Higher-dimensional twistor transforms using pure spinors

Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (euclidean) dimension d = 2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on ℝ2n. For d = 4 and d = 6, these spaces are ℂℙ1 and ℂℙ3 and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d > 6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations. © SISSA/ISAS 2005.

Jacobi script v sign-functions and discrete Fourier transforms

Properties of the Jacobi script v sign3-function and its derivatives under discrete Fourier transforms are investigated, and several interesting results are obtained. The role of modulo N equivalence classes in the theory of script v sign-functions is stressed. An important conjecture is studied. © 2006 American Institute of Physics.

Thermal investigation and infrared evolved gas analysis of solid trivalent lanthanide and yttrium alpha-hydroxyisobutyrates in N-2 and CO2 atmospheres

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Study of some volatile compounds evolved from the thermal decomposition of atenolol

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Social Parasite Evolved Reproductive Isolation from Its Fungus-Growing Ant Host in Sympatry

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The most relictual fungus-farming ant species cultivates the most recently evolved and highly domesticated fungal symbiont species

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Synthesis, evolved gas analysis (EGA) during pyrolysis and spectroscopic study of light lanthanide nicotinate in solid state

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Thermal degradation of both latex and latex cast films forming membranes: combined TG/FTIR investigation

Latex collected from natural rubber trees forming membranes can be used as biomaterials in several fields being the temperature a key parameter. Thermogravimetry (TG) coupled to Fourier transform infrared spectroscopy (FTIR) is a useful technique to investigate the thermal degradation of both latex and cast films (membranes), wich were obtained from Hevea brasiliensis (RRIM 600 clone) and used without stabilization. The membranes were prepared by casting the latex onto a glass substrate at 65 degrees C for 6 h. The thermal degradation was followed by FTIR spectra acquisition along the process, allowing the identification of the gaseous components evolved upon the thermal treatment. According to TG measurements, the main processes of thermal degradation of the latex and membranes occur at three temperature intervals for both.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

Parallel-recusive filter structures for the computation of discrete transforms

A general approach is presented for implementing discrete transforms as a set of first-order or second-order recursive digital filters. Clenshaw's recurrence formulae are used to formulate the second-order filters. The resulting structure is suitable for efficient implementation of discrete transforms in VLSI or FPGA circuits. The general approach is applied to the discrete Legendre transform as an illustration.

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )