Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool

The EMD algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of components, well separated in the time–frequency plane, each of which can be viewed as approximately harmonic locally, with slowly varying amplitudes and frequencies. The EMD has already shown its usefulness in a wide range of applications including meteorology, structural stability analysis, medical studies. On the other hand, the EMD algorithm contains heuristic and ad hoc elements that make it hard to analyze mathematically.In this paper we describe a method that captures the flavor and philosophy of the EMD approach, albeit using a different approach in constructing the components. The proposed method is a combination of wavelet analysis and reallocation method. We introduce a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and we prove that our method does indeed succeed in decomposing arbitrary functions in this class. We provide several examples, for simulated as well as real data.     

Spectral synthesis for coadjoint orbits of nilpotent Lie groups

We determine the space of primary ideals in the group algebra \(L^{1}(G) \) of a connected nilpotent Lie group by identifying for every \(\pi \in \widehat{G} \) the family \(\mathcal I^\pi \) of primary ideals with hull \(\{\pi \} \) with the family of invariant subspaces of a certain finite dimensional sub-space \(\mathcal P_Q^\pi \) of the space of polynomials \(\mathcal P(G) \) on G.     

Synthesis and characterization of new strontium 4-carboxyphenylphosphonates

Several new strontium 4-carboxyphenylphosphonates, i.e., two modifications of Sr(HOOCC₆H₄PO₃H)₂, SrH(OOCC₆H₄PO₃)·H₂O, Sr₃(OOCC₆H₄PO₃)₂·4H₂O and Sr₃(OOCC₆H₄PO₃)₂·5.7H₂O were prepared and characterized by elemental analysis, thermogravimetry, X-ray powder diffraction and infrared spectroscopy. It was found that the compositions of these compounds depend on the acidity of the reaction medium. In addition, the presented compounds are interconvertible in dependence on pH. The position of the acid hydrogen atom in SrH(OOCC₆H₄PO₃)·H₂O was determined from the IR spectra of the studied compounds.The structure of the β modification of Sr(HOOCC₆H₄PO₃H)₂ was solved from its X-ray powder diffraction pattern using an ab initio method (the FOX program) with subsequent Rietveld refinement in the FULLPROF program. The compound is monoclinic, with the space group P2₁/c (No. 14), a=49.88(2), b=7.867(2), c=5.602(3) Å, β=128.68(2)°, and Z=4. It has a one-dimensional structure with an inorganic part built of SrO₈ distorted tetragonal antiprisms.     

{Bis­[2‐(2‐oxido‐1‐naphthylmethylidene­amino)­phenyl] disulfide}chloroiron(III)

The crystal structure of the title compound, {bis­[2‐(2‐oxido‐2‐naphthyl­idene­amino)­phenyl] di­sulfide‐κ⁵O,N,S,N′,O′}chloroiron(III), [FeCl(C₃₄H₂₂N₂O₂S₂)], has been determined. The structure consists of monomeric iron(III) complexes with distorted octahedral coordination. The di­sulfide functions as a pentadentate ligand and the Fe^III atom is coordinated through two N, two O and one S atom, and one chloride ion. The distance between the second S atom and the Fe^III atom is a non‐bonding 3.8473 (14) Å.     

Determination of mercury in gasoline diluted in ethanol by GF AAS after cold vapor generation, pre-concentration in gold column and trapping on graphite tube

A simple method for the determination of mercury in gasoline samples diluted with ethanol by graphite furnace atomic absorption spectrometry (GF AAS) after cold vapor (CV) generation, pre-concentration in a gold column and trapping on a graphite tube is proposed. The methodology is based upon conventional analytical processes that can be performed by any laboratory with a chemical generation and gold amalgamation systems coupled to the atomic absorption spectrometer. The GF AAS temperature was optimized, being the retention, pyrolysis and atomization temperatures, respectively, 100 °C, 150 °C and 800 °C. Gasoline samples were prepared simply by forming a 2-fold diluted solution in ethanol. The mercury formed vapors by reacting the sample with the reducing agent were pre-concentrated in a gold column and further retained on a graphite tube, coated with gold as permanent modifier. Five samples from different gas stations around the UFSC Campus (Florianópolis, Brazil) were analyzed and the Hg concentrations were found to be in the range from 0.40 µg L^− 1 to 0.90 µg L^− 1. Calibration against aqueous standard solutions in acidic medium was carried out. The standard solutions had about the same viscosity as the gasoline diluted in ethanol. The relative standard deviations were lower than 2.4% for the samples. The limits of detection in the samples were 0.08 and 0.14 µg L^− 1, with and without pre-concentration in the gold column, respectively. The accuracy of the method was estimated by applying the recovery test and recovery values between 92 and 100% were obtained. A sample throughput of 4 h^− 1 was achieved. Simplicity and high detection capability are some of the qualities of the method.     

Increasing the solubility characteristics of fenofibrate with cyclodextrin

The incidence of genetic lipoprotein disorders, or hyperlipoproteinaemia, is currently increasing. Examinations were carried out on the hyperlipoproteinaemic drug fenofibrate and various cyclodextrin derivatives were applied to increase the solubility of this drug. Numerous products with several compositions (drug: CD mole ratio=2:1, 1:1, 1:2 or 1:3) were studied and three preparation methods (powder mixing, kneading and precipitation) were used. In vitro drug liberation and membrane diffusion examinations revealed compositions suitable for the preparation of a capsule dosage form (1:2 and 1:3 physical mixtures).Dedicated to Dr. Béla Selmeczi, university professor, with the best wishes for his 65th birthday.     

Tablet of Spondias mombin L. Developed from Nebulized Extract Prevents Gastric Ulcers in Mice via Cytoprotective and Antisecretory Effects

Spondias mombin L. (Anacardiaceae) has a worldwide distribution and is present in all regions of Brazil. Its leaves, flowers and bark are used as teas in folk medicine to treat diseases of the digestive system. This study aimed to evaluate the acute non-clinical toxicity, gastroprotective activity, and the related mechanisms of action of nebulized extract and tablets based on dried Spondias mombin (SmNE). SmNE screening showed the presence of flavonoids (0.65%), polyphenols (25.50%), where the major compound is gallic acid. In the acute oral toxicity assay, a dose of 2000 mg/kg of SmNE administered orally in Swiss mice did not induce any behavioral changes. SmNE (250 or 500 mg/kg p.o) significantly reduced the ulcerative lesion area when compared to the control group in ethanol and non-steroidal anti-inflammatory drug (NSAIDs) models. Results showed that treatment with SmNE (250 mg/kg) reduced acid secretion and gastric content, accompanied with an increase in pH. Previous administration of indomethacin and glibenclamide reversed the protection provided by SmNE, confirming the participation of prostaglandins (PGs) and ATP-sensitive potassium channels (KATP) in its gastroprotective effect. The SmNE tablets met the pharmacopeial quality requirements with gastroprotective activity and similar protection in comparison to the isolated extract administrated. In conclusion, SmNe has a gastroprotective activity related to cytoprotective mechanisms, such as the participation of endogenous prostaglandins and KATP channels, having an anti-secretory effect with systemic action. The formulation obtained presented gastroprotective effects similar to the administration of the extract, the tablets showed favorable compression characteristics by the direct route and met the pharmacopeial quality requirements.