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Abstrak :
Contains the proceedings that were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas. This book includes many relevant topics in approximation theory, such as abstract approximation, approximation with constraints, and interpolation and smoothing.

Abstrak :

Residual merupakan sisa dari peristiwa seismik setelah dilakukan koreksi Normal Moveout yang menyimpang pada offset tertentu. Residual moveout dapat diatasi dengan melakukan muting pada pemrosesan data seismik, namun proses tersebut dapat menyebabkan hilangnya informasi bawah permukaan. Reduksi residual moveout  dilakukan untuk mengurangi proses muting sehingga informasi bawah permukaan dapat dipertahankan. Beberapa peneliti telah melakukan modifikasi persamaan waktu tempuh hiperbolik menjadi persamaan waktu tempuh non-hiperbolik untuk memperoleh nilai kecepatan NMO dan eta yang lebih akurat pada Offset to Depth Ratio (ODR) yang besar, sehingga nilai residual moveout semakin kecil. Tujuan penelitian ini adalah meningkatkan nilai reduksi residual moveout pada offset panjang menggunakan Pendekatan Pada dan dikomparasi dengan metode persamaan waktu tempuh hiperbolik dan non-hiperbolik. Metode yang dilakukan dalam penelitian ini adalah melakukan pemodelan ke depan (forward modeling) struktur pelapisan bawah permukaan. Hasil residual moveout menggunakan Pendekatan Pada memiliki kemampuan resukdi residual terbaik. Hal ini  dapat dilihat dari nilai residual terkecil dibandingkan dengan metode hiperbolik dan Alkhalifah dan Fomel dan Stovas. Hasil residual moveout menggunakan Pendekatan Padé menghasilkan residual yang kecil dengan residual masing-masing layer adalah 0.002 s [0.2%], 0.002 s [0.133%] dan 0.003 s [0.157%].

 

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Residual is the remaining trace of seismict event after a NMO correction is deviated at a far offset. Residual moveout can be overcome by muting the processing of seismic data, but the process can cause loss of subsurface information. Reduction of residual moveout is done to reduce the muting process so that the subsurface information can be maintained. Some researchers have modified hyperbolic travel time equation to obtain a more accurate value NMO velocity and parameter an-ellipticity or etha on the large ODR, so that the residual moveout value is smaller mainly in large offset to depth ratio. The aims of research is to increase the reduction value of moveout residue at long offset data using Pada approximation then compare with several approximation. The method used in this study is to conduct a forward modeling of the subsurface coating structure.   The result is Pada Approximation method is obtained the best reducing residual of NMO. It can be seen from the smaller residual value of Pada Approximation than Hyperbolic, Alkhalifah and Fomel & Stovas method. The result of residual moveout using Padé Approximation have the smallest residual of each layer are 0.002 s [0.2%], 0.002 s [0.133%], and 0.003 s [0.157%].

 

Abstrak :
This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.

Abstrak :
These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7–10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. Previous conferences in the series were held in Austin, Texas (1973, 1976, 1980, 1992), College Station, Texas (1983, 1986, 1989, 1995), Nashville, Tennessee (1998), St. Louis, Missouri (2001), Gatlinburg, Tennessee (2004), and San Antonio, Texas (2007). Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation.

Abstrak :
The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.

Abstrak :
Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships. A mapping principle is presented to connect many of the methods. The eigenvalue problems studied are linear, and linearization is shown to give important information about nonlinear problems. Linear vector spaces and their properties are used to uniformly describe the eigenvalue problems presented that involve matrices, ordinary or partial differential operators, and integro-differential operators.

Abstrak :
Results and problems in the modern theory of best approximation, in which the methods of functional analysis are applied in a consequent manner. This modern theory constitutes both a unified foundation for the classical theory of best approximation and a powerful tool for obtaining new results.