Sharif Digital Repository

In this paper we consider the nonlinear third-order quasi-linear differential equationx‴+k2x′=εfx,x′,x″and obtain some simple conditions for the existence of a periodic solution for it. In so doing we use the implicit function theorem to prove a theorem about the existence of periodic solutions and consider one example to show the realizability of the conditions. The validity of the conditions for the parameter-free problemx‴+k2x′=fx,x′,x″also is considered. © 2001 Academic Press  

Sufficient conditions for the boundedness and regularity of a function, whose partial derivatives satisfy a certain set of equations, are presented. Energy methods are used to establish these results. The asymptotic behavior of the gradient toward a constant function is also investigated. © Sharif University of Technology  

Here we are concerned with the problem of the existence of periodic solution for certain second and third-order nonlinear differential equations. Our method here is to consider the problem as an eigenvalue problem and treat it by the topological degree theory. In particular we establish the conditions of the existence of periodic solution first for a simpler system which is homotopic to the original system and then generalize the obtained results for the focal system. The method employed here is applicable also for a system of nonlinear differential equations just with simple modifications. Finally, we present some specific examples numerically to show that the results are valid and... 

Here we are concerned with the existence of periodic solution for nonlinear non-autonomous third order system of ordinary differential equations with singular terms. Our method here is based on the topological method in the sense that we conclude some computable results for the focal system from a homotopic nonsingular system. The aim is to obtain sufficient conditions for which the system has periodic solution whenever the value of deformation with respect to the first variation of the nonsingular subsystem is sufficiently small. The method presented here is constructive in the sense that the existence of periodic orbits can be verified numerically as well as computed if any. For this, we... 

As a first endeavor, the aeroelastic responses of functionally graded carbon nanotube reinforced composite (FG-CNTRC) truncated conical curved panels subjected to aerodynamic load and axial compression are investigated. The nonlinear dynamic equations of FG-CNTRC conical curved panels are derived according to Green's strains and the Novozhilov nonlinear shell theory. The aerodynamic load is estimated in accordance with the quasi-steady Krumhaar's modified supersonic piston theory by taking into account the effect of the panel curvature. Matrix transform method along with the harmonic differential quadrature method (HDQM) are employed to solve the nonlinear equations of motion of the FG-CNTRC... 

In this brief, we use the alpha power law model for MOS devices to reach a more accurate modeling of CMOS buffers in very deep submicrometer technologies. We derive alpha model parameters of a CMOS buffer for 90-, 65-, and 45-nm technologies using HSPICE simulations. By analytical efforts we find the output resistance of a minimum-size buffer and compare it with those extracted from HSPICE simulations. We propose a new model for the output resistance of a given-size buffer in any technology, which demonstrates 3% error on average as opposed to the conventional model. Also a new buffer resistance is proposed analytically and numerically to calculate the crosstalk for interconnect analysis... 

The dynamics of nonlinear thin plates under influence of relatively heavy moving masses is considered. By expansion of the solution as a series of mode functions, the governing equations of motion are reduced to an ordinary differential equation for time development of vibration amplitude, which is Duffing's oscillator with time varying coefficients. Through the application of Banach's fixed-point theorem, the periodic solutions are predicted. The method presented in this paper is general so that the response of plate to moving force systems can also be considered. © 2002 Published by Elsevier Science Ltd  

The governing differential equation of the Duffing's oscillator with time varying coefficients is addressed. It is shown that the response of a flexible nonlinear plate can be simulated by such equation. Existence of the periodic behavior that is the most important regular solution is illustrated using Banach's fixed-point theorem  

This paper presents a mathematical model using Stochastic Activity Networks (SANs) to model a grid resource, and compute the throughput of a resource in servicing grid tasks, wherein the failure–repair behavior of the processors inside the resource is taken into account. The proposed SAN models the structural behavior of a grid resource and evaluates the combined performance and availability measure of the resource. Afterwards, the curve fitting technique is used to find a suitable function fitted to the throughput of a resource for grid tasks. Having this function and the size of each grid job based on its tasks, an algorithm is proposed to compute the makespan of each available resource to... 

Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean-Vlasov equation and a corresponding propagation of chaos result in the infinite population limit are proven. Our existence result for the McKean-Vlasov equation is based on the Euler approximation that is applied to this type of equation for the first time. © 2020 Institute of Mathematical Statistics  

We present a Lyapunov-type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature, most results concerning existence and uniqueness are obtained under regularity assumptions of the coefficients with respect to the Wasserstein distance. Some existence and uniqueness results for irregular coefficients have been obtained by considering the total variation distance. Here, we extend this approach to the control of the solution in some weighted total variation distance, that allows us now to derive a rather general weak uniqueness result, merely assuming measurability and certain integrability on the drift... 

Increase of nonlinear loads in industries has resulted in high levels of harmonic currents and consequently harmonic voltages in power networks. Harmonics have several negative effects such as higher energy losses and equipment life reduction. To reduce the levels of harmonics in power networks, different methods of harmonic suppression have been employed. The basic idea in all of these methods is to prevent harmonics from flowing into a power network at customer sides and the point of common coupling (PCC). Due to the costs, none of the existing mitigating methods result in a harmonic-free power system. The remaining harmonic currents, which rotate in a power network according to the system... 

Multivariate interpolation and approximation is a powerful tool for intuition of real world. In this paper we study Lebesgue function and Lebesgue constant for multivariate interpolation by conditionally positive definite RBFs. Also we give a conjecture about similar Bernstein and Erdös problem to multivariate case. © 2006 Elsevier Inc. All rights reserved  

In this paper, the existence of periodic solutions of autonomous ordinary differential equations of a 4th and 5th order is investigated. The method used is based on the Brower's degree theorem using the homotopy invariant a property of a topological degree. © Sharif University of Technology, April 2008  

In this paper, the third order differential equation x‴ + ψ (x′)x″ + (κ2 +ø (x))x′ + f(t, x = e(t) is considered. Under certain conditions on the functions appearing in the differential equation, the existence of periodic solutions is proved. Similar problems have been treated by authors in [4,6,7]. However, the method employed here is used by Reissig [1] and the results obtained are, in fact, a generalization of those in [1-3]. The conditions imposed on the nonlinear terms do not require the ultimate boundedness of all solutions. © Sharif University of Technology  

This paper deals with the dynamic analysis of Euler-Bernoulli beams at the resonant condition. The governing partial differential equation of the problem is converted into an ordinary differential equation by applying the well-known Fourier transform. The solution develops a Green's function method which involves establishing the Green's function of the problem, applying the pertinent boundary conditions of the beam. Due to the special conditions of the resonant situation, a significant obstacle arises during the derivation of the Green's function. In order to overcome this hurdle, however, the Fredholm Alternative Theorem is employed; and it is shown that the modified Green's function of... 

Abstract A system designer needs to estimate the behavior of a system interconnection based on different patterns of switching which happen around an interconnect. Two different scenarios are supposed to estimate the effect of interconnect issues on system performance. First, based on a normalization technique for decreasing the number of a transfer function variables, a definitive environment for one interconnect is considered and an optimized look-up-table for the wire time delay is generated. Using some sampling methods, fast accessible look-up-tables are proposed for CAD tools in very simple and small one. A 4×4×4 table for the wire delay is introduced which results in very fast...