Li–Yorke chaos in a coupled lattice system related with Belusov–Zhabotinskii reaction

Garca Guirao and Lampart (J Math Chem 48:66–71, 2010; J Math Chem 48:159–164, 2010) said that for non-zero couplings constant, the lattice dynamical system is more complicated. Motivated by this, in this paper, we prove that this coupled map lattice system is Li–Yorke chaotic for coupling constant ${0 < \epsilon <1 }$ .     

Chaos of a coupled lattice system related with the Belusov–Zhabotinskii reaction

In this paper we present a lattice dynamical system stated by Kaneko in (Phys Rev Lett, 65: 1391–1394, 1990) which is related to the Belusov-Zhabotinskii reaction. We prove that this CML (Coupled Map Lattice) system has positive topological entropy for zero coupling constant.     

A note on the principal measure and distributional ({\varvec{p, q}})-chaos of a coupled lattice system related with Belusov–Zhabotinskii reaction

García Guirao and Lampart in (J Math Chem 48:159–164, 2010) presented a lattice dynamical system stated by Kaneko in (Phys Rev Lett 65:1391–1394, 1990) which is related to the Belusov–Zhabotinskii reaction. In this paper, we prove that for any non-zero coupling constant $\varepsilon \in (0, 1)$ , this coupled map lattice system is distributionally $(p, q)$ -chaotic for any pair $0\le p\le q\le 1$ , and that its principal measure is not less than $(1-\varepsilon )\mu _{p}(f)$ . Consequently, the principal measure of this system is not less than $$\begin{aligned} (1-\varepsilon )\left( \frac{2}{3}+\sum \limits _{n=2}^{\infty }\frac{1}{n}\frac{2^{n-1}}{(2^{n}+1) (2^{n-1}+1)}\right) \end{aligned}$$ for any non-zero coupling constant $\varepsilon \in (0, 1)$ and the tent map $\Lambda $ defined by $$\begin{aligned} \Lambda (x)=1-|1-2x|,\quad x\in [0, 1]. \end{aligned}$$      

Comment on “A note on the principal measure and distributional (p,q)-chaos of a coupled lattice system related with Belusov–Zhabotinskii reaction”

In García Guirao and Lampart (J Math Chem 48:159–164, 2010) presented a lattice dynamical system stated by Kaneko (Phys Rev Lett 65:1391–1394, 1990) which is related to the Belusov–Zhabotinskii reaction. In this note, we give an example which shows that the proofs of Theorems 3.1 and 3.2 in [J Math Chem 51:1410–1417, 2013] are incorrect, and two open problems.     

The principal measure and distributional (p, q)-chaos of a coupled lattice system related with Belusov–Zhabotinskii reaction

García Guirao and Lampart (J Math Chem 48:66–71, 2010; J Math Chem 2 48:159–164, 2010) said that for non-zero couplings constant, the lattice dynamical system is more complicated. Motivated by this, in this paper, we prove that this coupled lattice system is distributionally (p, q)-chaotic for any pair 0?≤ p?≤ q?≤ 1 and its principal measure is not less than ${\frac{2}{3} + \sum_{n=2}^{\infty} \frac{1}{n} \frac{2^{n-1}}{(2^{n}+1)(2^{n-1}+1)}}$ for coupling constant ${0 < \epsilon < 1}$ .     

The principal measure and distributional (p, q)-chaos of a coupled lattice system with coupling constant \varepsilon =1 related with Belusov–Zhabotinskii reaction

We consider the following system coming from a lattice dynamical system stated by Kaneko (Phys Rev Lett, 65:1391–1394, 1990) which is related to the Belusov–Zhabotinskii reaction: $$\begin{aligned} x_{n}^{m+1}=(1-\varepsilon )f\left( x_{n}^{m}\right) +\frac{1}{2}\varepsilon \left[ f(x_{n-1}^{m})+f\left( x_{n+1}^{m}\right) \right] , \end{aligned}$$ where $m$ is discrete time index, $n$ is lattice side index with system size $L$ (i.e., $n=1, 2, \ldots , L$ ), $\varepsilon \ge 0$ is coupling constant, and $f(x)$ is the unimodal map on $I$ (i.e., $f(0)=f(1)=0$ , and $f$ has unique critical point $c$ with $0<c<1$ and $f(c)=1$ ). In this paper, we prove that for coupling constant $\varepsilon =1$ , this CML (Coupled Map Lattice) system is distributionally $(p, q)$ -chaotic for any $p, q\in [0, 1]$ with $p\le q$ , and that its principal measure is not less than $\mu _{p}(f)$ . Consequently, the principal measure of this system is not less than $\frac{2}{3}+\sum _{n=2}^{\infty }\frac{1}{n}\frac{2^{n-1}}{(2^{n}+1) (2^{n-1}+1)}$ for coupling constant $\varepsilon =1$ and the tent map $\Lambda $ defined by $\Lambda (x)=1-|1-2x|, x\in [0, 1]$ . So, our results complement the results of Wu and Zhu (J Math Chem, 50:2439–2445, 2012).     

