An implicit function theorem: Comment

In Ref. 1, Jittorntrum proposed an implicit function theorem for a continuous mappingF:R ⁿ ×R ^m R ⁿ, withF(x ⁰,y ⁰)=0, that requires neither differentiability ofF nor nonsingularity of _x F(x ⁰,y ⁰). In the proof, the local one-to-one condition forF(·,y):A R ⁿ R ⁿ for ally B is consciously or unconsciously treated as implying thatF(·,y) mapsA one-to-one ontoF(A, y) for ally B, and the proof is not perfect. A proof can be given directly, and the theorem is shown to be the strongest, in the sense that the condition is truly if and only if.     

超分子三维氢键网络：{[Cu(phen)3](SO4)(H3PCA)2(8H2O)}的晶体结构

A new complex， {[Cu(phen)₃](SO₄)(H₃PCA)₂(8H₂O)}， was synthesized and structurally characterized by single-crystal X-ray analysis. The complex is composed of copper cations， sulfate anions， 1，10-phenanthroline， protocatechuic acid and lattice water molecules. The structure of H₃PCA， SO₄^2- and waters comprises packing of anionic three-dimensional network by hydrogen bonds with cavities. The complex can be considered as a model of host/guest supramolecule. The three-dimensional hydrogen-bonding network is the host species. The Cu(phen)₃²⁺ cations， guest species， occupied the cavities of the host. And the results demonstrate that the form of protocatechuic acid at pH< 1 should be free ligand. CCDC： 191733.     

Reaction graphs and a construction of reaction networks

Summary A general definition of reaction graphs is presented. For a pair of isomeric molecular graphs and , related by a chemical transformation , the reaction graph is determined using a maximal common subgraph defined for vertex mapping . A binary operation defined for graphs constructed over the same vertex set enables us to decompose the reaction graph into the sum of prototype reaction graphs. A decomposition of an overall reaction graph can be advantageously used for the construction of a reaction network. An oriented path in this network beginning at and ending at corresponds to a breakdown of the transformation into a sequence of intermediates.     

Application of an artificial neural network (ANN) and piezoelectric chemical sensor array for identification of volatile organic compounds

A piezoelectric chemical sensor array was developed using four quartz crystals. Gas chromatographic stationary phases were used as sensing materials and the array was connected to an artificial neural network (ANN). The application of the ANN method proved to be particularly advantageous if the measured property (mass, concentration, etc.) should not be connected exactly to the signal of the transducers of the piezoelectric sensor. The optimum structure of neural network was determined by a trial and error method. Different structures were tried with several neurons in the hidden layer and the total error was calculated. The optimum values of primary weight factors, learning rate (η=0.15), momentum term (μ=0.9), and the sigmoid parameter (β=1) were determined. Finally, three hidden neurons and 900 training cycles were applied. After the teaching process the network was used for identification of taught analytes (acetone, benzene, chloroform, pentane). Mixtures of organic compounds were also analysed and the ANN method proved to be a reliable way of differentiating the sensing materials and identifying the volatile compounds.     

Supermolecular structures and flow birefringence in polymer solutions

Experimental studies of supermolecular structures and localized flow birefringence in solutions of high-molecular weight polymer are described. Advantage is taken of poly(ethylene oxide) and polyisobutylene. Supermolecular structures are examined with the aid of optical microscopy using freeze-dried samples of the polymer solutions. Birefringence is investigated that arises in planar elongational flow in a cross-slot cell. Flow velocities at which the onset of the localized birefringence occurs are determined. Then these velocities are correlated with viscoelastic characteristics of the solutions. The presence of a liquid-crystalline fibrillar network in the polymer solutions exhibiting flow birefringence is ascertained. The fibrils are birefringent objects. The fibrils are birefringent objects. The localized birefringence phenomenon is explained in term of the orientation of the fibrils in elongational flow. It has been shown that the onset of localized birefringence occurs at a critical Weissenberg number, the value of which is close to unity.     

Solutions of alkali soaps and water in fatty acids IX. The location of theL 2-phase in three-component systems of sodium soap — fatty acid — water,in view of the occurrence of acid soaps

Previous studies of the occurrence of acid soaps in systems containing a longchain sodium soap and the corresponding fatty acid, and the study of phase equilibria in the system sodium octanoate — octanoic acid — water, performed by our group at the beginning of the 1960s, show that the isotropic liquidL ₂-phase of the last mentioned system in its whole region of existence is situated in that part in which acid soaps occur. This provides an explanation for the fact that theL ₂-phase itself contains acid sodium octanoates in all regions. TheL ₂-phase has its origin in the water-free melt of fatty acid and neutral soap in which these components react with each other under the formation of an acid soap. When water is added to the system, this water-free acid soap is transformed into different hydrated acid soaps. In a large region of concentration, there is an extremely close relation between theL ₂-phase and the liquid-crystalline lamellarD-phase, which itself consists of hydrated acid soaps. At its outermost water-rich tip, theL ₂-phase is in equilibrium with theL ₁-phase of the system, just above the+LAC, that is, with the most dilute aqueous soap solution in which acid soap still may be formed in aqueous environment. Formation of acid soap is a fundamental requirement for the existence of this isotropic liquidL ₂-phase.     

