Marcinkiewicz–Zygmund inequalities

We study a generalization of the classical Marcinkiewicz–Zygmund inequalities. We relate this problem to the sampling sequences in the Paley–Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz–Zygmund inequalities.     

Pattern recognition and data mining software based on artificial neural networks applied to proton transfer in aqueous environments

In computational physics proton transfer phenomena could be viewed as pattern classification problems based on a set of input features allowing classification of the proton motion into two categories： transfer ＇occurred＇ and transfer ＇not occurred＇. The goal of this paper is to evaluate the use of artificial neural networks in the classification of proton transfer events, based on the feed-forward back propagation neural network, used as a classifier to distinguish between the two transfer cases. In this paper, we use a new developed data mining and pattern recognition tool for automating, controlling, and drawing charts of the output data of an Empirical Valence Bond existing code. The study analyzes the need for pattern recognition in aqueous proton transfer processes and how the learning approach in error back propagation （multilayer perceptron algorithms） could be satisfactorily employed in the present case. We present a tool for pattern recognition and validate the code including a real physical case study. The results of applying the artificial neural networks methodology to crowd patterns based upon selected physical properties （e.g., temperature, density） show the abilities of the network to learn proton transfer patterns corresponding to properties of the aqueous environments, which is in turn proved to be fully compatible with previous proton transfer studies.     

On the 2-adic valuation of the cardinality of elliptic curves over finite extensions of $$\mathbb {F}_{\varvec{q}} $$

In this paper we study the difference between the 2-adic valuations of the cardinalities \( \# E( \mathbb {F}_{q^k} ) \) and \( \# E( \mathbb {F}_q ) \) of an elliptic curve E over \( \mathbb {F}_q \). We also deduce information about the structure of the 2-Sylow subgroup \( E[ 2^\infty ]( \mathbb {F}_{q^k} ) \) from the exponents of \( E[ 2^\infty ]( \mathbb {F}_q ) \).     

Quantum dynamics study of the K+HF(v=0-2,j=0)-->KF+H reaction and comparison with quasiclassical trajectory results

Extensive quantum real wave packet calculations within the helicity decoupling approximation are used to analyze the influence of the HF vibrational excitation on the K+HF(v=0-2,j=0)-->KF+H reaction. Quantum reaction probabilities P and reaction cross sections sigma are compared with corresponding quasiclassical trajectory (QCT) results. Disregarding threshold regions for v=0 and 1 (v=2 has no threshold), both approaches lead to remarkably similar results, particularly for sigma, validating the use of the QCT method for this system. When moving from v=0 to v=1 there is a large increase in P and sigma, as expected for a late barrier system. For v=2 the reaction becomes exoergic and P approximately 0.95 (with the exception of large total angular momenta where centrifugal barriers play a role). While substantial vibrational enhancement of the reactivity is thus seen, it is still quite less than that inferred from experimental data in the intermediate and high collision energy ranges. The origin of this discrepancy is unclear.     

Analysis of electron delocalization in aromatic systems: individual molecular orbital contributions to para-delocalization indexes (PDI)

Our research group has recently defined two new aromaticity indexes based on the analysis of electron delocalization in aromatic species using the quantum theory of atoms-in-molecules. One of these indexes is the para-delocalization index (PDI) that measures the electronic delocalization between para-related carbon atoms in six-membered rings. In this paper, we show that this index can be partitioned into individual molecular orbital contributions. We have applied this PDI decomposition to several polycyclic aromatic hydrocarbons showing that this partitioning provides new insight into the origin of aromaticity.     

Autocatalytic demetalation of a Zn(salphen) complex provoked by unprotected N-heterocycles

The interaction of Zn(salphen) complex with biologically important structures such as (benz)imidazoles and purine has been studied and revealed in the case of unprotected purine and (benz)imidazole derivatives a demetalated product, whereas for structurally related 1-methyl-(benz)imidazole the formation of 1 : 1 coordination complexes was evidenced by NMR, MS and X-ray crystallography.     

Determination of carbosulfan and its metabolites in oranges by liquid chromatography ion-trap triple-stage mass spectrometry

Liquid chromatography ion-trap mass spectrometry LC-MSn has been successfully applied to identify and confirm carbosulfan and seven of its metabolites in oranges after pressurized liquid extraction (PLE) with dichloromethane. Mass spectra of carbosulfan and its metabolites were investigated using multiple stages of mass spectrometry. Although interpretation of the fragmentation pathways, based on mass spectra, enables structural elucidation and identification of these compounds, the proposed fragmentation pathways and ion structures need verification by exact mass measurements. The analytical method--PLE and LC-MS3 --was validated: limits of quantification (LOQ) ranged from 0.01 to 0.07 mg kg(-1); at this level, recoveries were 55-90% with RSDs (five replicate analyses) from 8 to 19%. The degradation of carbosulfan was determined in a laboratory study carried out in mature oranges (Valencia Late) and tangerines (Clementine of Nules) already harvested. Main degradation products of carbosulfan were carbofuran, 3-hydroxycarbofuran, 3-ketocarbofuran and dibutylamine.     

Preparation and structure of three solvatomorphs of the polymer [Co(dbm)2(4ptz)]n: spin canting depending on the supramolecular organization

The syntheses and X-ray structures of three isomeric 1D coordination polymers are reported. The complex [Co(dbm)2(MeOH)2] (1) was used as a precursor in these reactions. The preparation and structure of 1 is also presented; this mononuclear complex is in the cis configuration because this allows the formation of a network of intermolecular hydrogen bonds in the solid state. Reaction of 1 with 2,4,6-tris-(4-pyridyl)-1,3,5-triazine (4ptz) yields the polymers [Co(dbm)2(4ptz)]n.nTHF (2a), [Co(dbm)2(4ptz)]n.0.75nTHF.0.5nEt2O (2b), and [Co(dbm)2(4ptz)]n.3nDMF (2c) in the form of zigzag chains, instead of the expected honeycomb architectures. This is because of the establishment of extended pi-pi stacking throughout these solids, which could not have occurred otherwise. Compounds 2a, 2b, and 2c are solvatomorphs, and formation of either one of them depends on the exact conditions of crystallization, which lead to significant differences in the supramolecular organization of the chains. Bulk magnetic measurements on 2a reveal weak antiferromagnetic exchange within the chains and small ordering throughout the solid that results in the manifestation of the phenomenon of spin canting, whereas for 2c the different supramolecular organization causes the antiferromagnetic exchange not to result in spin canting.