Peculiarities of the electron energy spectrum in the Coulomb field of a superheavy nucleus

We consider the peculiarities of the electron energy spectrum in the Coulomb field of a superheavy nucleus and discuss the long history of an incorrect interpretation of this problem in the case of a pointlike nucleus and its current correct solution. We consider the spectral problem in the case of a regularized Coulomb potential. For some special regularizations, we derive an exact equation for the point spectrum in the energy interval (-m,m) and find some of its solutions numerically. We also derive an exact equation for charges yielding bound states with the energy E = -m; some call them supercritical charges. We show the existence of an infinite number of such charges. Their existence does not mean that the oneparticle relativistic quantum mechanics based on the Dirac Hamiltonian with the Coulomb field of such charges is mathematically inconsistent, although it is physically unacceptable because the spectrum of the Hamiltonian is unbounded from below. The question of constructing a consistent nonperturbative second-quantized theory remains open, and the consequences of the existence of supercritical charges from the standpoint of the possibility of constructing such a theory also remain unclear.     

Limit problems for a Fractional p-La placian as $${ p\to\infty}$$

The purpose of this work is the analysis of the solutions to the following problems related to the fractional p-Laplacian in a Lipschitzian bounded domain \({\Omega \subset \mathbb{R}^N}\),

$$\left\{\begin{array}{lll}-\int_{\mathbb{R}^N}\frac{|u(y)-u(x)|^{p-2}(u(y)-u(x))}{|x-y|^{\alpha p}}\;dy=f(x,u)\;\;&x\in \Omega,\\ u=g(x) &x\in\mathbb{R}^N\setminus \Omega,\end{array}\right.$$

where \({\alpha\in(0,1)}\) and the exponent p goes to infinity. In particular we will analyze the cases:

1. (i)
   \({f=f(x).}\)
    
2. (ii)
   \({f=f(u)=|u|^{\theta(p)-1} u \, {\rm with} \, 0 < \theta(p) < p -1 \, {\rm and} \, \lim_{p\to\infty}\frac{\theta(p)}{p-1}=\Theta < 1 \, {\rm with} \, g \geq 0.}\)
    

We show the convergence of the solutions to certain limit as \({p\to\infty}\) and identify the limit equation. In both cases, the limit problem is closely related to the Infinity Fractional Laplacian:

$$\mathcal{L}_\infty v(x)=\mathcal{L}_\infty^+ v(x)+\mathcal{L}_\infty^- v(x),$$

where

$$\mathcal{L}_\infty^+ v(x)=\sup_{y\in\mathbb{R}^N}\frac{v(y)-v(x)}{|y-x|^\alpha}, \quad \mathcal{L}_\infty^- v(x)=\inf_{y\in\mathbb{R}^N}\frac{v(y)-v(x)}{|y-x|^\alpha}.$$

     

Dissipativity in impulsive systems via Lyapunov functions

This paper deals with impulsive dissipative semidynamical systems. We present sufficient conditions to obtain dissipativity for autonomous and non‐autonomous systems by using Lyapunov functions. Also, some converse‐type results are presented.     

Electrochemical Characterization of Carbon Solidlike Paste Electrode Assembled Using Different Carbon Nanoparticles

Solid like carbon paste electrodes (SCPEs) are built using different carbon materials namely carbon black N110, N220, N375, N772 and acetylene black. The electrochemical behavior of these electrodes and the influence of carbon black/paraffin ratio were studied and the results were discussed and compared to other electrodes prepared with graphite, mesoporous carbon and nanopowder carbon. Cyclic voltammetry, amperometry and electrochemical impedance spectroscopy were employed for their electrochemical and analytical characterizations. Amperometric measurements using N110, N220, N375 SCPEs with solid paraffin, showed a linear response of benzoquinone concentration with a detection limit of 75, 32 and 171 nM respectively.     

Study of variables for optimization of the dye indosol adsorption process using red mud and clay as adsorbents

The effluents from the textile industry, which not properly treated or discharged directly into water bodies, are a serious environmental problem. In order to find options to solve this problem, in this study, it was evaluate two alternative adsorbents: red mud and smectite clay, to remove the dye Indosol dark-blue SF-BL SGR 240. Assays were performed in batch using the experimental design to optimize the process and evaluate the influence of pH, mass and agitation speed on the adsorption capacity of dye by each material. The results showed that the adsorption process was influenced by the amount of mass of the adsorbent, by the pH and the by interaction between pH and mass, thereby obtaining a removal of approximately 0.110 and 0.119 mg g^?1 with red mud and smectite clay respectively.     

