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 ${0 < \epsilon < 1}$ .     

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.     

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.     

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 ${0 < \epsilon <1 }$ .     

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

This paper is concerned with the following system which comes from a lattice dynamical system stated by Kaneko in (Phys Rev Lett 65:1391–1394, 1990) and is related to the Belusov–Zhabotinskii reaction: $$\begin{aligned} x_{n}^{m+1}=(1-\varepsilon )f(x_{n}^{m})+\frac{1}{2}\varepsilon \left[ f(x_{n-1}^{m})+f(x_{n+1}^{m})\right] , \end{aligned}$$ x n m + 1 = ( 1 ? ε ) f ( x n m ) + 1 2 ε [ f ( x n ? 1 m ) + f ( x n + 1 m ) ] , where $m$ m is discrete time index, $n$ n is lattice side index with system size $L$ L (i.e., $n=1, 2, \ldots , L$ n = 1 , 2 , … , L ), $\varepsilon $ ε is coupling constant, and $f(x)$ f ( x ) is the unimodal map on $I$ I (i.e., $f(0)=f(1)=0$ f ( 0 ) = f ( 1 ) = 0 and $f$ f has unique critical point $c$ c with $0<c<1$ 0 < c < 1 and $f(c)=1$ f ( c ) = 1 ). It is proved that for coupling constant $\varepsilon =1$ ε = 1 , this CML (Coupled Map Lattice) system is chaotic in the sense of Li–Yorke for each unimodal selfmap on the interval $I=[0, 1]$ I = [ 0 , 1 ] .     

NHC–Pd(II)–Im (NHC=N-heterocyclic carbene,Im=1-methylimidazole) complex catalyzed coupling reaction of arylboronic acids with carboxylic acid anhydrides in water

A well-defined N-heterocyclic carbene (NHC)–palladium chloride–imidazole complex exhibited high catalytic activity in the coupling reaction of arylboronic acids with carboxylic acid anhydrides in pure water under mild conditions. Under the optimal conditions, all reactions gave the desired coupling products in moderate to high yields.     

New strategy by a two-component heterogeneous catalytic system composed of Pd–PVP–Fe and heteropoly acid as co-catalyst for Suzuki coupling reaction

Research on Chemical Intermediates - We have developed a simple and efficient catalytic protocol composed of hollow palladium-poly(N-vinylpyrrolidone)-nano zero valent iron and H5PMo10V2O40...     

Well-defined NHC–Pd(II)–Im (NHC=N-heterocyclic carbene; Im=1-methylimidazole) complex catalyzed C–N coupling of primary amines with aryl chlorides

We report herein a well-defined NHC–Pd(II)–Im (NHC=N-heterocyclic carbene; Im=1-methylimidazole) complex catalyzed C–N coupling of primary amines with aryl chlorides. Under the optimal reaction conditions, a variety of primary amines can be coupled with aryl chlorides to give the amination products in good to high yields within 4 h. It is worthy of noting here that the NHC–Pd(II)–Im complex showed especially high catalytic activity toward challenging sterically hindered substrates including both of aryl amines and aryl chlorides. In addition, alkyl amines were also proved to be suitable reaction partners to give the corresponding amination products in good to high yields.     

Adducts and dimers of SFn+ (n = 1–5) with benzene,acetonitrile, and pyridine. Gas-phase generation and ab initio structures and thermochemistry

Pentaquadrupole (QqQqQ) mass spectrometry is used to explore the abilities of gaseous SF_n⁺ (n = 1–5) ions to form adducts and dimers with three π-electron rich molecules—benzene, acetonitrile, and pyridine, whereas ab initio calculations estimate most feasible structures, bond dissociation energies (BDEs), and reaction enthalpies of the observed products. With benzene, SF⁺ reacts by net H-by-SF^+· replacement. As suggested by the calculations, this novel benzene reaction forms ionized benzenesulfenyl fluoride, C₆H₅–SF^+·, via a Wheland-type intermediate that spontaneously loses a H atom. SF₃⁺ forms a rare, loosely bonded π complex with benzene, [Bz ⋯ SF₃]⁺, which is stable toward both H and HF loss. No dimer, Bz₂SF₃⁺, is formed. According to calculations, an unsymmetrically bonded, π-coordinated Bz₂SF₃⁺ dimer exists, i.e. (Bz–SF₃ ⋯ Bz)⁺, but its formation from [Bz ⋯ SF₃]⁺ is endothermic; hence, thermodynamically unfavorable. With acetonitrile, SF₂^+·, SF₃⁺, and SF₅⁺ form both adducts and dimers. CH₃–C^·N–SF₂⁺ (a new distonic ion) and CH₃CN–SF₅⁺ are covalently bonded, but CH₃CN ⋯ SF₃⁺ is loosely bonded. The binding natures of the acetonitrile adducts are reflected in the dimers; [CH₃CN–SF₂ ⋯ NCCH₃]^+· and [CH₃CN–SF₅ ⋯ NCCH₃]⁺ are unsymmetrically bonded, whereas [CH₃CN ⋯ SF₃ ⋯ NCCH₃]⁺ is symmetrically and loosely bonded. Such dimers as [CH₃CN ⋯ SF₃ ⋯ NCCH₃]⁺ are ideal for measurements of ion affinity via the Cooks’ kinetic method. With pyridine, only SF₃⁺ forms adduct and dimer. Py–SF₃⁺ is covalently bonded through nitrogen; [Py ⋯ SF₃ ⋯ Py]⁺ is loosely but unsymmetrically bonded. The unsymmetric 2.28 and 2.44 Å long N–S bonds in [Py ⋯ SF₃ ⋯ Py]⁺, which are expected to rapidly interconvert, result likely from steric hindrance that forces orthogonal alignment of the two pyridine rings. Most observed adducts and dimers display relatively high BDEs, i.e. they are formed in thermodynamically favorable reactions. The extents of dissociation of the adducts and dimers observed in MS³ experiments reflect the structures and BDEs predicted by the calculations.     

The reaction mechanism of a M (M = Mn,Fe, Co and Ni) atom inserted into a Fe8O12 cage

Research on Chemical Intermediates - The reaction process of a M (M?=?Mn, Fe, Co and Ni) atom associated and then interpolated into a Fe8O12 cage is calculated by using a PBE...     

Matrix IR spectra and quantum chemical studies of the reaction between difluorostannylene and hept-1-yne. The first direct observation of a carbene analog π-complex with alkne

IR studies of SnF₂ and hept-1-yne codeposited in an argon matrix at 12 K has revealed new bands at 540, 565, 1011, 2088 and 3256 cm^–1, assigned to the formation of a complex between SnF₂ and the alkyne. Quantum chemical AM1 and PM3 calculations confirm this assignment to the -complex of SnF₂ and the triple bond of hept-1-yne, and show that the complex forms without an activation barrier. The energy of the formation of the complex according to AM1 and PM3 calculations is 7.4 and 9.1 kcal/mol, respectively. The calculations indicate that the product of the cycloaddition of SnF₂ to a triple bond, stannyrene, is significantly less stable than the -complex.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 54–56, January, 1994.     

Simultaneous determination of hydride (Se) and non-hydride-forming (Ca,Mg, K,P, S and Zn) elements in various beverages (beer,coffee, and milk), with minimum sample preparation,by ICP–AES and use of a dual-mode sample-introduction system

A method has been developed enabling direct analysis (i.e. after dilution only) of beer, instant coffee, milk, and milk powder by ICP–AES. Analysis of the beverages after dilution with a low concentration of HNO₃ was used for accurate determination of essential minor and trace elements (Ca, Mg, K, P, S, and Zn). Selenium, introduced as the hydride, was determined simultaneously with the other non-hydride-forming elements using the commercial multi-mode sample-introduction system (MSIS). To obtain accurate results, however, some simple pre-treatment was needed. Analysis was also performed after microwave-assisted decomposition of the samples. Three different modes of sample-preparation, i.e. dilution only, partial decomposition (aqua regia treatment), and complete decomposition were compared. The results obtained by use of the three different sample-preparation methods were in very good agreement. Results from analysis of certified reference material (SRM 1459 non-fat milk powder) also verified the accuracy of the methods. The limit of detection obtained for Se using dual-mode sample introduction was 0.5 ng mL^–1, which corresponds to approximately 2 ng g^–1 in beer and approximately 4 ng g^–1 in coffee and milk when using the recommended procedure.     

Determination of cyromazine and melamine in chicken eggs using quick,easy, cheap,effective, rugged and safe (QuEChERS) extraction coupled with liquid chromatography–tandem mass spectrometry

A rapid and sensitive method has been developed for the simultaneous detection of cyromazine and melamine in chicken eggs using the quick, easy, cheap, effective, rugged and safe (QuEChERS) method coupled with liquid chromatography–tandem mass spectrometry (LC–MS/MS). The optimal extraction solvent for the liquid–liquid extraction was 5 mL of acetonitrile with a 0.1 M hydrochloric acid aqueous solution (99.5:0.5, v/v). The extract was cleaned with 0.5 g of anhydrous magnesium sulfate and 10 mg of graphitized carbon black. The analysis of cyromazine and melamine was accomplished by combining the use of an anion exchange LC column with tandem mass spectrometry in the positive electrospray ionization mode with selected reaction monitoring mode (SRM). The detection limits were 1.6 ng g⁻¹ for cyromazine and 8 ng g⁻¹ for melamine, and the quantitation limits were 5.5 ng g⁻¹ for cyromazine and 25 ng g⁻¹ for melamine. The recoveries of cyromazine and melamine in the spiked egg samples were 83.2% and 104.6%, respectively, with an relative standard deviation (RSD) of less than 18.1%. The intra-day and inter-day precisions, represented by the RSD, ranged from 1.5% to 8.8% and 6.8% to 14.3%, respectively. The proposed method was tested by analyzing chicken eggs from the markets and from the veterinary medicine laboratory. The concentrations of cyromazine and melamine detected in these samples were in the range of 20–94 ng g⁻¹. The results demonstrated that the QuEChERS method combined with LC–MS/MS is a simple, rapid and inexpensive method for the analysis of cyromazine and melamine in eggs.