and between oil and water contact. The production of oil wells in the field A ranges between 100-800 BOPD per well. The result of this study is expected to identify the oil zone and other prospects for further gas development.

Based on 3D seismic data and well data, the evaluation was carried out using one of spectral decomposition methods, the Continuous Wavelet Transform (CWT). The analysis was done using both well synthetic seismogram data and seismic trace that crossing-through the wells. Then CWT was run on both data. Referring to the result of the analysis, CWT was distributed across the field to identify the presence of low-frequency zone.

The results of the CWT analysis from well data and seismic trace data are shown on the crossplots between the amplitude and the frequency. They show a fairly good correlation. Gas zone shows the highest value of CWT amplitude at a frequency of 10-13 Hz and oil zone shows the highest value at a frequency of 17- 22 Hz. Amplitude values decreased in the higher frequencies. In the water zone, the value of the CWT amplitude is always lower in low to high frequencies. From the crossplot it can be concluded that the cut-off amplitude value for water zone is at 1.0 + E09. In any frequency, the CWT amplitudes below that value is nonhydrocarbon or water.

The result of spectral decomposition that is based the above analysis and distributed throughout the field is able to identify zones of prospects. In addition to that, the crossplot between the CWT value and the water saturation (Sw) in each oil, gas and water zone shows a correlation. High CWT amplitudes correlate to low water saturation, and vice versa."

"This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics."