The calculation of the detection efficiency in the calibration of gross alpha–beta systems

This paper presents a method for efficiency calibration of a measuring alpha–beta system PROTEAN ORTEC, MPC-2000-DP, using standard radioactive sources. The system is used to measure gross alpha–beta activity concentrations in environmental samples. The calculated efficiencies of detection were subsequently introduced in the system for two working geometries: measuring geometry—gross alpha–beta $ \varepsilon_{\alpha }^{g} $  = 31,37 ± 0.25 (%)—the alpha efficiency and $ \varepsilon_{\beta }^{g} $  = 44.94 ± 0.69 (%)—the beta efficiency, where the spillover factor is $ X_{\text{talk}}^{g} $  = 25.59 ± 0.50 (%) and measuring geometry up alpha–beta $ \varepsilon_{\alpha }^{u} $  = 36.23 ± 0.29 (%)—the alpha efficiency and $ \varepsilon_{\beta }^{u} $  = 48.53 ± 0.74 (%)—the beta efficiency, where the spillover factor is $ X_{\text{talk}}^{u} $  = 31.08 ± 0.60 (%).     

Volumetric Properties of the Nucleoside Thymidine in Aqueous Solution at T = 298.15 K and p = (10 to 100) MPa

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.     

Synergistic extraction of europium and americium into nitrobenzene by using hydrogen dicarbollylcobaltate and bis(diphenylphosphino)methane dioxide

Extraction of microamounts of europium and americium by a nitrobenzene solution of hydrogen dicarbollylcobaltate (H⁺B^?) in the presence of bis(diphenylphosphino)methane dioxide (DPPMDO, L) has been investigated. The equilibrium data have been explained assuming that the species $ {\text{HL}}^{ + } $ , $ {\text{HL}}_{2}^{ + } $ , $ {\text{ML}}_{2}^{3 + } $ , $ {\text{ML}}_{3}^{3 + } $ and $ {\text{ML}}_{4}^{3 + } $ (M³⁺ = Eu³⁺, Am³⁺) are extracted into the organic phase. The values of extraction and stability constants of the species in nitrobenzene saturated with water have been determined. It was found that the stability constants of the corresponding complexes $ {\text{EuL}}_{n}^{3 + } $ and $ {\text{AmL}}_{n}^{3 + } $ , where n = 2, 3 and L is DPPMDO, in water–saturated nitrobenzene are comparable, whereas in this medium the stability of the cationic species $ {\text{AmL}}_{4}^{3 + } $ (L = DPPMDO) is somewhat higher than that of $ {\text{EuL}}_{4}^{3 + } $ with the same ligand L.     

Excess Molar Volumes and Excess Isentropic Compressibilities of o-Toluidine + Tetrahydropyran with Pyridine or Benzene or Toluene Ternary Mixtures at 298.15, 303.15 and 308.15 K

The densities, ρ ₁₂₃, and speeds of sound, u ₁₂₃, of ternary o-toluidine (OT, 1) + tetrahydropyran (THP, 2) + pyridine (Py) or benzene or toluene (3) mixtures have been measured as a function of composition at 298.15, 303.15 and 308.15 K. Values of the excess molar volumes, $ V_{123}^{\text{E}} , $ and excess isentropic compressibilities, $ (\kappa_{\text{S}}^{\text{E}} )_{123} , $ of the studied mixtures have been determined by employing the measured experimental data. The observed thermodynamic properties were fitted with the Redlich–Kister equation to determine adjustable ternary parameters and standard deviations. The $ V_{123}^{\text{E}} $ and $ (\kappa_{\text{S}}^{\text{E}} )_{123} $ values were also analyzed in terms of Graph theory. It was observed that Graph theory correctly predicts the sign as well as magnitude of $ V_{123}^{\text{E}} $ and $ (\kappa_{\text{S}}^{\text{E}} )_{123} $ values of the investigated mixtures. Analysis of the data suggests strong interactions and a more close packed arrangement in OT (1) + THP (2) + Py (3) mixtures as compared to those of the OT (1) + THP (2) + benzene (3) or toluene (3) mixtures. This may be due to the presence of a nitrogen atom in Py which results in stronger interactions for the OT:THP molecular entity as compared to those with benzene or toluene.     

