We construct higher-dimensional analogues of the $\mathcal{I}^{\prime}$-curvature Case and Gover in all CR dimensions $n \geq 2$. Our $\mathcal{I}^{\prime}$-curvatures transform by a first-order linear differential operator under change contact form their total integrals are independent choice pseudo-Einstein on closed manifold. exhibit examples where these depend general form, thereby produce ...

where the pseudo-differential operator Λ = (−∆)α/2 with 0 < α ≤ 2 is defined by the Fourier transformation: Λ̂αu(ξ) = |ξ|αû(ξ). Moreover, we assume that λ ∈ {−1, 1} and p > 1. Nonlinear evolution problems involving fractional Laplacian describing the anomalous diffusion (or α-stable Lévy diffusion) have been extensively studied in the mathematical and physical literature (see [2, 11, 5] for refe...

We define a dynamical residue which generalizes the Guillemin–Wodzicki density of pseudo-differential operators. More precisely, given Schwartz kernel, definition refers to Pollicott–Ruelle resonances for dynamics scaling towards diagonal. apply this formalism complex powers wave operator and we prove that residues Lorentzian spectral zeta functions are residues. The shown have local geometric ...

An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.

we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...

In this paper, we propose a genetic algorithm, called GenSPN, for finding highly probable differential characteristics of substitution permutation networks (SPNs). A special fitness function and a heuristic mutation operator have been used to improve the overall performance of the algorithm. We report our results of applying GenSPN for finding highly probable differential characteristics of Ser...

in present paper acertain convolution operator of analytic functions is defined.moreover, subordination- and superordination- preserving propertiesfor a class of analytic operators defined on the space of normalizedanalytic functions in the open unit disk is obtained. we also applythis to obtain sandwich results and generalizations of some knownresults.

In this paper, we will use the Kohn’s ∂̄b-theory on CRhypersurfaces to derive some new results in CR-geometry. Main Theorem. LetM2n−1 be the smooth boundary of a bounded strongly pseudo-convex domain Ω in a complete Stein manifold V 2n. Then: (1) For n ≥ 3, M2n−1 admits a pseudo-Einstein metric. (2) Forn ≥ 2,M2n−1 admits a Fefferman metric of zero CRQ-curvature. (3) In addition, for a compact st...

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...