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In this study, the solutions of 2 + 1 -dimensional nonlinear Date–Jimbo–Kashiwara–Miwa (DJKM) equation are characterized, which can be used in mathematical physics to model water waves with low surface tension and long wavelengths. The integration scheme, namely, the extended direct algebraic method, is used to extract complex trigonometric, rational and hyperbolic functions. The complex-valued solutions represent traveling waves in different structures, such as bell-, V-, and W-shaped multiwaves. The results obtained in this article are novel and more general than those contained in the literature (Wang et al., 2014, Yuan et al., 2017, Pu and Hu 2019, Singh and Gupta 2018). Furthermore, the mechanical features and dynamical characteristics of the obtained solutions are demonstrated by three-dimensional graphics.

In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $ b $-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving $ (\alpha, \beta) $-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein.

The proposed work focuses on improving the performance of the traditional nonlinear saturation controller (NSC) algorithm. In this work, a tuning mechanism can be implemented by providing the NSC control unit with the measured speed $\Omega $ of the rotor from a shaft encoder device in order to introduce a tuned NSC (TNSC). In other words, we are going to tune the NSC’s natural frequency ${\omega _{c}}$ at one half of $\Omega $ such that $\Omega =2{\omega _{c}}$ . This TNSC is adopted to reduce the vibratory amplitudes of a 16-pole constant-stiffness rotor-Active magnetic bearings AMBs) system for a wide range of speeds and eccentricities. The whole controlled system is studied mathematically to seek its approximate solutions via the multiple scales technique. Different relations between the rotor’s amplitudes and its parameters are plotted so as to verify the proposed tuning mechanism and its crucial role in improving the NSC’s performance.

In this paper, the authors determine the number of infected cells and concentration of infected (viral) particles in plasma during HIV-1 (human immunodeficiency virus type one) infections using Shehu transformation. For this, the authors first defined some useful properties of Shehu transformation with proof and then applied Shehu transformation on the mathematical representation of the HIV-1 infection model. The mathematical model of HIV-1 infections contains a system of two simultaneous ordinary linear differential equations with initial conditions. Results depict that Shehu transformation is very effective integral transformation for determining the number of infected cells and concentration of viral particles in plasma during HIV-1 infections.

In this paper, we introduce a nonlinear vibrations analysis and dynamic responses of a vertical conveyor system under multi excitation forces. By adding the nonlinear proportional derivative controller (NPD) to the vibrating motion of the vertical vibration conveyor, the energy was transferred between uncontrolled and controlled system. We calculate the approximate solutions of the vibrating system utilizing the method of multiple scales. In addition, we investigate the stability at worst resonance cases using phase plane technique, equations of frequency response, and averaging method. The vertical vibration conveyor behavior was studied numerically at the values of its different parameters. The results exhibit the efficiency of NPD control unit to avoid the oscillations of the vertical conveyor system. Numerical simulations have been carried out using MAPLE and MATLAB software's to ensure the fidelity of our results. Comparisons are made between analytical and numerical results. Also, findings of the present work are discussed in details and compared with published works.

This article utilizes a nonlinear active vibration control to eliminate the helicopter blade flapping system oscillations having mixed excitation forces. The approximate solutions were calculated using the multiple scale perturbation technique. Furthermore, the stability and bifurcation analysis were investigated using the averaging method and Poincaré maps. In addition, numerical results exhibit the amplitude of the steady state against the detuning parameter and, the influences of all the parameters on the vibrating system behavior. Comparisons were carried out between analytical and numerical simulations to enclose the accuracy of our results. Finally, the current work is examined and compared to the published works.

The nonlinear dynamics control of a contact-mode atomic force microscopy (AFM) system with multi forces (harmonic and parametric excitation force) utilizing the time delay proportional derivative (PD) controller is investigated. The perturbation method is utilized to calculate the first-order approximate solutions for the AFM system. The stability of the AFM system is investigated at the worst resonance case by Lyapunov's first method. We also show the bifurcation diagrams of response curves using frequency response equations before and after control are performed. Furthermore, we focus on the effect of the time-delayed control and returns signals gain on the vibration amplitude and the stability analysis of the controlled system in primary, sub-harmonic resonance for different parameter variations. In addition, the numerical results are procured using MATLAB program. Eventually, validation curves are presented to estimate the nearness degree between the analytical predictions also numerical simulation. The obtained results exhibited that, the time-delayed PD control efficiency to put down the nonlinear oscillations of the system.