Computer-aided cooling curve thermal analysis of near eutectic Al–Si–Cu–Fe alloy

The effects of bismuth (Bi), antimony (Sb) and strontium (Sr) additions on the characteristic parameters of the evolution of aluminium dendrites in a near eutectic Al–11.3Si–2Cu–0.4Fe alloy during solidification at different cooling rates (0.6–2 °C) were investigated by computer-aided cooling curve thermal analysis (CA-CCTA). Nucleation temperature ( $ T_{\text{N}}^{{\alpha {\text{ - Al}}}} $ ) is defined with a new approach based on second derivative cooling curve. The results showed that $ T_{\text{N}}^{{\alpha {\text{ - Al}}}} $ increased with increasing cooling rate but both the growth temperature ( $ T_{\text{G}}^{{\alpha {\text{ - Al}}}} $ ) and the coherency temperature (T _DCP) decreased. Increase in the temperature difference for dendrite coherency ( $ T_{\text{N}}^{{\alpha {\text{ - Al}}}} - T_{\text{DCP}} $ ) with increasing cooling rate indicate a wider range of temperature before the dendrite can impinge on each other and higher fraction solid ( $ f_{\text{S}}^{\text{DCP}} $ ). Additions of Bi, Sb and Sr to the base alloy produced only a minor effect on $ T_{\text{N}}^{{\alpha {\text{ - Al}}}} $ . Additions of Bi and Sb resulted in an increase in fraction solid and an increase of 30 % in the value of $ T_{\text{N}}^{{\alpha {\text{ - Al}}}} \, - \,T_{\text{G}}^{{\alpha {\text{ - Al}}}} $ to almost 13 °C.     

Study on the Chromatographic Fingerprinting of Schisandra chinensis (Turcz.) Baill. by LC Coupled with Principal Component Analysis

Schisandra chinensis (Turcz.) Baill. is a rich source of lignans with diverse biological activities. Quantitative analysis and chromatographic fingerprinting of the fruitlets of the plant by liquid chromatography (LC) were performed in order to characterize and evaluate the region-related variation. Using the optimized LC method, satisfactory linearity and repeatability were obtained for all the test standards. This method was subsequently applied for the identification and quantitation of six lignans in fruitlets of Schisandra chinensis by comparing the retention time with that of authentic standards available. Principal component analysis (PCA) was also employed to assess the similarity and dissimilarity of the fingerprint profiles from different origins encompassing eleven areas from China and two samples from Japan. The work suggested that the fruitlets of Schisandra chinensis from Japan exhibited great difference with those from China as evidenced by the clear separation in the PCA scores plot as well as quantitative analysis e.g., schisandrin and deoxyschisandrin are 5.50 μg mg^?1 $ (\overline{X} ) $ and 0.90 μg mg^?1 $ (\overline{X} ) $ in the materials from China and 3.40 μg mg^?1 $ (\overline{X} ) $ and 1.90 μg mg^?1 $ (\overline{X} ) $ in the materials from Japan, respectively. Such a reliable method potentially provides an effective and convenient method for quality control of herbal medicine from different regions.     

The dissolution properties of N-guanylurea-dinitramide (FOX-12) in dimethyl sulfoxide (DMSO)

The enthalpy of dissolution of FOX-12 in dimethyl sulfoxide (DMSO) was measured by means of a RD496-III Calvet microcalorimeter at 298.15 K. Empirical formulae for the calculation of the enthalpy of dissolution ( $ \Updelta_{\text{diss}} H $ ), relative partial molar enthalpy ( $ \Updelta_{\text{diss}} H_{\text{partial}} $ ), and relative apparent molar enthalpy ( $ \Updelta_{\text{diss}} H_{\text{apparent}} $ ) were obtained from the experimental data of the enthalpies of dissolution of FOX-12 in DMSO. The kinetic equation that describes the dissolution process of FOX-12 in DMSO at 298.15 K is determined as $ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 8.5 \times 10^{ - 3} (1 - \alpha )^{0.59} $ .     

