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).     

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.     

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 ] .     

The reaction of dichlorocarbene with tertiary carboxamides : Preparation of α-chloromethylenelactams and (E)-chloroacrylamides

An easy method is described for the preparation of (E)-3-chloroacrylamides and α-chloromethylenelactams which is based on the simple treatment of tertiary carboxamides and lactams with dichlorocarbene.     

Design, testing and optimization of a neutron radiography system based on a Deuterium–Deuterium (D–D) neutron generator

Simulations show that significant improvement in imaging performance can be achieved through collimator design for thermal and fast neutron radiography with a laboratory neutron generator. The radiography facility used in the measurements and simulations employs a fully high-voltage-shielded, axial D–D neutron generator with a radio frequency driven ion source. The maximum yield of such generators is about 10¹⁰ fast neutrons per seconds (E = 2.45 MeV). Both fast and thermal neutron images were acquired with the generator and a Charge Coupled Devices camera. To shorten the imaging time and decrease the noise from gamma radiation, various collimator designs were proposed and simulated using Monte Carlo N-Particle Transport Code (MCNPX 2.7.0). Design considerations included the choice of material, thickness, position and aperture for the collimator. The simulation results and optimal configurations are presented.     

Co-crystal of (R,R)-1,2-cyclohexanediol with (R,R)-tartaric acid,a key structure in resolution of the (±)-trans-diol by supercritical extraction,and the related ternary phase system

A novel co-crystal of trans-(R,R)-1,2-cyclohexanediol and (R,R)-tartaric acid (with 1:1 molar ratio, 1) has been found to be a key crystalline compound in the improved resolution of (±)-trans-1,2-cyclohexanediol by supercritical fluid extraction. The molecular and crystal structure of this co-crystal, which crystallizes in orthorhombic crystal system (space group P2₁2₁2₁, a = 6.7033(13) Å, b = 7.2643(16), c = 24.863(5), Z = 4), has been solved by single crystal X-ray diffraction (R = 0.064). The packing arrangement consists of two dimensional layers of sandwich-like sheets, where the inner part is constructed by double layers of tartaric acids which hydrophilicity is “covered” on both upper and bottom side by cyclohexanediols with the hydrophobic cyclohexane rings pointing outward. Thus, a rather complex hydrogen bonding pattern is constructed. The relatively high melting point (133 °C) observed by both simultaneous TG/DTA and DSC, and the main features of FTIR-spectrum of 1 are explained by the increased stability of this crystal structure. DSC studies on binary mixtures of co-crystal 1 with (R,R)-1,2-cyclohexanediol or (R,R)-tartaric acid, revealed eutectic temperatures of T_eu = 100 or 131 °C, respectively. Between (S,S)-1,2-cyclohexanediol and (R,R)-tartaric acid a eutectic temperature of T_eu = 85 °C have also been observed. The phase relations have been confirmed by powder X-ray diffraction, as well.     

Synthesis,structure, and photoluminescence of a (4,6)-connected Cu(I)–CN–triazolate framework built with a unique heptanuclear hybrid cluster

A 3-D Cu(I)–CN–triazolate hybrid coordination polymer, {Cu₉(NH₂-BPT)₂(BPT)₂(CN)₇}_n (1) (NH₂-BPT = 4-amino-3,5-bis(3-pyridyl)-1,2,4-triazole, BPT = 3,5-bis(3-pyridyl)-1,2,4-triazole), has been synthesized via self-assembly of NH₂-BPT, CuCN, and K₃Fe(CN)₆ under hydrothermal conditions. Single-crystal X-ray diffraction data show that four of the five independent copper centers in 1 have a three-coordinated trigonal coordination geometry, and the remaining copper center has a two-coordinated linear geometry. Three Cu ions are linked by one cisoid-BPT and two CN^? to form a 16-membered ring subunit, which is joined by the two-coordinate copper center via the triazole N(4)-position to generate an unprecedented [Cu₇(BPT)₂(CN)₄] hybrid heptanuclear cluster. Each heptanuclear motif is linked to two adjacent [Cu₇] clusters through four CN^? anions, and further to four [Cu–CN–Cu] binuclear clusters through two transoid-NH₂-BPT ligands. Each of these [Cu–CN–Cu] units is linked to four neighboring heptanuclear motifs. The overall geometry is a 3-D (4,6)-connected topological framework with Schläfli symbol of (4^4?×?6²)(4^4?×?6^10?×?8). Compound 1 also exhibits high thermal stability and strong green fluorescence emission at 536?nm in the solid state.     

