On Equivalence Relations in Ordered Sets

A relationship between equivalence relations in finite ordered sets and linear decompositions is presented.     

A quadratically convergent local algorithm on minimizing sums of the largest eigenvalues of a symmetric matrix

In this paper, we consider the problem on minimizing sums of the largest eigenvalues of a symmetric matrix which depends on the decision variable affinely. An important application of this problem is the graph partitioning problem, which arises in layout of circuit boards, computer logic partitioning, and paging of computer programs. Given 0, we first derive an optimality condition which ensures that the objective function is within error bound of the solution. This condition may be used as a practical stopping criterion for any algorithm solving the underlying problem. We also show that, in a neighborhood of the minimizer, the optimization problem can be equivalently formulated as a smooth constrained problem. An existing algorithm on minimizing the largest eigenvalue of a symmetric matrix is shown to be applicable here. This algoritm enjoys the property that if started close enough to the minimizer, then it will converge quadratically. To implement a practical algorithm, one needs to incorporate some technique to generate a good starting point. Since the problem is convex, this can be done by using an algorithm for general convex optimization problems (e.g., Kelley's cutting plane method or ellipsoid methods), or an algorithm specific for the optimization problem under consideration (e.g., the algorithm developed by Cullum, Donath, and Wolfe). Such union ensures that the overall algorithm has global convergence with quadratic rate. Finally, the results presented in this paper are readily extended on minimizing sums of the largest eigenvalues of a Hermitian matrix.Some of results in this paper were given in [19] without proofs.     

Distribution for fermionic discrete lattice gas within the canonical ensemble

The distinct deviations from the Fermi-Dirac statistics ascertained recently at low temperatures for a one-dimensional, spinless fermionic discrete lattice gas with conserved number of noninteracting particles hopping on the non-degenerated, well-separated single-particle energy levels are studied in numerical and theoretical terms. The generalized distribution is derived in the formn(h)={Y _h exp [(_h–)]+1{su–1 valid even in the thermodynamic limit, when the discreteness of the energy levels is kept. This distribution demonstrates good agreement with the data obtained numerically both by the canonical partition function technique and by Monte Carlo simulation.     

一个新的连接性指数对脂肪醇的QSPR/QSAR研究

在分子拓扑理论的基础上 ,提出了一个新的连接性指数nχz,并用 nχz 研究了脂肪醇化合物在水中的溶解度 (Sw)、正辛醇 /水分配系数 (Kow)及对水生生物急性毒性 (-LC50 ) ,给出了相关方程 ,研究结果表明 ,相关性良好 ,新方法计算方便 ,物理意义明确 ,预测值与相应的实验值较吻合     

Influence of surfactant vesicles and their polymerization on the complex formation between indoleacetate and methylviologen

 The association constant K between methylviologen MV and indoleacetate IA was decreased by the addition of cationic vesicles, and the K increased at high vesicle concen-trations. The influence of the polymerization of surfactants with different chain lengths on K was different. The concentration dependence of K was analyzed by a theory in terms of the partition coefficients of reactants between the bulk solvent phase and the local vesicle environment. The theoretical partition coefficients were determined graphically. The measured depen-dence of K on vesicle concentration was satisfactorily reproduced by the theory. When dimyrystyldiallylammonium bromide (DMAB) was added to the complex, the polymerization of the surfactant increased the partition coefficients of IA and the complex but decreased that of MV. However, the polymerization of dicetyldiallylammonium bromide (DCAB) showed the reverse tendency. The influence of polymerization on K or the partition coefficient was discussed in terms of the difference in the polymerization mechanism due to the differences in the distance between the neighboring nonpolymerized surfactant molecules and the polymerization induced change in that distance. Received: 10 May 1996 Accepted: 27 August 1996     

Atoms-in-molecules from the Stockholder Partition of the Molecular Two-electron Distribution

The effective one-electron distributions of bonded atoms obtained from the “stockholder” partition of the molecular two-electron density are reported. These two-electron stockholder (S) atoms are compared with their one-electron analogs represented by the corresponding Hirshfeld (H) one-electron stockholder pieces of the molecular electron density. The influence of the exchange (Fermi) and Coulomb correlation between electrons on the resultant shapes of bonded atoms is investigated The vertical (for the fixed molecular electron density) and horizontal (involving the electron density displacement) correlation influences on the two-electron stockholder atoms are examined. The two sets of bonded stockholder atoms in the near-dissociation bond-elongated diatomics are compared for different approximations of the electron correlation effects. The cluster components in atomic resolution of the S-partitioning scheme are investigated for illustrative homonuclear and heteronuclear diatomics: H₂, LiH, HF, LiF, and N₂. This framework facilitates an understanding of the origins of the observed differences between the S and H variants of Atoms-in-Molecules. With the exception of hydrogen atoms, especially in light molecules, the two sets of bonded atoms were found to be practically identical. For H₂ and LiH the S atoms were shown to exhibit a distinctly higher degree of the bonding character, compared to their H analogs. The main electron correlation effects have been found to be well represented already at the exchange-only level, e.g., in the unrestricted Hartree–Fock (UHF) theory. An inclusion of the extra vertical Coulomb correlation exerts a marginal moderating influence on the ionic/covalent composition of the chemical bond already predicted by the UHF approximation, in the direction of a slightly more covalent (less ionic) bond character. The horizontal shifts of the molecular density due to Coulomb correlation, relative to the UHF reference, often act in the opposite direction.     

