In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo (MCMC) paradigm. This paper studies how many steps of the underlying Markov chain are required to get samples (approximately) from the uniform distribution on the boundary of the set, for sets with an upper bound on the curvature of the boundary. Our main theo...

We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted periodic boundary condition and the open boundary condition. We determine the most general form of the integrable twisted periodic boundary condition by consideri...

The goal of this paper is to present the finite element scheme for solving the Earth potential problems in 3D domains above the Earth surface. To that goal we formulate the boundary-value problem (BVP) consisting of the Laplace equation outside the Earth accompanied by the Neumann as well as the Dirichlet boundary conditions (BC). The 3D computational domain consists of the bottom boundary in t...

We consider the coulomb gas model on the upper half plane with different boundary conditions, namely Drichlet, Neuman and mixed. We related this model to SLE(κ, ρ) theories. We derive a set of conditions connecting the total charge of the coulomb gas, the boundary charges, the parameters κ and ρ. Also we study a free fermion theory in presence of a boundary and show with the same methods that i...

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an l × l box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length l in the boundary is bounded by δl, where δ < 1. We show that for any such boundary condition, when the temperature is suff...

The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integr...