Mathematical Physics (MP)
http://hdl.handle.net/20.500.11824/16
2019-07-22T08:17:57ZA Lê-Greuel type formula for the image Milnor number
http://hdl.handle.net/20.500.11824/992
A Lê-Greuel type formula for the image Milnor number
Nuño-Ballesteros J.J.; Pallarés Torres I.
Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n-1},0)\to (\mathbb{C}^{n},0)$ the transverse slice of $f$ with respect to $p$. We prove that the sum of the image Milnor numbers $\mu_I(f)+\mu_I(g)$ is equal to the number of critical points of $p|_{X_s}\colon X_s\to\mathbb{C}$ on all the strata of $X_s$, where $X_s$ is the disentanglement of $f$ (i.e., the image of a stabilisation $f_s$ of $f$).
2019-02-01T00:00:00ZExamples of varieties with index one on C1 fields
http://hdl.handle.net/20.500.11824/990
Examples of varieties with index one on C1 fields
Dan A.; Kaur I.
Let K be the fraction field of a Henselian discrete valuation ring with algebraically closed residue field k. In this article we give a sufficient criterion for a projective variety over such a field to have index 1.
2019-04-16T00:00:00ZRestoring property of the Michelson-Sivashinsky equation
http://hdl.handle.net/20.500.11824/985
Restoring property of the Michelson-Sivashinsky equation
Trucchia A.; Pagnini G.
In this paper we propose a derivation of the Michelson-Sivashinsky
(MS) equation that is based on front propagation only, in opposition to
the classical derivation based also on the flow field. Hence, the characteristics of the flow field are here reflected into the characteristics of the
fluctuations of the front positions. As a consequence of the presence of
the nonlocal term in the MS equation, the probability distribution of
the fluctuations of the front positions results to be a quasi-probability
distribution, i.e., a density function with negative values. We discuss
that the appearance of these negative values, and so the failure of the
pure diffusive approach that we adopted, is mainly due to a restoring
property that is inherent to the phenomenology of the MS equation.
We suggest to use these negative values to model local extinction and
counter-gradient phenomena.
2019-01-01T00:00:00ZPerverse sheaves on semi-abelian varieties -- a survey of properties and applications
http://hdl.handle.net/20.500.11824/977
Perverse sheaves on semi-abelian varieties -- a survey of properties and applications
Liu Y.; Maxim L.; Wang B.
We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various restrictions on the homotopy type of complex algebraic manifolds (expressed in terms of their cohomology jump loci), homological duality properties of complex algebraic manifolds, as well as new topological characterizations of semi-abelian varieties.
2019-05-01T00:00:00Z