in this paper sufficient conditions of oscillation of all of nonlinear second order neutral differential eqiation and sifficient conditions for nonoscillatory soloitions to onverage to zero are obtained

The aim of this paper is to present method for solving ordinary differential equations of eighth order with two point boundary conditions. We propose two-point osculatory interpolation to construct polynomial solution.

In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynami

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time

This paper constructs a new linear operator associated with a seven parameters Mittag-Leffler function using the convolution technique. In addition, it investigates some significant second-order differential subordination properties with considerable sandwich results concerning that operator.

The major aim of this work is to apply a technique, Elzaki transform (ET), which is an iterative analytical technique to achieve an approximate analytical solution for some applications of nonlinear differential equations. This technique depends on applying ET which has been used to break down the partial differential equation solution into an infinite number of components. Moreover, some illustrative examples are given and the results obtained indicate the proposed method’s accuracy, efficiency, and reliability. Results like this demonstrate how effective and efficient this method is in resolving problems of this kind. Therefore, using fractional differential equations as a model, our suggested approach can be used to analyze the

A taxonomic keys was established of book and bark lice Order Psocoptera to isolated insects in Iraq from different localities of Baghdad and Babylon provinces. Thirteen species belong to eight genera and five families have been studied and described in details, these species were recorded for the first time in Iraq. These species are: Belaphopsocus badonneli New, 1971; Belaphotroctes oculeris Bodonnel, 1973; Embodopsocosis newi Bodonnel, 1973; Epipsocus stigamaticus Mockeord, 1991; Lepinotus huoni Schmidt and New, 2008; Liposcelies decolor Peramane 1925 Liposcelies paeta Pearman 1942 Liposclies bostrychphila Badonnel 1931; Liposclies brunnea Mostchulsky 1852; Liposclies entoophila Enderlein 1907; Neopsocopsis minuscule Li 2002 ;

Two decades after replacing the OAU, the AU’s record is best measured not by communiqués but by how fast it converts rules into results on the ground. In March 2022, the African Union’s Peace and Security Council (PSC) authorised the transition from AMISOM to ATMIS in Somalia — a reminder that, two decades after the African Union (AU) replaced the Organisation of African Unity (OAU), the Union’s rules are judged by execution, not intent. This article argues that the AU’s legal and institutional redesign shortened the warning‑to‑decision cycle and raised the credibility of enforcement, but performance still hinges on finance, logistics and political will. Where mandates are matched with money, enabling capabilities and enforc

Criticism is inherently impolite and a face-threatening act generally leading to conflicts among interlocutors. It is equally challenging for both native and non-native speakers, and needs pre-planning before performing it. The current research examines the production of non-institutional criticism by Iraqi EFL university learners and American native speakers. More specifically, it explores to what extent Iraqi EFL learners and American native speakers vary in (i) performing criticism, (ii) mitigating criticism, and (iii) their pragmatic choices according to the contextual variables of power and distance. To collect data, a discourse-completion task was used to elicit written data from 20 Iraqi EFL learners and 20 American native speaker