Let Λ be a basic finite dimensional algebra over an algebraically closed field K. Tameness of the representation type of Λ – the only situation in which one can, at least in principle, meaningfully classify all finite dimensional representations of Λ – is a borderline phenomenon. However, even in the wild scenario, it is often possible to obtain a good grasp of the “bulk” of d-dimensional repre...

‎let $g$ be a finite group‎. ‎we say that the derived covering number of $g$ is finite if and only if there exists a positive integer $n$ such that $c^n=g'$ for all non-central conjugacy classes $c$ of $g$‎. ‎in this paper we characterize solvable groups $g$ in which the derived covering number is finite‎.‎

That is, W0 is the set of all finite products of the generators, allowing repetitions. Let W signify the larger multiplicative semigroup generated by W0 together with {1/2}. We call W the wild semigroup and W0 the Wooley semigroup. The question we consider is: Which integers belong to these semigroups? The sets of integer elements W(Z) := W ∩ Z and W0(Z) := W0 ∩ Z themselves form multiplicative...

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

Given a Heegaard splitting of a three-manifold Y , we consider the SL(2,C) character variety of the Heegaard surface, and two complex Lagrangians associated to the handlebodies. We focus on the smooth open subset corresponding to irreducible representations. On that subset, the intersection of the Lagrangians is an oriented d-critical locus in the sense of Joyce. Bussi associates to such an int...

Matching dependencies (mds) have recently been proposed [10] in order to make dependencies tolerant to various information representations, and proved [13] useful in data quality applications such as record matching. Instead of strict identification function in traditional dependency syntax (e.g., functional dependencies), mds specify dependencies based on similarity matching quality. However, ...

Strong learning of context-free grammars is the problem of learning a grammar which is not just weakly equivalent to a target grammar but isomorphic or structurally equivalent to it. This is closely related to the problem of defining a canonical grammar for the language. The current proposal for strong learning of a small class of CFGs uses grammars whose nonterminals correspond to congruence c...