We consider an indecomposable representation of a cyclic p-group Z pr over a field of characteristic p. We show that the top degree of the corresponding ring of coinvariants is less than (r 2+3r)pr 2 . This bound also applies to the degrees of the generators for the invariant ring of the regular representation.

This is the third, and last, of a series of papers dealing with oriented regular representations. Here we complete the classification of finite groups that admit an oriented regular representation (or ORR for short), and give a complete answer to a 1980 question of László Babai: “Which [finite] groups admit an oriented graph as a DRR?” It is easy to see and well-understood that generalised dihe...

New representation results for three families of regular languages are stated, using a special kind of shuue operation, namely the synchronized shuue. First, it is proved that the family of regular star languages is the smallest family containing the language (a + bc) and closed under synchronized shuue and length preserving morphism. The second representation result states that the family of "...

We determined the degree to which the response modulation of macaque inferior temporal (IT) neurons corresponds to perceptual versus physical shape similarities. IT neurons were tested with four groups of shapes. One group consisted of variations of simple, symmetrical (i.e. regular) shapes that differed in nonaccidental properties (NAPs, i.e. viewpoint-invariant), such as curved versus straigh...

The regular representation of an essentially finite 2-group G in the 2-category 2Vectk of (Kapranov and Voevodsky) 2-vector spaces is defined and cohomology invariants classifying it computed. It is next shown that all hom-categories in Rep 2Vectk pGq are 2-vector spaces under quite standard assumptions on the field k, and a formula giving the corresponding “intertwining numbers” is obtained wh...

Let denote a bipartite distance-regular graph with diameter D ≥ 3 and valency k ≥ 3. Let θ0 > θ1 > · · · > θD denote the eigenvalues of and let qh i j (0 ≤ h, i, j ≤ D) denote the Krein parameters of . Pick an integer h (1 ≤ h ≤ D − 1). The representation diagram = h is an undirected graph with vertices 0, 1, . . . , D. For 0 ≤ i, j ≤ D, vertices i, j are adjacent in whenever i = j and qh i j =...

In this paper we give a partial answer to a 1980 question of Lazslo Babai: “Which [finite] groups admit an oriented graph as a DRR?” That is, which finite groups admit an oriented regular representation (ORR)? We show that every finite non-solvable group admits an ORR, and provide a tool that may prove useful in showing that some families of finite solvable groups admit ORRs. We also completely...

in recent years, many changes have been observed in buying culture of customers and developing chain stores in iran. moreover, need to be more competition in business environments made necessary the stablishment of chain stores, the creation of competitive advantage and long relations to the costumers. regular marketing is a response to stores requirement when establishing such a win-win long r...

Translated into the language of representations of quivers, a challenge in matrix pencil theory is to find sufficient and necessary conditions for a Kronecker representation to be a subfactor of another Kronecker representation in terms of their Kronecker invariants. The problem is reduced to a numerical criterion for a Kronecker representation to be a subrepresentation of another Kronecker rep...

Relief representation is a difficult problem. The surface of the Earth cannot be defined by a physical or mathematical representation but can be approximated by digital elevation models (DEM), triangular irregular networks (TIN), and contour lines. Each representation carries approximation errors. A DEM introduces the greatest errors because we assume that the surface of the Earth can be approx...