Effective Differential Nullstellensatz for Ordinary DAE Systems with Constant Coefficients

We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants $K$ of characteristic $0$. Let $\vec{x}$ be a set of $n$ differential variables, $\vec{f}$ a finite family of differential polynomials in the ring $K\{\vec{x}\}$ and $f\in K\{\vec{x}\}$ another polynomial which vanishes at every solution of the differential equation system $\vec{f}=0$ in any differentially closed field containing $K$. Let $d:=\max\{\deg(\vec{f}), \deg(f)\}$ and $\epsilon:=\max\{2,{\rm{ord}}(\vec{f}), {\rm{ord}}(f)\}$. We show that $f^M$ belongs to the algebraic ideal generated by the successive derivatives of $\vec{f}$ of order at most $L = (n\epsilon d)^{2^{c(n\epsilon)^3}}$, for a suitable universal constant $c>0$, and $M=d^{n(\epsilon +L+1)}$. The previously known bounds for $L$ and $M$ are not elementary recursive

On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations

This paper is mainly devoted to the study of the differentiation index and the order for quasi-regular implicit ordinary differential algebraic equation (DAE) systems. We give an algebraic definition of the differentiation index and prove a Jacobi-type upper bound for the sum of the order and the differentiation index. Our techniques also enable us to obtain an alternative proof of a combinatorial bound proposed by Jacobi for the order. As a consequence of our approach we deduce an upper bound for the Hilbert-Kolchin regularity and an effective ideal membership test for quasi-regular implicit systems. Finally, we prove a theorem of existence and uniqueness of solutions for implicit differential systems

A Geometric Index Reduction Method for Implicit Systems of Differential Algebraic Equations

This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely algebraic (polynomial) equation plus an under-determined ODE (that is, a semi-explicit DAE system of differentiation index 1) in as many variables as the order of the input system. This can be done by means of a Kronecker-type algorithm with bounded complexity

L’attività di ricerca universitaria nelle scienze sociali e la nuova disciplina sul trattamento dei dati personali

Il presente contributo si pone come scopo quello di inquadrare gli effetti della disciplina europea e interna in tema di «trattamento dei dati personali» delle persone fisiche nell’ambito dell’attività di ricerca scientifica universitaria, in particolare quella delle scienze sociali. Ciò ha comportato la necessità di esaminare gli effetti sull’attività del personale docente, ma anche sull’amministrazione, parti di una stessa organizzazione che opera in direzione di un interesse pubblico. Nel contributo si considera contestualmente la disciplina europea e quella interna, a partire dal Codice della privacy, sino a ricomprendervi le specifiche regole deontologiche nonché la regolamentazione specifica degli atenei

Generalized Quantifiers: Logic and Language

The Generalized Quantifiers Theory, I will argue, in the second half of last Century has led to an important rapprochement, relevant both in logic and in linguistics, between logical quantification theories and the semantic analysis of quantification in natural languages. In this paper I concisely illustrate the formal aspects and the theoretical implications of this rapprochement

Some metaphysical implications of the category of potentiality

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