1. THE RIEMANN–LEBESGUE LEMMA. In its usual form, the Riemann– Lebesgue Lemma reads as follows: If f ∈ L1 and f̂ (s) = ∫∞ −∞ eisx f (x) dx is its Fourier transform, then f̂ (s) exists and is finite for each s ∈ R and f̂ (s) → 0 as |s| → ∞ (s ∈ R). This result encompasses Fourier sine and cosine transforms as well as Fourier series coefficients for functions periodic on finite intervals. When the i...

INTRODUCTION Andrei Andreyevich Markov was a Russian mathematician born in 1856. Markov's main interests were in number theory, continued fractions, and approximation theory. He studied under P. Chebyshev and worked in the field of probability theory. Markov pioneered work in the area of stochastic processes by creating a model called a Markov chain—a random walk on a state space. His work has ...

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Microtubules turn over rapidly arc Kirschner recalls that the mid-1980s “was a very innovative time.” While the era was giving rise to stonewashed jeans and rap music, cell biology was entering new territory as it finally went molecular. For cell biologists who, like Kirschner, were interested in the cytoskeleton, there was an even more exciting possibility: the modification of interesting prot...

—Multimedia groupware systems provide rich support for distributed team work. Yet effective design of these systems is difficult because they must cater to complex human and social factors. Rapid prototyping partially mitigates this, for it allows designers to build, deploy, test and quickly evolve design ideas. The problem is that multimedia groupware is hard to prototype because distributed m...

Current approaches to adaptive game AI require either a high quality of utilised domain knowledge, or a large number of adaptation trials. These requirements hamper the goal of rapidly adapting game AI to changing circumstances. In an alternative, novel approach, domain knowledge is gathered automatically by the game AI, and is immediately (i.e., without trials and without resource-intensive le...

Dermatofibroma, also known as "fibrous histiocytoma", is a benign dermal or subcutaneous poorly circumscribed proliferation of spindle-shaped fibroblasts and macrophages in the dermis. Although it is commonly present as a brownish nodule the legs of females, it may also arise on the upper extremities, trunk, and rarely on the head. The exact pathogenesis is unclear. However, it is widely believ...

Data gathering in the physical world is tedious and often risky. Robots are ideally suited for such applications. The objective of a data gathering robot is to travel between two points maximizing the information it gains while not exceeding energy or cost constraints. This problem can be formalized as that of finding budgeted routes in a graph such that the reward collected by the route is max...

Volume 95 No. 5 May 2012 a newborn Male, delivered by Caesarean section after induction at 41 weeks of gestation for failure to progress, was admitted to the Women and Infants’ Hospital (WIH) Neonatal Intensive Care Unit (NICU) with a large vascular mass on his left knee (Figure 1). Routine prenatal US had been normal and the pregnancy had been uneventful. Physical examination at delivery was o...

We review the quest of modeling rapidly rotating stars during the past 40 years and detail the challenges to be taken up by models facing new data from interferometry, seismology, spectroscopy... We then present the progress of the ESTER project aimed at giving a physically self-consistent model for the structure and evolution of rapidly rotating stars.