The extent of molecular orientation at liquid/vapor interface of pyridine and its alkyl derivatives by molecular dynamics simulation

In this paper, molecular dynamics simulation was performed to investigate the liquid∕vapor interfacial structure of neat polar liquids. Large-scale ensembles of liquid pyridine and its alkyl derivatives, 4-methylpyridine and 4-ethylpyridine, were simulated by classical molecular dynamics at 298 K. For the liquid system of low polarity, the surface density profile of the atoms meet exactly at the middle of interfacial region, and atoms of hydrophobic nature can be hardly discriminated from hydrophilic ones in either vapor or liquid sides. For a liquid system of high polarity, the density profile of atoms with different nature is highly discriminated all over the interfacial region, and as the polarity increases, a dense region of atomic density is clearly developed in the subsurface region. The recognized bivariate method was also used to study the molecular orientational distribution quantitatively. Orientational analysis of the three liquid systems indicates that the pyridine ring plane in the outmost surface tends to be vertical. Its tendency in the innermost interfacial region is parallel. The orientational states available to 4-ethylpyridine and pyridine are discriminated by predicting the possibility of a bisector-wise tumbling for the ring plane in pyridine and a side-wise tumbling in 4-ethylpyridine. The orientational distribution maps explain the trend of experimental surface tension and surface entropy. As the dipole moment of these liquids increases with the alkyl chain length, the surface structural profile changes from a regular definite one to a surface of complex atomic structure involving a dense phase near the interface. The development of dense region in alkyl derivatives is the result of segregation of molecules due to the alkyl group, which is captured and discriminated by molecular dynamics simulation even when the length of a short alkyl chain is increased by one carbon atom.     

Students’ ways of understanding a proof

We present a model for describing the growth of students’ understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important transitions in this path. The other path focuses on the surface-level form of the proof, and the use of symbolic representations. At the end of this path, students understand how and why symbolic computations formally establish a claim, at a syntactic level. We make distinctions between states in the model and illustrate them with examples from early secondary students’ mathematical activity. We then apply the model to one student’s developing understanding in order to show how the model works in practice. We close with some suggestions for further research.     

Highly Efficient,Four Component,One-pot Synthesis of Tetrasubstituted Imidazoles Using a Catalytic Amount of FeCl<Subscript>3</Subscript> · 6H<Subscript>2</Subscript>O

Summary. An efficient and improved procedure for the synthesis of tetrasubstituted imidazoles by FeCl₃ · 6H₂O catalyzed four-component one-pot synthesis in refluxing ethanol is described.     

Preparation of Co3O4 nanoparticles by nonhydrolytic thermolysis of [Co(Pht)(H2O)]n polymers

Benzenedicarboxylate complexes, especially phthalate ones, can be significant precursors for the preparation of nano-sized metal and metal oxides. The injection of organic surfactants such as oleic acid (OA) and triphenylphosphine into molecular precursors has yielded samples with size control, narrow size distributions and crystallinity of individual nanocrystals. Fourier transform infrared and X-ray photoelectron spectroscopy revealed that the OA molecules were adsorbed on the ferromagnetic nanoparticles by chemisorption. The temperature-dependent magnetization curve in zero-field-cooled and field-cooled exhibit weak ferromagnetism of the Co₃O₄ nanoparticles. At 300 K the remanent magnetization is 0.02 emu/g, the coercive field is 441 Oe and the magnetization at saturation is 1.05 emu/g.     

Tunable optical filter based on Sagnac phase-shift using single optical ring resonator

In this paper, a single optical ring resonator connected to a Sagnac loop is used to demonstrate theoretically a novel narrow band optical filter response that is based on Sagnac phase-shift Δφ. The given filter structure permits the Sagnac rotation to control the filter response. It is shown that by changing the Sagnac rotation rate, we can tune the filter response for desired bandwidths. To increase the wavelength selectivity of the filter, the Sagnac phase-shift should be as small as possible that is limited by the loop length. For Δφ=0.1 rad, the obtained FWHM is 2.63 MHz for tuning loop length of 2 m. The simulation response agrees fairly with the recently reported experimental result.     

Some generalizations of torsion-free Crawley groups

In this paper we investigate two new classes of torsion-free Abelian groups which arise in a natural way from the notion of a torsion-free Crawley group. A group G is said to be an Erd?s group if for any pair of isomorphic pure subgroups H,K with G/H ? G/K, there is an automorphism of G mapping H onto K; it is said to be a weak Crawley group if for any pair H,K of isomorphic dense maximal pure subgroups, there is an automorphism mapping H onto K. We show that these classes are extensive and pay attention to the relationship of the Baer-Specker group to these classes. In particular, we show that the class of Crawley groups is strictly contained in the class of weak Crawley groups and that the class of Erd?s groups is strictly contained in the class of weak Crawley groups.     

Powers of the Vertex Cover Ideal of a Chordal Graph

In this article, Cohen–Macaulay chordal graphs and generalized star graphs are studied to show that all powers of the vertex cover ideal of such graphs have linear quotients. Moreover, it is shown that the Alexander dual of the clique complex of any chordal graph is vertex decomposable.     

Fuzzy quasi C*-algebra

At the present paper, the new concepts of fuzzy quasi norm, fuzzy Banach space, fuzzy quasi continuity and fuzzy quasi boundedness is introduced. Furthermore, we define the fuzzy quasi operator norm and also it is shown that the set all of fuzzy quasi bounded operator from X to Y is fuzzy quasi Banach space. Finally, we have introduced and investigated some notions and some results on *-algebra theory.