Study of Malachite Green Fading in Water–Ethanol–Ethylene Glycol Ternary Mixtures

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.     

Thermochemical Properties of n-Undecylammonium Bromide Monohydrate C11H28BrNO(s)

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.     

CORAL: QSPRs of enthalpies of formation of organometallic compounds

Available on the Internet the CORAL software gives reasonable good prediction for standard enthalpy of formation for selected organometallic compounds (n = 132). The approach is tested using five random splits of the considered data into the sub-training set (n = 32–49), calibration set (n = 36–51), test set (n = 10–29), and the validation set (n = 22–41). Compounds of the validation set are not involved in building up the models. The average statistical quality of prediction is the following: correlation coefficient ( $\overline{R^{2}} )$ R 2 ¯ ) $0.991\pm 0.005$ 0.991 ± 0.005 and standard error of estimation ( $\overline{s} )$ s ¯ ) $22.9 \pm 5.6$ 22.9 ± 5.6  kJ/mol.     

Heats of formation of the amino acids re-examined by means of W1-F12 and W2-F12 theories

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.     

A thermodynamic study of complexation of 18-crown-6 with Zn2+, Tl+, Hg2+ and {\text{UO}}^{{{\text{2 + }}}}_{{\text{2}}} cations in acetonitrile-dimethylformamide binary media and study the effect of anion on the stability constant of (18C6-Na+) complex in methanol solutions

The equilibrium constants and thermodynamic parameters for complex formation of 18-crown-6(18C6) with Zn²⁺, Tl⁺, Hg²⁺ and $ {\text{UO}}^{{{\text{2 + }}}}_{{\text{2}}} $ cations have been determined by conductivity measurements in acetonitrile(AN)-dimethylformamide(DMF) binary solutions. 18-crown-6 forms 1:1 complexes [M:L] with Zn²⁺, Hg²⁺ and $ {\text{UO}}^{{{\text{2 + }}}}_{{\text{2}}} $ cations, but in the case of Tl⁺ cation, a 1:2 [M:L₂] complex is formed in most binary solutions. The thermodynamic parameters ( $ \Delta {\text{H}}^{ \circ }_{{\text{c}}} $ and $ \Delta {\text{S}}^{ \circ }_{{\text{c}}} $ ) which were obtained from temperature dependence of the equilibrium constants show that in most cases, the complexes are enthalpy destabilized but entropy stabilized and a non-monotonic behaviour is observed for variations of standard enthalpy and entropy changes versus the composition of AN/DMF binary mixed solvents. The obtained results show that the order of selectivity of 18C6 ligand for these cations changes with the composition of the mixed solvent. A non-linear relationship was observed between the stability constants (logK_f) of these complexes with the composition of AN/DMF binary solutions. The influence of the $ {\text{ClO}}^{ - }_{{\text{4}}} $ , $ {\text{NO}}^{ - }_{{\text{3}}} $ and $ {\text{Cl}}^{ - } $ anions on the stability constant of (18C6-Na⁺) complex in methanol (MeOH) solutions was also studied by potentiometry method. The results show that the stability of (18C6-Na⁺) complex in the presence of the anions increases in order: $ {\text{ClO}}^{ - }_{{\text{4}}} $  >  $ {\text{NO}}^{ - }_{{\text{3}}} $  >  $ {\text{Cl}}^{ - } $ .     

Densities and Volumetric Properties of Butyl Acrylate + 1-Butanol, or +2-Butanol, or +2-Methyl-1-propanol, or +2-Methyl-2-propanol Binary Mixtures at Temperatures from 288.15 to 318.15 K

