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Abstrak :
Titik x dikatakan titik tetap dari sembarang pemetaan T jika dan hanya jika T x = x. Berbagai hasil mengenai teorema titik tetap telah dibuktikan pada ruang metrik. Seiring berkembangnya bidang analisis matematis, semakin banyak matematikawan yang berhasil membuktikan teorema titik tetap di berbagai ruang dan pemetaan. Namun, tidak banyak hasil mengenai teorema titik tetap yang telah dibuktikan pada ruang dislocated quasi b-metric. Ruang dislocated quasi b-metric adalah salah satu bentuk perluasan dari ruang metrik dimana jarak antara dua buah titik yang sama tidak harus bernilai nol yaitu d(x, x) =/= 0 serta sifat simetri yaitu d(x, y) = d(y, x) tidak berlaku di ruang ini. Pada skripsi ini, akan dibuktikan kembali teorema-teorema mengenai ketunggalan titik tetap pada ruang dislocated quasi b-metric untuk sembarang pemetaan. Pada Skripsi ini juga akan dibahas mengenai teorema titik tetap untuk pemetaan tipe F-kontraktif pada ruang yang sama. ......A point x is said to be a fixed point of a mapping T on a nonempty set X if and only if T x = x. Many results regarding the fixed point theorem have been proved on metric spaces. As the field of mathematical analysis develops, more and more mathematicians have succeeded in proving fixed point theorems in various spaces and mappings. However, not many results regarding the fixed point theorem have been proved on dislocated quasi b-metric spaces. Dislocated quasi b-metric space is one of the extensions of metric space where the distance between two equal points does not have to be zero i.e. d(x, x) =/= 0 and the symmetry property i.e. d(x, y) = d(y, x) does not apply in this space. In this thesis, we will prove the theorems on the uniqueness of fixed points on dislocated quasi b-metric spaces for any mapping. This thesis also discusses the fixed point theorem for F-contractive type mappings in the same space.

Abstrak :
Metode magnetotelluric (MT) merupakan metode yang efektif dalam memetakan kondisi bawah permukaan. Pada data MT, sering ditemukan adanya pergeseran statik yang disebabkan oleh beberapa hal, antara lain adalah heterogenitas di dekat permukaan, efek topografi ataupun kontak vertikal. Jika hal ini dibiarkan, maka akan menyebabkan kesalahan interpretasi pada resistivitas dan kedalaman. Untuk mengatasi fenomena ini dapat dilakukan dengan menggunakan data Time Domain Electromagnetic (TDEM). Namun hal itu harus dilakukan dengan menggunakan peralatan yang mahal dan akan menghabiskan waktu dan biaya operasional yang besar. Untuk mengatasi hal tersebut, upaya pemecahan masalah pergeseran statik terus dikembangkan antara lain dengan metode Complex Kriging (Cokriging), Perata-rataan (averaging), atau dengan menggunakan geomagnetic transfer function. Penelitian ini difokuskan pada pemecahan masalah pergeseran statik dengan membuat software berbasis Matlab menggunakan metode Cokriging dan Peratarataan. Pengujian kedua metode tersebut dilakukan dengan menggunakan data sintetik dan data riil. Dari kedua metode tersebut didapat kesimpulan bahwa metode Perata-rataan memberikan hasil yang lebih baik. ......Magnetotelluric method (MT) is an effective method to map the subsurface conditions. In the MT data, often found the existence of static shift can be caused by several things, among others, is the heterogeneity near the surface, the effect of topography or vertical contacts. If this is allowed, it will cause errors of interpretation in resistivity and depth. To overcome this phenomenon can be done using data Time Domain Electromagnetic (TDEM). But it must be done by using expensive equipment and will spend the time and operational costs are great. To overcome this, the static shift problem solving efforts continue to be developed include the method of Complex Kriging (Cokriging), Averaging, or by using geomagnetic transfer function. This study focused on problems solving of static shift by creating software based Matlab using Cokriging and Averaging. Testing the two methods are conducted using synthetic data and real data. Of the two methods could be concluded that the Averaging method gives better results.

Abstrak :
This book is devoted to the Beltrami equations that play a significant role in geometry, analysis and physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations