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1.
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).  相似文献   

2.
Accurate low and high-lying bound states of Tietz–Hua oscillator potential are presented. The radial Schrödinger equation is solved efficiently by means of the generalized pseudospectral method that enables optimal spatial discreti zation. Both $\ell =0$ and rotational states are considered. Ro-vibrational levels of six diatomic molecules viz., H $_2$ , HF, N $_2$ , NO, O $_2$ , O $_2^+$ are obtained with good accuracy. Most of the states are reported here for the first time. A detailed analysis of variation of eigenvalues with $n, \ell $ quantum numbers is made. Results are compared with literature data, wherever possible. These are also briefly contrasted with the Morse potential results.  相似文献   

3.
Partial molal volumes ( $V_{\phi} ^{0}$ ) and partial molal compressibilities ( $K_{\phi} ^{0}$ ) for glycine, L-alanine, L-valine and L-leucine in aqueous potassium fluoride solutions (0.1 to 0.5?mol?kg?1) have been measured at T=(303.15,308.15,313.15 and 318.15) K from precise density and ultrasonic speed measurements. Using these data, Hepler coefficients ( $\partial^{2}V_{\phi} ^{0}/\partial T^{2}$ ), transfer volumes ( $\Delta V_{\phi} ^{0}$ ), transfer compressibilities ( $\Delta K_{\phi} ^{0}$ ) and hydration number (n H) have been calculated. Pair and triplet interaction coefficients have been obtained from the transfer parameters. The values of $V_{\phi} ^{0}$ and $K_{\phi} ^{0}$ vary linearly with increasing number of carbon atoms in the alkyl chain of the amino acids. The contributions of charged end groups ( $\mathrm{NH}_{3}^{+}$ , COO?), CH2 group and other alkyl chains of the amino acids have also been estimated. The results are discussed in terms of the solute?Ccosolute interactions and the dehydration effect of potassium fluoride on the amino acids.  相似文献   

4.
Different binders of Portland cement, calcium aluminate cement and calcium sulphate (PC/CAC/C $ {\bar{\text{S}}} $ ) have been investigated to determinate the influence the CAC and C $ {\bar{\text{S}}} $ amount in the reactions mechanism. Several mixtures were studied, ratios of 100, 85/15 and 75/25 of PC/CAC with 0, 3 and 5 % of C $ {\bar{\text{S}}} $ . Conduction calorimetric technique was used to follow the hydration during 100 h. The XRD and FTIR techniques were used as support in the analysis of the hydration products. The results have shown that the studied ternary systems form an extra amount of ettringite, and changes in the reactions mechanism with respect to a PC. The reactions mechanism depends on the CAC and C $ {\bar{\text{S}}} $ amount present in the different binders.  相似文献   

5.
The acid?Cbase behavior of $\mathrm{Fe}(\mathrm{CN})_{6}^{4-}$ was investigated by measuring the formal potentials of the $\mathrm{Fe}(\mathrm{CN})_{6}^{3-}$ / $\mathrm{Fe}(\mathrm{CN})_{6}^{4-}$ couple over a wide range of acidic and neutral solution compositions. The experimental data were fitted to a model taking into account the protonated forms of $\mathrm{Fe}(\mathrm{CN})_{6}^{4-}$ and using values of the activities of species in solution, calculated with a simple solution model and a series of binary data available in the literature. The fitting needed to take account of the protonated species $\mathrm{HFe}(\mathrm{CN})_{6}^{3-}$ and $\mathrm{H}_{2}\mathrm{Fe}(\mathrm{CN})_{6}^{2-}$ , already described in the literature, but also the species $\mathrm{H}_{3}\mathrm{Fe}(\mathrm{CN})_{6}^{-}$ (associated with the acid?Cbase equilibrium $\mathrm{H}_{3}\mathrm{Fe}(\mathrm{CN})_{6}^{-}\rightleftharpoons \mathrm{H}_{2}\mathrm{Fe}(\mathrm{CN})_{6}^{2-} + \mathrm{H}^{+}$ ). The acidic dissociation constants of $\mathrm{HFe}(\mathrm{CN})_{6}^{3-}$ , $\mathrm{H}_{2}\mathrm{Fe}(\mathrm{CN})_{6}^{2-}$ and $\mathrm{H}_{3}\mathrm{Fe}(\mathrm{CN})_{6}^{-}$ were found to be $\mathrm{p}K^{\mathrm{II}}_{1}= 3.9\pm0.1$ , $\mathrm{p}K^{\mathrm{II}}_{2} = 2.0\pm0.1$ , and $\mathrm{p}K^{\mathrm{II}}_{3} = 0.0\pm0.1$ , respectively. These constants were determined by taking into account that the activities of the species are independent of the ionic strength.  相似文献   

6.
The leading term in the large- $N$ asymptotics of the isomer count of fullerenes with $N$ carbon atoms is extracted from the published enumerations for $N\le 400$ with the help of methods of series analysis. The uncovered simple $N^9$ scaling is distinct from isomer counts of most classes of chemical structures that conform to mixed exponential/power-law asymptotics. The second leading asymptotic term is found to be proportional to $N^{25/3}$ . A conjecture concerning isomer counts of the IPR fullerenes is also formulated.  相似文献   

7.
N-1-Naphthylethylenediamine dihydrochloride monomethanolate (N-NEDHME) was tested as a corrosion inhibitor for copper in 2 M HNO3 solution using the standard gravimetric technique at 303–343 K. N-NEDHME acts as an inhibitor for copper in an acidic medium. Inhibition efficiency increases with increase in concentration of N-NEDHME but decreases with a rise in temperature. Thermodynamic parameters such as adsorption heat ( $ \Updelta H_{\text{ads}}^\circ $ ), adsorption entropy ( $ \Updelta S_{\text{ads}}^\circ $ ) and adsorption free energy ( $ \Updelta G_{\text{ads}}^\circ $ ) were obtained from experimental data of the temperature studies of the inhibition process at five temperatures ranging from 303 to 343 K. Kinetic parameters activation such as $ E_{a} $ , $ \Updelta H_{\text{a}}^\circ $ , $ \Updelta S_{\text{a}}^\circ $ and pre-exponential factors have been calculated and are discussed. Adsorption of N-NEDHME on the copper surface in 2 M HNO3 follows the Langmuir isotherm model.  相似文献   

8.
The lower energy levels of the protactinium (Pa) atom are unusually difficult to treat theoretically. Pa is located where the 6d and 5f energies cross; simple calculations consistently put the electron configurations $5f^16d^27s^2$ and $5f^26d^17s^2$ in the incorrect order. We have used multireference spin?Corbit configuration interaction to compute the energies of these states to determine which additional interactions need to be included. We also discuss the less common J 1 j coupling scheme suggested for these atomic states with applications also to the $5f^16d^2$ and $5f^26d^1$ states of $\hbox{Pa}^{2+}$ .  相似文献   

9.
A Kekulé structure of a benzenoid or a fullerene $\Gamma $ Γ is a set of edges $K$ K such that each vertex of $\Gamma $ Γ is incident with exactly one edge in $K$ K . The set of faces in $\Gamma $ Γ that have exactly three edges in $K$ K are called the benzene faces of $K$ K . The Fries number of $\Gamma $ Γ is the maximum number of benzene faces over all possible Kekulé structures for $\Gamma $ Γ . The Clar number is the maximum number of independent benzene faces over all possible Kekulé structures for $\Gamma $ Γ . It is often assumed, but never proved, that some set of independent benzene faces giving the Clar number is a subset of a set of benzene faces giving the Fries number. In Hartung (The Clar structure of fullerenes, Ph.D. Dissertation. Syracuse University, 2012) it is shown that this assumption is false for a large class of fullerenes. In this paper, we prove that this assumption is valid for a large a class of benzenoids.  相似文献   

10.
A Kekulé structure for a benzenoid or a fullerene $\Gamma $ is a set of edges $K$ such that each vertex of $\Gamma $ is incident with exactly one edge in $K$ , i.e. a perfect matching. All fullerenes admit a Kekulé structure; however, this is not true for benzenoids. In this paper, we develop methods for deciding whether or not a given benzenoid admits a Kekulé structure by constructing Kekulé structures that have a high density of benzene rings. The benzene rings of the Kekulé structure $K$ are the faces in $\Gamma $ that have exactly three edges in $K$ . The Fries number of $\Gamma $ is the maximum number of benzene rings over all possible Kekulé structures for $\Gamma $ and the set of benzene rings giving the Fries number is called a Fries set. The Clar number is the maximum number of independent benzene rings over all possible Kekulé structures for $\Gamma $ and the set of benzene rings giving the Clar number is called a Clar set. Our method of constructing Kekulé structures for benzenoids generally gives good estimates for the Clar and Fries numbers, often the exact values.  相似文献   

11.
Photoelectrochemical, photoelectrocatalytic, and electrochemical processes of silicon anodic oxidation and hydrogen evolution in aqueous HF solution are discussed in terms of thermodynamic stability of Si, oxides SiO, SiO2, and Si surface hydrides. It is shown that photoelectrochemical oxidation of n-type low-resistivity silicon to SiO2 is catalyzed by Si $^{+}$ photo-hole formation, whereas in the case of p-type Si, the feasibility of this reaction is predetermined by p-type conductivity. It is suggested that anodic oxidation of Si goes through the stage of SiO oxide formation and its subsequent oxidation to SiO2. Such mechanism accounts for chemical inertness of Si phase in HF solutions as well as for selective, anisotropic, and isotropic etching of Si within E ranges from $-0.5$ to 0.35 V, $0.35-0.8~V,$ and $E > 0.8$ V, respectively. Hydrogen evolution reaction on Si surface proceeds at very large overpotential ( $\geq 0.5$ V) through the stage of surface Si hydride formation: $\mathrm {Si + H_{2}O + e^{-} \rightarrow (SiH)_{surf} + OH^{-}}$ (the rate determining step) and $\mathrm {(SiH)_{surf} + H_{2}O + e^{-} \rightarrow Si + H_{2} + OH^{-}}$ . Illumination-related effects of surface reactions relevant to selective and anisotropic etching and nano/micro-structuring of Si surface are discussed.  相似文献   

12.
The heat capacity and density of KNCS-N-methylpyrrolidone (MP), Cd(NCS)2-MP, and KNCS-Cd(NCS)2-MP solutions at 298.15 K are studied by means of calorimetry and densitometry. Standard partial molar heat capacities and volumes ( $\bar C^\circ _{p,2} $ and $\bar V^\circ _2 $ ) of the studied electrolytes in MP are calculated. Standard values of heat capacity $\bar C^\circ _{p,i} $ and volume $\bar V^\circ _i $ of NCS? ions in MP at 298.15 K are determined. Values of the heat capacity and volume changes upon the formation of the three-component system KNCS-Cd(NCS)2-MP from binary solutions are obtained and discussed.  相似文献   

13.
We have obtained accurate heats of formation for the twenty natural amino acids by means of explicitly correlated high-level thermochemical procedures. Our best theoretical heats of formation, obtained by means of the ab initio W1-F12 and W2-F12 thermochemical protocols, differ significantly (RMSD = 2.3 kcal/mol, maximum deviation 4.6 kcal/mol) from recently reported values using the lower-cost G3(MP2) method. With the more recent G4(MP2) procedure, RMSD drops slightly to 1.8 kcal/mol, while full G4 theory offers a more significant improvement to 0.72 kcal/mol (max. dev. 1.4 kcal/mol for glutamine). The economical G4(MP2)-6X protocol performs equivalently at RMSD = 0.71 kcal/mol (max. dev. 1.6 kcal/mol for arginine and glutamine). Our calculations are in excellent agreement with experiment for glycine, alanine and are in excellent agreement with the recent revised value for methionine, but suggest revisions by several kcal/mol for valine, proline, phenylalanine, and cysteine, in the latter case confirming a recent proposed revision. Our best heats of formation at 298 K ( $\Delta H_{f,298}^{\circ }$ ) are as follows: at the W2-F12 level: glycine ?94.1, alanine $-$ 101.5, serine $-$ 139.2, cysteine $-$ 94.5, and methionine $-$ 102.4  kcal/mol, and at the W1-F12 level: arginine $-$ 98.8, asparagine $-$ 146.5, aspartic acid $-$ 189.6, glutamine $-$ 151.0, glutamic acid $-$ 195.5, histidine $-$ 69.8, isoleucine $-$ 118.3, leucine $-$ 118.8, lysine $-$ 110.0, phenylalanine $-$ 76.9, proline $-$ 92.8, threonine $-$ 149.0, and valine $-$ 113.6 kcal/mol. For the two largest amino acids, an average over G4, G4(MP2)-6X, and CBS-QB3 yields best estimates of $-$ 58.4 kcal/mol for tryptophan, and of $-$ 117.5 kcal/mol for tyrosine. For glycine, we were able to obtain a “quasi-W4” result corresponding to $\hbox {TAE}_e$  = 968.1, $\hbox {TAE}_0$  = 918.6, $\Delta H_{f,298}^{\circ }=-90.0$ , and $\Delta H_{f,298}^{\circ }=-94.0$  kcal/mol.  相似文献   

14.
Sound speeds have been measured for aqueous solutions of the nucleoside thymidine at T = 298.15 K and at the pressures p = (10, 20, 40, 60, 80, and 100) MPa. The partial molar volumes at infinite dilution, $ V_{2}^{\text{o}} $ , the partial molar isentropic compressions at infinite dilution, $ K_{S,2}^{\text{o}} $ , and the partial molar isothermal compressions at infinite dilution, $ K_{T,2}^{\text{o}} $ $ \{ K_{T,2}^{\text{o}} = - (\partial V_{2}^{\text{o}} /\partial p)_{T} \} $ , have been derived from the sound speeds at elevated pressures using methods described in our previous work. The $ V_{2}^{\text{o}} $ and $ K_{T,2}^{\text{o}} $ results were rationalized in terms of the likely interactions between thymidine and the aqueous solvent. The $ V_{2}^{\text{o}} $ results were also compared with those calculated using the revised Helgeson–Kirkham–Flowers (HKF) equation of state.  相似文献   

15.
The determination of the weighted $L_p$ norms of the real orthogonal polynomials of hypergeometric type $\left\{ y_n(x)\right\} $ is not only a very important problem per se in the theory of special functions, but also because of their recent entropic characterization and applications in quantum chemistry, quantum physics and information theory. Indeed, they essentially describe the $p$ th-order Rényi and Tsallis entropies of the numerous quantum systems whose wavefunctions are controlled by these polynomials. Moreover, for different values of $p$ , up to a constant factor, these norms characterize various fundamental and experimentally accessible quantities of many-electron systems. As well, the $L_p$ norms have been used to develop and interpret all energy components in the density-functional theory of the ground-state of atoms and molecules. The asymptotics of these quantities when $n \rightarrow \infty $ and $p>0$ have been recently calculated for Hermite polynomials, although not yet for Laguerre and Jacobi polynomials. Here, we determine the asymptotics ( $p\rightarrow \infty $ , $n$ fixed) of the weighted $L_p$ norms for general orthogonal polynomials in terms of the weight function and the coefficients of the second-order hypergeometric differential equation that they satisfy, and we apply it to the three classical families of real orthogonal polynomials. Moreover we analyse and discuss the monotonicity of this asymptotics, and we carry out a detailed numerical study of it.  相似文献   

16.
The heat capacity and density of solutions of calcium and cadmium nitrates in N-methylpyrrolidone (MP) at 298.15 K are studied by calorimetry and densimetry. The obtained data are discussed in relation to certain features of solvation and complex formation in solutions of these salts. The standard partial molar heat capacities and volumes ( $\overline {C_{p^2 }^0 }$ and $\overline {V_2^0 }$ ) of the electrolytes in MP are calculated. The standard heat capacities $\overline {C_{p^i }^0 }$ and volumes $\overline {V_i^0 }$ of Ca2+ and Cd2+ ions in MP at 298.15 K were determined, along with the contribution from specific interactions to the values of $\overline {C_{p^i }^0 }$ and $\overline {V_i^0 }$ of Cd2+ ions in MP solution.  相似文献   

17.
The rate constant of malachite green (MG+) alkaline fading was measured in water–ethanol–ethylene glycol ternary mixtures. This reaction was studied under pseudo-first-order conditions at 283–303 K. In each series of experiments, the concentration of ethanol was kept constant and the concentration of ethylene glycol was changed. It was shown that due to hydrogen bonding and hydrophobic interaction between MG+ and alcohol molecules the observed reaction rate constant, $ k_{\text{obs}} $ , increased in the water–ethanol–ethylene glycol ternary mixtures. The fundamental rate constants of MG+ fading in these solutions ( $ k_{1} $ , $ k_{ - 1} $ and $ k_{2} $ ) were obtained by the SESMORTAC model. Analysis of $ k_{1} $ and $ k_{2} $ values in solutions containing constant ethanol concentrations show that in low concentrations of ethylene glycol, hydrogen bonding formed between ethanol and ethylene glycol molecules and in high concentrations of ethylene glycol, ethanol as a solvent for ethylene glycol affected the reaction rate.  相似文献   

18.
The crystal structure of n-undecylammonium bromide monohydrate was determined by X-ray crystallography. The crystal system of the compound is monoclinic, and the space group is P21/c. Molar enthalpies of dissolution of the compound at different concentrations m/(mol·kg?1) were measured with an isoperibol solution–reaction calorimeter at T = 298.15 K. According to the Pitzer’s electrolyte solution model, the molar enthalpy of dissolution of the compound at infinite dilution ( $ \Updelta_{\text{sol}} H_{\text{m}}^{\infty } $ ) and Pitzer parameters ( $ \beta_{\text{MX}}^{(0)L} $ and $ \beta_{\text{MX}}^{(1)L} $ ) were obtained. Values of the apparent relative molar enthalpies ( $ {}^{\Upphi }L $ ) of the title compound and relative partial molar enthalpies ( $ \bar{L}_{2} $ and $ \bar{L}_{1} $ ) of the solute and the solvent at different concentrations were derived from experimental values of the enthalpies of dissolution.  相似文献   

19.
The shell density approximation to the electron-pair radial density of atoms is applied to the inner $D_< (r)$ and outer $D_> (r)$ densities, which are two components of the single-electron density $D(r)$ . The inner and outer densities are found to be expressed by product sums of shell densities and shell distributions or their complements. The expressions clarify physical meaning of the two densities and give examples for constructing two-electron properties from single-electron properties. Examination of the 53 atoms He through Xe shows that the quantum similarity indices between the original and approximate densities, bounded by 0 (complete dissimilarity) and 1 (complete similarity), are never smaller than 0.99998 and 0.99987 for the inner and outer densities, respectively. The local nature of the shell density and the monotonically increasing property of the shell distribution are used to derive simple shellwise lower and upper bounds to $D_< (r)$ and $D_> (r)$ in terms of $D(r)$ and the numbers of shell electrons. Numerical tests of the bounds demonstrate their utility.  相似文献   

20.
The densities, ρ 12, and speeds of sound, u 12, of 1-ethyl-3-methylimidazolium tetrafluoroborate (1) + N-methylformamide or N,N-dimethylformamide (2) binary mixtures at (293.15. 298.15. 303.15, 308.15 K), and excess molar enthalpies, $ H_{12}^{\text{E}} $ H 12 E , of the same mixtures at 298.15 K have been measured over the entire mole fraction range using a density and sound analyzer (Anton Paar DSA-5000) and a 2-drop microcalorimeter, respectively. Excess molar volume, $ V_{12}^{\text{E}} $ V 12 E , and excess isentropic compressibility, $ \left( {\kappa_{S}^{\text{E}} } \right)_{12} $ ( κ S E ) 12 , values have been calculated by utilizing the measured density and speed of sound data. The observed data have been analyzed in terms of: (i) Graph theory and (ii) the Prigogine–Flory–Patterson theory. Analysis of the $ V_{12}^{\text{E}} $ V 12 E data in terms of Graph theory suggest that: (i) in pure 1-ethyl-3-methylimidazolium tetrafluoroborate, the tetrafluoroborate anion is positioned over the imidazoliun ring and there are interactions between the hydrogen atom of (C–H{edge}) and proton of the –CH3 group (imidazolium ring) with fluorine atoms of tetrafluoroborate anion, and (ii) (1 + 2) mixtures are characterized by ion–dipole interactions to form a 1:1 molecular complex. Further, the $ V_{12}^{\text{E}} $ V 12 E , $ H_{12}^{\text{E}} $ H 12 E and $ \left( {\kappa_{S}^{\text{E}} } \right)_{12} $ ( κ S E ) 12 values determined from Graph theory compare well with their measured experimental data.  相似文献   

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