Immobilization of α-amylase in vinyl-polymer-based interpenetrating polymer networks

Semi-interpenetrating polymer networks (IPNs) of poly(ethylene glycol), poly(vinyl alcohol) and polyacrylamide were prepared as a support for enzyme immobilization and kinetic studies were performed for the immobilization of -amylase. The effect of IPN composition on the extent of immobilization was investigated and the percentage of relative activity of the immobilized enzyme was evaluated as a function of the chemical architecture of the IPNs, pH and temperature, taking starch as a substrate. The kinetic constants and the maximum reaction velocity were also evaluated. The IPNs were characterized by IR spectral analysis.     

Surface Energy of Silica-TEOS-PDMS Ormosils

Inverse gas chromatography (IGC) was applied to characterize the surface energy of organically modified silicates (ormosils) by measuring the interaction of molecular organic probes with the ormosil surface. Ormosils were prepared by the sol-gel method by the reaction of TEOS (tetraethoxysilane), PDMS (polydimethylsiloxane) and different types of silica (Aerosil 130, Aerosil 200 and Aerosil 380). The isosteric heat of adsorption, q _st, and the dispersive component of the surface energy, _s ^D, were estimated by using the retention volume of different nonpolar and polar probes at infinite dilution. The dispersive component shows an increase as the specific surface area of the silica is increased from 29.6 mJ/m² to 51.4 mJ/m² at 60°C. Such values are lower than that obtained for aerosil particles meaning that PDMS chains impede the interaction with silanol groups located on the silica surface. The specific interaction parameter, I^SP, and the enthalpy of specific adsorption, H _a ^SP, of polar probes on the ormosil surface were also measured in order to obtain the acid-base character of ormosil surface. The H _a ^SP, was correlated with the donor, DN, and the acceptor, AN, numbers of the probes to quantify the acidic, K _A, and the basic, K _B, parameters of the substrate surface. The obtained results suggest that the silica particles were covered by PDMS chains in a different way depending on the type of silica used. The values of K _A and K _B suggest that the ormosil surface is amphoteric, with predominantly acceptor electron sites.     

从溶胀平衡研究玻璃态高聚物的凝聚缠结网络

在13~15℃室温条件下对聚苯乙烯(PS)颗粒在二氧六环/水混合溶剂中的溶胀情况进行目视观察,可以看到,当减小混合溶剂二氧六环/水中的水含量时,PS颗粒从玻璃态到溶胀的玻璃态、溶胀的高弹态、流体态的转变,与PS颗粒升温时从玻璃态到高弹态、流体态的转变相对应.选定混合溶剂二氧六环/水(水6·8wt%)对一个单分散PS试样(Mw=1·68×105)在30℃进行分相平衡和溶胀平衡的测定.分相平衡是先将PS/二氧六环/水(混合溶剂水含量6·8wt%)体系加热到130℃使PS溶解成一均相溶液,然后在冷却过程中分相,在30℃达分相平衡(30天)时,浓相高分子体积浓度p″=0·304,稀相几乎为纯溶剂.从Flory-Huggins相平衡理论得出此体系的高分子-溶剂相互作用参数χ=0·63.本工作使用的单分散PS试样在选定的混合溶剂,即二氧六环/水(水6·8wt%)中,30℃时不能溶解只能溶胀,单分散PS颗粒淬冷试样(密度ρp=1·0451g/mL)到达溶胀平衡(80天)时浓相高分子体积浓度p″=0·308.而此淬冷试样经在80℃热处理100h后的老化试样(ρp=1·0470g/mL)达溶胀平衡(70天)时p″=0·312.从溶胀过程中浓相体积变化曲线可知试样经在80℃热处理过程中凝聚网络趋向于更均一,更接近热处理温度下的平衡态,试样密度增大,网络产生了新的链间凝聚,物理交联密度增大(凝聚点间分子量减小).从溶胀平衡理论并取χ=0·63(分相平衡)可得到淬冷试样的物理交联点间分子量Mc=11·6×104,老化试样的物理交联点间分子量Mc=6·9×104.实验结果说明溶胀过程及溶胀平衡的测定可以反映玻璃态高聚物中的凝聚网络结构的细节,而且非常敏感.     

{[Cu4(nip)4(4，4′-bipy)4(DMF)4]·CH3OH}n配合物的合成与晶体结构

A coordination polymer, {[Cu₄(nip)₄(4，4′-bipy)₄(DMF)₄]·CH₃OH}_n, have been synthesized by the layer method using 5-nitroisophthalic acid (H₂nip), Cu(CH₃COOH)₂ and 4,4′-bipyridine(4,4′-bipy) with three solutions in a marrow tube and structurally characterized by X-ray single-crystal structure analysis. The results indicated that the nip ligand has a μ₂ mono-atomic bridging-monodentate coordination mode and the structure is a two-dimensional network. CCDC: 623420.