353 research outputs found

### On isoperimetric inequalities with respect to infinite measures

We study isoperimetric problems with respect to infinite measures on $R ^n$.
In the case of the measure $\mu$ defined by $d\mu = e^{c|x|^2} dx$, $c\geq 0$,
we prove that, among all sets with given $\mu-$measure, the ball centered at
the origin has the smallest (weighted) $\mu-$perimeter. Our results are then
applied to obtain Polya-Szego-type inequalities, Sobolev embeddings theorems
and a comparison result for elliptic boundary value problems.Comment: 25 page

### Quantum tricriticality in transverse Ising-like systems

The quantum tricriticality of d-dimensional transverse Ising-like systems is
studied by means of a perturbative renormalization group approach focusing on
static susceptibility. This allows us to obtain the phase diagram for 3<d<4,
with a clear location of the critical lines ending in the conventional quantum
critical points and in the quantum tricritical one, and of the tricritical line
for temperature T \geq 0. We determine also the critical and the tricritical
shift exponents close to the corresponding ground state instabilities.
Remarkably, we find a tricritical shift exponent identical to that found in the
conventional quantum criticality and, by approaching the quantum tricritical
point increasing the non-thermal control parameter r, a crossover of the
quantum critical shift exponents from the conventional value \phi = 1/(d-1) to
the new one \phi = 1/2(d-1). Besides, the projection in the (r,T)-plane of the
phase boundary ending in the quantum tricritical point and crossovers in the
quantum tricritical region appear quite similar to those found close to an
usual quantum critical point. Another feature of experimental interest is that
the amplitude of the Wilsonian classical critical region around this peculiar
critical line is sensibly smaller than that expected in the quantum critical
scenario. This suggests that the quantum tricriticality is essentially governed
by mean-field critical exponents, renormalized by the shift exponent \phi =
1/2(d-1) in the quantum tricritical region.Comment: 9 pages, 2 figures; to be published on EPJ

### Finsler Hardy inequalities

In this paper we present a unified simple approach to anisotropic Hardy
inequalities in various settings. We consider Hardy inequalities which involve
a Finsler distance from a point or from the boundary of a domain. The sharpness
and the non-attainability of the constants in the inequalities are also proved.Comment: 31 pages. We add "Note added to Proof" in Introduction and several
reference

### Neural networks for driver behavior analysis

The proliferation of info-entertainment systems in nowadays vehicles has provided a really cheap and easy-to-deploy platform with the ability to gather information about the vehicle under analysis. With the purpose to provide an architecture to increase safety and security in automotive context, in this paper we propose a fully connected neural network architecture considering positionbased features aimed to detect in real-time: (i) the driver, (ii) the driving style and (iii) the path. The experimental analysis performed on real-world data shows that the proposed method obtains encouraging results

### On the behaviour of the solutions to $p$-Laplacian equations as $p$ goes to $1$

In the present paper we study the behaviour as $p$ goes to $1$ of the weak
solutions to the problems
$\begin{cases}
-\operatorname{div} \bigl(|\nabla u_p|^{p-2}\nabla u_p\bigr)=f
&\text{in } \Omega\\
u_p=0 &\text{on } \partial\Omega,
\end{cases}$
where $\Omega$ is a bounded open set of ${\mathbb R}^N$ $(N\ge 2)$ with
Lipschitz boundary and p > 1. As far as the datum $f$ is
concerned, we analyze several cases: the most general one is $f\in
W^{-1,\infty}(\Omega)$. We also illustrate our results by means of
remarks and examples

### The isoperimetric problem for a class of non-radial weights and applications

We study a class of isoperimetric problems on R+ N where the densities of the weighted volume and weighted perimeter are given by two different non-radial functions of the type |x|kxN Î±. Our results imply some sharp functional inequalities, like for instance, Caffarelli-Kohn-Nirenberg type inequalities

### Interface mapping in two-dimensional random lattice models

We consider two disordered lattice models on the square lattice: on the
medial lattice the random field Ising model at T=0 and on the direct lattice
the random bond Potts model in the large-q limit at its transition point. The
interface properties of the two models are known to be related by a mapping
which is valid in the continuum approximation. Here we consider finite random
samples with the same form of disorder for both models and calculate the
respective equilibrium states exactly by combinatorial optimization algorithms.
We study the evolution of the interfaces with the strength of disorder and
analyse and compare the interfaces of the two models in finite lattices.Comment: 7 pages, 6 figure

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