For d ≥ 1 and α ∈ (0, 2), consider the family of pseudo differential operators {∆ + b∆α/2; b ∈ [0, 1]} on Rd that evolves continuously from ∆ to ∆ + ∆α/2. In this paper, we establish a uniform boundary Harnack principle (BHP) with explicit boundary decay rate for nonnegative functions which are harmonic with respect to ∆ + b∆α/2 (or equivalently, the sum of a Brownian motion and an independent ...

We introduce and study a new class of spaces, namely $beta-$topological vector spaces via $beta-$open sets. The relationships among these spaces with some existing spaces are investigated. In addition, some important and useful characterizations of $beta-$topological vector spaces are provided.  

Branch-and-bound (B&B) is a well-known and general combinatorial optimisation technique that is used especially for NP-hard problems where no special purpose algorithm is known. Because of the high problem complexity, parallel implementations are required for speeding up the computations. Algorithms with high and stable efficiency, i.e., utilisation of the processing elements (PEs), are desired...