We establish an integral representation of a right inverse of the Askey-Wilson finite difference operator on L2 with weight (1−x2)−1/2. The kernel of this integral operator is θ′4/θ4 and is the Riemann mapping function that maps the open unit disc conformally onto the interior of an ellipse. Running title: An Inverse Operator 1990 Mathematics Subject Classification: Primary 33D45, 42C10, Second...

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

In this paper, extension of the EQ-logic by the ∆connective is introduced. The former is a new kind of many-valued logic which based on EQ-algebra of truth values, i.e. the algebra in which fuzzy equality is the fundamental operation and implication is derived from it. First, we extend the EQ-algebra by the ∆ operation and then introduce axioms and inference rules of EQ∆-logic. We also prove th...

R. Meyer and E. Mares [10] studied the logic CNR, a classical relevant logic with a modal connective. Such logic is of type S4. As it has been noted in [10], the addition of a modal operator in the language of classical relevant logic and the axioms φ ∧ ψ → (φ ∧ ψ) and (φ ∧ ψ) → ( φ ∧ ψ) do not necessarily produce theorems such that as (φ→ ψ) → φ → ψ or (♦φ→ ψ) → (φ→ ψ). These formulas are well...

Modal Kleene algebras are Kleene algebras enriched by forward and backward box and diamond operators. We formalise the symmetries of these operators as Galois connections, complemetarities and dualities. We study their properties in the associated operator algebras and show that the axioms of relation algebra are theorems at the operator level. Modal Kleene algebras provide a unifying semantics...

A special algebra called EQ-algebra has been recently introduced by Vilém Novák. Its original motivation comes from fuzzy type theory, in which the main connective is fuzzy equality. EQ-algebras have three binary operations meet, multiplication, fuzzy equality and a unit element. They open the door to an alternative development of fuzzy (manyvalued) logic with the basic connective being fuzzy e...

We study the interior spike solutions to a steady state problem of the shadow system of the Gierer-Meinhardt system arising from biological pattern formation. We rst show that at a nondegenerate peak point the interior spike solution is locally unique and then we establish the spectrum estimates of the associated linearized operator. We also prove that the corresponding solution to the shadow s...

We examine a time dependent singularly perturbed convection-diffusion problem, where the convective coefficient contains an interior layer. A smooth transformation is introduced to align the grid to the location of the interior layer. A numerical method consisting of an upwinded finite difference operator and a piecewise-uniform Shishkin mesh is constructed in this transformed domain. Numerical...

Abstract We have shown that in holographic superconductivity theory for 3+1 dimensional system, the scaling dimension of Cooper pair operator can be obtained as a quantized value if we request scalar function describing order parameter is finite inside black hole well outside. This should contrasted to usual situation where set mass squared by hand. Our method applied any parameters.