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"Rock compressibility is an important formation rock properties. It influences various processes in reservoir and rock formations that encompass from sources of reservoir driving energy, changes in other reservoir properties, to land subsidence. "

"This monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it embodies the classical versions of these lemma, together with the well known as well as the most recent extensions of them due to Barndorff-Nielsen, Balakrishnan and Stepanov, Erdos and Renyi, Kochen and Stone, Petrov and the present author. The versions of the second Borel-Cantelli Lemma for pair wise negative quadrant dependent sequences, weakly *-mixing sequences, mixing sequences (due to Renyi) and for many other dependent sequences are all included. The special feature of the book is a detailed discussion of a strengthened form of the second Borel-Cantelli Lemma and the conditional form of the Borel-Cantelli Lemmas due to Levy, Chen and Serfling. All these results are well illustrated by means of many interesting examples. All the proofs are rigorous, complete and lucid. An extensive list of research papers, some of which are forthcoming, is provided. The book can be used for a self study and as an invaluable research reference on the present topic."

"Formulasi skema numerik sebagai diskretisasi ruang terutama untuk persamaan diferensial parsial hiperbolik nonlinear dikembangkan secara berkelanjutan. Hal ini dilakukan untuk memperbaiki berbagai aspek yang menjadi masalah utama dalam penyelesaian persamaan tersebut, diantaranya: diskontinuitas, spektrum skala aliran yang luas, dan kestabilan numerik. Pada bagian awal penelitian ini, dilakukan formulasi alternatif untuk indikator smoothness skema targeted ENO (TENO). Studi kestabilan numerik dan approximate dispersion relation (ADR) memberikan nilai parameter q1=2, q2=3 dan q1=1, q2=6. Berdasarkan ADR ditentukan bahwa indikator smoothness skema TENO dengan parameter q1=1, q2=6 memberikan disipasi numerik paling rendah dan dispersi yang baik. Pada bagian berikutnya, diusulkan reformulasi skema TENO menggunakan polinomial Hermite. Skema Hermite TENO (HTENO) ini mempunyai beberapa keuntungan dibandingkan skema yang telah ada sebelumnya, antara lain rekonstruksi yang lebih ringkas dan mempunyai disipasi numerik yang rendah dengan dimanfaatkannya strategi pemilihan stensil berbasis skema TENO. Selanjutnya, diformulasikan global reference smoothness indicator baru untuk skema yang diusulkan. Perhitungan fluks dan integrasi waktu secara berturut-turut diselesaikan dengan metode Lax-Friedrichs lokal dan strong-stability-preserving Runge-Kutta orde ketiga. Pada penelitian ini, didemonstrasikan uji numerik skema HTENO pada persamaan skalar dan persamaan Euler untuk fluida kompresibel dalam satu- dan dua-dimensi. Pada uji numerik tersebut, skema numerik yang diusulkan memberikan disipasi numerik yang rendah, peningkatan performa penangkapan diskontinuitas dan memberikan resolusi fluktuasi aliran berskala kecil yang baik sebagaimana skema TENO.

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Formulation of the numerical schemes as spatial discretization, particularly for nonlinear hyperbolic partial differential equations, is developed continuously. Those works improve various aspects that become the main problem to solve these equations, including discontinuity, a broad spectrum of flow scales, and numerical stability. At the beginning of this research, an alternative formulation for the smoothness indicator of the targeted ENO (TENO) scheme was carried out. The study of numerical stability and approximate dispersion relation (ADR) give parameter values ​​ q1=2, q2=3 and q1=1, q2=6. Based on the ADR, TENO’s smoothness indicator with the parameters q1=1, q2=6 gives the lowest numerical dissipation and good dispersion.

In the next section, we propose a reformulation of the TENO scheme using Hermite polynomials. The Hermite TENO (HTENO) reconstructions offer major advantages over earlier reconstructions; namely, it is a compact Hermite-type reconstruction and has low dissipation by virtue of TENO’s stencil voting strategy. Next, new high-order global reference smoothness indicators for the proposed scheme are formulated. The flux calculation and time integration were carried out by using the local Lax-Friedrichs and the third-order strong-stability-preserving Runge-Kutta method, respectively. In this research, numerical tests of the HTENO scheme on scalar equations and Euler equations of compressible flow in one- and two-dimensions are demonstrated. In these tests, the proposed scheme gives low numerical dissipation, improves the shock-capturing performance and inherits the good small-scale resolution of the TENO scheme."