Degrevlex Gröbner bases of generic complete intersections

In this paper, we study the Hilbert–Samuel function of a generic standard graded K-algebra

K[X₁,…,X_n]/(g₁,…,g_m)

when refined by an (ℓ)-adic filtration, ℓ being a linear form. From this we obtain a structure theorem which describes the stairs of a generic complete intersection for the degree-reverse-lexicographic order. We show what this means for generic standard (or Gröbner) bases for this order; in particular, we consider an “orderly filling up” conjecture, and we propose a strategy for the standard basis algorithm which could be useful in generic-like cases.     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

Le saut en zéro de la fonction de décalage spectral

We give a formula for the jump at zero of the spectral shift function associated with Schrödinger operator on manifolds with conical ends. We show that, according to its decay, a zero energy resonant state has a non-integer contribution.     

Equation of motion of small bodies in relativity

There is proven a theorem, to the effect that a material body in general relativity, in a certain limit of sufficiently small size and mass, moves along a geodesic.     

SHI induced modification in CR-39 polycarbonate by positron annihilation lifetime studies

CR-39 is a polycarbonate widely used as SSNTD for recording nuclear charged particles and in other applications. Latent ion tracks produced in the polymers due to the damage produced by the passage of Swift Heavy Ions contain amorphous material with highest degree of disorder, changing the free volume properties which have strong correlation with the macroscopic properties of the material. Positron annihilation lifetime spectroscopy (PALS) provides direct information about the dimension, content and hole size distribution of free volume in polymers. The effect of irradiation of ⁴⁰Ar (14.9 MeV/n) ions on CR-39 polycarbonate by Positron Annihilation Lifetime Spectroscopy (PALS) is reported here. PALS provides a non-destructive and non-interfering probe, having high detection efficiency for free volume hole properties. From o-Ps lifetime mean free volume hole radius and average free volume of the micro-voids have been calculated. PAL measurement shows an increase in free volume on irradiation.     

The convergence rate of continued fractions representing solutions of a Riccati equation

The aim of this note is to generalize and apply results on matrix continued fractions representing the solution of discrete matrix Riccati equations. Assuming uniform bounds for the norm of the matrix coefficients of the continued fraction, the minimal and maximal solutions of the corresponding algebraic Riccati equation can be accurately enclosed.