It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for non-negative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized Bessel function, the Dunkl kernel. Radia...

This paper generalizes the notion of the backbone of a CNF formula to capture also equations between literals. Each such equation applies to remove a variable from the original formula thus simplifying the formula without changing its satisfiability, or the number of its satisfying assignments. We prove that for a formula with n variables, the generalized backbone is computed with at most n+1 s...

This guide to the neurological disorder cerebral autosomal dominant arteriopathy with subcortical infarcts and leuco encephalopathy (CADASIL) is specifically targeted at psychiatrists. The aims are to enhance awareness, provide educational clinical information and offer practical guidance on management of the disorder. An overview of diagnostic algorithms and recent research is also provided. M...

In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.

We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals [Formula: see text] and [Formula: see text] depending on a parameter [Formula: see text], which contains an earlier result in the particular case [Formula: see text].

We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal polynomials.

In this work we study families of pairs of window functions and lattices which lead to Gabor frames which all possess the same frame bounds. To be more precise, for every generalized Gaussian g, we will construct an uncountable family of lattices [Formula: see text] such that each pairing of g with some [Formula: see text] yields a Gabor frame, and all pairings yield the same frame bounds. On t...