Classification of torsion-free genus zero congruence groups

We study and classify all torsion-free genus zero congruence subgroups of the modular group.

     

A ruthenium(II) complex with p‐cymene and (S)‐2‐(anilinomethyl)pyrrolidine

The title compound, [(S)‐2‐(anilino­methyl)­pyrrolidine‐N,N′]‐chloro(η⁶‐para‐cymene)­ruthenium(II) chloride, [RuCl‐(C₁₀H₁₄)(C₁₁H₁₆N₂)]Cl, has been synthesized by the reaction of [RuCl₂(p‐cymene)]₂ (p‐cymene is para‐iso­propyl­toluene) with (S)‐2‐(anilinomethyl)­pyrrolidine in triethyl­amine/2‐propanol. The Ru atom is in a pseudo‐tetrahedral environment coordinated by a chloride ligand, the aromatic hydro­carbon is linked in a η⁶ manner and the amine is linked via its two N atoms. The chloride anion is involved in hydrogen bonding with the di­amine moieties through N—H?Cl interactions, with N?Cl distances of 3.273 (4) and 3.352 (4) Å.     

New insights into the development of ordered structure in poly(ethylene terephthalate), II Results from transmission infrared spectroscopy of thin films

To complement our earlier work involving external reflection infrared spectroscopy of PET, a set of thin PET films with different crystalline structures (amorphous, strain-induced crystallinity, thermally induced crystallinity) was prepared and analyzed in detail in the transmission mode. In analogy with the reflection work, factor analysis was used to generate three basis spectra corresponding to three distinct structures: G = an arrangement involving gauche glycol conformers and disordered terephthalate groups; TX = an arrangement involving trans glycol conformers and disordered terephthalate groups (probably a mixture of cis and trans conformers); and TC = the all-trans arrangement found in the true crystalline phase. The TX structure is believed to play an important role in the widely reported “intermediate” phase of PET, which is particularly significant in cold-drawn samples. The transmission spectra confirm the validity of the reflection spectra and also provide more detailed information. In addition, analysis of two biaxially oriented industrial films has provided further information on the geometry of certain vibrational modes. Overall, the results lead to a better understanding of the complex crystalline structure of PET and its relationship to the infrared spectrum.     

Effects of Geomaterial-Originated Fillers on Microstructure and Mechanical/Physical Properties of α- and β-Chitosan-Based Films

Edible films and coatings with good mechanical/physical properties are highly required for carrying medical substances and food packaging. So, solvent-cast films of α- or β-chitosan filled with palygorskite, montmorillonite or geopolymer-containing material (GCM), were prepared, and the effects of their clay contents (up to 50 wt.%) on the mechanical/physical properties were assessed. The microstructure of the films was investigated using FT-IR spectroscopy, SEM and thermal analysis. The results showed that, except for the films composed of GCM and β-chitosan, the mechanical properties of the films with limited (up to 5 wt.%) to moderate (5–25 wt.%) amounts of fillers increased as a result of the attractive electrostatic forces formed between the fillers and chitosan functional groups (–NH₃⁺, CH₂OH and NHCOCH₃). However, due to the occurrence of coarse aggregates, the strength of filler-rich films declined. The addition of fillers led to an increase in porosity and water absorption of the films, but it had irregular effects on their wettability and water vapor transmission rate. These observations as well as the thermal stability of the films were discussed in relation to the characterization results.     

On descent alternating direction method with LQP regularization for the structured variational inequalities

Optimization Letters - By reviewing the Logarithmic–quadratic proximal (LQP) method, in this paper we suggest and analyze a new LQP alternating direction scheme for the separable constrained...     

A new projection and contraction method for linear variational inequalities

In this paper, we presented a new projection and contraction method for linear variational inequalities, which can be regarded as an extension of He's method. The proposed method includes several new methods as special cases. We used a self-adaptive technique to adjust parameter β at each iteration. This method is simple, the global convergence is proved under the same assumptions as He's method. Some preliminary computational results are given to illustrate the efficiency of the proposed method.