In this paper we have introduced the concept of γ-b-open sets and studied some of their properties.

For d ≥ 1 and α ∈ (0, 2), consider the family of pseudo differential operators {∆+b∆; b ∈ [0, 1]} on R that evolves continuously from ∆ to ∆ + ∆. 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∆ (or equivalently, the sum of a Brownian motion and an independent symmetric α-st...

For d ≥ 1 and α ∈ (0, 2), consider the family of pseudo differential operators {∆+b∆α/2; b ∈ [0, 1]} on R that evolves continuously from ∆ to ∆ + ∆. 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∆ (or equivalently, the sum of a Brownian motion and an independent symmetric α...

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...