Commutator subgroups of the power subgroups of?some Hecke groups

Let q??3 be a prime and let H(?? _q ) be the Hecke group associated to q. Let m be a positive integer and H ^m (?? _q ) be the mth power subgroup of H(?? _q ). In this work, we study the commutator subgroups of the power subgroups H ^m (?? _q ) of H(?? _q ). Then, we give the derived series for all triangle groups of the form (0;2,q,n) for n a positive integer, since there is a nice connection between the signatures of the subgroups we studied and the signatures of these derived series.     

A Computer Program to Help Resolution of Complex and Poorly Resolved Cu2+ and VO2+ Ions Doped Single Crystals Electron Paramagnetic Resonance Spectra

Complex and poorly resolved Cu²⁺ and VO²⁺ doped single-crystal electron paramagnetic resonance (EPR) spectra are some of the serious problems that exist in this area. In order to help the resolution of this sort of spectra, and for easily resolvable spectra as well, a versatile computer program known as EPR RESolution, or EPRES, is presented. All detectable line positions in the single-crystal spectra taken in three mutually perpendicular planes are given as input. The program plots these line positions. The user then manually determines the lines by selecting the true data points on the plot and fitting them to a well-known variation function. If selection is not suitable, the process is canceled and renewed. By this process, as many resolvable lines as in the spectra can be resolved and determined. The user then groups the resolved lines according to the paramagnetic center to which they belong. This includes the attribution of correct nuclear spin I and M _I to correct lines. After this step, hyperfine and g tensor elements can be found, constructed, and diagonalized.

[Supplemental materials are available for this article. Go to the publisher's online edition of Spectroscopy Letters for the following free supplemental resource: a copy of the EPRES computer program.]     

ESR of Gamma Irradiation and Ultraviolet Photolysis Products in Some Tetrasubstituted Ammonium Compounds

Abstract

The electron spin resonance of gamma and ultraviolet irradiated tetrabutylammonium halides [CH₃(CH₂)₃]₄NX (X=I,Cl,Br), tetrabutylammonium hydrogen sulfate [CH₃(CH₂)₃]₄NHSO₄, tetrabutylammonium periodate [CH₃(CH₂)₃]₄NIO₄, and ultraviolet photolyzed tetramethylammonium iodide, (CH₃)₄NI, and tetramethylphosphonium iodide, (CH₃)₄PI have been investigated between 140 and 350 K. The gamma and ultraviolet irradiation damage centers in tetrabutylammonium compounds were attributed to CH₃—CH^…—CH^…—CH₂, radicals, and ultraviolet photolysis damage centers in tetramethylammonium and phosphonium iodides were attributed to ?H₃ radicals. The g values of both radicals are found to be isotropic and g = 2.0030 and 2.0037 respectively to the methylallyl and the methyl radicals. The hyperfine coupling constants of the free electron to the protons in the radicals are reported and discussed.     

A comprehensive study for selective removal of Cr(VI) by asymmetric imidazolium bromide salts as environmentally-friendly extractant

The study was to determine selective removal and recovery of Cr(VI) from acidic media by solvent extraction (SX) using asymmetric imidazolium-based room temperature imidazolium bromide salts (ARTILs) as the extractants. The relevant parameters on the extraction and the stripping of Cr(VI) were investigated to identify optimum conditions. The optimum conditions were determined as equilibration time 5 minutes, acid concentration and type 0.5?mol/L H₂SO₄, stirring speed 1200?rpm, extractant concentration and type 0.5?mol/L ARTIL5, phase ratio 2.0 and stripping reagent type, and concentration 2.0?mol/L NH₃. In optimum conditions, decyl substituted ARTIL was best in extraction process about 99.7% of extraction rate, whereas moderately hydrophobic pentyl substituted ARTIL was best in stripping process about 70.0% of stripping rate. Also, the optimized process was found as so selective toward Cr(VI) in the presence of the other metal ions with an environmental-friendly liquid–liquid–based SX method.     

Lithium Accommodation in a Redox‐Active Covalent Triazine Framework for High Areal Capacity and Fast‐Charging Lithium‐Ion Batteries

The synthesis of a new type of redox‐active covalent triazine framework (rCTF) material, which is promising as an anode for Li‐ion batteries, is reported. After activation, it has a capacity up to ≈1190 mAh g^?1 at 0.5C with a current density of 300 mA g^?1 and a high cycling stability of over 1000 discharge/charge cycles with a stable Coulombic efficiency in an rCTF/Li half‐cell. This rCTF has a high rate performance, and at a charging rate of 20C with a current density of 12 A g^?1 and it functions well for over 1000 discharge/charge cycles with a reversible capacity of over 500 mAh g^?1. By electrochemical analysis and theoretical calculations, it is found that its lithium‐storage mechanism involves multi‐electron redox‐reactions at anthraquinone, triazine, and benzene rings by the accommodation of Li. The structural features and progressively increased structural disorder of the rCTF increase the kinetics of infiltration and significantly shortens the activation period, yielding fast‐charging Li‐ion half and full cells even at a high capacity loading.     

New method to measure the K-shell absorption jump factor in some rare-earth elements

The Compton scattering of 59.54 keV gamma rays by an Al scatterer has been used as a primer source at scattering angles from 48 to 118° by using a Si(Li) detector, and this primer gamma ray has been send to absorbers including Gd, Tb, Dy, Ho and Er. A new method has been developed to determine the K-shell absorption jump factor of elements and compounds. This method is based on simultaneous measurement of fluorescence radiation and scattered radiation, thus avoiding the problems with measuring the source strength and source-to-detector solid angle. In this method, the jump factor is effected from the scattering angle. Evident energies near to K-absorption edges of each lanthanide element have been determined for chosen angles, after the incident photon energy (59.5 keV) is exposed to Compton scattering from Al (secondary source). The experimental absorption jump factors are compared with the theoretical estimates and literature experimental values.     

EPR spectra of Cu(2+) in KH(2)PO(4) single crystals

Cu(2+) doped single crystals of KH(2)PO(4) were investigated using EPR technique at room temperature. The spectra of the complex contains large number of overlapping lines. Five sites are resolved and four of them are compatible with the tetragonal symmetry, and the fifth one belongs to an interstitial site. The results are discussed and compared with previous studies. Detailed investigation of the EPR spectra indicate that Cu(2+) substitute with K(+) ions. The principal values of the g and hyperfine tensors and the ground state wave function of Cu(2+) ions are obtained.     

Oxidation of Alcohols to Carbonyl Compounds, Benzylic Carbons to their Ketones, and Arenes to their Quinones with Molecular Oxygen in Subcritical Water

Summary. Molecular oxygen is used as an efficient oxidant for the conversion of alcohols into carbonyl compounds, benzylic carbons to their ketones, and arenes to their quinones in subcritical water in the absence of catalysts. The procedure utilizes water and does not require support materials and metal salts.     

SOME SUBGROUPS OF THE EXTENDED HECKE GROUPS (H)(λq)

The authors consider the extended Hecke groups H(λq) generated by T(z) =-1 / z, S(z) = -1/(z+λq) and R(z) = 1 / -z with λq = 2cos(π/q) for q ≥ 3 an integer. Inthis paper, the even subgroup He(λq), the second commutator subgroup H"(λq) and theprincipal congruence subgroups Hp(λq) of the extended Hecke groups H(λq) are studied.Also, relations between them are given.