The impact of Newtonian heating on a time-dependent fractional magnetohydrodynamic (MHD) Maxwell fluid over an unbounded upright plate is investigated. The equations for heat, mass and momentum are established in terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) fractional derivatives. The solutions are evaluated by employing Laplace transforms. The change in the momentum profile due to variability in the values of parameters is graphically illustrated for all three C, CF and ABC models. The ABC model has proficiently revealed a memory effect.

A number of mathematical methods have been developed to determine the complex rheological behavior of fluid’s models. Such mathematical models are investigated using statistical, empirical, analytical, and iterative (numerical) methods. Due to this fact, this manuscript proposes an analytical analysis and comparison between Sumudu and Laplace transforms for the prediction of unsteady convective flow of magnetized second grade fluid. The mathematical model, say, unsteady convective flow of magnetized second grade fluid, is based on nonfractional approach consisting of ramped conditions. In order to investigate the heat transfer and velocity field profile, we invoked Sumudu and Laplace transforms for finding the hidden aspects of unsteady convective flow of magnetized second grade fluid. For the sake of the comparative analysis, the graphical illustration is depicted that reflects effective results for the first time in the open literature. In short, the obtained profiles of temperature and velocity fields with Laplace and Sumudu transforms are in good agreement on the basis of numerical simulations.

In this article, we are interested in some well-known dynamic inequalities on time scales. For this reason, we will prove some new Hermite–Hadamard (H-H) and Opial dynamic inequalities on time scales. The main results here will be derived via the dynamic integration by parts and chain rule formulas on time scales. In addition, we will extend and unify the inequalities for the convex functions.

We consider a class of initial fractional Liouville-Caputo difference equations (IFLCDEs) and its corresponding initial uncertain fractional Liouville-Caputo difference equations (IUFLCDEs). Next, we make comparisons between two unique solutions of the IFLCDEs by deriving an important theorem, namely the main theorem. Besides, we make comparisons between IUFLCDEs and their \begin{document}$ \varrho $\end{document}-paths by deriving another important theorem, namely the link theorem, which is obtained by the help of the main theorem. We consider a special case of the IUFLCDEs and its solution involving the discrete Mittag-Leffler. Also, we present the solution of its \begin{document}$ \varrho $\end{document}-paths via the solution of the special linear IUFLCDE. Furthermore, we derive the uniqueness of IUFLCDEs. Finally, we present some test examples of IUFLCDEs by using the uniqueness theorem and the link theorem to find a relation between the solutions for the IUFLCDEs of symmetrical uncertain variables and their \begin{document}$ \varrho $\end{document}-paths.

In this paper, we explored the nonlinear dynamics behavior and vibration suppression of a nonlinear electromechanical oscillator system under harmonic and parametric excitation. The model comprises of an electrical part coupled to mechanical part and displayed by a coupled nonlinear ordinary differential equations. The analytical up to second order approximate solutions are sought applying the method of multiple scales method. We utilized the time-series and method of averaging to analyze the response and stability of the solutions at the worst resonance cases. We checked the results of perturbation solution through numerical simulations and the effects of different system parameters have been reported. Comparison between analytical and numerical solutions is obtained. Also, the numerical results are obtained using MAPLE and MATLAB algorisms.

Integral transformations are essential for solving complex problems in business, engineering, natural sciences, computers, optical science, and modern mathematics. In this paper, we apply a general integral transform, called the Jafari transform, for solving a system of ordinary differential equations. After applying the Jafari transform, ordinary differential equations are converted to a simple system of algebraic equations that can be solved easily. Then, by using the inverse operator of the Jafari transform, we can solve the main system of ordinary differential equations. Jafari transform belongs to the class of Laplace transform and is considered a generalization to integral transforms such as Laplace, Elzaki, Sumudu, G\_transforms, Aboodh, Pourreza, etc. Jafari transform does not need a large computational work as the previous integral transforms. For the Jafari transform, we have studied some valuable properties and theories that have not been studied before. Such as the linearity property, scaling property, first and second shift properties, the transformation of periodic functions, Heaviside function, and the transformation of Dirac’s delta function, and so on. There is a mathematical model that describes the cell population dynamics in the colonic crypt and colorectal cancer. We have applied the Jafari transform for solving this model.

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

This paper studied the nonlinear vibration and resonance of a Cartesian manipulator system carrying an intermediate end effector under mixed excitations. The multiple scales method is applied to get the approximate solutions of this system of the second-order differential equation. Furthermore, the analytical solution obtained the amplitudes and phases of the response from the first-order differential equation governing. We extracted all worst resonance cases and studied it numerically. The numerical solutions and response amplitude of this system are also studied and discussed. We analyzed the stability of the steady-state solution of a Cartesian manipulator system using frequency response equations and phase plane technique at the worst resonance cases. Comparison between analytical and numerical solutions is obtained. We determined both bifurcation diagrams and stability using Poincare maps. Also, the numerical results are obtained using MAPLE and MATLAB algorithms.

An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition and its properties. Furthermore, there is a strong correlation between convexity and symmetry concepts. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the last few years. In this study, by using a new identity, we establish some new fractional weighted Ostrowski-type inequalities for differentiable quasi-convex functions. Further, further results for functions with a bounded first derivative are given. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtain. The obtained results generalize and refine certain known results.

In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability weighted moments, moments of (reversed) residual lifetime, entropy and order statistics. After producing the general class, two of the corresponding parametric statistical models are outlined. The hazard rate function of the sub-models can take a variety of shapes such as increasing, decreasing, unimodal, and Bathtub shaped, for different values of the parameters. Furthermore, the sub-models of the introduced family are also capable of modelling symmetric and skewed data. The parameter estimation of the special models are discussed by numerous methods, namely, the maximum likelihood, simple least squares, weighted least squares, Cramér-von Mises, and Bayesian estimation. Under the Bayesian framework, we have used informative and non-informative priors to obtain Bayes estimates of unknown parameters with the squared error and generalized entropy loss functions. An extensive Monte Carlo simulation is conducted to assess the effectiveness of these estimation techniques. The applicability of two sub-models of the proposed family is illustrated by means of two real data sets.

This study reflects the behaviorof nanoparticles shape on (Ag-TiO2)/water hybrid nanofluid flow toward the horizontal permeable stretching shrinking cylinder. The effect of suction and injection parameters is also considered. Three different shapes (sphere, blade, and lamina) of Ag and TiO2 are used in this study. The boundarylayer equations of the problem are transformed to a setof non-linearODEs and the analytical solution of these non-linear ODEsis conducted. Thehomotopyanalysis method (HAM) is applied to findthe analytical resultsof the problem. The obtained results are also compared with the already published article by Sandeep et al.Spectacular characteristics of hybrid nanofluid flow quantities are carried out with a special focus on velocity f ' η profile, temperature θ η profileand Nusselt number Nu . With the impact of pertinent parameters, the temperature and Nusselt number profiles show that the sphereshape nanoparticles have better temperature disturbance and heat transfer on hybrid nanofluid flow.

The main aim of this paper is to propose a new and simple algorithm namely the optimal q-homotopy analysis method (Oq-HAM), to obtain approximate analytical solutions of the convection diffusion (CD) equation. Comparison of Oq-HAM with the homotopy analysis method (HAM) and the homotopy perturbation method (HPM) is made. The results reveal that the Oq-HAM has more accuracy than the others. Finally, numerical example is given to illustrate the accuracy and stability of this method. Comparison of the approximate solution with the exact solutions shows that the proposed method is very efficient and computationally attractive. A new efficient approach is proposed to obtain the optimal value of convergence controller parameter ℏ to guarantee the convergence of the obtained series solution. Keywords: Optimal q-homotopy analysis method, Convergence-control parameter, Convection diffusion equation

This research paper investigates the numerical solutions of the (1 + 1)-dimensional Ito equation through the extended simplest equation (ESE) method. This model is considered as well-known in quantum mechanics and nonlinear optics, which represents the height of the water’s free surface above a flat bottom. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. Diverse novel computational solutions are constructed and demonstrated through three distinct types of sketches. The stability of our obtained solutions is investigated by using Hamiltonian system’s characterizations. The novelty of our paper is explained by comparing our obtained solutions with the previously evaluated computational solutions with different computational schemes.

In this article, the iteration transform method is used to evaluate the solution of a fractional-order dark optical soliton, bright optical soliton, and periodic solution of the nonlinear Schr&ouml, dinger equations. The Caputo operator describes the fractional-order derivatives. The solutions of some illustrative examples are presented to show the validity of the proposed technique without using any polynomials. The proposed method provides the series form solutions, which converge to the exact results. Using the present methodology, the solutions of fractional-order problems as well as integral-order problems are calculated. The present method has less computational costs and a higher rate of convergence. Therefore, the suggested algorithm is constructive to solve other fractional-order linear and nonlinear partial differential equations.

In this paper, we study the dynamics, transfer of energy and control of the vibrations of micro-electromechanical system (MEMS) gyroscope with linear and nonlinear parametric excitations. This leads to two-degree-of-freedom system. The coupling of the system equations is responsible for energy transfers of the two vibration modes (drive mode and sense mode) and for the resonance in MEMS gyroscope. The resulting governing equation is in the form of a cubic Mathieu equation coupled to a Duffing equation. The averaging method is applied to obtain the frequency response equations near simultaneous sub-harmonic and internal resonance. The stability of the steady-state solution near the worst resonance case is studied and discussed. The effects of the different parameters on the two modes of system behavior are studied numerically. Poincare maps are used to determine stability and plot bifurcation diagrams. Comparison between optimal linear feedback control and active control via negative nonlinear cubic velocity feedback in the presence of parameter uncertainties and noise measurement are done. The numerical results of stability, phase planes and time history are achieved using MATLAB and MAPLE programs.

In this paper, a study for nonlinear saturation controller (NSC) is presented that used to suppress the vibration amplitude of a structural dynamic model simulating nonlinear composite beam at simultaneous sub-harmonic and internal resonance excitation. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities of the feedback gain and a two-to-one internal resonance. The analytical solution for the system and the nonlinear saturation controller are obtained using method of multiple time scales perturbation up to the second order approximation. All possible resonance cases were extracted at this approximation order and studied numerically. The stability of the system at the worst resonance case (Ω = 2ωs and ωs = 2ωc) is investigated using both frequency response equations and phase-plane trajectories. The effects of different parameters on the system and the controller are studied numerically. The effect of some types of controller on the system is investigated numerically. The simulation results are achieved using Matlab and Maple programs.

In this article, the performance and working fluid selection for an organic Rankine cycle-vapor compression refrigeration (ORC–VCR) integrated system activated by renewable energy is investigated. The performance of the system is described by the system coefficient of performance (COPS), and the refrigerant mass flow rate per kilowatt refrigeration capacity (m˙total). Twenty-three pure substances are proposed as working fluids for the integrated system. The basic integrated system performance is assessed and compared using the proposed working fluids. The basic VCR cycle works between 35 and 0 °C, while the basic ORC works between 35 and 100 °C. The impacts of different operating parameters such as the evaporator, the boiler, and the condenser temperatures on the ORC–VCR system performance are also examined. The results show that the cyclopentane accomplished the highest system performance under all investigated operating conditions. Accordingly, among the examined 23 working fluids, cyclopentane is the most appropriate working fluid for the integrated system from the viewpoints of environmental concerns and system performance. Nevertheless, due to its high flammability, further restrictions should be taken. The basic integrated system COPS, refrigeration effect, and the corresponding m˙total utilizing cyclopentane are 0.654, 361.3 kW, and 0.596 × 10−2 kg/(s kW), respectively.

In the present work, the coupling of two non-linear oscillators of the main system and absorber representing ultrasonic cutting process is investigated. This leads to a two-degree-of-freedom system subjected to multi-external excitation force. The aim of this work is to control the main system behavior at simultaneous primary and internal resonance condition, where the system damage is probable. Multiple scale perturbation method is applied to obtain the solution up to the second order approximations. The different resonance cases are reported and studied numerically. The stability of the system is investigated applying both phase-plane and frequency response techniques. The effects of the different parameters of the absorber on the system behavior are studied numerically. Comparison with the available published work is reported.

The knowledge of the prevalence of spinal cord disorders (SCD) is important to understand specific causes in each part of the worldand to allow to potentially adapt health care and public policy including law enforcement to the main causes. SCD have important personal, biopsychological, socio-economic, short-term and long-term consequences. An SCD is the underlying cause for 1 of every 40 patients admitted to a major trauma centre. The affected population consists primarily of young male adults. The aim of the present study was to determine the prevalence and cause of SCD in Al-Quseir City, using a door-to-door method. The total of inhabitants was 33,285 in Al-Quseir City screened by 3 specialists of neurology. Suspected cases were subjected to full clinical assessment and MRI or CT of the spine. The prevalence rate of SCD was 63/100,000 for the total population. Traumatic spinal cord injury had a prevalence of 18/100,000, while non-traumatic SCD was found in 45/100,000. Degenerative cervical disc prolapse was the most common aetiology of SCD with a prevalence rate of 27/100,000.

In this paper, the nonlinear dynamic behavior of a string-beam coupled system subjected to external, parametric and tuned excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system which are described by a set of ordinary differential equations with two degrees of freedom. The case of 1:1 internal resonance between the modes of the beam and string, and the primary and combined resonance for the beam is considered. The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system and obtain approximate solutions up to and including the second-order approximations. All resonance cases are extracted and investigated. Stability of the system is studied using frequency response equations and the phase-plane method. Numerical solutions are carried out and the results are presented graphically and discussed. The effects of the different parameters on both response and stability of the system are investigated. The reported results are compared to the available published work.

The present study deals with the response of a two-degree-of-freedom (2DOF) system with quadratic coupling under parametric and harmonic excitations. The method of multiple scale perturbation technique is applied to solve the nonlinear differential equations and obtain approximate solutions up to and including the second order approximations. All resonance cases are extracted and investigated. Stability of the system is studied using frequency response equations and phase-plane method. Numerical solutions are carried out and the results are presented graphically and discussed. The effects of the different parameters on both response and stability of the system are investigated. The reported results are compared to the available published work.

The nonlinear behavior of an elastic cable subjected to harmonic excitation is studied and solved. The method of multiple scales perturbation is applied to analyze the response of the nonlinear system near the simultaneous principle primary and internal resonance. The stability of the proposed analytic nonlinear solution near the simultaneous primary-internal resonance is studied and the stability condition is investigated. The effect of different parameters on the steady state responses of the vibrating system is studied and discussed using frequency response equations. The numerical solutions and chaotic response of the nonlinear system of the elastic cable for different parameters are also studied.

Vibrations are usually undesired phenomena as they may cause damage or destruction of the system. However, sometimes they are desirable, as in ultrasonic machining (USM). In such case, the problem is a complicated one, as it is required to reduce the vibration of the machine head and have reasonable amplitude for the tool. In the present work, the coupling of two non-linear oscillators of the tool holder and tool representing ultrasonic cutting process is investigated. This leads to a two-degree-of-freedom system subjected to multi-external excitation force. The aim of this work is to control the tool holder behavior at simultaneous primary and internal resonance condition and have high amplitude for the tool. Multiple scale perturbation method is applied to obtain a solution up to the second order approximations. Other different resonance cases are reported and studied numerically. The stability of the system is investigated applying both phase-plane and frequency response techniques. The effects of the different parameters of the tool on the system behavior are studied numerically. Comparison with the available published work is reported.

The dynamic response of mechanical and civil structures subject to high-amplitude vibration is often dangerous and undesirable. Sometimes controlled vibration is desirable as in ultrasonic machining (USM). Ultrasonic machining (USM) is the removal of material by the abrading action of grit-loaded liquid slurry circulating between the workpiece and a tool vibrating perpendicular to the workface at a frequency above the audible range. A high-frequency power source activates a stack of magnetostrictive material, which produces a low-amplitude vibration of the toolholder. This motion is transmitted under light pressure to the slurry, which abrades the workpiece into a conjugate image of the tool form. This can be achieved via passive and active control methods. In this paper, multi-tool techniques are used in the ultrasonic machining via reducing the vibration in the tool holder and providing reasonable amplitudes for the tools represented by the absorbers. The coupling of the tool holder and absorbers simulating ultrasonic cutting process are investigated. This leads to a multi-degree-of-freedom system subject to external and tuned excitation forces. Multiple scale perturbation method is applied to obtain the solution up to the second order approximation. Different resonance cases are reported and studied numerically. The stability of the system is investigated applying both phase-plane and frequency response techniques. The effects of the different parameters of the absorbers on the system behavior are studied numerically. Comparison with the available published work is reported.

Ultrasonic machining (USM) is of particular interest for the machining of non-conductive, brittle materials such as engineering ceramics. In this paper, a multi-tool technique is used in USM to reduce the vibration in the tool holder and have reasonable amplitude for the tools. This can be done via dynamic absorbers. The coupling of four non-linear oscillators of the tool holder and tools representing ultrasonic cutting process are investigated. This leads to a four-degree-of-freedom system subjected to multi-external and multi-parametric excitation forces. The aim of this work is to control the tool holder behavior at simultaneous primary, sub-harmonic and internal resonance condition. Multiple scale perturbation method is used to obtain the solution up to the second order approximations. The different resonance cases are reported and studied numerically. The stability of the system is investigated by using both phase-plane and frequency response techniques. The effects of the different parameters of the tools on the system behavior are studied numerically. Comparison with the available published work is reported.

