Active sound control in composite regions

In active sound control, noise shielding of a target region is achieved via additional sources (called controls) situated at the perimeter of the region. The sources protect the target region by adjusting the acoustic field near the boundary of the region. In the present paper a numerical model of active sound control based on surface potentials in 3D bounded composite regions is numerically studied. In the composite region setup, it is required that the regions be shielded from noise while allowing admissible sound that is generated in the shielded regions to be preserved. The admissible sound is usually required to propagate freely inside the protected regions or in a (selective) predetermined pattern. The adjusting approach used here does not require any knowledge of the sound sources or the properties of the propagation medium in order to obtain the controls. Moreover, the approach differs sharply from some other approaches where the detailed knowledge of the sound sources and the propagation medium is required. For the first time, numerical test cases involving both free communication and predetermined communication pattern between the regions in three dimensions are considered. In all test cases, these regions are effectively shielded from the noise while any present admissible sound is preserved. In addition, selective propagation of the admissible sound between the regions is enforced. The effect of the number of controls on their operation is also studied. Whether admissible sound is present or not, the level of noise cancellation decreases linearly as fewer controls are used. In addition to the increase in size of the interference zone, the controls become individually distinguishable.     

Extended Gerber–Shiu functions in a risk model with interest

We consider a compound Poisson risk model with interest. The Gerber–Shiu discounted penalty function is modified with an additional penalty for reaching a level above the initial capital. We show that the problem can be split into two independent problems; an original Gerber–Shiu function and a first passage problem. We also consider the case of negative interest. Finally, we apply the results to a model considered by Embrechts and Schmidli (1994).     

Tighter uncertainty principles for periodic signals in terms of frequency

In this study, we propose some new uncertainty principles for periodic signals with sharper lower bounds than those in the existing ones. The improved lower bounds, in particular, are related to the frequency of the signal. Three examples are employed to demonstrate sharpness of the new uncertainty principles. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence and uniqueness of optimal solutions for multirate partial differential algebraic equations

The numerical simulation of electric circuits including multirate signals can be done by a model based on partial differential algebraic equations. In the case of frequency modulated signals, a local frequency function appears as a degree of freedom in the model. Thus the determination of a solution with a minimum amount of variation is feasible, which allows for resolving on relatively coarse grids. We prove the existence and uniqueness of the optimal solutions in the case of initial-boundary value problems as well as biperiodic boundary value problems. The minimisation problems are also investigated and interpreted in the context of optimal control. Furthermore, we construct a method of characteristics for the computation of optimal solutions in biperiodic problems. Numerical simulations of test examples are presented.     

Approximation properties for solutions to non‐Lipschitz stochastic differential equations with Lévy noise

In this paper, we consider the non‐Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Lévy noise, and the approximation theorems for the solutions to these two kinds of equations will be proposed respectively. Non‐Lipschitz condition is much weaker condition than the Lipschitz one. The simplified equations will be defined to make its solutions converge to that of the corresponding original equations both in the sense of mean square and probability, which constitute the approximation theorems. Copyright © 2014 John Wiley & Sons, Ltd.     

Signal moments for the short‐time Fourier transform associated with Hardy–Sobolev derivatives

The short‐time Fourier transform has been shown to be a powerful tool for non‐stationary signals and time‐varying systems. This paper investigates the signal moments in the Hardy–Sobolev space that do not usually have classical derivatives. That is, signal moments become valid for non‐smooth signals if we replace the classical derivatives by the Hardy–Sobolev derivatives. Our work is based on the extension of Cohen's contributions to the local and global behaviors of the signal. The relationship of the moments and spreads of the signal in the time, frequency and short‐time Fourier domain are established in the Hardy–Sobolev space. Copyright © 2014 John Wiley & Sons, Ltd.     

Variational Solution of Stochastic Schrödinger Equations With Power-Type Nonlinearity

We investigate a Schrödinger problem with multiplicative Gaussian noise term and power-type nonlinearity on a bounded one-dimensional domain. In order to prove the existence and uniqueness of the variational solution, a further process will be introduced which allows to transform the stochastic nonlinear Schrödinger problem into a pathwise one. Galerkin approximations and compact embedding results are used.     

Existence of frequency modes coupling seismic waves and vibrating tall buildings

We prove in this paper an existence result for frequency modes coupling seismic waves and vibrating tall buildings. The derivation from physical principles of a set of equations modeling this phenomenon was done in previous studies. In this model all vibrations are assumed to be anti-plane and time harmonic so the two dimensional Helmholtz equation can be used. A coupling frequency mode is obtained once we can determine a wavenumber such that the solution of the corresponding Helmholtz equation in the lower half plane with relevant Neumann and Dirichlet conditions at the interface satisfies a specific integral equation at the base of an idealized tall building. Although numerical simulations suggest that such wavenumbers should exist, as far as we know, to date, there is no theoretical proof of their existence. This is what this present study offers to provide.     

Influence of the automotive Start/Stop system on noise emission: Experimental study

One of the most common environmental impacts of road transportation is the traffic noise. Linked to this, Start/Stop is a technology which has demonstrated to save fuel by powering off the engine when the vehicle is stopped, such as in front of a traffic light, and restarting the engine instantly when the driver pushes back the pedal brake to proceed. The technology helps also to reduce the CO₂ emission, playing a key role in a way to accomplish stringent emission norms for vehicle manufacturer. However, we are not sure whether it reduces the noise emission and how much? Thus, the main aim of this work is to assess the engine noise emissions of a vehicle incorporating a Start/Stop system in urban traffic, and compare it with those radiated by the mean traffic stream. Experimental results demonstrate that there are no contributions of the Start/Stop system to reduce meaningfully the engine noise in urban traffic.