1‐Octanol/Water Partition Coefficients of 1Alkyl‐3‐methylimidazolium Chloride

The solubilities of 1alkyl‐3‐methylimidazolium chloride, [C_nmim][Cl], where n=4, 8, 10, and 12, in 1octanol and water have been measured by a dynamic method in the temperature range from 270 to 370 K. The solubility data was used to calculate the 1octanol/water partition coefficients as a function of temperature and alkyl substituent. The melting point, enthalpies of fusion, and enthalpies of solid–solid phase transitions were determined by differential scanning calorimetry, DSC. The solubility of [C_nmim][Cl], where n=10 or 12 in 1octanol is comparable and higher than that of [C₄mim][Cl] in 1octanol. Liquid 1n‐octyl‐3‐methylimidazolium chloride, [C₈mim][Cl], is not miscible with 1octanol and water, consequently, the liquid–liquid equilibrium, LLE was measured in this system. The differences between the solubilities in water for n=4 and 12 are shown only in α₁ and γ₁ solid crystalline phases. Additionally, the immiscibility region was observed for the higher concentration of [C₁₀mim][Cl] in water. The intermolecular solute–solvent interaction of 1butyl‐3‐methylimidazolium chloride with water is higher than for other 1alkyl‐3‐methylimidazolium chlorides. The data was correlated by means of the UNIQUAC ASM and two modified NRTL equations utilizing parameters derived from the solid–liquid equilibrium, SLE. The root‐mean‐square deviations of the solubility temperatures for all calculated data are from 1.8 to 7 K and depend on the particular equation used. In the calculations, the existence of two solid–solid first‐order phase transitions in [C₁₂mim][Cl] has also been taken into consideration. Experimental partition coefficients (log P) are negative at three temperatures; this is evidence for the possible use of these ionic liquids as green solvents.     

Interfacial tension of alkylglucosides in different APG/oil/water systems

The interfacial performance of pure alkylglucosides (C₈G₁, C₁₀G₁ and C₁₂G₁) and of technical grade alkylpolyglucoside (APG) surfactants was investigated in three different water/oil systems (decane, isopropylmyristate and 2-octyldodecanol). From the dependence of the interfacial tension on the surfactant concentration below the CMC the cross-sectional area of the molecules at the decane/water interface was estimated. The plateau values of the interfacial tension at the CMC _c are independent of temperature and almost independent of added electrolyte in the decane/water system. The ability of the surfactants to lower the oil/water interfacial tension is most pronounced for the nonpolar oil. The partition coefficient of the surfactant between oil and water phase (k _c) was estimated from the CMC and the observed break point of the interfacial tension after equilibration of the two phases. In decane/water,k _c is nearly zero for all surfactants studied. For the polar oils,k _c increases with the chain length of the surfactant up tok _c10 for C₁₂G₁ in octyldodecanol/water. The values of _c in the different oil/water systems appear to be correlated withk _c and exhibit a minimum neark _c=1.     

Horseradish peroxidase extraction and purification by aqueous two-phase partition

The effect of poly(ethyleneglycol) (PEG) molecular weight, system pH, and sodium chloride concentration on the partitioning behavior of horseradish peroxidase fromArmomcia rusticana root extract was investigated in poly(ethyleneglycol)/sodium phosphate systems. PEG molecular weight strongly affects the enzyme partition coefficient, whereas pH variation from 5.5 to 8.0 has little effect. The addition of sodium chloride (8% w/w) to a PEG 1540/phosphate system, pH 7.0, raises the peroxidase partition coefficient 13.5-fold without important changes in that of total horseradish root proteins. Moreover, these conditions allow direct homogenization of theA. rusticana roots with the selected aqueous two-phase system with the clear top phase containing over 90% of the enzyme and the purification factor being 4.8.     

Identification and thermodynamic treatment of several types of large-amplitude motions

We present a partially automated method for the thermodynamic treatment of large-amplitude motions. Starting from the molecular geometry and the Hessian matrix, we evaluate anharmonic partition functions for selected vibrational degrees of freedom. Supported anharmonic vibration types are internal rotation and inversion (oscillation in a double-well potential). By heuristic algorithms, we identify internal rotations in most cases automatically from the Hessian eigenvectors, and we also estimate the parameters of anharmonic partition functions (e.g., potential barrier, periodicity, and symmetry number) with thermodynamically sufficient precision. We demonstrate the validity of our schemes by comparison to pointwise calculated ab initio potential curves.