In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liou...

On q-Di®erence Equations Moemen H. Abu-Risha Department of Mathematics Cairo University, Eygpt E-mail: [email protected] We give an investigation of some properties of solutions of linear q¡di®erence equations de ̄ned on an interval [a;1): The cases a = 0 and a > 0 are essentially di®erent. The study of the latter case is necessary for the derivation of asymptotic formulae and oscil...

We introduce invariant sample measures to nonautonomous random dynamical systems, and consider the behaviors of a stochastic $ p $-Laplacian equation with multiplicative noise on bounded domain. first use asymptotic priori estimate method prove existence (L^2, L^q) $-pullback attractors for generated system. Then, we establish Liouville type theorem in L^2 this equation. Moreover, are carried b...

• We study degenerate second order operators with “Euler-type” degeneracy. show boundary continuity assuming only local boundedness. strongly constrain behaviors near the and infinity. prove a Liouville theorem for global solutions just class of second-order boundary-degenerate elliptic equations in two dimensions minimal regularity assumptions. maximum principle Harnack inequality at and, boun...

In this paper we discuss various aspects of non-compact models of CFT of the type: ∏NL j=1{N = 2 Liouville theory}j ⊗ ∏NM i=1{N = 2 minimal model}i and ∏NL j=1{SL(2;R)/U(1) supercoset}j⊗ ∏NM i=1 {N = 2 minimal model}i. These models are related to each other by T-duality. Such string vacua are expected to describe non-compact Calabi-Yau compactifications, typically ALE fibrations over (weighted)...

We present the quantization of the Liouville model defined in light-cone coordinates in (1,1) signature space. We take advantage of the representation of the Liouville field by the free field of the Backlünd transformation and adapt the approch by Braaten, Curtright and Thorn [1] . Quantum operators of the Liouville field ∂+φ, ∂−φ, e , e are constructed consistently in terms of the free field. ...

Quantum theory of dilaton gravity is studied in 2+ ǫ dimensions. Divergences are computed and renormalized at one-loop order. The mixing between the Liouville field and the dilaton field eliminates 1/ǫ singularity in the Liouville-dilaton propagator. This smooth behavior of the dilaton gravity theory in the ǫ → 0 limit solves the oversubtraction problem which afflicted the higher orders of the ...

We consider a quantum system composed of a small part, having finitely many degrees of freedom, interacting with a free, spatially infinitely extended Bose gas. An equilibrium state for the uncoupled system is given by the product state where the small part is in the Gibbs state at some temperature T > 0, and the Bose gas is in a state where a spatially homogeneous Bose-Einstein Condensate is i...

We consider stationary solutions to the three-dimensional Navier-Stokes equations for viscous incompressible flows in the presence of a linear strain. For certain class of strains we prove a Liouville type theorem under suitable decay conditions on vorticity fields.