The preparation of conducting polyaniline–silver and poly(p-phenylenediamine)–silver nanocomposites in liquid and frozen reaction mixtures

The oxidation of aniline with silver nitrate in 1 mol L⁻¹ acetic acid at 20 °C yielded a composite of two conducting components, polyaniline and silver; the acceleration with 1 mol% of p-phenylenediamine is needed for efficient synthesis. The yield and molecular weight increased when aniline was copolymerized with 10 mol% p-phenylenediamine. Such product displayed metallic conductivity below 180 K and semiconductor type above this temperature. As the result, the conductivity was the same at 100 and 300 K. The oxidation of p-phenylenediamine alone with silver nitrate also produced a conducting composite having the conductivity of 1,750 S cm⁻¹ despite the assumed nonconductivity of poly(p-phenylenediamine). The present study demonstrates that all oxidations proceeded also in frozen reaction mixtures at −24 °C, i.e., in the solid state. In most cases, molecular weights of polymer component increased, the conductivity of composites with silver improved, to 2,990 S cm⁻¹ for poly(p-phenylenediamine)–silver, and remained high after deprotonation with 1 mol L⁻¹ ammonium hydroxide.

     

Determination of glyphosate and AMPA in surface and waste water using high-performance ion chromatography coupled to inductively coupled plasma dynamic reaction cell mass spectrometry (HPIC–ICP–DRC–MS)

A novel method employing high-performance cation chromatography in combination with inductively coupled plasma dynamic reaction cell mass spectrometry (ICP–DRC–MS) for the simultaneous determination of the herbicide glyphosate (N-phosphonomethylglycine) and its main metabolite aminomethyl phosphonic acid (AMPA) is presented. P was measured as ³¹P¹⁶O⁺ using oxygen as reaction gas. For monitoring the stringent target value of 0.1 μg L⁻¹ for glyphosate, applicable for drinking and surface water within the EU, a two-step enrichment procedure employing Chelex 100 and AG1-X8 resins was applied prior to HPIC–ICP–MS analysis. The presented approach was validated for surface water, revealing concentrations of 0.67 μg L⁻¹ glyphosate and 2.8 μg L⁻¹ AMPA in selected Austrian river water samples. Moreover, investigations at three waste water-treatment plants showed that elimination of the compounds at the present concentration levels was not straightforward. On the contrary, all investigated plant effluents showed significant amounts of both compounds. Concentration levels ranged from 0.5–2 μg L⁻¹ and 4–14 μg L⁻¹ for glyphosate and AMPA, respectively.     

The Ln–Cu(II)–Hpic–H2BDC system showing interesting production variety upon different reaction conditions: hydrothermal synthesis,structures, thermostability,and magnetism

Herein, we report research regarding the Ln–Cu(II)–Hpic–H₂BDC system, where Ln, Hpic, and H₂BDC are lanthanide ions, picolinic acid, and 1,2-benzenedicarboxylic acid, respectively. Under different reaction temperatures (160°C and 170°C), the self-assembly of Gd₂O₃, CuCl₂, Hpic, and H₂BDC in water at pH = 2 adjusted by HClO₄ generates two Ln-containing coordination compounds, GdCu(pic)(PhCOO)₄ (1) and Gd(pic)(BDC)(µ-H₂O)₂(H₂O) (2) (PhCOOH = benzenecarboxylic acid). Under the same reaction conditions, if Gd₂O₃ is replaced by Pr₃O₄, then polymer Pr₄(BDC)₆(µ-H₂O)₂ (3) is obtained. The structural features are 1-D tape or 2-D irregular (6, 3) net. We also explored their phase purity by X-ray diffraction analysis and evaluated their thermostability by thermogravimetric analysis studies.     

