An improved blow‐up criterion for smooth solutions of the two‐dimensional MHD equations

Our main object is to establish a regularity criterion with p≥q > 1 for the incompressible magnetohydrodynamics equations with zero magnetic diffusivity. Copyright © 2016 John Wiley & Sons, Ltd.     

Irreducible buchsbaum curves

For every biliaison class C _M of Buchsbaum curves of π ³ we prove that the leftmost shift in which there are smooth and connected curves is the same as for irreducible curves. As a consequence, every irreducible Buchsbaum curve has a flat deformation with cohomology and Hartshorne-Rao module constant which is smooth and connected.     

Nonlinear Neutral Delay Differential Equations of Fourth-Order: Oscillation of Solutions

The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included.     

Parabolic Herz spaces and their applications

This note is a natural continuation of the study started in Ragusa (2009) [11]. For Herz spaces endowed with a parabolic metric we prove regularity results for weak solutions to divergence form parabolic equations having discontinuous coefficients, using the boundedness of integral operators and commutators generated using VMO functions and Calderón–Zygmund operators.     

A Solution of a Nonsymmetric Theory of Gravitation

The field equations of a proposed nonsymmetrictheory of gravitation are solved exactly for the case ofa static and spherically symmetric point singularity.The physical consequences of the solution are analyzed for the precession of perihelia,deflection of light, red-shift and radar-echodelay.     

On the reducibility of the postulation Hilbert scheme

We give a condition in terms of the possible graded Betti numbers compatible with a given Hilbert functionH of 0-dimensional subschemes of ℙ ⁿ which implies the reducibility of the postulation Hilbert scheme and of its subscheme which parametrizes reduced subschemes with Hilbert functionH.     

Sulle algebre per cui vale il teorema degli zeri di Hilbert generalizzato

Riassunto In questo lavoro studiamo quelleA-algebreB, chiamate algebre di Hilbert, in cui è vera una generalizzazione del teorema degli zeri di Hilbert. In particolare studiamo alcune proprietà che implicano cheB sia un'algebra di Hilbert e proviamo il passaggio di queste proprietà rispetto a certi cambiamenti di base. Infine studiamo alcuni anelli di frazioni dell'anello dei polinomi sopra un corpo algebricamente chiusoK ed in un insieme di indeterminate di cardinalità non inferiore a quella diK.

---

Summary In this paper we study thoseA-algebrasB, named Hilbert algebras, in which a generalization of Hilbert's Nullstellensatz is verified. Particularly we look at some properties implying thatB is an Hilbert algebra and we prove the passage of this property with respect to certain base change. At last we study some rings of fractions of the polynomial ring generated over an algebrically closed fieldK by a set of indeterminates with cardinality greater or equal then the cardinality ofK.

---

---

Lavoro eseguito nell'ambito dei gruppi di ricerca del C.N.R.