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pro vyhledávání: '"Alessandro De Paris"'
Autor:
Alessandro De Paris
Publikováno v:
Le Matematiche, Vol 70, Iss 2, Pp 3-18 (2015)
At the time of writing, the general problem of finding the maximal Waring rank for homogeneous polynomials of fixed degree and number of variables (or, equivalently, the maximal symmetric rank for symmetric tensors of fixed order and in fixed dimensi
Externí odkaz:
https://doaj.org/article/40cc77e4ec564da7802ab4b953a42a0b
Autor:
Alessandro De Paris
Publikováno v:
Mathematics, Vol 6, Iss 11, p 247 (2018)
We present the state-of-the-art on maximum symmetric tensor rank, for each given dimension and order. After a general discussion on the interplay between symmetric tensors, polynomials and divided powers, we introduce the technical environment and th
Externí odkaz:
https://doaj.org/article/90342282944a4095a084a29ed9f75c4e
The theory of connections is central not only in pure mathematics (differential and algebraic geometry), but also in mathematical and theoretical physics (general relativity, gauge fields, mechanics of continuum media). The now-standard approach to t
Publikováno v:
Communications in Algebra. 47:5443-5461
We discuss a possible noncommutative generalization of the notion of an equivariant vector bundle. Let $A$ be a $\mathbb{K}$-algebra, $M$ a left $A$-module, $H$ a Hopf $\mathbb{K}$-algebra, $\delta:A\to H\otimes A:=H\otimes_{\mathbb{K}} A$ an algebra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94692b11f63cb28ecb6b68c035b2b974
https://doi.org/10.1080/00927872.2019.1631320
https://doi.org/10.1080/00927872.2019.1631320
We explicitly fix a mistake in a preliminary statement of our previous paper on the conductor at a multiplanar singularity. The correction is not immediate and, though the mistake does not affect correctness of the subsequent results, the wrong state
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::061305075198a78ac8d21cc21a0443b4
Autor:
Alessandro De Paris, Edoardo Ballico
A notion of open rank, related with generic power sum decompositions of forms, has recently been introduced in the literature. The main result here is that the maximum open rank for plane quartics is eight. In particular, this gives the first example
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::422f55184ee2e105a4e9d05e234eb177
http://hdl.handle.net/11588/671582
http://hdl.handle.net/11588/671582
Autor:
Alessandro De Paris
We exhibit, for each positive even degree, a ternary form of rank strictly greater than the maximum rank of monomials. Together with an earlier result in the odd case, this gives a lower bound of $$\begin{aligned} \left\lfloor \frac{d^2+2d+5}{4}\righ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::01e543aa66a3f29548458bed064904a5
Publikováno v:
Scientific Reports
Scientific reports (Nature Publishing Group) 6 (2016). doi:10.1038/srep24091
info:cnr-pdr/source/autori:Marasco A, De Paris A, Migliore M/titolo:Predicting the response of olfactory sensory neurons to odor mixtures from single odor response/doi:10.1038%2Fsrep24091/rivista:Scientific reports (Nature Publishing Group)/anno:2016/pagina_da:/pagina_a:/intervallo_pagine:/volume:6
Scientific reports (Nature Publishing Group) 6 (2016). doi:10.1038/srep24091
info:cnr-pdr/source/autori:Marasco A, De Paris A, Migliore M/titolo:Predicting the response of olfactory sensory neurons to odor mixtures from single odor response/doi:10.1038%2Fsrep24091/rivista:Scientific reports (Nature Publishing Group)/anno:2016/pagina_da:/pagina_a:/intervallo_pagine:/volume:6
The response of olfactory receptor neurons to odor mixtures is not well understood. Here, using experimental constraints, we investigate the mathematical structure of the odor response space and its consequences. The analysis suggests that the odor r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9294429c16fe69b4dd5860f1675e73e1
https://doi.org/10.1038/srep24091
https://doi.org/10.1038/srep24091
Autor:
Alessandro De Paris
Let $\operatorname{r_{max}}(n,d)$ be the maximum Waring rank for the set of all homogeneous polynomials of degree $d>0$ in $n$ indeterminates with coefficients in an algebraically closed field of characteristic zero. To our knowledge, when $n,d\ge 3$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3df76a6343f2e042c1000077b9027128
http://hdl.handle.net/11588/634821
http://hdl.handle.net/11588/634821
Publikováno v:
Communications in Algebra. 36:2969-2978
Let A be a noetherian local k-algebra with residue field k and associated graded ring G(A). Let 𝔟 be the conductor of A in its normalization , which we assume to be regular and finite over A. Assume also that Proj(G(A)) is reduced and . Let r be t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::008971365d8b7656f7aeb85f9c2fe52e
https://doi.org/10.1080/00927870802110367
https://doi.org/10.1080/00927870802110367