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Note On Jakimovski-Leviatan Operators Preserving e x

Abstract

In the present article, a modification of Jakimovski-Leviatan operators is presented which reproduce constant and e x functions. We prove uniform convergence order of a quantitative estimate for the modified operators. We also give a quantitative Voronovskya type theorem.

Open access
Optical solitons to the fractional Schrödinger-Hirota equation

Abstract

This study reaches the dark, bright, mixed dark-bright, and singular optical solitons to the fractional Schrödinger-Hirota equation with a truncated M-fractional derivative via the extended sinh-Gordon equation expansion method. Dark soliton describes the solitary waves with lower intensity than the background, bright soliton describes the solitary waves whose peak intensity is larger than the background, and the singular soliton solutions is a solitary wave with discontinuous derivatives; examples of such solitary waves include compactions, which have finite (compact) support, and peakons, whose peaks have a discontinuous first derivative. The constraint conditions for the existence of valid solutions are given. We use some suitable values of the parameters in plotting 3-dimensional surfaces to some of the reported solutions.

Open access
Probing for stomach using the Focused Impedance Method (FIM)

Abstract

For probing deep organs of the body using electrical impedance, the conventional method is to use Electrical Impedance Tomography (EIT). However, this would be a sophisticated machine and will be very expensive when a full 3D EIT is developed in the future. Furthermore, for most low income countries such expensive devices may not deliver the benefits to a large number of people. Therefore, this paper suggests the use of simpler techniques like Tetrapolar Impedance Measurement (TPIM) or Focused Impedance Method (FIM) in probing deeper organs. Following a method suggested earlier by one of the authors, this paper studies the possibility of using TPIM and FIM for the stomach. Using a simplified model of the human trunk with an embedded stomach, a finite element simulation package, COMSOL, was used to obtain transfer impedance values and percentage contribution of the stomach region in the total impedance. For this work, judicious placement of electrodes through qualitative visualizations based on point sensitivity equations and equipotential concepts were made, which showed that reasonable contribution of the stomach region is possible through the use of TPIM and FIM. The contributions were a little over 20% which is of similar order of the cross-sectional area percentage of the stomach with respect to that of the trunk. For the case where the conductivity of the stomach region was assumed about 4 times higher, the contributions increased to about 38%. Through further studies this proposed methods may contribute greatly in the study of deeper organs of the body.

Open access
Psychological correlates of nonspecific electrodermal responses

Abstract

Spontaneous fluctuations in electrodermal responses are known as nonspecific electrodermal responses (NS.EDRs). The use of NS.EDRs as a tool in applied psychophysiological research has resulted in a variety of publications. NS.EDRs are examined separately as associated with the (as a biomarker of) levels of anxiety. The aim of this study was to compare changes (in terms of amplitude, frequency and time components) in NS.EDRs at two different (pre and post of an external stimulus) resting phases. NS.EDRs (nonspecific skin conductance responses (NS.SCRs), nonspecific skin potential responses (NS.SPRs), and nonspecific skin susceptance responses (NS.SSRs)) were recorded from 50 apparently healthy volunteers simultaneously at the same skin area. They were scored as NS.SCRs and NS.SSRs for changes greater than 0.02 μS and NS.SPRs greater than 0.02 mV. It was found that NS.EDRs, in particular NS.SCRs and NS.SPRs, were significantly changed in the second resting period, following the specific stimulus. More specifically, the amplitude of NS.EDRs were significantly decreased for NS.SCRs (p<0.001) and for NS.SPRs (p<0.005), but NS.SSRs remained stable. Moreover, the rise time of NS.SCRs was decreased in the second resting time. Furthermore, the frequency of responses was also changed. The computed NS.EDRs, in particular NS.SCRs and NS.SPRs could be of psychological interest and be used to study the electrodermal responses in detail. NS.SSRs were found to be robust with respect to nonspecific stimuli at various relaxation periods and their role was found to be less important in analysis of NS.EDRs in comparison to NS.SCRs and NS.SPRs at low frequency (20 Hz AC current). This should be considered in analysis of NS.EDRs. The computed NS.EDRs, especially NS.SCRs and NS.SPRs may be used as a useful measure of arousal due to their fast response and sensitivity to nonspecific stimuli and may also be used in assessment of individual differences.

Open access
Questioning the aloe vera plant and apple memristors

Abstract

Non-linear electrical properties of a (biological) tissue can be revealed by non-linear electrical measurements, which means that the applied stimulus itself affects the measurement. If resulting voltage–current plots exhibit pinched hysteresis loops, the underlying tissue may be classified as a memristor, a state dependent resistor. The aloe vera plant and apples have been found to be memristors. However, polarization processes on the electrodes are also non-linear and may affect the measurement. Apples and aloe vera conduct electrical current very well and it is likely that the recordings are actually dominated by the polarization impedance of the electrodes. Here, we study the non-linear properties of aloe vera and apples with two different measurement electrode types. Furthermore, we measured also on the extracted liquids from one aloe vera leaf and one apple, leading to similar results. We concluded, unlike previous studies on these subjects, that the memristive properties originate from electrochemical reactions on the electrodes rather than the apples or aloe vera themselves.

Open access
The new extended rational SGEEM for construction of optical solitons to the (2+1)–dimensional Kundu–Mukherjee–Naskar model

Abstract

This work proposes the new extended rational sinh-Gordon equation expansion technique (SGEEM). The computational approach is formulated based on the well-known sinh-Gordon equation. The proposed technique generalizes the sine-Gordon/sinh-Gordon expansion methods in a rational format. The efficiency of the suggested technique is tested on the (2+1)imensional Kunduukherjeeaskar (KMN) model. Various of optical soliton solutions have been obtained using this new method. The conditions which guarantee the existence of valid solitons are given.

Open access
On graphs with equal dominating and c-dominating energy

Abstract

Graph energy and domination in graphs are most studied areas of graph theory. In this paper we try to connect these two areas of graph theory by introducing c-dominating energy of a graph G. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.

Open access
Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation

Abstract

In this article, we attain new analytical solution sets for nonlinear time-fractional coupled Burgers’ equations which arise in polydispersive sedimentation in shallow water waves using exp-function method. Then we apply a semi-analytical method namely perturbation-iteration algorithm (PIA) to obtain some approximate solutions. These results are compared with obtained exact solutions by tables and surface plots. The fractional derivatives are evaluated in the conformable sense. The findings reveal that both methods are very effective and dependable for solving partial fractional differential equations.

Open access
Yang-Laplace Decomposition Method for Nonlinear System of Local Fractional Partial Differential Equations

Abstract

The basic motivation of the present study is to extend the application of the local fractional Yang-Laplace decomposition method to solve nonlinear systems of local fractional partial differential equations. The differential operators are taken in the local fractional sense. The local fractional Yang-Laplace decomposition method (LFLDM) can be easily applied to many problems and is capable of reducing the size of computational work to find non-differentiable solutions for similar problems. Two illustrative examples are given, revealing the effectiveness and convenience of the method.

Open access
Word series high-order averaging of highly oscillatory differential equations with delay

Abstract

We show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word series techniques to obtain high-order averaged equations for differential equations without delay.

Open access