Differential operator without dense range

LASERS WITHOUT INVERSION: DENSITY OPERATOR METHOD

A quantum theory of a two and three-level laser with injected atomic coherence is developed by using a density operator method, to the best of our knowledge, for the first time. The initial atomic coherence plays an essential role. At steady state, the equation of motion for the density operator yields to exhibit laser without inversion and a phase locking but no threshold for the laser fie...

SOLVING A CLASS OF GENERALIZED LYAPUNOV OPERATOR DIFFERENTIAL EQUATIONS WITHOUT THE EXPONENTIAL OPERATOR FUNCTION A bstract

Airy equation with memory involvement via Liouville differential operator

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

Bi-concave Functions Defined by Al-Oboudi Differential Operator

The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

Dense Multi-view 3D-reconstruction Without Dense Correspondences

We introduce a variational method for multi-view shapefrom-shading under natural illumination. The key idea is to couple PDE-based solutions for single-image based shapefrom-shading problems across multiple images and multiple color channels by means of a variational formulation. Rather than alternatingly solving the individual SFS problems and optimizing the consistency across images and chann...