A non-empty subset of a topological space is irreducible if whenever it is covered by the union of two closed sets, then already it is covered by one of them. Irreducible sets occur in proliferation: (1) every singleton set is irreducible, (2) directed subsets (which of fundamental status in domain theory) of a poset are exactly its Alexandroff irreducible sets, (3) directed subsets (with respe...

abstract. in this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

the aim of this note is to characterize the finite groups in which all non-linear irreducible characters have distinct zero entries number.

The fundamental construct of numerical algebraic geometry is the representation of an irreducible algebraic set, A, by a witness set, which consists of a polynomial system, F , for which A is an irreducible component of V(F ), a generic linear space L of complementary dimension to A, and a numerical approximation to the set of witness points, L ∩A. Given F , methods exist for computing a numeri...

Irreducible trinomials of given degree n over F2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F2. A condition for divisibility of selfreciprocal trinomials by irreducible poly...

Let A = (aij ) ∈ Rn×n,N = {1, . . . , n} and DA be the digraph (N, {(i, j); aij > −∞}). The matrix A is called irreducible if DA is strongly connected, and strongly irreducible if every maxalgebraic power of A is irreducible. A is called robust if for every x with at least one finite component, A(k) ⊗ x is an eigenvector of A for some natural number k. We study the eigenvalue–eigenvector proble...

The classical McKay correspondence for finite subgroups G of SL(2,C) gives a bijection between isomorphism classes of nontrivial irreducible representations of G and irreducible components of the exceptional divisor in the minimal resolution of the quotient singularity A2C/G. Over non algebraically closed fields K there may exist representations irreducible over K which split over K. The same i...

The state-of-the-art Galois field GF ð2Þ multipliers offer advantageous space and time complexities when the field is generated by some special irreducible polynomial. To date, the best complexity results have been obtained when the irreducible polynomial is either a trinomial or an equally spaced polynomial (ESP). Unfortunately, there exist only a few irreducible ESPs in the range of interest ...

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.