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"A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localized pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation. For such exactly solvable problems, the inverse scattering transform provides the general solution of their initial value problems. It is equally surprising that some of these exactly solvable problems arise naturally as models of physical phenomena. Simply put, the inverse scattering transform is a nonlinear analog of the Fourier transform used for linear problems. Its value lies in the fact that it allows certain nonlinear problems to be treated by what are essentially linear methods."

"Pencitraan gelombang mikro telah banyak diterapkan pada berbagai bidang, salah satunya adalah pencitraan payudara untuk diagnosis kanker/tumor. Teknik pencitraan ini berpotensi menjadi modalitas komplementer untuk modalitas yang sudah ada, terutama untuk aplikasi pendeteksian dini. Sistem pencitraan gelombang mikro untuk deteksi tumor/kanker payudara memerlukan sensitivitas tinggi untuk mendeteksi jaringan abnormal yang memiliki sedikit kontras pada payudara dengan kepadatan tinggi. Tesis ini mengusulkan simulasi sistem pencitraan gelombang mikro kualitatif berbasis inverse scatteringdengan metode sensitivity-maps. Metode ini memperhitungkan medan yang dihamburkan objek sebagai data pengukuran. Metode ini memanfaatkan pengukuran dua jenis objek sebagai kalibrasi sistem: objek referensi sebagai latar yang tidak terdapat penghambur dan objek kalibrasi berupa objek kecil sebagai penghambur untuk mendapatkan respon impuls dari sistem. Penggunaan objek kalibrasi membuat metode ini memiliki sensitivitas yang tinggi. Objek yang diuji terdiri dari objek dengan kontras dielektrik rendah dan objek dengan banyak kontras dielektrik (multi-kontras). Rekonstruksi dilakukan pada tiga jenis data pengukuran S-Parameter yaitu , , dan gabungan keduanya. S-parameter diukur pada beberapa frekuensi, yaitu 3, 10, 14, 15, 16, 20 GHz, dan penggabungan seluruh frekuensi tersebut (multi-frekuensi). Hasil simulasi pencitraan menunjukkan sistem mampu merekonstruksi objek dielektrik dengan akurat. Selain analisis kualitatif, parameter elative root mean squared error (RRMSE) dan structural similarity index (SSIM) digunakan untuk menganalisis citra hasil rekonstruksi secara kuantitatif. Hasil rekonstruksi menunjukkan pengukuran  dengan multi-frekuensi memiliki kualitas citra terbaik dengan nilai RRMSE 0,1272 dan SSIM 0,9076. Sistem pencitraan yang dirancang juga berhasil merekonstruksi phantom multi-kontras secara akurat dengan RRMSE 0,1434 dan SSIM 0,4609.

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Microwave imaging has been widely applied in various fields, one of which is breast imaging for cancer/tumor diagnosis. This imaging technique has the potential to be a complementary modality to existing modalities, especially for early detection applications. Microwave imaging systems for breast tumor/cancer detection require high sensitivity in order to detect abnormal tissue which has little contrast in high-density breasts. This thesis proposes a simulation of a qualitative microwave imaging system based on inverse scattering using the sensitivity-maps method. This method takes into account the scattered field of the object as measurement data. This method utilizes the measurement of two types of objects as system calibration: a reference object as a scatterer-free background and a calibration object in the form of a small object as a scatterer to obtain an impulse response from the system. The use of calibration objects makes this method has high sensitivity. The object under test (OUT) consists of an object with low dielectric contrast and an object with multiple dielectric contrast (multi-contrast). Reconstruction was carried out on three types of S-Parameter measurement data, namely  and a combination of both. S-parameters are measured at several frequencies which are 3, 10, 14, a15, 16, 20 GHz, and the combination of all these frequencies (multifrequency). Imaging simulation results show the system is capable of reconstructing dielectric objects accurately. In addition to qualitative analysis, the relative root mean squared error (RRMSE) and structural similarity index (SSIM) parameters were used to analyze the reconstructed image quantitatively. The reconstruction results show that the multi-frequency  measurement has the best image quality with RRMSE values of 0.1272 and SSIM of 0.9076. The designed imaging system also successfully reconstructed multi-contrast phantom accurately with RRMSE of 0.1434 and SSIM of 0.4609. "

"Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems."

