Solubility and metastable zone width of DL‐tartaric acid in aqueous solution

Solubility and metastable zone width (MSZW) of DL‐tartaric acid (DL‐TA) in aqueous solution have been determined. Solubility of DL‐TA was measured in the temperature range from 0 to 50 °C at atmospheric pressure by means of the conventional polythermal method using Turbidity Monitoring Technique, which was verified by a gravimetric method. The dissolution enthalpy and entropy of DL‐TA were then calculated from the solubility data using van't Hoff equation. Two approaches was used to estimate the nucleation kinetics from the measured metastable zone width data, the self‐consistent approach and the approach based on 3D nucleation. In addition, the metastable zone width slightly decreases with increasing agitation rate and was independent of working volume.     

A FPTAS for computing a symmetric Leontief competitive economy equilibrium

In this paper, we consider a linear complementarity problem (LCP) arisen from the Nash and Arrow–Debreu competitive economy equilibria where the LCP coefficient matrix is symmetric. We prove that the decision problem, to decide whether or not there exists a complementary solution, is NP-complete. Under certain conditions, an LCP solution is guaranteed to exist and we present a fully polynomial-time approximation scheme (FPTAS) for approximating a complementary solution, although the LCP solution set can be non-convex or non-connected. Our method is based on approximating a quadratic social utility optimization problem (QP) and showing that a certain KKT point of the QP problem is an LCP solution. Then, we further show that such a KKT point can be approximated with a new improved running time complexity ${{O}((\frac{n^4}{\epsilon})\log\log(\frac{1}{\epsilon}))}$ arithmetic operation in accuracy ${\epsilon \in (0,1)}$ . We also report preliminary computational results which show that the method is highly effective. Applications in competitive market model problems with other utility functions are also presented, including global trading and dynamic spectrum management problems.     

Subgraph extraction and metaheuristics for the maximum clique problem

The maximum clique problem involves finding the largest set of pairwise adjacent vertices in a graph. The problem is classic but still attracts much attention because of its hardness and its prominent applications. Our work is based on the existence of an order of all the vertices whereby those belonging to a maximum clique stay close enough to each other. Such an order can be identified via the extraction of a particular subgraph from the original graph. The problem can consequently be seen as a permutation problem that can be addressed efficiently by metaheuristics. We first design a memetic algorithm (MA) for this purpose. Computational experiments conducted on the DIMACS benchmark instances clearly show that our MA not only outperforms existing genetic approaches, but it also compares very well to state-of-the-art algorithms regarding the maximal clique size found after different runs. Furthermore, we show that a hybridization of MA with an iterated local search (ILS) improves the stability of the algorithm. This hybridization (MA-ILS) permits to find two distinct maximal cliques of size 79 and one of size 80 for the C2000.9 instance of the DIMACS benchmark.     

Exact solutions of a two-fluid model of two-phase compressible flows with gravity

We aim at determining and computing a class of exact solutions of a two-fluid model of two-phase flows with/without gravity. The model is described by a non-hyperbolic system of balance laws whose characteristic fields may not be given explicitly, making it perhaps impossible to solve the Riemann problem. First, we investigate Riemann invariants in the linearly degenerate characteristic fields and obtain a surprising result on the corresponding contact waves of the model without gravity. Second, even when gravity is allowed, we show that smooth stationary solutions can be governed by a system of differential equations in divergence form, which determines jump relations for any stationary discontinuity wave. Using these relations, we establish a nonlinear equation for the pressure and propose a method to compute the pressure and then the equilibria resulted by a stationary wave.     

