Isentropic partial molal compressibilities of alcohols in propylene carbonate at 25°C

The isentropic coefficients of compressibility of the homologous series of alcohols and diols R _n CH₂OH (n=2–6), CH₃CHOHR _n (n=1–5), 1,2-propanediol, 1,3- 1,4- and 2,3-butanediol, 1,5-pentanediol, and 1,7-heptanediol dissolved in propylene carbonate have been measured at 25°C. Isentropic partial molal compressibilities and group partial molal compressibilities at infinite dilution have been evaluated. The isentropic partial molal compressibilities of these alcohols and diols have been compared with the corresponding values in water. This comparison shows that the values in propylene carbonate are higher than in water by a factor of 10 due to an increased compressibility of the solvation sheath around nonpolar groups in PC.     

SYNTHESIS AND CHARACTERIZATION OF PHTHALAZINONE POLY(ARYL ETHER SULFONE KETONE)WITH CARBONYL GROUP*

A kind of novel heat-resistant, high performance engineering thermoplastic phthalazinone poly(aryl ether sulfoneketone) (PPESK) containing a carboxyl group in its side chain was prepared by the nucleophilic displacement reaction of 4-(4-hydroxylphenyl)-1(2H)-phthalazinone with di(4-chlorophenyl) sulfone, 4,4'-difluoro-benzophenone and phenolphthalin insulfolane in the presence of K_2CO_3 to produce high molecular weight polymers which can be dissolved in some polarsolvents such as chloroform and nitrobenzene at room temperature and can be easily can into flexible, yellowish andtransparent films. PPESK is an amorphous polymer having a decomposition temperature above 400℃, which indicates that ithas high thermal stability. At the same time, the thermal properties of PPESKs with dicyandiamide (DICY) as curing agentindicated that the heat-resistance properties of the PPESKs are improved after curing. The apparent activation energy (ΔE) ofthe cross-linking reaction and the reaction order (n) of PPESK/DICY were found to be 52.2 kJ/mol and ca. 1.0, respectively.Therefore, the cross-linking reaction is approximately a first order reaction.     

The computation of the representation matrices of the generators of the unitary group

A method is presented for the efficient computation of the representation matrices of the unitary group, U(n) in the Gelfand—Tsetlin basis (corresponding to the usual spin-symmetry adapted basis for an N electron CI). The present scheme is conceptually and computationally attractive in that it is formulated directly in terms of Weyl tableaux and also that it permits simultaneous basis vector generation and matrix element evaluation. In addition the basis vectors are ordered so that subsequent restriction to the three dimensional rotation group is facilitated. An illustrative example is also presented.Taken in part from a thesis submitted to the University of London in partial fulfilment of the requirements for the degree of PhD.     

New functional microspheres with active succinimide groups

Radiation-induced polymerization of monomers, for example N-methacryl-oxysuccinimide (MASu) and diethylene glycol dimethacrylate (2G), in ethyl propionate, was performed from +25°C to –78°C. The copoly (MASu/2G) microspheres were obtained in MASu monomer compositions of 30 wt % or below. The average particle diameter of copoly(MASu/2G, 20/80 wt %) microspheres obtained at irradiation temperatures of 25°, 0°, and –43 °C were 0.81±0.29, 0.63±0.26, and 0.90±0.43 m, respectively. No microspheres were formed when irradiated at –78 °C. The reactivity of the succinimide groups on the surface of copoly(MASu/2G, 20/80 wt%) microspheres was checked by reacting with ethylene diamine. The maximal amount of reacting succinimide groups was 9.4±0.5 nol/g, which corresponds to about 1 % of the total number of succinimide groups in the microsphere.     

Regio- and stereoselective reactions of a rhodanine derivative with optically active 2-methyl- and 2-phenyloxirane

The reaction of a rhodanine derivative (=(Z)-5-benzylidene-3-phenyl-2-thioxo-1,3-thiazolidin-4-one; 1) with (S)-2-methyloxirane (2) in the presence of SiO₂ in dry CH₂Cl₂ for 10 days led to two diastereoisomeric spirocyclic 1,3-oxathiolanes 3 and 4 with the Me group at C(2) (Scheme 2). The analogous reaction of 1 with (R)-2-phenyloxirane (5) afforded also two diastereoisomeric spirocyclic 1,3-oxathiolanes 6 and 7 bearing the Ph group at C(3) (Scheme 3). The structures of 3, 4, 6, and 7 were confirmed by X-ray crystallography (Figs. 1 and 2). These results show that oxiranes react selectively with the thiocarbonyl group (CS) in 1. Furthermore, the nucleophilic attack of the thiocarbonyl S-atom at the SiO₂-activated oxirane ring proceeds with high regio- and stereoselectivity via an S_N2-type mechanism.     

