Polynomial group laws. II

Polynomial design of deadbeat control laws

Homogeneous Multiplicative Polynomial Laws Are Determinants

Let R be a ring and let B be a commutative ring. Let p : R −→ B be a homogeneous multiplicative polynomial law of degree n. The main result of this paper is to show that p is essentially a determinant, in the sense that p is obtained from a determinant by left and right composition with ring homomorphisms. This is achieved using results on the invariants of matrices in positive characteristic d...

Polynomial endomorphisms of the Cuntz algebras arising from permutations. II —Branching laws of endomorphisms—

For a subgroup H of a group G, an irreducible decomposition of π|H for an irreducible representation π of G is one of main study in representation theory([12]). When such decomposition holds, the decomposition formula is called a branching law. This is reformulated as the branching which is brought by the inclusion map ι from H to G, that is, ι∗(π) ≡ π ◦ ι gives a map from RepG to RepH. In gene...

On the $s^{th}$ Derivative of a Polynomial-II

The paper presents an $L^{r}-$ analogue of an inequality regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle of arbitrary radius but greater or equal to one. Our result provides improvements and generalizations of some well-known polynomial inequalities.

Phase-II Monitoring of AR (1) Autocorrelated Polynomial Profiles

In some statistical process control applications, quality of a process or product can be characterized by a relationship between a response and one or more independent variables, which is typically referred to a profile. In this paper, polynomial profiles are considered to monitor processes in which there is a first order autoregressive relation between the error terms in each profile. A remedi...