Sharif Digital Repository

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... 

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  

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 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  

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 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... 

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... 

In this paper, jitter due to both capacitive and inductive coupling is studied. Maximum frequency of driving signal on a wire is limited by its input rise time, fall time, pulse width, and the coupling effect from its neighbors. The analytical expressions to estimate the deterministic jitter time due to these effects are presented. The estimation is based on the fastest and slowest approximation of the signal waveform components. Also, we have extracted the eye opening parameters of the eye diagram. The inductance effects significance is shown on eye opening and jitter time. The 45nm technology is used for estimating the horizontal and vertical eye opening and jitter time. The presented... 

Crosstalk due to the capacitive and inductive coupling has adverse effect on the circuit performance. In this paper crosstalk voltage and its induced power are studied for a stochastic environment bus with specific physical structure. Input switching pattern, driver, and load are swept in wide range for VLSI application to study crosstalk variation. Crosstalk and power is extracted to drive mean and standard deviation for implemented structures. The crosstalk mean and its induced power get lower with increasing of the load and driver resistance. This phenomenon is proportional to shrinking the technology  

The present research deals with bifurcation and vibration responses of a composite truncated conical shell with embedded single-walled carbon nanotubes (SWCNTs) subjected to an external pressure and axial compression simultaneously. The distribution of reinforcements through the thickness of the shell is assumed to be either uniform or functionally graded. The equations of motion are established using Green-Lagrange type nonlinear kinematics within the framework of Novozhilov nonlinear shell theory. Linear membrane prebuckling analysis is conducted to extract the prebuckling deformations. The stability equations are derived by applying the adjacent equilibrium criterion to the prebuckling... 

Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method (GMLSM) and then, discrete equations of motion based on Lagrange's equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between... 

The aeroelastic flutter characteristics of a functionally graded carbon nanotube reinforced composite (FG-CNTRC) truncated conical shell under simultaneous actions of a hydrostatic pressure and yawed supersonic airflow are scrutinized. The nonlinearity in geometry of the conical shell is considered in Green–Lagrange sense and the model is derived according to the Novozhilov nonlinear shell theory. The aerodynamic pressure is modeled based on the quasi-steady Krumhaar's modified supersonic piston theory by considering the effect of the panel curvature and flow yaw angle. Parametric studies are conducted to investigate the effects of boundary conditions, semi-vertex angle, distribution and...