Variational approximations for renormalization group transformations

Approximate recursion relations which give upper and lower bounds on the free energy are described. Optimal calculations of the free energy can then be obtained by treating parameters within the renormalization equations variationally. As an example, a particularly simple lower bound approximation which preserves the symmetry of the Hamiltonian (the one-hypercube approximation) is described. The approximation is applied to both the Ising model and the Wilson-Fisher model. At the fixed point a parameter is set variationally and critical indices are calculated. For the Ising model the agreement with the exact results atd = 2 is surprisingly good, 0.1%, and is good atd=3 and evend=4. For the Wilson-Fisher model the recursion relation is reduced to a one-dimensional integral equation which can be solved numerically givingv=0.652 atd=3, or by expansion in agreement with the results of Wilson and Fisher to leading order in . The method is also used to calculate thermodynamic functions for thed = 2 Ising model; excellent agreement with the Onsager solution is found.Supported in part by the National Science Foundation under Grants Nos. MPS73-04886A01 and GH-41512 and by the Brown University Materials Research Laboratory supported by the National Science Foundation. M.C.Y. was supported by a grant from the Scientific and Technical Research Council of Turkey.     

Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call it M-homotopy), discuss its properties and applications. They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001. The difference between them is that the weak graph map homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over the graph homotopy transformation. As its applications, they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph. Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.     

Surface Modification Strategy for Enhanced NO2 Capture in Metal–Organic Frameworks

The interaction strength of nitrogen dioxide (NO₂) with a set of 43 functionalized benzene molecules was investigated by performing density functional theory (DFT) calculations. The functional groups under study were strategically selected as potential modifications of the organic linker of existing metal–organic frameworks (MOFs) in order to enhance their uptake of NO₂ molecules. Among the functional groups considered, the highest interaction energy with NO₂ (5.4 kcal/mol) was found for phenyl hydrogen sulfate (-OSO₃H) at the RI-DSD-BLYP/def2-TZVPP level of theory—an interaction almost three times larger than the corresponding binding energy for non-functionalized benzene (2.0 kcal/mol). The groups with the strongest NO₂ interactions (-OSO₃H, -PO₃H₂, -OPO₃H₂) were selected for functionalizing the linker of IRMOF-8 and investigating the trend in their NO₂ uptake capacities with grand canonical Monte Carlo (GCMC) simulations at ambient temperature for a wide pressure range. The predicted isotherms show a profound enhancement of the NO₂ uptake with the introduction of the strongly-binding functional groups in the framework, rendering them promising modification candidates for improving the NO₂ uptake performance not only in MOFs but also in various other porous materials.     

概率语言多属性群决策方法及其在新型智慧城市市民获得感评价中的应用

针对公众参与的语言信息多属性群决策问题,研究了考虑参与者满意度的概率语言多属性群决策方法。首先,根据参与者的语言评价信息确定并规范化概率语言决策矩阵。然后,对大群体进行共识分析,由最大化参与者群体的满意度构建线性规划模型,确定参与者群组的权重;构造正、负理想方案的评价向量,构建多目标规划模型,用拉格朗日乘子法求解属性权重;定义各方案的加权贴近度,并以此对方案进行排序和优选。最后,通过新型智慧城市市民获得感评价案例验证了模型的可行性和有效性。     

Perturbative Power Counting,Lowest-Index Operators and Their Renormalization in Standard Model Effective Field Theory

We study two aspects of higher dimensional operators in standard model effective field theory.We first introduce a perturbative power counting rule for the entries in the anomalous dimension matrix of operators with equal mass dimension.The power counting is determined by the number of loops and the difference of the indices of the two operators involved,which in turn is defined by assuming that all terms in the standard model Lagrangian have an equal perturbative power.Then we show that the operators with the lowest index are unique at each mass dimension d,i.e.,(H~?H)~(d/2)for even d≥4,and(L~TεH)C(L~TεH)~T(H~?H)~((d-5)/2)for odd d≥5.Here H,L are the Higgs and lepton doublet,andε,C the antisymmetric matrix of rank two and the charge conjugation matrix,respectively.The renormalization group running of these operators can be studied separately from other operators of equal mass dimension at the leading order in power counting.We compute their anomalous dimensions at one loop for general d and find that they are enhanced quadratically in d due to combinatorics.We also make connections with classification of operators in terms of their holomorphic and anti-holomorphic weights.