The densities, ρ, of binary mixtures of butyl acrylate with 1-butanol, 2-butanol, 2-methyl-1-propanol, and 2-methyl-2-propanol, including those of the pure liquids, were measured over the entire composition range at temperatures of (288.15, 293.15, 298.15, 303.15, 308.15, 313.15, and 318.15) K and atmospheric pressure. From the experimental data, the excess molar volume $ V_{\text{m}}^{\text{E}} $ V m E , partial molar volumes $ \overline{V}_{\text{m,1}} $ V ¯ m,1 and $ \overline{V}_{\text{m,2}} $ V ¯ m,2 , and excess partial molar volumes $ \overline{V}_{\text{m,1}}^{\text{E}} $ V ¯ m,1 E and $ \overline{V}_{\text{m,2}}^{\text{E}} $ V ¯ m,2 E , were calculated over the whole composition range as were the partial molar volumes $ \overline{V}_{\text{m,1}}^{^\circ } $ V ¯ m,1 ° and $ \overline{V}_{\text{m,2}}^{^\circ } $ V ¯ m,2 ° , and excess partial molar volumes $ \overline{V}_{\text{m,1}}^{{^\circ {\text{E}}}} $ V ¯ m,1 ° E and $ \overline{V}_{\text{m,2}}^{{^\circ {\text{E}}}} $ V ¯ m,2 ° E , at infinite dilution,. The $ V_{\text{m}}^{\text{E}} $ V m E values were found to be positive over the whole composition range for all the mixtures and at each temperature studied, indicating the presence of weak (non-specific) interactions between butyl acrylate and alkanol molecules. The deviations in $ V_{\text{m}}^{\text{E}} $ V m E values follow the order: 1-butanol < 2-butanol < 2-methyl-1-propanol < 2-methyl-2-propanol. It is observed that the $ V_{\text{m}}^{\text{E}} $ V m E values depend upon the position of alkyl groups in alkanol molecules and the interactions between butyl acrylate and isomeric butanols decrease with increase in the number of alkyl groups at α-carbon atom in the alkanol molecules.     

Thermodynamic study of metal corrosion and inhibitor adsorption processes in copper/N-1-naphthylethylenediamine dihydrochloride monomethanolate/nitric acid system: part 2

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.     

Compound-specific isotope analysis of benzotriazole and its derivatives

Compound-specific isotope analysis (CSIA) is an important tool for the identification of contaminant sources and transformation pathways, but it is rarely applied to emerging aquatic micropollutants owing to a series of instrumental challenges. Using four different benzotriazole corrosion inhibitors and its derivatives as examples, we obtained evidence that formation of organometallic complexes of benzotriazoles with parts of the instrumentation impedes isotope analysis. Therefore, we propose two strategies for accurate $\delta^{13}$ C and $\delta^{15}$ N measurements of polar organic micropollutants by gas chromatography isotope ratio mass spectrometry (GC/IRMS). Our first approach avoids metallic components and uses a Ni/Pt reactor for benzotriazole combustion while the second is based on the coupling of online methylation to the established GC/IRMS setup. Method detection limits for on-column injection of benzotriazole, as well as its 1-CH $_{3}$ -, 4-CH $_{3}$ -, and 5-CH $_{3}$ -substituted species were 0.1–0.3 mM and 0.1–1.0 mM for δ¹³C and δ¹⁵N analysis respectively, corresponding to injected masses of 0.7–1.8 nmol C and 0.4–3.0 nmol N, respectively. The Ni/Pt reactor showed good precision and was very long-lived ( $>$ 1000 successful measurements). Coupling isotopic analysis to offline solid-phase extraction enabled benzotriazole-CSIA in tap water, wastewater treatment effluent, activated sludge, and in commercial dishwashing products. A comparison of $\delta ^{13}$ C and $\delta ^{15}$ N values from different benzotriazoles and benzotriazole derivatives, both from commercial standards and in dishwashing detergents, reveals the potential application of the proposed method for source apportionment.     

