Biased random walks on random graphs

These notes cover one of the topics programmed for the St Petersburg School in Probability and Statistical Physics of June 2012. The aim is to review recent mathematical developments in the field of random walks in random environment. Our main focus will be on directionally transient and reversible random walks on different types of underlying graph structures, such as $\mathbb{Z}$, trees and $\mathbb{Z}^d$ for $d\geq 2$.Comment: Survey based one of the topics programmed for the St Petersburg School in Probability and Statistical Physics of June 2012. 64 pages, 16 figure

Common Structures in 2,3 and 4D Simplicial Quantum Gravity

Two kinds of statistical properties of dynamical-triangulated manifolds (DT mfds) have been investigated. First, the surfaces appearing on the boundaries of 3D DT mfds were investigated. The string-susceptibility exponent of the boundary surfaces ($\tilde{\gamma}_{st}$) of 3D DT mfds with $S^{3}$ topology near to the critical point was obtained by means of a MINBU (minimum neck baby universes) analysis; actually, we obtained $\tilde{\gamma}_{st} \approx -0.5$. Second, 3 and 4D DT mfds were also investigated by determining the string-susceptibility exponent near to the critical point from measuring the MINBU distributions. As a result, we found a similar behavior of the MINBU distributions in 3 and 4D DT mfds, and obtained $\gamma_{st}^{(3)} \approx \gamma_{st}^{(4)} \approx 0$. The existence of common structures in simplicial quantum gravity is also discussed.Comment: 3 pages, latex, 3 ps figures, uses espcrc2.sty. Talk presented at LATTICE97(gravity

Geological Structure Analysis to Determine the Direction of the Main Stress at Western Part of Kolok Mudik, Barangin District, Sawahlunto, West Sumatera

On the study area there are three types of structure, those are fault, fold and joint. Types of fault were found  in the study area, reverse fault with the strike/dip is N215oE/75o, normal fault has a fault directions N22oE and N200oE with pitch 35o, and dextral fault with pitch 10o and strike N219oE. Fold and joint structures used to determine the direction of the main stress on the study area. Further, an analysis used stereonet for data folds and joints. So that from the data got three directions of main stress, those are Northeast – Southwest (T1), North – South (T2) and Southeast – Northwest (T3). On the Northeast – Southwest (T1) stress there are four geological structures, anticline fold at ST.3 , syncline folds at ST. 13a, ST. 13b, ST. 13c and ST. 33, chevron fold at ST. 44 and joint at ST. 2. On the North – South (T2) stress there are three geological structures, those are syncline fold at ST. 35, anticline fold at ST. 54 and joints at ST. 41, ST. 46 and ST. 47. On the Southeast – Northwest (T3) stress were also three geological structures, those are chevron fold at ST 42a, overturned fold at ST. 42b, syncline fold at ST. 42c and joints at ST. 5 and ST. 34

On hypercomplex pseudo-Hermitian manifolds

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal invariance and the conformal equivalence of the basic types manifolds are studied. A known example is characterized in relation to the obtained results.Comment: 12 pages, presented on The Sixth International Workshop on Complex Structures and Vector Fields, St Konstantin, Bulgaria, 3-6 September 200