2008 DEC 30 - (VerticalNews.com) -- According to a study from the United States, "A good portion of Gatteschi's research publications-about 65%-is devoted to asymptotics of special functions and their zeros."

  "Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi's and Whittaker's form," wrote W. Gautschi and colleagues, Purdue University ...read more

  2008 AUG 4 - (VerticalNews.com) -- "Let H be a Hilbert space of finite dimension d, such as the finite signals l(2)(d) or a space of multivariate orthogonal polynomials, and n>= d. There is a finite number of tight frames of n vectors for H which can be obtained as the orbit of a single vector under the unitary action of an abelian group G (of symmetries of the frame). Each of these so called harmonic frames or geometrically uniform frames can be obtained from the character table of G in a simple way," scientists writing in the journal Numerical Algorithms report ...read more

  2008 JUN 23 - (VerticalNews.com) -- "Consider an information network with threats called attackers; each attacker uses a probability distribution to choose a node of the network to damage. Opponent to the attackers is a protector entity called defender; the defender scans and cleans from attacks some part of the network (in particular, a link), which it chooses independently using its own probability distribution," researchers in Nicosia, Cyprus report ...read more