Proton Transport in a Highly Conductive Porous Zirconium‐Based Metal–Organic Framework: Molecular Insight

The water stable UiO‐66(Zr)‐(CO₂H)₂ MOF exhibits a superprotonic conductivity of 2.3×10^?3 S cm^?1 at 90 °C and 95 % relative humidity. Quasi‐elastic neutron scattering measurements combined with aMS‐EVB3 molecular dynamics simulations were able to probe individually the dynamics of both confined protons and water molecules and to further reveal that the proton transport is assisted by the formation of a hydrogen‐bonded water network that spans from the tetrahedral to the octahedral cages of this MOF. This is the first joint experimental/modeling study that unambiguously elucidates the proton‐conduction mechanism at the molecular level in a highly conductive MOF.     

Determination of low‐molecular‐weight amines and ammonium in saline waters by ion chromatography after their extraction by steam distillation

A new method was developed for the determination of ammonium ion, monomethylamine and monoethylamine in saline waters by ion chromatography. Steam distillation was used to eliminate matrix interferences. Variables such as distillation time, concentration of sodium hydroxide solution and analyte mass were optimized by using a full two‐level factorial (2³) design. The influence of steam distillation on the analytical curves prepared in different matrices was also investigated. Limits of detection of 0.03, 0.05 and 0.05 mg/L were obtained for ammoniumion, monomethylamine and monoethylamine, respectively. Saline water samples from the Brazilian oil industry, containing sodium and potassium concentrations between 2.0–5.2% w/v and 96–928 mg/L, respectively, were analyzed. Satisfactory recoveries (90–105%) of the analytes were obtained for all spiked samples, and the precision was ≤ 7% (n = 3). The proposed method is adequate for analyzing saline waters containing sodium to ammoniumion, monomethylamine and monoethylamine concentration ratios up to 28 000:1 and potassium to ammonium, monomethylamine and monoethylamine concentration ratios up to 12 000:1.     

Study of the application of multiway multivariate techniques to model data from an industrial fermentation process

Several multivariate statistical techniques have been extensively proposed for monitoring industrial processes. In this paper, multiway extensions of two such techniques: multiway principal component analysis (MPCA) and multiway partial least squares regression (MPLS) were applied to a large data set from an industrial pilot-scale fermentation process to improve process knowledge. The MPCA model is able to diagnose faults occurring in the process whether they affect or not process productivity while the MPLS model enables the prediction of final product concentration and the detection of faults that will influence the fermentation productivity.     

X-ray scattering and multivariate analysis for classification of organic samples: a comparative study using Rh tube and synchrotron radiation

This work compares the performance of X-ray tube induced and synchrotron induced energy dispersive X-ray fluorescence in generating scattering profiles when organic samples are irradiated. In the first case, this effect produces sharper peaks, well defined in the spectra, whereas synchrotron-induced scatter are seen as broad bands. These effects may be used for classifying simple materials like graphite, coke, activated carbon and carbon nanotubes, all having the same composition but different structures, using multivariate data analysis. In a second sample set, the method was applied to liquid samples of different alcohols (methanol, ethanol, 1-propanol and 2-propanol). Classifications were obtained in both cases independent of the X-ray source (synchrotron radiation or X-ray tube radiation), showing that the use of chemometric tools combined with X-ray spectrometry can efficiently distinguish organic samples by using scattering effects.     

An automatic falling drop system based on multicommutation process for photometric chlorine determination in bleach

In this work an automatic photometric procedure for the determination of chlorine in bleach samples employing N,N′-diethyl-p-phenylenediamine (DPD) as chromogenic reagent is described. The procedure was based on a falling drop system where the analyte (Cl₂) was collected by a DPD solution drop (50 μL) after its delivery from the sample bulk that was previously acidified. The flow system was designed based on the multicommutation process assembling a set of three-way solenoid valves, which under microcomputer control afforded facilities to handle sample and reagent solution in order to control analyte delivering and solution drop generation. The analyte volatilization was improved by coupling online a little heating device. The detection system comprised a green LED (515 nm) and a phototransistor. Aiming to prove the usefulness of the proposed procedure a set of bleach samples was analyzed. Comparing the results with those obtained with reference method no significant difference at 95% confidence level was observed. Other profitable features such as a linear response ranging from 15 up to 100 mg L⁻¹ Cl₂ (R = 0.999); a detection limit of 4.5 mg L⁻¹ Cl₂ estimated based on the 3σ criterion; a relative standard deviation of 2.5% (n = 10) using a typical bleach sample containing 25.0 mg L⁻¹ Cl₂; a consumption of 55 μg of DPD per determination; and a analytical frequency of 20 determinations per hour were also achieved.