Two inversion formulas for enumerating words in the free monoid by θ-adjacencies are applied in counting pairs of permutations by various statistics. The generating functions obtained involve refinements of bibasic Bessel functions. We further extend the results to finite sequences of permutations. ∗This work is partially supported by EC grant CHRX-CT93-0400 and PRC Maths-Info †Financial suppor...

Some notes on analytical derived loudspeaker arrays with uniform radiation characteristics are presented. The array coefficients are derived via analytical means and compared with so-called maximal flat sequences known from telecommunications and information theory. It appears that the newly derived array, i.e., the quadratic phase array, has a higher efficiency than the Bessel array and a flat...

A fifth-order CMOS continuous-time Bessel filter with a tunable 6to IS-MHZ cutoff frequency is described. This fully balanced transconductance-capacitor (G~ – C) leapfrog filter achieves a dynamic range of 55 dB while dissipating 96 mW in a 5-V 0.9-pm CMOS process. The on-chip master–slave tuning system uses a voltage-controlled oscillator (VCO).

We show that the use of operational methods and of multi-index Bessel functions allow the derivation of generating functions, involving the product of an arbitrary number of Laguerre polynomials. ∗2000 Mathematics Subject Classification. 33C45, 44A45. †E-mail:[email protected] ‡E-mail:[email protected] §E-mail:[email protected] ¶E-mail:[email protected] 270 G. Dattol...

Generalizing the notion of placing rooks on a Ferrers board leads to a new class of combinatorial models and a new class of rook polynomials. Connections are established with absolute Stirling numbers and permutations, Bessel polynomials, matchings, multiset permutations, hypergeometric functions, Abel polynomials and forests, and polynomial sequences of binomial type. Factorization and recipro...

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

Clustered regularly interspaced palindromic repeats (CRISPR) and CRISPR-associated (Cas) proteins, particularly Cas9, have provided unprecedented control on targeting editing specific DNA sequences. If the target sequences are prone to folding into noncanonical secondary structures, such as G-quadruplex (GQ), conformational states activity of CRISPR–Cas9 complex may be influenced, but impact ha...