A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

Fractionation and purification of antioxidant peptides from Chinese sturgeon (Acipenser sinensis) protein hydrolysates prepared using papain and alcalase 2.4L

Protein hydrolysates have the potential to be natural and safer sources of bioactive peptides. In this study, two proteases were used to hydrolyze Chinese sturgeon (Acipenser sinensis) protein, and the hydrolysates were then purified to yield antioxidant peptides. The degree of hydrolysis of 23.56 % and 18.14 % was obtained using papain and alcalase 2.4L, respectivly, and hydrolysates had 96.80 % and 87.24 % total amino acid content, respectivly. The papain hydrolysate (PH) and alcalase 2.4L hydrolysate (AH) showed good antioxidant activity against DPPH^? (IC₅₀ of 3.64 and 3.15 mg/mL) and ABTS^?+ (IC₅₀ of 1.92 and 1.58 mg/mL), respectively. The low-molecular-weight (<1000 Da) fraction of both hydrolysates demonstrated the highest antiradical activity (IC₅₀ of 2.59 and 2.31 mg/mL, DPPH) and (IC₅₀ of 1.54 and 1.36 mg/mL, ABTS), respectively. Nine peptides were separated from both hydrolysates using reverse phase high performance liquid chromatography (RP-HPLC). The IC₅₀ for ABTS^?+ scavenging activity of peptide P5 with valine, glycine and asparagine (MW of 282.13 Da) from PH, and peptide P3 with histidine, glycine and alanine (MW of 302.74 Da) from AH was 0.89 and 0.72 mg/mL, respectively. The fractions and purified peptides obtained from Chinese sturgeon hydrolysates could be utilized as natural antioxidant substitutes in pharmaceuticals and food products.     

Determination of the Enthalpies of Vaporization of Cyclic Organic Peroxides by Correlation of Changes in Gas Chromatographic Retention Times

Liquid and solid cyclic peroxides derived from aliphatic ketones are explosive materials so their enthalpies of vaporization and other thermodynamic or condensed-phase properties cannot be measured directly. In this work the enthalpies of vaporization of peroxides at 298.15 K were estimated simply from gas chromatographic retention times measured at different temperatures. The technique correlates changes in the retention times of compounds whose enthalpies of vaporization are known (called the reference series), with those of the compounds of interest. If t _R′ is the adjusted retention time (retention time of each compound minus the retention time of unretained diethyl ether, used as solvent) a plot of ln t _R′ against 1/T for each compound (reference compounds and cyclic peroxides) results in a straight line (r ² > 0.99 for all compounds). The enthalpy of transfer from solution to the vapor state (Δ_sol^g H _m) can be obtained by multiplying the slope by the gas constant (R). A second plot correlates the enthalpies of transfer from solution to the vapor state (Δ_sol^g H _m), as measured by gas–liquid chromatography (GLC), with enthalpies of vaporization of reference materials (Δ_vap H _m at 298.15 K) available in the literature. C₉–C₁₅ fatty acid methyl esters and hydrocarbons were used as reference compounds. The enthalpies of vaporization of the cyclic organic peroxides were calculated from the equation of the line obtained in this second correlation, the slope of which was Δ_vap H _m (at 298.15 K)/Δ^g _sol H _m. The experiments were performed under isothermal conditions with a DB-5 capillary column, flame-ionization detection (FID), and nitrogen as carrier gas. The column temperature was varied over a range of at least 30–70 K between 403 and 473 K, with chromatograms being acquired at 10 K intervals. Enthalpies of vaporization of cyclic organic peroxides are not available in the literature, and the values given in this paper, obtained by gas chromatography, are the first to be reported.     

Thermal Decomposition of Bi(III), Cd(II), Pb(II) and Cu(II) Thiocyanates

Thermal decomposition of Bi(SCN)₃, Cd(SCN)₂, Pb(SCN)₂ and Cu(SCN)₂ has been studied. The thermal analysis curves and the diffraction patterns of the solid intermediate and final products of the pyrolysis are presented. The gaseous products of the decomposition (SO₂ and CO₂) were detected and quantitatively determined. Thermal, X-ray and chemical analyses have been used to establish the nature of the reactions occurring at each stage in the decomposition.This revised version was published online in November 2005 with corrections to the Cover Date.     

2-Polyfluoroalkylchromones. 9. Synthesis and structures of 5-(2-hydroxyaryl)-7-polyfluoroalkyl-1,4,8-triazabicyclo[5.3.0]dec-4-enes

2-Polyfluoroalkylchromones reacted with diethylenetriamine at 20 °C to form the corresponding 1,4,8-triazabicyclo[5.3.0]dec-4-ene derivatives. The crystal structures of 5-(2-hydroxyphenyl)-7-trifluoromethyl-1,4,8-triazabicyclo[5.3.0]dec-4-ene and 1-(2-aminoethyl)-7-(2-hydroxy-5-methoxyphenyl)-5-(1,1,2,2-tetrafluoroethyl)-2,3-dihydro-1H-1,4-diazepine were established by X-ray diffraction analysis.     

Determination of acidic sites and binding toxic metal ions on cumin surface using nonideal competitive adsorption model

A fundamental study of the application of cumin biomass in the recovery of Cu and Zn metal ion uptake from food and drinks is carried out at different pH's and at fixed ionic strength. The chemical characteristics of protein in cumin seeds were investigated. Results showed that cumin contains 18.25% crude protein, which includes 18 amino acids. The main reactive groups on protein cumin are amino and carboxylic groups of dicarboxylic amino acids, leading to a pH-dependent charge. Therefore, the cumin surface is considered as a heterogeneous system. To describe protonation behavior in a heterogeneous cumin biomass (cumin/0.1 M NaNO(3)) system, acid-base titrations have been performed with conductometric and potentiometric titration. Measurement of the reactivity of cumin surface in the adsorption of Cu and Zn metal ions and determination of metal binding at different pH's were also carried out. To solve broad and ill-defined titration curves, a simplified version of nonideal competitive analysis (NICA) by Plette et al.) was applied. The results show that the sorption of the bivalent metal ions onto the whole surface of cumin could be attributed to a monodentate binding to one site mainly carboxylic-type site.     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Qualitative evaluation of aromatic herbs by direct headspace GC analysis. Applications of the method and comparison with the traditional analysis of essential oils

GC headspace analyses of various aromatizing herbs have been compared with those relating to the essential oils, obtained by steam distillation, of the same plants. In this way it was possible to establish the most significant differences between the composition of a herb flavor and that of its essential oil. In particular, we observed some very volatile compounds in the headspace samples which were absent from the essential oil; these components may make an important contribution to the herb flavor. The identification of these substances is still in progress.     

A Sensitive Spectrophotometric Determination of Nitrite in Water and Soil

A highly sensitive spectrophotometric method for the determination of nitrite in water and soil has been developed. The reaction of nitrite with acidified potassium iodide to liberate iodine which oxidizes leuco‐crystal violet (LCV) to form crystal violet having absorption maxima at 590 nm forms the bases of this method. In aqueous medium the system obeys Beer's law in the range of 0.1 to 1.0 μg per 25 mL (0.004–0.04 ppm), while in an extractive system the range is 0.025–0.25 μg in 100 mL (0.00025–0.0025 ppm). The molar absorptivity and Sandell's sensitivity were found to be 1.54 × 10⁶ 1 mol^?1 cm^?1 and 44 pg cm^?2, respectively.