1 We introduce the fundamentals of cyclic multirate systems and filter banks and present a number of important differences between the cyclic and noncyclic (traditional) cases. Some of the additional freedom offered by cyclic systems is pointed out, and a number of open issues are summarized.

A complete extension theorem for linear codes over a module alphabet and the symmetrized weight composition is proved. It is shown that an extension property with respect to arbitrary weight function does not hold for module alphabets with a noncyclic socle.

A mononuclear iron(III) complex of a noncyclic tetradentate monoamido ligand, Fe(III)mpaq, catalyses the oxidation of Orange II, guaiacol, ABTS and Amplex Red with H2O2 in aqueous solutions at neutral pH. Under identical conditions, other structurally related nonheme iron complexes showed only negligible activities.

It is shown that in the units of augmentation one of an integral group ring ZG of a finite group G, a noncyclic subgroup of order p, for some odd prime p, exists only if such a subgroup exists in G. The corresponding statement for p = 2 holds by the Brauer–Suzuki theorem, as recently observed by W. Kimmerle.

While most approaches to geometric quantum computation are based on phases in cyclic evolution, noncyclic gates have been proposed increase further the flexibility. these remove dynamical phase of computational basis, they do not, general, it from eigenstates time evolution operator, which makes nature ambiguous. Here, we resolve this ambiguity by proposing a scheme for genuinely gates. These o...

We demonstrate that the technique for calculating length of two-block matrix algebras, developed by author earlier, can be used to calculate lengths group algebras Abelian groups. find algebra a noncyclic order 2p2, where p > 2 is prime number, over field characteristic p, namely, we prove this equal 3p−2.