For every n divisible by 4, we construct a square matrix H of size n, with coeecients 1, such that H H t nI mod 32. This solves the 32-modular version of the classical Hadamard conjecture. We also determine the set of lengths of 16-modular Golay sequences. 0. Introduction Hadamard matrices can be constructed from various binary sequences, either from Golay complementary sequences, or Williamson...

A Diophantine m-tuple is a set of m positive integers with the property that product of any two of its distinct elements is one less then a square. In this survey we describe some problems and results concerning Diophantine m-tuples and their connections with Fibonacci numbers.

We consider the set of quadruples of matrices defining singular linear time-invariant dynamical systems and show that there is a one-to-one correspondence between this set and a subset of the set of polynomial matrices of degree two. This correspondence preserves the equivalence relations introduced in both sets (feedback-similarity and strict equivalence): two quadruples of matrices are feedba...

CI de gestion de l’alimentation • Des alimentations PCMCIA ultra-minces qui s’insèrent dans les cartes (MAX606/607) 22 de type 1 et de type 2 • Un contrôleur élévateur génère une sortie fixe (5V) ou réglable (3V à 16,5V) (MAX608) 22 • Les régulateurs linéaires SOT-23 ayant la plus faible chute de tension (MAX8863/8864) 23 fournissent 50mA Commutateurs analogiques et multiplexeurs • Des commutat...

Figure 1: An Apollonian Circle Packing Apollonius’s Theorem states that given three mutually tangent circles, there are exactly two circles which are tangent to all three. Apollonian circle packings are produced by repeating the construction of mutually tangent circles to fill all remaining spaces. A remarkable consequence of Descartes’ Theorem is if the initial four tangent circles have integr...

Determination of maximal resolvable packing number and minimal resolvable covering number is a fundamental problem in designs theory. In this article, we investigate the existence of maximal resolvable packings of triples by quadruples of order v (MRPQS(v)) and minimal resolvable coverings of triples by quadruples of order v (MRCQS(v)). We show that an MRPQS(v) (MRCQS(v)) with the number of blo...

We investigate Residue Number Systems (RNS) of special type which were recently shown to be useful for some computations in embedded systems. develop an algorithm derivation all quadruples RNS under investigation subject certain restrictions.