Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

On the efficacy of Fourier series approximations for pricing European options

This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the halfrange cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together,these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

Small-amplitude cyclic voltammetry: Part I. A simple fourier synthesis approach

Current-potential relationships are derived for small-amplitude periodic inputs for linear electrochemical systems using a Fourier synthesis procedure. Specific results have been obtained for a triangular potential waveform for two simple model systems.

Negligible evidence for regional genetic population structure for two shark species Rhizoprionodon acutus (Rüppell, 1837) and Sphyrna lewini (Griffith & Smith, 1834) with contrasting biology

Biodiversity of sharks in the tropical Indo-Pacific is high, but species-specific information to assist sustainable resource exploitation is scarce. The null hypothesis of population genetic homogeneity was tested for scalloped hammerhead shark (Sphyrna lewini, n = 237) and the milk shark (Rhizoprionodon acutus, n = 207) from northern and eastern Australia, using nuclear (S. lewini, eight microsatellite loci; R. acutus, six loci) and mitochondrial gene markers (873 base pairs of NADH dehydrogenase subunit 4). We were unable to reject genetic homogeneity for S. lewini, which was as expected based on previous studies of this species. Less expected were similar results for R. acutus, which is more benthic and less vagile than S. lewini. These features are probably driving the genetic break found between Australian and central Indonesian R. acutus (F-statistics; mtDNA, 0.751–0.903, respectively; microsatellite loci, 0.038–0.047 respectively). Our results support the spatially homogeneous monitoring and management plan for shark species in Queensland, Australia.

Lucien Levy-Bruehl, Albert Einstein, Franz Oppenheimer, Arthur Liebert and his son, Paul Tillich, unidentified woman and Mrs. Charles Blondel outside the Grand Hotel Curhaus during the Davoser Hochschulkurse; Davos, Switzerland Portraits Groups

The Davoser Hochschulkurse took place for the first time in 1928. Mainly university teachers from Germany, France, Switzerland (perhaps elsewhere) offered lectures to students recovering from tuberculosis at the health resort in the Swiss mountains. The lecturers were accommodated at the Grand Hotel Curhaus, where the lectures also took place.

Small amplitude cyclic voltammetry - a simple fourier synthesis approach

Abstaract is not available.

On the Fourier refinement of protein structures

The situation normally encountered in the high-resolution refinement of protein structures is one in which the inaccurate positions of P out of a total of N atoms are known whereas those of the remaining atoms are unknown. Fourier maps with coefficients (FN -- F'P) × exp (i[alpha]'P) and (mFN -- nF'P) exp (i[alpha]'P), where FN is the observed structure factor and F'P and [alpha]'P are the magnitude and the phase angle of the calculated structure factor corresponding to the inaccurate atomic positions, are often used to correct the positions of the P atoms and to determine those of the Q unknown atoms. A general theoretical approach is presented to elucidate the effect of errors in the positions of the known atoms on the corrected positions of the known atoms and the positions of the unknown atoms derived from such maps. The theory also leads to the optimal choice of parameters used in the different syntheses. When the errors in the positions of the input atoms are systematic, their effects are not taken care of automatically by the syntheses.

Evaluation of two-dimensional quantizers for Fourier transform binary holograms

Quantization formats of four digital holographic codes (Lohmann,Lee, Burckhardt and Hsueh-Sawchuk) are evaluated. A quantitative assessment is made from errors in both the Fourier transform and image domains. In general, small errors in the Fourier amplitude or phase alone do not guarantee high image fidelity. From quantization considerations, the Lee hologram is shown to be the best choice for randomly phase coded objects. When phase coding is not feasible, the Lohmann hologram is preferable as it is easier to plot.

Eberstadt-Seligmann Family Collection 1772-1885

Family tree; six original family letters dealing with private affairs.

Ehrenberg-Rosenzweig Family Collection 1772-1930

The collection contains correspondence among members of the Ehrenberg and Rosenzweig families, including letters from Franz Rosenzweig, Adam Rosenzweig and Richard Ehrenberg, as well as with other parties, including Leopold Zunz, Adelheid Zunz, Claire von Gluemer, and Heinrich Heine (copies only). Also included are engagement contracts, marriage banns, school curricula and certificates, character references, eulogies, family histories, and other documents concerning family members. This material also reflects much of the history of the Samsonschule in Wolfenbuettel of which members of the Ehrenberg family were principals.

A novel method for the age estimation of Saddletail snapper (Lutjanus malabaricus) using Fourier Transform-near infrared (FT-NIR) spectroscopy

Near infrared (NIR) spectroscopy was investigated as a potential rapid method of estimating fish age from whole otoliths of Saddletail snapper (Lutjanus malabaricus). Whole otoliths from 209 Saddletail snapper were extracted and the NIR spectral characteristics were acquired over a spectral range of 800–2780 nm. Partial least-squares models (PLS) were developed from the diffuse reflectance spectra and reference-validated age estimates (based on traditional sectioned otolith increments) to predict age for independent otolith samples. Predictive models developed for a specific season and geographical location performed poorly against a different season and geographical location. However, overall PLS regression statistics for predicting a combined population incorporating both geographic location and season variables were: coefficient of determination (R2) = 0.94, root mean square error of prediction (RMSEP) = 1.54 for age estimation, indicating that Saddletail age could be predicted within 1.5 increment counts. This level of accuracy suggests the method warrants further development for Saddletail snapper and may have potential for other fish species. A rapid method of fish age estimation could have the potential to reduce greatly both costs of time and materials in the assessment and management of commercial fisheries.

Effect of fourier domain quantization on matched filtering

It is shown that the use of a coarsely quantized binary digital hologram as a matched filter on an optical computer does not degrade signal-to-noise ratio (SNR) appreciably.

Schneeberger-Saenger Collection 1837-1845

Business ledger in Yiddish (1837-1845)