Saturation phenomena may occur in non-linear vibrating systems. This phenomena is very useful in suppressing the undesired vibrations. In the present work saturation is investigated in a non-linear oscillating system subject to multi-parametric excitation. The system represents the vibration of a single-degree-of-freedom (SDOF) cantilever or the wing of an aircraft. Multiple scale perturbation method is applied to the system to obtain solution up to and including third-order approximations. The saturation phenomena is investigated at one of the extracted resonance cases. Other resonance cases are studied numerically. Effects of different parameters on saturation phenomena are studied. Stability of the system is investigated applying both frequency response function (FRF) and phase-plane trajectories. Some recommendations are given by the end of the work regarding best system behavior.

In this paper, a non-linear explicit one step method is presented for solving stiff differential systems which characterize several kinds of linear reactions and diffusion from biochemistry, physiology, etc. The accuracy and stability properties of the method are investigated and shown to yield at least fifth-order and A-stable. The method is consistent and convergent. Some differential systems arising in chemical reactions are solved to illustrate the performance and accuracy of the method. Received: November 21, 2013 c © 2014 Academic Publications, Ltd. url: www.acadpubl.eu Correspondence author 342 E.R. El-Zahar, Y.S. Hamed, H.M. Habib AMS Subject Classification: 65L05

Hamdy El-Tallawy,1 Wafa Farghaly,1 Nabil Metwally,2 Tarek Rageh,1 Ghaydaa A Shehata,1 Reda Badry,1 Esam El Moselhy,2 Mahmoud Hassan,2 Mohamed M Sayed,3 Ahmed A Abdelwarith,1 Y Hamed,2 I Shaaban,2 Talal Mohamed,4 Mohamed Abd El Hamed,1 MR Kandil1 1Department of Neurology, Faculty of Medicine, Assiut University, Assiut, Egypt; 2Department of Neurology and Public Health, Faculty of Medicine, Al-Azhar University (Assiut branch), Assiut, Egypt; 3Department of Neurology, Faculty of Medicine, Sohag University, Sohag, Egypt; 4Department of Neurology, Faculty of Medicine, Qena University, Qena, Egypt Abstract: Methodology and strategy play a very important role in epidemiological studies. Determination of the study area, geographical features, facilities, difficulties, and key personnel from the same area are important factors for successful methodology. Over 31 months (July 1, 2009 to January 31, 2012), a screening and an examination survey were carried out to ascertain the prevalence of epilepsy, stroke, dementia, cerebellar ataxia, migraine, cerebral palsy, Parkinsonism, chorea, athetosis, dystonia, trigeminal neuralgia, Bell's palsy, multiple sclerosis, spinal cord disorders, and attention deficit hyperactivity disorders in Al Quseir, Red Sea Governorate, Egypt. A total of 33,285 people were screened by three neurologists in a door-to-door manner, including every door, using a standardized Arabic questionnaire to detect any subject with a neurological disorder. The methodological aspects of this project were carried out through eight phases: (1) data collection; (2) preparation; (3) screening; (4) case ascertainment; (5) investigations; (6) classifications; (7) data entry; and (8) statistics and tabulations. The results of this study reveal that the total prevalence of neurological disorders in Al Quseir was 4.6% and higher among females (5.2%) than males (3.9%). The highest prevalence was recorded in the elderly population (60+ years [8.0%]) and among the age group 18–39 years (5.4%). Keywords: methodological aspects, demographic data, prevalence

This paper adds a negative velocity feedback to the dynamical system of twin-tail aircraft to suppress the vibration. The system is represented by two coupled second-order nonlinear differential equations having both quadratic and cubic nonlinearities. The system describes the vibration of an aircraft tail subjected to both multi-harmonic and multi-tuned excitations. The method of multiple time scale perturbation is adopted to solve the nonlinear differential equations and obtain approximate solutions up to the third order approximations. The stability of the proposed analytic solution near the simultaneous primary, combined and internal resonance is studied and its conditions are determined. The effect of different parameters on the steady state response of the vibrating system is studied and discussed by using frequency response equations. Some different resonance cases are investigated numerically