Ince-Gaussian series representation of the two-dimensional fractional Fourier transform

We introduce the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptical coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded-index media whose eigenmodes in elliptical coordinates are derived for the first time to our knowledge. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence among the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation among the three definitions.     

Generation of hyperentangled photon pairs

We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric down-conversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode, and time energy. We also produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2 x 2 x 3 x 3 system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.     

Numerical blow‐up for the porous medium equation with a source

We study numerical approximations of positive solutions of the porous medium equation with a nonlinear source, where m > 1, p > 0 and L > 0 are parameters. We describe in terms of p, m, and L when solutions of a semidiscretization in space exist globally in time and when they blow up in a finite time. We also find the blow‐up rates and the blow‐up sets, proving that there is no regional blow‐up for the numerical scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

Domination by Positive Narrow Operators

We prove that each positive operator from a Köthe function-space E() to a Banach lattice F with a narrow majorant is itself narrow provided the norm on F is order continuous. We also prove that every l ²-strictly singular regular operator from L ^p[0,1], 1p < , to a Banach lattice F is narrow, provided F has an order continuous norm.     

Acoustic Analysis of Pathological Voices Compressedwith MPEG System

The MPEG-1 Layer 3 compression schema of audio signal, commonly known as mp3, has caused a great impact in recent years as it has reached high compression rates while conserving a high sound quality. Music and speech samples compressed at high bitrates are perceptually indistinguishable from the original samples, but very little was known about how compression acoustically affects the voice signal. A previous work with normal voices showed a high fidelity at high-bitrate compressions both in voice parameters and the amplitude-frequency spectrum. In the present work, dysphonic voices were tested through two studies. In the first study, spectrograms, long-term average spectra (LTAS), and fast Fourier transform (FFT) spectra of compressed and original samples of running speech were compared. In the second study, intensities, formant frequencies, formant bandwidths, and a multidimensional set of voice parameters were tested in a set of sustained phonations. Results showed that compression at high bitrates (96 and 128 kbps) preserved the relevant acoustic properties of the pathological voices. With compressions at lower bitrates, fidelity decreases, introducing some important alterations. Results from both works, Gonzalez and Cervera and this paper, open up the possibility of using MPEG-compression at high bitrates to store or transmit high-quality speech recordings, without altering their acoustic properties.     

Stereo‐ and Regioselective Alkyne Hydrometallation with Gold(III) Hydrides

The hydroauration of internal and terminal alkynes by gold(III) hydride complexes [(C^N^C)AuH] was found to be mediated by radicals and proceeds by an unexpected binuclear outer‐sphere mechanism to cleanly form trans‐insertion products. Radical precursors such as azobisisobutyronitrile lead to a drastic rate enhancement. DFT calculations support the proposed radical mechanism, with very low activation barriers, and rule out mononuclear mechanistic alternatives. These alkyne hydroaurations are highly regio‐ and stereospecific for the formation of Z‐vinyl isomers, with Z/E ratios of >99:1 in most cases.     

An improved synthesis of alpha-carbolines under microwave irradiation

[reaction: see text]. Alpha-carbolines are interesting core structures for designing DNA-interacting small molecules. However, these compounds are not commercially available and their synthetic methods are low yielding or time consuming. The shortest synthetic route, the modified Graebe-Ullmann reaction, has been optimized by using microwave heating in four different types of apparatus to give shorter reaction times and enhanced yields. Optimized conditions enabled the preparation of a small library of alpha-carbolines.     

Self-assembling porphyrin-modified peptides

[structure: see text] We report the synthesis and characterization of a novel supramolecular assembly that features long-range electronic coupling between porphyrins covalently attached to a designed peptide scaffold. The resulting construct self-assembles to form extended organized aggregates in which the porphyrins engage in exciton coupling.     

Path integral formulation of Roothaan's equations

The generating functional Z(N) of the molecular orbital theory of N electrons has been projected into a subspace of atomic orbitals. By application of the saddle-Point approximataions to the corresponding effective action, a set of equations of motion results. These equations are the classical Roothaan's equations of quantum chemistry.