Modal theory for the two-frequency mutual coherence function in random media: general theory and plane wave solution: I

In this paper, the modal expansion theory is presented as a new analytical approach together with the resulting new physical parameters. In particular, the features of an arbitrary power-law structure function are investigated. The exact expression for the Gaussian spectrum is rederived. An approximate analytical expression for the two-frequency coherence function evaluated at equal positions for the Kolmogorov spectrum is presented and comparison with the numerical solution in the literature exhibits a remarkable agreement. As a result of the modal decomposition, general properties for a transversally homogeneous and isotropic medium are demonstrated, such as the exponential decay of the amplitude of the solution and the linear phase behaviour at large propagation distances.     

Dynamics of N = 2 supersymmetric gauge theories in three dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N _f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.     

On the Constructions of the Non-Abelian p 3-Extensions Over ℚ

Let p be an odd prime, and let G be one of the two non-abelian groups of order p ³. Ledet [3 Ledet , A. ( 2000 ). Generic and explicit realization of small p-groups . Journal of Symbolic Computation 30 : 859 – 865 . [Google Scholar]] described explicit G-extensions over the rationales in special cases. In this article, we generalize his results and show how non-tame G-extensions can be constructed having exactly two ramified primes.     

MRI inter-slice reconstruction using super-resolution

MRI reconstruction using super-resolution is presented and shown to improve spatial resolution in cases when spatially-selective RF pulses are used for localization. In 2-D multislice MRI, the resolution in the slice direction is often lower than the in-plane resolution. For certain diagnostic imaging applications, isotropic resolution is necessary but true 3-D acquisition methods are not practical. In this case, if the imaging volume is acquired two or more times, with small spatial shifts between acquisitions, combination of the data sets using an iterative super-resolution algorithm gives improved resolution and better edge definition in the slice-select direction. Resolution augmentation in MRI is important for visualization and early diagnosis. The method also improves the signal-to-noise efficiency of the data acquisition.     

The incompressible Navier–Stokes equations from black hole membrane dynamics

We consider the dynamics of a d+1 space–time dimensional membrane defined by the event horizon of a black brane in (d+2)-dimensional asymptotically Anti-de Sitter space–time and show that it is described by the d-dimensional incompressible Navier–Stokes equations of non-relativistic fluids. The fluid velocity corresponds to the normal to the horizon while the rate of change in the fluid energy is equal to minus the rate of change in the horizon cross-sectional area. The analysis is performed in the Membrane Paradigm approach to black holes and it holds for a general non-singular null hypersurface, provided a large scale hydrodynamic limit exists. Thus we find, for instance, that the dynamics of the Rindler acceleration horizon is also described by the incompressible Navier–Stokes equations. The result resembles the relation between the Burgers and KPZ equations and we discuss its implications.     

The onset of coulomb explosions in polyatomic molecules

With the development of high intensity femtosecond lasers, the ionisation and dissociation dynamics of molecules has become an area of considerable interest. Using the technique of femtosecond laser mass spectrometry (FLMS), the molecules carbon disulphide, pyrimidine, toluene, cyclohexanone and benzaldehyde are studied with pulse widths of 50 fs in the near infrared (IR) wavelength region (790 nm). Results are presented and contrasted for laser beam intensities around 10(15) and 10(16) W cm(-2). For the lower intensities, the mass spectra yield dominant singly charged parent ions. Additionally, the appearance of doubly charged parent ions is evident for carbon disulphide, toluene and benzaldehyde with envelopes of doubly charged satellite species existing in these local regions. Carbon disulphide also reveals a small triply charged component. Such atomic-like features are thought to be a strong fingerprint of FLMS at these intensities. However, upon increasing the laser intensity to approximately 10(16) W cm(-2), parent ion dominance decreases and the appearance of multiply charged atomic species occurs, particularly carbon. This phenomenon has been attributed to Coulomb explosions in which the fast absorption of many photons may produce transient highly ionised parent species which can subsequently blow apart. Copyright 1999 John Wiley & Sons, Ltd.     

The Minimal Number of Cyclic Generators of the Symmetric and Alternating Groups

The aim of this note is to find the minimal number of generators of the symmetric group S _n and alternating group A _n , when the generators are cycles of length at most k. The approach is constructive.     

Meson production in p + d reactions

Total and differential cross sections for the reactions p + d → ³He + m ⁰ with m=π, η and p + d → ³H+π⁺ were measured with the GEM detector at COSY for beam momenta between threshold and the maximum of the corresponding baryon resonance. For both reactions a strong forward-backward asymmetry was found. The data were compared with model calculations. The aspect of isospin symmetry breaking is studied. Representing the GEM Collaboration