The q–deformation Uq(h4) of the harmonic oscillator algebra is defined and proved to be a Ribbon Hopf algebra. Associated with this Hopf algebra we define an infinite dimensional braid group representation on the Hilbert space of the harmonic oscillator, and an extended Yang–Baxter system in the sense of Turaev. The corresponding link invariant is computed in some particular cases and coincides...

‎The controlled harmonic oscillator with retarded damping‎, ‎is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems‎. ‎In this paper‎, ‎to solve this problem‎, ‎we presented an analytical method‎. ‎This approach is based on the homotopy perturbation method‎. ‎The solution procedure becomes easier‎, ‎simpler and mor...

This paper proposes a hybrid control scheme for the synchronization of two chaotic Duffing oscillator system, subject to uncertainties and external disturbances. The novelty of this scheme is that the Linear Quadratic Regulation (LQR) control, Sliding Mode (SM) control and Gaussian Radial basis Function Neural Network (GRBFNN) control are combined to chaos synchronization with respect to extern...

The simplest N = 2 supersymmetric quantum mechanical system is realized in terms of the bosonic creation and annihilation operators obeying either ordinary or deformed Heisenberg algebra involving Klein operator. The construction comprises both the exact and spontaneously broken supersymmetry cases with the scale of supersymmetry breaking being governed by the deformation parameter. Proceeding ...

Perhaps the simplest Colpitts oscillator to construct and get running. Because there is no load on the inductor a high "Q" circuit results with a high L/C. Colpitts Oscillator Tutorial and the theory behind the design of the Colpitts Oscillator which uses a LC Oscillator tank circuit to generate sine waves. The Colpitts Oscillator Circuit Characterised By Tapping The Midpoint Of The Capacitive ...

Spintronic oscillators are nanodevices that are serious candidates for CMOS integration due to their compactness and easy frequency tunability. For a crystal oscillator to work, there must exist a feedback path with properly What practical circuits do is design such that we have a phase-shift of 180. A double balanced down conversion oscillator mixer using 90 nm CMOS technology is proposed in a...

In this paper, an intuitive analysis of a phase noise reduction technique is done, and then a modified structure is proposed to achieve higher phase noise reduction than the original one. This method reduces the impact of noise sources on the phase noise by decreasing closed-loop gain in zero-crossings points and moving this high closed-loop gain to the non-zero-crossings points. This reduction...

We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We truncate the hierarchy of flow equations such that the results are at least correct up to second order perturbation theory in the coupling. For the anharmon...

The Matsuoka oscillator has been used to control various robots that perform rhythmic movements. The oscillator-driven control system usually takes a feedback structure. While the oscillator actuates some part of a controlled object, some state variable of the object is fed back to the oscillator. An important property of this control scheme is that the oscillator comes to drive the object at i...