1,809 research outputs found
The Principles of Environmental Protection*
In the context of Global Goals (without poverty, zero hunger, health and well-being, quality education, gender equality, clean water and sanitations, clean and affordable energy, decent work and economic growth, industry, innovation and infrastructure, reducing inequalities, sustainable cities and communities, responsible consumption and production, climate action, aquatic life, earth life, peace, justice and efficient institutions, partenerships for achieving the objectives) it is important to join the fight to achieve these goals, advocating for the Right to a Healthy Environment. In my article I will try to analyze the way in which various institutional arrangements regarding the current climate crisis can have a pozitive impact on the environment and society
From Random Matrices to Stochastic Operators
We propose that classical random matrix models are properly viewed as finite
difference schemes for stochastic differential operators. Three particular
stochastic operators commonly arise, each associated with a familiar class of
local eigenvalue behavior. The stochastic Airy operator displays soft edge
behavior, associated with the Airy kernel. The stochastic Bessel operator
displays hard edge behavior, associated with the Bessel kernel. The article
concludes with suggestions for a stochastic sine operator, which would display
bulk behavior, associated with the sine kernel.Comment: 41 pages, 5 figures. Submitted to Journal of Statistical Physics.
Changes in this revision: recomputed Monte Carlo simulations, added reference
[19], fit into margins, performed minor editin
Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble
A time series delta(n), the fluctuation of the nth unfolded eigenvalue was
recently characterized for the classical Gaussian ensembles of NxN random
matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble
as a function of beta (zero or positive) by Monte Carlo simulations. The
fluctuation of delta(n) and the autocorrelation function vary logarithmically
with n for any beta>0 (1<<n<<N). The simple logarithmic behavior reported for
the higher-order moments of delta(n) for the GOE (beta=1) and the GUE (beta=2)
is valid for any positive beta and is accounted for by Gaussian distributions
whose variances depend linearly on ln(n). The 1/f noise previously demonstrated
for delta(n) series of the three Gaussian ensembles, is characterized by
wavelet analysis both as a function of beta and of N. When beta decreases from
1 to 0, for a given and large enough N, the evolution from a 1/f noise at
beta=1 to a 1/f^2 noise at beta=0 is heterogeneous with a ~1/f^2 noise at the
finest scales and a ~1/f noise at the coarsest ones. The range of scales in
which a ~1/f^2 noise predominates grows progressively when beta decreases.
Asymptotically, a 1/f^2 noise is found for beta=0 while a 1/f noise is the rule
for beta positive.Comment: 35 pages, 10 figures, corresponding author: G. Le Cae
Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
We solve the loop equations of the -ensemble model analogously to the
solution found for the Hermitian matrices . For \beta=1y^2=U(x)\beta((\hbar\partial)^2-U(x))\psi(x)=0\hbar\propto
(\sqrt\beta-1/\sqrt\beta)/Ny^2-U(x)[y,x]=\hbarF_h-expansion at arbitrary . The set of "flat"
coordinates comprises the potential times and the occupation numbers
\widetilde{\epsilon}_\alpha\mathcal F_0\widetilde{\epsilon}_\alpha$.Comment: 58 pages, 7 figure
Fragmentation Properties of Three-membered Ring Heterocyclic Molecules by Partial Ion Yield Spectroscopy: C2H4O and C2H4S
We investigated the photofragmentation properties of two three-membered ring heterocyclic molecules, C2H4O and C2H4S, by total and partial ion yield spectroscopy. Positive and negative ions have been collected as a function of photon energy around the C 1s and O 1s ionization thresholds in C2H4O, and around the S 2p and C 1s thresholds in C2H4S. We underline similarities and differences between these two analogous systems. We present a new assignment of the spectral features around the C K-edge and the sulfur L2,3 edges in C2H4S. In both systems, we observe high fragmentation efficiency leading to positive and negative ions when exciting these molecules at resonances involving core-to-Rydberg transitions. The system, with one electron in an orbital far from the ionic core, relaxes preferentially by spectator Auger decay, and the resulting singly charged ion with two valence holes and one electron in an outer diffuse orbital can remain in excited states more susceptible to dissociation. A state-selective fragmentation pattern is analyzed in C2H4S which leads to direct production of S2+ following the decay of virtual-orbital excitations to final states above the double-ionization threshold
On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures
This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev
inequalities for a class of Boltzmann-Gibbs measures with singular interaction.
Such measures allow to model one-dimensional particles with confinement and
singular pair interaction. The functional inequalities come from convexity. We
prove and characterize optimality in the case of quadratic confinement via a
factorization of the measure. This optimality phenomenon holds for all beta
Hermite ensembles including the Gaussian unitary ensemble, a famous exactly
solvable model of random matrix theory. We further explore exact solvability by
reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting
the Hermite-Lassalle orthogonal polynomials as a complete set of
eigenfunctions. We also discuss the consequence of the log-Sobolev inequality
in terms of concentration of measure for Lipschitz functions such as maxima and
linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional
Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics
225
- …