Dissipative dynamics of a harmonic oscillator: A nonperturbative approach

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.

Professional learning places and spaces: The staffroom as a site of beginning teacher induction and transition

This paper argues that the staffroom is an important professional learning space where beginning teachers interact to understand who they are and the nature of their professional work. The authors highlight the theoretical importance of space and place in the construction and negotiation of beginning teacher subjectivities. To illustrate the staffroom as a particular place where important professional learning could occur the authors use two narratives based on the lived experiences of two beginning teachers, one in a primary context, the other secondary. The authors conclude by calling for greater research attention to the significance of the staffroom and its interaction with teacher subjectivities. At the level of practice we also call for the teaching profession to recognise staffrooms as important sites of professional learning and places that should support induction and mentoring of beginning teachers. Such recognition could enhance the retention, satisfaction, and effectiveness of new and experienced teachers alike.

A Team of Continuous-Action Learning Automata for Noise-Tolerant Learning of Half-Spaces

Learning automata are adaptive decision making devices that are found useful in a variety of machine learning and pattern recognition applications. Although most learning automata methods deal with the case of finitely many actions for the automaton, there are also models of continuous-action-set learning automata (CALA). A team of such CALA can be useful in stochastic optimization problems where one has access only to noise-corrupted values of the objective function. In this paper, we present a novel formulation for noise-tolerant learning of linear classifiers using a CALA team. We consider the general case of nonuniform noise, where the probability that the class label of an example is wrong may be a function of the feature vector of the example. The objective is to learn the underlying separating hyperplane given only such noisy examples. We present an algorithm employing a team of CALA and prove, under some conditions on the class conditional densities, that the algorithm achieves noise-tolerant learning as long as the probability of wrong label for any example is less than 0.5. We also present some empirical results to illustrate the effectiveness of the algorithm.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Proximinality in Banach spaces

In this paper, we study approximatively τ-compact and τ-strongly Chebyshev sets, where τ is the norm or the weak topology. We show that the metric projection onto τ-strongly Chebyshev sets are norm-τ continuous. We characterize approximatively τ-compact and τ-strongly Chebyshev hyperplanes and use them to characterize factor reflexive proximinal subspaces in τ-almost locally uniformly rotund spaces. We also prove some stability results on approximatively τ-compact and τ-strongly Chebyshev subspaces.

The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) to provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) to provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Space-Vector-Based Hybrid Pulsewidth Modulation Techniques for Reduced Harmonic Distortion and Switching Loss

Novel switching sequences can be employed in spacevector-based pulsewidth modulation (PWM) of voltage source inverters. Differentswitching sequences are evaluated and compared in terms of inverter switching loss. A hybrid PWM technique named minimum switching loss PWM is proposed, which reduces the inverter switching loss compared to conventional space vector PWM (CSVPWM) and discontinuous PWM techniques at a given average switching frequency. Further, four space-vector-based hybrid PWM techniques are proposed that reduce line current distortion as well as switching loss in motor drives, compared to CSVPWM. Theoretical and experimental results are presented.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.