Thermodynamic properties of polymorphic forms of theophylline. Part II: The enthalpies of solution in water at 298.15 K

The enthalpies of solution $ \Updelta_{sol}^{{}} H_{m}^{{}} $ of polymorphic forms I and II of theophylline in water at 298.15 K using the isoperibol solution calorimeter have been determined in the range of concentration (0.311–1.547) · 10^?3 /mol · kg^?1. The enthalpies of hydration $ \Updelta_{hyd}^{{}} H_{m}^{o} $ were determined from the experimentally obtained the enthalpies of solution for aqueous solutions and previously determined enthalpies of sublimation $ \Updelta_{s}^{g} H_{m}^{o} . $      

Thermal analysis, phase transitions and molecular reorientations in [Sr(OS(CH3)2)6](ClO4)2

Thermal analysis (TG/DTG/QMS), performed for [Sr(OS(CH₃)₂)₆](ClO₄)₂ in a flow of argon and in temperature range of 295–585 K, indicated that the compound is completely stable up to ca. 363 K, and next starts to decompose slowly, and in the temperature at ca. 492 K looses four (CH₃)₂SO molecules per one formula unit. During further heating [Sr(DMSO)₂](ClO₄)₂ melts and simultaneously decomposes with explosion. Differential scanning calorimetry (DSC) measurements performed in the temperature range of 93–370 K for [Sr(DMSO)₆](ClO₄)₂ revealed existence of the following phase transitions: glass ? crystal phase Cr5 at T _g  ≈ 164 K (235 K), phase Cr5 → phase Cr4 at $ T_{\text{c6}}^{\text{h}} $  ≈ 241 K, phase Cr4 → phase Cr3 at $ T_{\text{c5}}^{\text{h}} $  ≈ 255 K, phase Cr3 → phase Cr2 at $ T_{\text{c4}}^{\text{h}} $  ≈ 277 K, phase Cr2 ? phase Cr1 at $ T_{\text{c3}}^{\text{h}} $  ≈ 322 K and $ T_{\text{c3}}^{\text{c}} $  ≈ 314 K, phase Cr1 ? phase Rot2 at $ T_{\text{c2}}^{\text{h}} $  ≈ 327 K and $ T_{\text{c2}}^{\text{c}} $  ≈ 321 K and phase Rot2 ? phase Rot1 at $ T_{\text{c1}}^{\text{h}} $  ≈ 358 K and $ T_{\text{c1}}^{\text{c}} $  ≈ 347 K. Entropy changes values of the phase transitions at $ T_{\text{c1}}^{\text{h}} $ and $ T_{\text{c2}}^{\text{h}} $ (?S ≈ 79 and 24 J mol^?1 K^?1, respectively) indicated that phases Rot1 and Rot2 are substantially orientationally disordered. The solid phases (Cr1–Cr5) are more or less ordered phases (?S ≈ 7, 10, 4 and 3 J mol^?1 K^?1, respectively). Phase transitions in [Sr(DMSO)₆](ClO₄)₂ were also examined by Fourier transform middle infrared spectroscopy (FT-MIR). The characteristic changes in the FT-MIR absorption spectra of the low- and high-temperature phases observed at the phase transition temperatures discovered by DSC allowed us to relate these phase transitions to the changes of the reorientational motions of DMSO ligands and/or to the crystal structure changes.     

A proposed family of variationally correlated first-order density matrices for spin-polarized three-electron model atoms

In early work of March and Young (Phil Mag 4:384, 1959), it was pointed out for spin-free fermions that a first-order density matrix (1DM) for $N-1$ particles could be constructed from a 2DM ( $\Gamma $ ) for $N$ fermions divided by the diagonal of the 1DM, the density $n(\mathbf{r}_1)$ , as $2\Gamma (\mathbf{r}_1,\mathbf{r}^{\prime }_2;\mathbf{r}_1,\mathbf{r}_2)/n(\mathbf{r}_1)$ for any arbitrary fixed $\mathbf{r}_1$ . Here, we thereby set up a family of variationally valid 1DMS constructed via the above proposal, from an exact 2DM we have recently obtained for four electrons in a quintet state without confining potential, but with pairwise interparticle interactions which are harmonic. As an indication of the utility of this proposal, we apply it first to the two-electron (but spin-compensated) Moshinsky atom, for which the exact 1DM can be calculated. Then the 1DM is found for spin-polarized three-electron model atoms. The equation of motion of this correlated 1DM is exhibited and discussed, together with the correlated kinetic energy density, which is shown explicitly to be determined by the electron density.     

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).     

Heat capacity and density of solutions of calcium and cadmium nitrates in N-methylpyrrolidone at 298.15 K

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.