Reaction of acetyl- and 1,1′-diacetylferrocene with isatin (Pfitzinger reaction)

An efficient method for the synthesis of 2-ferrocenyl-substituted quinoline-4-carboxylic acids via the reaction of acetyl- and 1,1′-diacetylferrocene with isatin under the conditions of the Pfitzinger reaction was developed. Starting from the obtained acids methyl esters, amides, N-methyl-N-methoxyamides, and oximes (at one of the free acetyl groups) of some of these compounds were synthesized.     

Synthesis, characterization, and electron transfer reaction of some surfactant–cobalt(III) complex ions

Abstract  

The surfactant complex ion cis-[Co(tmd)₂(C₁₂H₂₅NH₂)₂]³⁺ (tmd = 1,3-propanediamine, C₁₂H₂₅NH₂ = dodecylamine) has been synthesized and characterized by elemental analysis and spectral data. In addition we have determined the critical micelle concentration of the surfactant–cobalt(III) complex and studied the kinetics and mechanism of the complex with ferrocyanide anion. The reaction is found to be second order, and the second-order rate constant increases with increasing initial concentration of the surfactant–cobalt(III) complex due to the presence of self-micelles formed by the complex itself. The thermodynamic parameters were determined. The results have been analyzed.     

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...     

The reaction of (trifluoromethyl)dialkylaminoboranes with HF,HCl and HBr. X-Ray structure investigation of the amineboranes (CF3)2B(X)NHMe2, X  F and OH

The reactions of CF₃B(NMe₂)₂ (I) and (CF₃)₂BNMe₂ (II) with HX (X  F, Cl and Br) have been investigated. Additions with preservation of the BC bonds to yield species with tetracoordinate boron, along with some BN cleavage, were observed. While I formed boronium salts CF₃B(X)(NHMe₂)₂⁺X⁻ with X  Cl and Br, CF₃BF₂ · NHMe₂ (V) was obtained with HF. On the other hand, reactions of II with HX yielded the 1 : 1 adducts (CF₃)₂B(X) · HNMe₂ in each case. Of these, the species with X  F (VI) and X  OH (IX) (obtained by hydrolysis) were examined by single crystal X-ray diffraction. Surprisingly, no difference was found between the average BC bond lengths of these borates (VI 1.612(8), IX 1.624(4) Å) and that of II. The implications of this observation for BCF₃ bonding are discussed.     

Phase state diagram of a poly(amic acid)–solvent–nonsolvent system

Phase behavior and structure formation was studied using optical interferometry, nephelometry, and refractometry in the polymer–solvent–nonsolvent system for DMF solutions of two poly(amic acids): based on 3,3′,4,4′-benzophenonetetracarboxylic acid dianhydride and meta-phenylenediamine (PAA-1) and pyromellitic acid dianhydride and 4,4′-oxydianiline (PAA-2). Distilled water and its mixtures with DMF were used as a nonsolvent. According to the results of the study, isothermal cross sections of the phase state diagram in the threecomponent system were plotted, the position of the critical point, the spinodal, and the conodes were determined, the movement of the figurative points in the system was traced depending on the nonsolvent composition.     

The asymmetric hetero-Diels–Alder reaction and addition of allylic organometallics to 10-N,N-dicyclohexylsulphamoyl-(2R)-isobornyl glyoxylate

The recent development of very effective chiral auxiliaries has led to the design of 10-N,N-dicyclohexylsulphamoyl-(R)-isoborneol, which is similar to Oppolzer's (2R)-bornane-10,2-sultam but less effective on account of a less rigid structure. 10-N,N-Dicyclohexylsulphamoyl-(R)-isobornyl glyoxylate was examined in Diels–Alder and organometallic addition reactions. The results obtained were compared with those achieved by application of N-glyoxyloyl-(2R)-bornane-10,2-sultam.