Emanuele Sgroi- Doctor of Philosophy
- PhD at University of Messina
Emanuele Sgroi
- Doctor of Philosophy
- PhD at University of Messina
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Publications (9)
We study from an algebraic and geometric viewpoint Hamiltonian operators which are sum of a non-degenerate first-order homogeneous operator and a Poisson tensor. In flat coordinates, also known as Darboux coordinates, these operators are uniquely determined by a triple composed by a Lie algebra, its most general non-degenerate quadratic Casimir and...
It is known that Q-conditional symmetries of the classical Burgers’ equation express in terms of three functions satisfying a coupled system of Burgers-like equations. The search of conditional symmetries of this system leads to a system of five coupled Burgers-like equations. Using the latter system as a starting point, and iterating the procedure...
Let [Formula: see text] be a finite simple graph on [Formula: see text] non-isolated vertices, and let [Formula: see text] be its binomial edge ideal. We determine almost all pairs [Formula: see text], where [Formula: see text] ranges over all finite simple graphs on [Formula: see text] non-isolated vertices, for any [Formula: see text].
Lie groups of symmetries of differential equations constitute a fundamental tool for constructing group-invariant solutions. The number of subgroups is potentially infinite and so the number of invariant solutions; thus, it is crucial to obtain a classification of subgroups in order to have an optimal system of inequivalent solutions from which all...
It is known that $Q$-conditional symmetries of the classical Burgers' equation express in terms of three functions satisfying a coupled system of Burgers-like equations. The search of conditional symmetries of this system leads to a system of five coupled Burgers-like equations. Iterating the procedure, an infinite hierarchy of systems made of an o...
The v-function of a graded filtration I = {I [k] } k≥0 is introduced. Under the assumption that I is Noetherian, we prove that the v-function v(I [k]) is an eventually quasi-linear function. This result applies to several situations, including ordinary powers, and integral closures of ordinary powers, among others. As another application, we invest...
Let $I$ be a graded ideal of a standard graded polynomial ring $S$ with coefficients in a field $K$. The asymptotic behaviour of the $\text{v}$-number of the powers of $I$ is investigated. Natural lower and upper bounds which are linear functions in $k$ are determined for $\text{v}(I^k)$. We call $\text{v}(I^k)$ the $\text{v}$-function of $I$. Unde...
Let $G$ be a finite simple graph with $n$ non isolated vertices, and let $J_G$ its binomial edge ideal. We determine all pairs $(\mbox{projdim}(J_G),\mbox{reg}(J_G))$, where $G$ ranges over all finite simple graphs with $n$ non isolated vertices, for any $n$.