"The soliton is a dramatic concept in nonlinear science. What makes this book unique in the treatment of this subject is its focus on the properties that make the soliton physically ubiquitous and the soliton equation mathematically miraculous. Here, on the classical level, is the entity field theorists have been postulating for years: a local traveling wave pulse; a lump-like coherent structure; the solution of a field equation with remarkable stability and particle-like properties. It is a fundamental mode of propagation in gravity- driven surface and internal waves; in atmospheric waves; in ion acoustic and Langmuir waves in plasmas; in some laser waves in nonlinear media; and in many biologic contexts, such as alpha- helix proteins. This is not an encyclopedia of information on solitons in which every sentence is interrupted by either a caveat or a reference. Rather, Newell has tried to tell the story of the soliton as he would have liked to have heard it as a graduate student, with some historical development, lots of motivation, and frequent attempts to relate the topic at hand to the big picture. The book begins with a history of the soliton from its first sighting to the discovery of the inverse scattering method and recent ideas on the algebraic structure of soliton equations. Chapter 2 focuses on the universal nature of these equations and how and why they arise in physical and engineering contexts as asymptotic solvability conditions. The third chapter deals with the inverse scattering method and perturbation theories. Chapter 4 introduces the t-function and discusses the relations between the various methods for constructing solutions to the soliton equations and their various properties. Finally, an algebraic structure for the equations is provided in Chapter 5."

"Lapangan Talavera seluas 230km2 adalah lapangan migas yang berada di Cekungan Sumatera Utara yang merupakan salah satu cekungan mature di Indonesia. Lapangan ini diduga memiliki fitur stratigrafi berupa chanel dan delta dengan perlapisan batu pasir yang tipis sehingga tidak dapat terdeteksi dalam peta seismik konvensional. Dalam penelitian ini dipilih atribut seismik dekomposisi spektral berbasis Continuous Wavelet Transform (CWT) yang dapat mengekstrak informasi frekuensi dari peta seismik fungsi waktu menjadi peta fungsi waktu-frekuensi. Hasilnya diharapkan akan dapat digunakan untuk mendelineasi fitur stratigrafi dan mengetahui penyebaran lapisan batu pasir (batuan reservoar). Sementara atribut RMS amplitude digunakan untuk melihat distribusi kandidat reservoar sekaligus menjadi data pembanding dan pendukung informasi yang didapat dari atribut dekomposisi spektral. Pada akhirnya, hasil penellitian ini akan sangat berguna bagi perhitungan cadangan rinci, yang akan sangat tergantung pada geometri dan kualitas reservoar. Selain itu, juga akan berguna bagi perencanaan produksi pada fase eksploitasi. Dari hasil penelitian ini didapatkan tiga fasies reservoar dan hubungan korelasi yang kuat antara metode dekomposisi spektral dengan ekstraksi atribut RMS amplitude. Dengan atribut RMS amplitude dapat dilihat distribusi reservoar berdasarkan tingginya nilai amplitudo. Sementara untuk delineasi batu pasir secara lebih rinci diperoleh dari hasil analisa dekomposisi spektral.

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Talavera is a 230km2 area of the oil and gas field located in the North Sumatra Basin, which is one mature basins in Indonesia. This field has allegedly stratigraphic features such as channels and delta sandstone with thin bedding that can not be detected in conventional seismic map.

In this study, seismic attribute spectral decomposition based on Continuous Wavelet Transform ( CWT ) is selected to extract the frequency information from the seismic map time domain becomes a seismic map time - frequency domain. The results are expected to be used to delineate the stratigraphic and geographic distribution of feature layers of sandstone (reservoir rock) . While the RMS amplitude attribute is used to look at the distribution of the reservoir as well as a candidate benchmark data and supporting information obtained from spectral decomposition attributes. In the end, this study results will be useful for a detailed calculation of reserves, which will depend on the geometry and quality of the reservoir. In addition, it will also be useful for the planning of production in the exploitation phase.

From the results of this study, the three reservoir facies and a strong correlation between the spectral decomposition method with RMS amplitude attribute extraction are detected. With RMS amplitude attribute can be seen by the high value of reservoir distribution amplitude . As for the delineation of sandstone in more detail the results obtained from the spectral decomposition analysis."