A test for strict sign-regularity

A stable test for strict sign regularity

A stable test to check if a given matrix is strictly sign regular is provided. Among other nice properties, we prove that it has an optimal growth factor. The test is compared with other alternative tests appearing in the literature, and its advantages are shown.

Weight Functions and Sign Regularity

We examine the question of how the ranking between di erent distributions with respect to a one-parameter family of weight functions depend on the parameter. We argue that in this context sign regularity of the family of weight functions is a natural condition to consider. Several classical economical examples are shown to satisfy this condition. We use sign regularity to obtain results on the ...

Lipschitz regularity for minima without strict convexity of the Lagrangian

We give, in a non-smooth setting, some conditions under which (some of) the minimizers of ∫ Ω f (∇u(x)) dx + g(x,u(x)) dx among the functions in W1,1(Ω) that lie between two Lipschitz functions are Lipschitz. We weaken the usual strict convexity assumption in showing that, if just the faces of the epigraph of a convex function f :Rn → R are bounded and the boundary datum u0 satisfies a generali...

A Regularity Test for Pushdown Machines

(when q, t > 1) where q is the number of control states of the pushdown machine and t is the size of the pushdown tape alphabet. Therefore, one solution to our problem is to test all finite state machines of that size or less to see if one of them recognizes the same set as the pushdown machine. The method of proof is to take the pushdown machine and extract a finite state machine which is equi...

Commentary on Toward a Test for Strict Liability in Torts