High-average-power free-electron lasers often rely on energy-recovering linacs. In a high-efficiency free electron laser, the main limitation to high average power stems from the fractional energy spread induced by the free-electron laser process. Managing beams with large fractional energy spread while simultaneously avoiding beam losses is extremely challenging and relies on intricate longitu...

Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of ...

Ultra-wideband (UWB) communications systems provide extremely high data rates while using low transmit power relative to narrowband systems. Recent research concludes that such systems have characteristics that make them appropriate for highspeed wireless network applications. One of the distinguishing aspects of the UWB signal is an extremely high fractional bandwidth when compared with conven...

A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. Stability conditions are obtained for the fully discrete schemes under the consideration. The numerical results are ...

Modified Laplace transformation method at finite temperature: application to infra-red problems of N component φ 4 theory ABSTRACT Modified Laplace transformation method is applied to N component φ 4 theory and the finite temperature problem in the massless limit is reexamined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orde...

We use the angular power spectrum of the Cosmic Microwave Background, measured during the North American test flight of the Boomerang experiment, to constrain the geometry of the universe. Within the class of Cold Dark Matter models, we find that the overall fractional energy density of the universe, Ω, is constrained to be 0.85 ≤ Ω ≤ 1.25 at the 68% confidence level. Combined with the COBE mea...

The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many th...

We present an analytic study for subdiffusive escape of overdamped particles out of a cusp-shaped parabolic potential well which are driven by thermal, fractional Gaussian noise with a 1/omega 1-alpha power spectrum. This long-standing challenge becomes mathematically tractable by use of a generalized Langevin dynamics via its corresponding non-Markovian, time-convolutionless master equation: W...