3,002 research outputs found
On homogeneous warped product Einstein metrics
In this article we study homogeneous warped product Einstein metrics and its
connections with homogeneous Ricci solitons. We show that homogeneous
-Einstein manifolds (which are the bases of homogeneous warped
product Einstein metrics) are one-dimensional extensions of algebraic solitons.
This answers a question from a paper of C. He, P. Petersen and W. Wylie, where
they prove the converse statement. Our proof is strongly based on their
results, but it also makes use of sharp tools from the theory of homogeneous
Ricci solitons. As an application, we obtain that any homogeneous warped
product Einstein metric with homogeneous base is diffeomorphic to a product of
homogeneous Einstein manifolds.Comment: 9 page
Immortal homogeneous Ricci flows
We show that for an immortal homogeneous Ricci flow solution any sequence of
parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton.
This is established by constructing a new Lyapunov function based on curvature
estimates which come from real geometric invariant theory.Comment: Final version, to appear in Invent. Mat
RELATIVISTIC-DFT STUDY OF THE ELECTRONIC STRUCTURE, BONDING AND ENERGETIC OF THE [ReF8]Ö¾ AND [UF8]2- IONS
Indexación: Web of Science; Scielo.In this study we evaluated the importance of the relativistic effects (scalar and spin-orbit) on the description of the electronic structure, bonding and the energetic of the [ReF8]- and [UF8]2- ions. We described the bonding interaction between ligands and metal center using the energy decomposition analysis (EDA) proposed by Morokuma and Ziegler, in which it can be appreciated a strong ionic behavior for both ions since the electrostatic interaction energy (∆Ezlestat) is greater than the orbitalic interaction energy (∆EOrb). Furthermore, a qualitative analysis using the mapping of the electrostatic potential over the total electronic density evidence an increase of the ionic character, as well as, the polarization of the electronic density as U > Re. The electron localization function (ELF) corroborates the bonding analysis because of the lack of di-synaptic basins on the metal-ligand bonding region.http://ref.scielo.org/jcbd4
Improving Missing Data Imputation with Deep Generative Models
Datasets with missing values are very common on industry applications, and
they can have a negative impact on machine learning models. Recent studies
introduced solutions to the problem of imputing missing values based on deep
generative models. Previous experiments with Generative Adversarial Networks
and Variational Autoencoders showed interesting results in this domain, but it
is not clear which method is preferable for different use cases. The goal of
this work is twofold: we present a comparison between missing data imputation
solutions based on deep generative models, and we propose improvements over
those methodologies. We run our experiments using known real life datasets with
different characteristics, removing values at random and reconstructing them
with several imputation techniques. Our results show that the presence or
absence of categorical variables can alter the selection of the best model, and
that some models are more stable than others after similar runs with different
random number generator seeds
Exact predictions from Edwards ensemble vs. realistic simulations of tapped narrow two-dimensional granular columns
We simulate via a Discrete Element Method the tapping of a narrow column of
disk under gravity. For frictionless disks, this system has a simple analytic
expression for the density of states in the Edwards volume ensemble. We compare
the predictions of the ensemble at constant compactivity against the results
for the steady states obtained in the simulations. We show that the steady
states cannot be properly described since the microstates sampled are not in
correspondence with the predicted distributions, suggesting that the postulates
of flat measure and ergodicity are, either or both, invalid for this simple
realization of a static granular system. However, we show that certain
qualitative features of the volume fluctuations difficult to predict from
simple arguments are captured by the theory.Comment: 11 pages, 6 figure
On the reduction of 4-oxo-4h-benzopyran-3-carbaldehydes : global and local electrophilicity patterns
The theoretical global and local electrophilicity patterns of substituted and chelated
4-oxo-4H-benzopyran-3-carbaldehydes (formylchromones) have been evaluated using the electrophilicity
index proposed by Parr et al [J. Am. Chem. Soc. 1999, 121, 1922]. The complexation of formylchromones
with aluminum predicts a strong electrophilic character of these compounds against nucleophiles.
Local response at the active sites may also be assessed in terms of a global contribution described by
the global electrophilicity, and a local contribution described by the variations in electrophilic
Fukui function at those sites. The highest local electrophilicity is found at the formyl group of
the chelated formylchromones, in spite of that, the highest positive charge is located on the pyrone
carbonyl group. This result is consistent with the experimental observed reactivity displayed by
4-oxo-4H-benzopyran-3-carbaldehydes in the presence of 2-propanol and alumina
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