A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

One concern in using photonic band-gap fiber (PBGF) as a gas sensor is the response time. In this type of the gas sensors, response time is the time required for gas to diffuse into the hollow-core. So considering a large hollow-core PBGF (HC-PBGF), the response time can be significantly reduced. But in the large HC-PBGF, the fundamental issue is the presence of higher order modes (HOMs). Somet...

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorith...

Granular cell tumor is a rare benign neoplasm most commonly appears in the head and neck region, especially in the tongue, cheek mucosa, and palate. Occurrence in limbs is even rarer. These tumors account for approximately 0.5% of all soft tissue tumors. Granular cell tumor can also affect other organs including skin, breast, and lungs. Local recurrence and metastasis is potentially higher in m...

 We investigate the existence of some‎ ‎large sets of size nine‎. ‎The large set $LS[9](2,5,29)$ is constructed and‎ ‎existence of the family $LS[9](2,5,27l+j)$ for $lgeq 1, ‎2leq‎ ‎j