Optical precursors in the singular and weak dispersion limits

Comment on ”Optical precursors in the singular and weak dispersion limits”

Dispersion Evaluation In Optical Wave Guides

One of the factors which limits the transmission capacity of the fiber optics communication channel is the material dispersion. Exact analytical study of the material dispersion is often complex and involves calculating the derivatives of the refractive index of the core. These calculations are too cumbersome to do, especially for high-order derivatives. So material dispersion has only been stu...

Dispersion Evaluation In Optical Wave Guides

One of the factors which limits the transmission capacity of the fiber optics communication channel is the material dispersion. Exact analytical study of the material dispersion is often complex and involves calculating the derivatives of the refractive index of the core. These calculations are too cumbersome to do, especially for high-order derivatives. So material dispersion has only been stu...

Lieb mode in a quasi-one-dimensional bose-einstein condensate of atoms.

We calculate the dispersion relation associated with a solitary wave in a quasi-one-dimensional Bose-Einstein condensate of atoms confined in a harmonic, cylindrical trap in the limit of weak and strong interactions. In both cases, the dispersion relation is linear for long-wavelength excitations and terminates at the point where the group velocity vanishes. We also calculate the dispersion rel...

Weak log-majorization inequalities of singular values between normal matrices and their absolute values

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...