In this work we derive two families of radix-4 factorizations for the FFT (Fast Fourier Transform) that have the property that both inputs and outputs are addressed in natural order. These factorizations are obtained from another two families of radix-2 algorithms that have the same property. The radix-4 algorithms obtained have the same mathematical complexity (number of multiplications and ad...

Permutation decoding is a technique which involves finding a subset S, called PD-set, of the permutation automorphism group of a code C in order to assist in decoding. A method to obtain s-PD-sets of minimum size s + 1 for partial permutation decoding for binary linear Hadamard codes Hm of length 2 , for all m ≥ 4 and 1 < s ≤ ⌊ 2−m−1 1+m ⌋ , is described. Moreover, a recursive construction to o...

An elusive permutation group is a transitive permutation group with no fixed point free elements of prime order, or equivalently, no nontrivial semiregular subgroups. We provide several new constructions of elusive groups, some of which enable us to build elusive groups with new degrees.

We give a mathematical analysis of the “time-reversal mirror”, in what concerns phenomena described by the genuine acoustic equation with Dirichlet or impedance boundary conditions. An ideal situation is first considered, followed by the boundary-data, impedance and internal time-reversal methods. We explore the relationship between local decay of energy and accuracy of the method, and explain ...

When time reversal is broken the viscosity tensor can have a non vanishing odd part. In two dimensions, and only then, such odd viscosity is compatible with isotropy. Elementary and basic features of odd viscosity are examined by considering solutions of the wave and Navier-Stokes equations for hypothetical fluids where the stress is dominated by odd viscosity.

We present a linear algebraic formulation for a class of index transformations such as Gray code encoding and decoding, matrix transpose, bit reversal, vector reversal, shuues, and other index or dimension permutations. This formulation uniies, simpliies, and can be used to derive algorithms for hypercube multiprocessors. We show how all the widely known properties of Gray codes and some not so...

In this tutorial paper, the basic principles of the ultra wideband impulse radio (IR-UWB) technology are covered. Pulse construction and signaling formats are discussed, along with channel models suited to the IR-UWB system design and assessment. Some reception techniques are also presented, with emphasis on the time reversal. The paper also highlights some applications of the IR-UWB technology.

Abstract. We compute the production of particles from the gravitational field of an expanding mass shell. Contrary to the situation of Hawking radiation and the production of cosmological perturbations during cosmological inflation, the example of an expanding mass shell has no horizon and no singularity. We apply the method of ‘ray-tracing’, first introduced by Hawking, and calculate the energ...

Reversal learning has been widely used to probe the implementation of cognitive flexibility in the brain. Previous studies in monkeys identified an essential role of the orbitofrontal cortex (OFC) in reversal learning. However, the underlying circuits and molecular mechanisms are poorly understood. Here, we use the T-maze to investigate the neural mechanism of olfactory reversal learning in Dro...

All-optical spin reversal presents a new opportunity for spin manipulations, free of a magnetic field. Most of all-optical-spin-reversal ferromagnets are found to have a perpendicular magnetic anisotropy (PMA), but it has been unknown whether PMA is necessary for spin reversal. Here we theoretically investigate magnetic thin films with either PMA or in-plane magnetic anisotropy (IMA). Our resul...