Minimal non-FC-groups have been largely investigated and their structure is well-known. Minimal non-CC-groups, a first generalization of minimal non-FC-groups, have been investigated more recently and their complete description is still unknown. The present paper deals with generalizations of the notion of minimal non-FC-group in the context of locally nilpotent and locally solvable groups.

This paper formulates the problem of determining the degrees of all polynomial entries in a minimal polynomial basis of a polynomial matrix by using only the degree structure of the given matrix. Using a block Toeplitz matrix structure corresponding to the given polynomial matrix, it is shown that the degrees of the elements in its minimal polynomial basis, in the generic case, depend only on t...

In response to hypertension, arterioles remodel their structure, the heart develops myocardial hypertrophy, and the kidney reduces creatinine clearance and increases albuminuria. To better understand the interrelations among the target organs involved in hypertension, we evaluated minimal forearm vascular resistances--a hemodynamic index of arteriolar structure derived from mean blood pressure ...

It is proved that all groups of finite U -rank that have the descending chain condition on definable subgroups are totally transcendental. A corollary is that any stable group that is definable in an o-minimal structure is totally transcendental of finite Morley rank. Motivation for this paper is a problem concerning stable groups definable in ominimal structures. One theorem is that any defina...

Minimal Lagrangian submanifolds of a Kähler manifold represent a very interesting class of submanifolds as they are Lagrangian with respect to the symplectic structure of the ambient space, while minimal with respect to the Riemannian structure. In this paper we study minimal Lagrangian immersions of the universal cover of closed surfaces (of genus g ≥ 2) in CH, with prescribed data (σ, tq), wh...

An ordered structure is called o-minimalistic if it has all the first-order features of an o-minimal structure. In this paper, we concentrate on a well-known fragment DCTC (Definable Completeness/Type Completeness) and generalize o-minimal properties to this more general situation (dimension theory, monotonicity, Hardy structures, quasi-cell decomposition) upon replacing finiteness by discreten...

Minimal recursion semantics (MRS) is a framework for computational semantics that is suitable for parsing and generation and that can be implemented in typed feature structure formalisms. We discuss why, in general, a semantic representation with minimal structure is desirable and illustrate how a descriptively adequate representation with a nonrecursive structure may be achieved. MRS enables a...

We prove an analog of the Szemerédi-Trotter theorem in the plane for definable curves and points in any o-minimal structure over an arbitrary real closed field R. One new ingredient in the proof is an extension of the well known crossing number inequality for graphs to the case of embeddings in any o-minimal structure over an arbitrary real closed field.