in this paper, some results of singh, gopalakrishna and kulkarni (1970s) have been extended to higher order derivatives. it has been shown that, if $sumlimits_{a}theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $t(r, f)sim t(r, f^{(k)}), rrightarrowinfty$ if $theta(infty, f)=1$ and $t(r, f)sim (k+1)t(r, f^{(k)}), rrightarrowinfty$ if $th...

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A new approach to the transient pulse compression by stimulated Brillouin scattering (SBS) is presented. The theoretical analysis involving the time-dependent SBS gain in explicit form leads to a nonlinear system of partial differential equations, solved numerically by a generalization of the split-step method. It is shown theoretically and confirmed experimentally that the phonon lifetime is n...

In this paper, we apply Theorem 3.2 of [G. M. Lee, L.-J. Lin, J. Nonlinear Convex Anal., 18 (2017), 1781–1800] to study the variational inequality over split equality fixed point problems for three finite families of strongly quasi-nonexpansive mappings. Then we use this result to study variational inequalities over split equality for three various finite families of nonlinear mappings. We give...

The propagation of optical pulses in a single mode fiber is analyzed by solving nonlinear Schrödinger (NLS) equation numerically. The propagation is modeled using a split-step wavelet method, analogous to the split-step Fourier method, while retaining the advantages of the wavelet transform. Pulses and pulse sequences are accommodated with equal ease, as is frequency chirping of the light sourc...

We analyze the interplay of nonlinearity and dispersion in a dispersion-decreasing photonic bandgap Bragg fiber as a new platform for generating parabolic pulses. A suitably designed linearly tapered, low-index-contrast, solid-core Bragg fiber – amenable to fabrication by conventional modified chemical vapor deposition technology – is shown to yield stable parabolic pulses. The fiber design was...

We propose an exponential time-differencing method based on the leapfrog scheme for numerical integration of the generalized nonlinear Schrödinger-type equations. The key advantage of the proposed method over the widely used Fourier split-step method is that in the new method, numerical instability at high wavenumbers is strongly suppressed. This allows one to use time steps that considerably e...

in the paper‎, ‎some new existence theorems of maximal elements for‎ ‎$mathscr{f}_{c,theta}$-mappings and $mathscr{f}_{c,theta}$-majorized mappings are established‎. ‎as applications, ‎some new existence theorems of equilibrium points for‎ ‎one-person games‎, ‎qualitative games and generalized games are obtained‎. ‎our results unify and generalize most known results‎ ‎in recent literature‎.

Background/aim: Based on mechanical considerations, the authors have developed a new approach to weakening oculomotor muscles. They present the biomechanical considerations that have encouraged them to explore this approach, and compare it with existing surgical techniques. Results of application to patients are given in the companion paper, and do not require an analytical understanding of the...