The general nonlinear fourth order differential equation, x"""" + f(1) (x,x"x "",x""")x""" + f(2) (x,x",x "")x "" + f(3)(x,x")x" + f(4)(x,x\",x "",x""",t)x = p(t) is considered. It is proved that if the functions f(i) accept certain sufficient conditions, then there exists a bounded space for state variables, in which the equation has periodic answer. For this purpose we use the existence of Green"s function and Schauder"s theorem.

In this paper, a differential transform method (DTM) is used to find the numerical solution of the linear and nonlinear Westervelt equation. Exact solution can also be achieved by the known forms of the series solution. In this paper, we present the definition and operation of the three-dimensional differential transform and investigate the particular exact solution of system of partial differential equations that usually arise in applied mechanic by a three-dimensional differential transform method. The numerical result of the present method is presented and compared with the exact solution that is calculated by the Laplace transform method.

‎‎‎‎In the present work the oscillatory behavior of the solutions of a nonlinear generalization of Euler equation will be considered in which the‎ ‎nonlinearities satisfy the smoothness conditions which guarantee‎ ‎the uniqueness of solutions of initial value problems‎. ‎However‎, ‎no‎ ‎conditions of sub(super)linearity are assumed‎. ‎Some new‎ ‎sufficient conditions are established ensuring oscillation of all‎ ‎solutions of this equation‎. ‎Examples are also provided to illustrate‎ ‎the relevance of the main results‎.

This paper presents a new technique for nonlinear continuous-time observer design based on the differential state-dependent Riccati equation (SDRE) filter, with guaranteed exponential stability. Although impressive results have rapidly emerged from the use of SDRE designs for observers and filters, the underlying theory is yet scant and there remain many unanswered questions such as stability and convergence. In this paper, Lyapunov stability analysis is used to obtain the required conditions for exponential stability of the estimation error dynamics. Furthermore, through a simulation study of a second order nonlinear model, which satisfies the stability conditions, the promising performance of the proposed observer is demonstrated. Finally, in order to examine the effectiveness of the proposed method, it is applied to highly nonlinear flux and angular velocity estimation problem for induction machines. The simulation results verify how effectively the modification proposed in this paper can increase the region of attraction and the observer error decay rate.

In this paper, a novel device, namely heterojunction electron-hole bilayer tunnel field effect transistor (HJ-EHBTFET), is proposed which outperforms conventional tunnel field effect transistor (TFET) in terms of electrical performance. The use of lattice matched InAs/Al0.6Ga0.4Sb material combination results in a broken band gap configuration, making it highly suitable for high speed ultra-low applications, as it requires smaller gate bias for the onset of tunneling. The impact of critical design parameters on the device performance is comprehensively investigated. The proposed device utilizes electrical doping instead of physical doping for the creation of tunneling junction, which effectively addresses the problem of low solubility of dopants in heavily doped III-V materials. The top gate and bottom gate workfunction are critical design parameters that effectively modulated the electrically induced charges at the tunneling junction and consequently, affect the tunneling rate. In order to obtain the lowest possible transition voltage for the onset of tunneling, a variation matrix of threshold voltage variation is computed as a function of gate electrode workfunction. Through this process, a step-like behavior from off-state to on-state has been achieved, with a subthreshold swing of 3 mV/dec and on/off current ratio of 5.8×1012, thereby paving the way for the design of low-power high-speed digital computing systems.

This paper is devoted to obtaining some new sufficient conditions for the oscillation of all solutions of first order nonlinear differential equations with several deviating arguments. Finally, an illustrative example related to our results is given.