We characterize strong F-regularity, a property associated with tight closure, in a large class of rings. A special case of our results is a workable criterion in complete intersection rings. Tight closure is a recently introduced operation linked to a variety of results in commutative algebra. Among the major results achieved with its use are a generalization of the Direct Summand Conjecture f...

We show that in superlattices with alternating superconducting (S) and ferromagnetic (F) layers the spontaneous magnetic field induced due to electromagnetic proximity effect becomes dramatically enhanced compared previously studied S/F bilayers. The reveals itself for in-plane orientation of moments both anti-ferromagnetic ordering F layers. In finite size samples decays from sample surface to...

The reformulation-linearization technique (RLT), introduced in [H.D. Sherali and W.P. Adams. A Hierarchy of Relaxations Between the Continuous and Convex Hull Representations for Zero-One Programming Problems, SIAM Journal on Discrete Mathematics, 3(3):411–430, 1990], provides a way to compute a hierarchy of linear programming bounds on the optimal values of NP-hard combinatorial optimization p...

System F-bounded is a second order lambda calculus with subtyping. It extends system F≤ (see [Cardelli Wegner 85, Curien Ghelli 92, Ghelli 90, Cardelli et al. 91]) in that bounds of typed quantification may contain the bounded variable. In object-oriented terms, this feature allows one to write functions which accept parameters belonging to all the classes which inherit from one class. F-bounde...

We study the coefficients of algebraic functions ∑ n≥0 fnz n. First, we recall the too-little-known fact that these coefficients fn always admit a closed form. Then we study their asymptotics, known to be of the type fn ∼ CAnnα. When the function is a power series associated to a contextfree grammar, we solve a folklore conjecture: the critical exponents α cannot be 1/3 or −5/2; they in fact be...

Classically, formal orthogonal polynomials are studied with respect to a linear functional, which gives rise to a moment matrix with a Hankel structure. Moreover, in most situations, the moment matrix is supposed to be strongly regular. This implies a number of algebraic properties which are well known, like for example the existence of a three-term recurrence relation (characterised by a tridi...