Mobility of water molecules in Li+, Na+ and Cs+ ionic forms of Nafion membrane studied by NMR

Correlation times and diffusion coefficients of water molecules were measured for the first time by ¹H spin relaxation and pulsed field gradient NMR in Li⁺, Na⁺ and Cs⁺ ionic forms of Nafion 117 membrane. Hydration numbers of Li⁺, Na⁺ and Cs⁺ cations were calculated. It was shown that at high humidity macroscopic transfer is controlled by the local translational motion of water molecules.     

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Theoretical studies on the influence of metallic cations on ring opening of propylene oxide catalyzed by metal-salen complexes

We studied the ring opening of propylene oxide (PO) by salen-M coordinated OH⁻ group [M = Al(III), Sc(III), Cr(III), Mn(III), Fe(III), Co(II), Co(III), Ni(II), Cu(II), Zn(II), Ru(III) and Rh(III)]. The results show that the ring-opening energy barriers for M(II) complexes are much lower than those with M(III) complexes in the gas phase, and the barriers correlate linearly with the negative charges on the OH⁻ group and the Fukui function condensed on the OH⁻ group. The nucleophilicity ordering in the gas phase can be rationalized by the ratio of formal positive charges/radius of M cations. Solvent effect greatly increases the barriers of M(II) complexes but slightly changes the results of M(III) ones, making the barriers similar. Analysis indicates that the reaction heats are linearly proportional to the reverse reaction barriers. The relationships established here can be used to estimate the ring-opening barriers and to screen epoxide ring-opening catalysts.     

Phase transition in the one-dimensional pair-hopping model with unusual one-electron hopping

By modifying the conventional one-electron hopping behavior, we study effects of an occupation-dependent hopping on the ground state of the half-filled one-dimensional pair-hopping model. At weak coupling, the use of bosonization and renormalization-group analysis techniques helps to derive the phase diagram. Such unusual hopping is shown to drive a spin-gap transition and to introduce a new region where the triplet superconducting instability dominates for positively small pair-hopping interaction.     

Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores

In this paper, we describe a result on self-conjugate $(s,s+1)$-core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of $(\stackrel{￣}{s},\stackrel{￣}{s+1})$-core partitions and the number of $(s,s+1)$-core shifted Young diagrams with the fixed number of shifted corners.     

Measured and Predicted Solubility Phase Diagrams of Quaternary Systems LiBr-NaBr-MgBr2-H2O and LiBr-KBr-MgBr2-H2O at 298.15 K

The stable phase equilibria of quaternary systems LiBr-NaBr-MgBr₂-H₂O and LiBr-KBr-MgBr₂-H₂O at 298.15 K were studied by both experimental measurement(isothermal solution saturation method) and theoretical prediction(Pitzer model). The solubilities of the saturated solution have been determined experimentally and two stable phase diagrams and relevant water diagrams of the two quaternary systems were obtained. Results show that quaternary system LiBr-NaBr-MgBr₂-H₂O is hydrate II type as NaBr and NaBr·2H₂O coexistence. Its phase diagram consists of only one invariant point, four univariant curves, and five crystallization fields. The quaternary system LiBr-KBr-MgBr₂-H₂O is a complex type as the double salt KBr·MgBr₂·6H₂O formed. In addition to this double salt, the three single salts LiBr·2H₂O, KBr and MgBr₂·6H₂O also crystallize. In this paper, the solubilities of phase equilibria in above quaternary systems were also calculated by the Pitzer's electrolyte solution model. All the needed parameters can be obtained from the literature or be fitted by experimental data. On the Basis of the experimental and calculated results, the phase diagram of the quaternary system was plotted for comparison. It shows that the calculation results are consistent with the experimental ones.