I point out that an “infinite-dimensional, homogeneous, pregeometry” on a structure M is the same thing as a generically stable type p(x) such that (p(x), x = x) is strongly regular. I also discuss the case of quasi-minimal structures and groups.

In 1959 S.S. Shrikhande wrote a paper concerning L2 association schemes [11]. Out of this paper arose a strongly regular graph with parameters (16, 6, 2, 2) that was not isomorphic to L2(4). This graph turned out to be important in the study of strongly regular graphs as a whole. In this paper, we survey the various constructions and properties of this graph.

Let V be a real finite dimensional representation of a compact Lie group G. It is well-known that the algebra R[V ] of G-invariant polynomials on V is finitely generated, say by σ1, . . . , σp. Schwarz [38] proved that each G-invariant C-function f on V has the form f = F (σ1, . . . , σp) for a Cfunction F on R. We investigate this representation within the framework of Denjoy–Carleman classes....

The group PGL(2, q) has an embedding into PGL(3, q) such that it acts as the group fixing a nonsingular conic in PG(2, q). This action affords a coherent configuration R(q) on the set L(q) of non-tangent lines of the conic. We show that the relations can be described by using the cross-ratio. Our results imply that the restrictions R+(q) and R−(q) of R(q) to the set L+(q) of secant (hyperbolic)...

Abstract In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of given mapping at certain point. Then, discuss Hoffman estimation achieve results for estimate distance set solutions system linear equalities . The advantage our is that it allows one calculate coefficient error bound.

In this paper, we consider a generalization of Ebenbauer’s differential equation for non-symmetric matrix diagonalization to a flow on arbitrary complex semisimple Lie algebras. The flow is designed in such a way that the desired diagonalizations are precisely the equilibrium points in a given Cartan subalgebra. We characterize the set of all equilibria and establish a Morse-Bott type property ...