Prediction of allergic reaction risk of Shenmai injection based on real-world evidence coupled with UPLC–Q-TOF-MS

The allergic reaction (AR) of Chinese herbal injection (CHI) has become one of the most noticeable focuses of public health in China. However, it still remains a considerable controversy as to whether low-molecular-weight components in CHI have potential sensitization. In this study, the relationship between AR and low-molecular-weight component profile of Shenmai injection was explored by an interdisciplinary technology integrating real-world evidence and ultra-performance liquid chromatography–quadrupole time-of-flight mass spectroscopy (UPLC–Q-TOF-MS). The AR information of hospitalized patients was obtained by comprehensively analyzing real-world evidence from January 2015 to June 2019 at two Chinese hospitals. The UPLC–Q-TOF-MS was exploited to systematically investigate the low-molecular-weight component profile with 50–1500 m/z mass range, and 3725 MS1 peaks were detected. The optimized partial least squares discriminant analysis model was established to map the influence of low-molecular-weight components on AR. The results of this study showed that high levels of organic acids administered intravenously might be a potential risk factor for inducing AR. By using this method, Shenmai injection with high AR risk could be recognized precisely with 100% accuracy before clinical use.     

A computational modeling of two dimensional reaction–diffusion Brusselator system arising in chemical processes

In this article, the authors proposed a modified cubic B-spline differential quadrature method (MCB-DQM) to show computational modeling of two-dimensional reaction–diffusion Brusselator system with Neumann boundary conditions arising in chemical processes. The system arises in the mathematical modeling of chemical systems such as in enzymatic reactions, and in plasma and laser physics in multiple coupling between modes. The MCB-DQM reduced the Brusselator system into a system of nonlinear ordinary differential equations. The obtained system of nonlinear ordinary differential equations is then solved by a four-stage RK4 scheme. Accuracy and efficiency of the proposed method successfully tested on four numerical examples and obtained results satisfy the well known result that for small values of diffusion coefficient, the steady state solution converges to equilibrium point $(B,A/B)$ if $1-A+B^{2}>0$ .     

A new coupled wavelet-based method applied to the nonlinear reaction–diffusion equation arising in mathematical chemistry

In this paper, we have applied the wavelet-based coupled method for finding the numerical solution of Murray equation. To the best of our knowledge, until now there is no rigorous Legendre wavelets solution has been reported for the Murray equation. The highest derivative in the differential equation is expanded into Legendre series, this approximation is integrated while the boundary conditions are applied using integration constants. With the help of Legendre wavelets operational matrices, the Murray equation is converted into an algebraic system. Block pulse functions are used to investigate the Legendre wavelets coefficient vectors of nonlinear terms. The convergence of the proposed method is proved. Finally, we have given a numerical example to demonstrate the validity and applicability of the method. Moreover the use of proposed wavelet-based coupled method is found to be simple, efficient, less computation costs and computationally attractive.     

Direct determination of copper in urine using a sol–gel optical sensor coupled to a multicommutated flow system

In this work, a multicommutated flow system incorporating a sol–gel optical sensor is proposed for direct spectrophotometric determination of Cu(II) in urine. The optical sensor was developed by physical entrapment of 4-(2-pyridylazo)resorcinol (PAR) in sol–gel thin films by means of a base-catalysed process. The immobilised PAR formed a red 2:1 complex with Cu(II) with maximum absorbance at 500 nm. Optical transduction was based on a dual-colour light-emitting diode (LED) (green/red) light source and a photodiode detector. The sensor had optimum response and good selectivity towards Cu(II) at pH 7.0 and its regeneration was accomplished with picolinic acid. Linear response was obtained for Cu(II) concentrations between 5.0 and 80.0 g L^–1, with a detection limit of 3.0 g L^–1 and sampling frequency of 14 samples h^–1. Interference from foreign ions was studied at a 10:1 (w/w) ion:Cu(II) ratio. Results obtained from analysis of urine samples were in very good agreement with those obtained by inductively coupled plasma mass spectrometry (ICP–MS); there was no significant differences at a confidence level of 95%.     

