ON CERTAIN CLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

In the present investigation we define a new class of meromorphic functions on the punctured unit disk △*:= {z ∈ C : 0 < |z| < 1} by making use of the generalized Dziok-Srivastava operator H l m [α1 ]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.     

Analytic approximation of the blow‐up time for nonlinear differential equations by the ADM–Padé technique

We present a new approach to calculate analytic approximations of blow‐up solutions and their critical blow‐up times. Our approach applies the Adomian decomposition–Padé method to quickly and easily compute the critical blow‐up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

On the role of nonlinearities in the Boussinesq-type wave equations

Longitudinal mechanical waves in biomembranes are described by a Boussinesq-type wave equation. It is shown that in this case the nonlinearities are of a different type compared with conventional models of solids. The governing equation analysed in this paper is the improved Heimburg–Jackson model with two dispersive terms. The soliton-type solutions of such a wave equation are found and analysed. The existence of solitons depends on the ratio of nonlinear terms and the width of solitons is governed by dispersive terms.     

Novel Mittag-Leffler stability of linear fractional delay difference equations with impulse

In this letter we propose a class of linear fractional difference equations with discrete-time delay and impulse effects. The exact solutions are obtained by use of a discrete Mittag-Leffler function with delay and impulse. Besides, we provide comparison principle, stability results and numerical illustration.     

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

For nonlinear Schrödinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed.     

Effect of variation in signal amplitude and transit time on reliability analysis of ultrasonic time of flight diffraction characterization of vertical and inclined cracks

The variation of amplitude and transit time of the diffracted signal from the crack-tip in complex geometry components and their resulting effect on the probability of detection (POD) and probability of sizing (POS) was studied. The diffracted signal amplitude has been evaluated from the standard expressions for diffraction coefficient, spatial attenuation and the transit time from the respective mathematical models for both vertical and inclined cracks. The same parameters namely the signal amplitude and the transit time have been measured through experiments conducted on simulated test specimens. It has been observed that the analytical and experimental results compare well with each other. Based on this result the trend and shape (width of the transition zone) of the POD/POS curves can be predicted.     

Guiding functions and periodic solutions for inclusions with causal multioperators

In the present paper, the method of guiding functions is applied to study the periodic problem for a differential inclusion with a causal multioperator. At first we consider the case when the multioperator is closed and convex-valued. Then the case of a non-convex-valued and lower semicontinuous right-hand part is considered. Thereafter, the theory is extended to the case of non-smooth guiding functions.     

Global persistence of geometrical structures for the Boussinesq equation with no diffusion

Our main aim is to investigate the temperature patch problem for the two-dimensional incompressible Boussinesq system with partial viscosity: the initial temperature is the characteristic function of some simply connected domain with 𝒞^1,𝜀 Hölder regularity. Although recent results ensure that the 𝒞¹ regularity of the patch persists for all time, whether higher order regularity is preserved has remained an open question. In the present paper, we give a positive answer to that issue. We also study the higher dimensional case, after prescribing an additional smallness condition involving critical Lebesgue or weak-Lebesgue norms of the data, so as to get a global-in-time statement. All our results stem from general properties of persistence of geometrical structures (of independent interest), that we establish in the first part of the paper.     

Energy harvesting from a magnetic levitation system

Numerical and experimental studies of a magnetic levitation harvester are presented in the paper. The idea is based on the motion of permanent cylinder magnet in a coil exploited for energy harvesting. The novel model is based on a new definition of the coupling coefficient (inductive coefficient) which relates mechanical and an electrical components. The performed static and dynamics experimental tests show that this coefficient is a nonlinear function of the magnet position, and highly depends on the magnet coordinate in the coil, in such a way that the maximum energy is obtained in a coil ends. The comparison between classical – fixed value model – and novel nonlinear model of the inductive coefficient is presented for selected cases. The most essential differences are presented.