New class of Preyssler-lanthanide complexes with modified and extended structures tuned by the lanthanide contraction effect

A family of polyoxometalate compounds based on Preyssler anions and lanthanide cations, K(5)Na(5)[{Pr(4)(H(2)O)(12)(pydc)(4)}{Na(H(2)O)P(5)W(30)O(110)}]·46H(2)O (1, H(2)pydc = pyridine-2,6-dicarboxylic acid), Na(7)[{Pr(4)(H(2)O)(20)(pydc)(2)(Ac)}{Na(H(2)O)P(5)W(30)O(110)}]·23H(2)O (2), and Na(10)H(2) [{Ln(2)(H(2)O)(10)(pydc)(2)}{Na(H(2)O)P(5)W(30)O(110)}]·XH(2)O (Ln = Sm 3, Eu 4, Gd 5; X = 11 for 3 and 5, 13 for 4), have been synthesized and characterized by elemental analysis and single crystal X-ray diffraction. Compound 1 exhibits a two-dimensional honeycomb layer which is built up from unique {Pr(4)} metallacycles and Preyssler anions. Remarkably, the strong involvement of the sodium countercations leads to the formation of a unique three-dimensional open architecture with one-dimensional channels. The 2D grid layer of compound 2 is constructed by the longest currently known rare-earth metal clusters {Pr(8)} and Preyssler anions. Isostructural compounds 3, 4, and 5, obtained by introduction of the intermediate lanthanide ions into the above reaction system, exhibit bisupporting [{Ln(2)(H(2)O)(10)(pydc)(2)}{Na(H(2)O)P(5)W(30)O(110)}](12-) polyoxometalate cluster structures. The magnetic properties of compounds 1 and 2 and the luminescent properties of compounds 3 and 4 are discussed in this paper.     

Novel flavanes from Livistona halongensis

A study of the chemical constituents of a methanolic extract of the roots of Livistona halongensis (Arecaceae) led to the isolation of two new flavanes, 2S,3S-3,5,7,3'-tetrahydroxy-5'-methoxyflavane (1) and 3,7,3'-trihydroxy-5'-methoxyflavane 5-O-beta-glucopyranoside (2), together with trans-3,5,3',5'-tetrahydroxy-4-methoxystilbene, saccharose and beta-sitosterol-3-O-beta-glucopyranoside. The structures of these compounds were elucidated on the basis of spectroscopic data.     

Swelling properties of pH‐responsive hydrophobically modified hydrogels of poly(methacrylic acid‐co‐diallylammonium salt) in aqueous solution

Using diallylmethyl alkyl ammonium salts (CCX) (X is alkyl's chain length, represents 12, 14, 16, and 18, respectively) as a comonomer of methacrylic (MAA), hydrophobically modified hydrogels of poly diallylmethyl alkyl ammonium salts‐methacrylic acid (PCCX‐MAA) were prepared by free radical copolymerization in aqueous solution. The synthetic conditions, such as dosage of cross‐linking agent, reaction concentration and length of alkyl chain were studied in detail. Results indicated that the swelling degree of hydrogels was decreased with dosage of cross‐linking agent, or monomer concentration increased at different pH. Incorporation of the different length of alkyl chain hydrophobic CCX units on PMAA chains by random distribution can change reswelling kinetics. The required time for reaching equilibrium swelling state was longest for PCC16‐MAA. Copyright © 2011 John Wiley & Sons, Ltd.     

Computational studies on ethylene addition to nickel bis(dithiolene)

The density functionals B3LYP, B3PW91, BMK, HSE06, LC-ωPBE, M05, M06, O3LYP, TPSS, ω-B97X, and ω-B97XD are used to optimize key transition states and intermediates for ethylene addition to Ni(edt)(2) (edt = S(2)C(2)H(2)). The efficacy of the basis sets 6-31G**, 6-31++G**, cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ is also examined. The geometric parameters optimized with different basis sets and density functionals are similar and agree well with experimental values. The ω-B97XD functional gives relative energies closest to those from CCSD, while M06 and HSE06 yield results close to those from CCSD(T). CASSCF and CASSCF-PT2 calculation results are also given. Variation of the relative energies from different density functionals appears to arise, in part, from the multireference character of this system, as confirmed by the T1 diagnostic and CASSCF calculations.