Determination of diuretics in human urine using HPLC coupled with magnetic solid-phase extraction based on a metal–organic framework

Magnetic solid-phase extraction (MSPE) employing a metal–organic framework (Fe₃O₄@UiO-66-OH) combined with high-performance liquid chromatography was developed for the determination of trace diuretics in urine. The structure and properties of Fe₃O₄@UiO-66-OH were investigated using X-ray diffraction, infrared spectroscopy, scanning electron microscopy and vibrating sample magnetometry. Magnetic solid-phase extraction conditions, such as adsorbent amount and solution pH, were optimized using response surface methodology. Under the optimal conditions, the method resulted in excellent linearity with a high correlation coefficient (r > 0.99), satisfactory intraday repeatability (1.78–2.99%), low limits of detection (0.08–0.23 ng/ml), and good recoveries in urine samples (between 93.5 and 103%). Fe₃O₄@UiO-66-OH based on MSPE is a novel pretreatment technique for the detection of trace diuretics in urine.     

A study on the reaction of 2''''-hydroxychalcones with I_2-H_2SO_4-DMSO system

The reaction of 2'-hydroxychalcones with I_2-H_2SO_4-DMSO system has been studied. The results obtained by us are entirely different from those reported in the literature. The mechanism of this reaction has also been investigated.     

Structure–reactivity relationship in bimolecular elimination reactions based on the condensed graph of a reaction

By means of a structural representation of the chemical reactivity as a condensed graph a model predicting rate constants of the bimolecular elimination reaction is derived for the first time. The model developed enables the prediction of rate constants of reactions proceeding in different solvents or water-organic mixtures at different temperatures. It demonstrates a good predictive performance: a mean square deviation of predicted values from experimental ones is less than 0.7 logarithmic units. An outlier analysis shows that prediction errors are mainly due to the imperfection of the training data containing unique reactions. The model is available for users at arsole.u-strasbg.fr.     

A DFT study on the effect of hydrogen bonding on the reaction of a μ-benzoquinone diruthenium complex with acetylene

A DFT study was carried out to investigate the reaction mechanisms of a model μ-benzoquinone diruthenium complex {CpRu(μ-H)}₂(μ-η²:η²-C₆H₄O₂), derived from the experimental compound {Cp*Ru(μ-H)}₂(μ-η²:η²-C₆H₃RO₂) (R = H or R = Me, Cp* = η⁵-C₅Me₅), with acetylene both in aprotic and protic solvents. Results of calculations show that the influence of the solvent methanol on the reaction is mainly on the step of acetylene coordination. Enhanced hydrogen bonding is the reason for acceleration of the reaction in protic solvent, which is supported by NBO charge analysis.     

Studies on a new solid–liquid Cs separation using the ionic liquid extraction system in comparison with the conventional adsorption

The process characteristics of a new solid–liquid Cs⁺ separation from the radioactive liquid waste using a crown ether dicyclohexano-18-crown-6 as an extractant and an ionic liquid of 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide were studied. The physicochemical properties of the precipitate containing Cs⁺ which is an solid–liquid extraction product were investigated to identify the solid–liquid phase separability and Cs⁺ loading. The Cs⁺ separation process performances were compared experimentally with those of the conventional adsorption system for pretreatment requirement and the amount of Cs⁺ waste. It was observed that the solid–liquid separation method using ILs has high Cs⁺ separation performance especially in the low Cs⁺ concentration.

     

Suzuki reaction with aryl bromides at room temperature in the presence of a simple “ligand-free” catalytic system

Possibility was examined of using the simplest catalytic system (palladium salt and NaOH) in ethanol or in a mixture of ethanol and water as a catalyst precursor in order to obtain high product yields in the Suzuki reaction with nonactivated aryl bromides at room temperature without an inert atmosphere or ligand additives.