707 research outputs found
Tomographic inversion of focusing operators
No full textSeismic images of the structure of the earth are a prerequisite for finding new hydrocarbon reservoirs. The quality of a seismic images is highly dependent on the accuracy of the velocity model of the subsurface. Conventional imaging consists of an iterative process between obtaining the image using a velocity model, and updating this model by investigating the properties of the image. The Common Focal Point (CFP) method makes it possible to analyze and treat seismic data in a fundamentally different way as it uses a two-step approach: 1) two-way reflection data are transformed into one-way data by estimating focusing operators, and 2) these focusing operators are used to estimate the velocity model by tomographic inversion. This second step, the tomographic inversion of focusing operators, is the subject of this thesis. This research contains two important new aspects. First, the use of focusing operators in (3D) velocity model estimation. Second the data-driven approach of the method. Some additional concepts like the inclusion of a priori information, the joint inversion of P and S-wave operators, and the new concept of the focal point clouds, by which the adequacy of the velocity model can be analyzed, are also addressed. After evaluation of the method of tomographic inversion of focusing operators on both synthetic and real data it can be concluded that the method results in accurate velocity models and is capable of dealing with complex subsurface models.Applied Science
Some common fixed point theorems for weakly compatible mappings
No full textAbstractJungck's [G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771–779] notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non-self mappings in complete convex metric spaces. We improve on the method of proof used by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9–12] and Ahmed and Rhoades [A. Ahmed, B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl. Math. 32 (2001) 1247–1254] and obtain generalization of some known results. In particular, a theorem by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9–12] is generalized and improved
On |A|<sub><i>k</i></sub>summability factors of infinite series
No full textIn an earlier paper (Rhoades. B. E. and Savaş, E. Some necessary conditions for absolute matrix summability factors. Indian J. Pure Appl. Math., 2002. 33(7), 1003-1009) the authors obtained necessary conditions for the series ?an to be absolutely summable of order k by a triangular matrix. In this paper we present sufficient conditions for absolute matrix summability factors. As a corollary we obtain a result of N. Singh (On |N?,pn| summability factors of infinite series. Indian J. Math., 1968, 10, 19-24)
An absolute double summability factor theorem
No full textIn an earlier paper Savas and Rhoades [Ekrem Savaş, B.E. Rhoades, A note on | A |k summability factors, Nonlinear Anal. 66 (2007) 1879-1883. [1]] obtained a summability factor theorem for absolute summability of order k ? 1. In this paper we extend that result to doubly infinite matrices. © 2008 Elsevier Ltd. All rights reserved
Fixed point theorems in generalized patially ordered G-metric spaces
No full textIn this paper, we consider the concept of a
-distance on a complete partially ordered G-metric space and prove some fixed point theorems
The convergence of matrix transforms for certain Markov chains
No full textAbstractIn this paper it is shown that, for certain classes of matrices, the matrix transform of a periodic strongly ergodic stochastic matrix P converges
Double absolute summability factor theorems and applications
No full textIn an earlier paper the first author [Ekrem Savas, Factors for | A |k summability of infinite series, Comput. Math. Appl. 53 (7) (2007) 1045-1049. [3]] obtained a summability factor theorem for absolute summability of the order k ? 1. In this paper we extend that result to doubly infinite matrices. © 2007 Elsevier Ltd. All rights reserved
Common fixed point theorems for maps under a contractive condition of integral type
No full textAbstractTwo common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007–4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149–153]
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