We have fabricated several varieties of micro and nanomechanical resonators and have studied their phase response when driven at their natural frequency with and without parametric pumping. We found that micron-sized paddle oscillators with submicron-sized supports had resonant frequencies in the 3-10 MHz range for their translational mode. Due to the stretching of the support beams, the effect...

Fractional calculus has many advantages. Under consideration of this paper is a (2+1)-dimensional non-linear local fractional heat conduction equation with arbitrary degree non-linearity. Backlund transformation reduced form the constructed by Painleve analysis. Based on transformation, some exact non-differentiable solutions are obtained. To gain more insights obtained solutions, two constrain...

We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by ...

The paper presents an overview of linearization methods of the non-linear state equation. The linearization is developed from the point of view of the application in the theoretical electrotechnics. Some aspects of these considerations can be used in the control theory. In particular the main emphasis is laid on three methods of linearization, i.e.: Taylor’s series expansion, optimal linearizat...

This paper presents the derivations of the voltage transfer functions of the amplifier A, the feedback network β, and the loop gain T of the common-drain (CD) Colpitts oscillator, using the small-signal model of the CD Colpitts oscillator. The derivation of the characteristic equation of the CD Colpitts oscillator is presented. Using the characteristic equation, the equation for the oscillation...

The field of mathematical finance has gained significant attention since Black and Scholes (1973) published their Nobel Prize work in 1973. Using some simplifying economic assumptions, they derived a linear partial differential equation (PDE) of convection–diffusion type which can be applied to the pricing of options. The solution of the linear PDE can be obtained analytically. In this paper we...

In a medium where a photoreactive species produces N equally photoreactive radicals, by combining the Lambert-Beer law for the decay of light intensity, as a beam propagates into the medium, with the kinetic equation, one obtains a generalization of the Wegscheider equation from photobleaching theory. It is shown that this equation can be solved exactly, but implicitly, and can be reduced to a ...

In addition to the passive observation of a non­ linear oscillator and the description of the measured data with Lyapounow exponents [1, 2], fractal dimensions [3-5], entropies [6], etc. it is possible to charcterize a non-linear oscillator by an active method, namely by determining its response to specific perturbations. The resonances of harmonic systems which are brought about by a sinusoida...