A decomposition of partitions and numerical sets

Semigroup Forum - The aim of this work is to exhibit a decomposition of partitions of natural numbers and numerical sets. In particular, we obtain a decomposition of a sparse numerical set into the...     

Development of an inexpensive and sensitive method for the determination of low quantity of arsenic species in water samples by CPE-FAAS

The simple and rapid preconcentration technique using cloud point extraction (CPE) was applied for the determination of As(V) and total inorganic arsenic (As(V) plus As(III)) in water samples by means of FAAS. As(V) has formed an ion-pairing complex with Pyronine B in the presence of cetyl pyridinium chloride (CPC) at pH 8.0 and extracted into the non-ionic surfactant Triton X-114, after centrifugation the surfactant-rich phase was separated and diluted with 1.0 mol L⁻¹ HNO₃ in methanol. The proposed method is very versatile and economic because it exclusively used conventional FAAS. After optimization of the CPE conditions, a preconcentration factor of 120, the detection and quantification limits of 1.67 and 5.06 μg L⁻¹ with a correlation coefficient of 0.9978 were obtained from the calibration curve constructed in the range of 5.0-2200 μg L⁻¹. The relative standard deviation, RSD as a measure of precision was less than 4.1% and the recoveries were in the range of 98.2-102.4%, 97.4-101.2% and 97.8-101.1% for As(V), As(III) and total As, respectively. The method was validated by the analysis of standard reference materials, TMDA-53.3 and NIST 1643e and applied to the determination of As(III) and As(V) in some real samples including natural drinking water and tap water samples with satisfactory results. The results obtained (34.70 ± 1.08 μg L⁻¹ and 60.25 ± 1.07 μg L⁻¹) were in good agreement with the certified values (34.20 ± 1.38 μg L⁻¹ and 60.45 ± 1.78 μg L⁻¹).     

Synthesis, characterization, tautomerism and theoretical study of some new Schiff base derivatives

New Schiff base derivatives were prepared by the condensation of 5-chloro and 5-bromo salicylaldehyde with bis(o-aminophenol)ethers. Five bis(o-nitrophenol)ether compounds were synthesized using some ditosylate, 1,3-dibromopropane and 1,4-dibromobuthane with o-nitrophenol. These compounds were reduced to bis(o-aminophenol)ethers. The products have been characterized by elemental analysis, FTIR, 1H, 13C NMR, HETCOR and HMBC spectroscopic techniques. The tautomerisms of all of the Schiff bases compounds were determined in DMSO, CHCl3, C2H5OH and C6H12 solvents and in both acidic and basic media using the UV-vis spectrophotometric method. The heat of formation (ΔHf), enthalpy (ΔH), entropy (ΔS), Gibbs free energy (ΔGf and ΔG), stable isomers, conformations and tautomers of the synthesized compounds are calculated using the MOPAC2009 (PM6) program.     

A study on quantum chemical calculations of 3-, 4-nitrobenzaldehyde oximes

The molecular geometry, vibrational frequencies, 1H and 13C NMR chemical shifts, UV-vis spectra, HOMO-LUMO analyses, molecular electrostatic potentials (MEPs), , thermodynamic properties and atomic charges of 3- and 4-Nitrobenzaldehyde oxime (C7H6N2O3) molecules have been investigated by using Hartree-Fock (HF) and density functional theory (DFT/B3LYP) methods with the 6-311++G(d, p) basis set. The calculated optimized geometric parameters (bond lengths and bond angles), the vibrational frequencies calculated and 13C and 1H NMR chemical shifts values for the mentioned compounds are in a very good agreement with the experimental data. Furthermore, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) have been simulated and the transition states, energy band gaps and molecular electrostatic potential (MEP) maps for each oxime compound have been determined. Additionally, we also report the infrared intensities and Raman activities for the compounds under study.     

The Synthesis and Acid-Catalyzed Hydrolysis of N-(4-Substitutedphenyl)-O-Benzenedisulfonimides

Abstract

The acid catalyzed hydrolyses of some cyclic disulfonimides, N-(4-substitutedphenyl)-o-benzenedisulfonimides (1a–d) have been studied in concentrated aqueous acidic solutions. Analysis of the data by the Excess Acidity Method, activation parameters, substituent, and solvent deuterium isotope effect are all indicate hydrolysis by an A-1 mechanism in the studied range.     

Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence

The propagation characteristics of higher-order annular Gaussian (HOAG) beams in turbulence are investigated. From a HOAG source plane excitation, the average intensity of the receiver plane is developed analytically. This formulation is verified against the previously derived HOAG beam solution in free space. The graphical outputs indicate that, upon traveling in turbulent atmosphere, the HOAG beam will undergo different stages of evolution. At intermediate propagation distances, it will attempt to concentrate the energy near the origin. In this process, the appearance of the single higher-order primary beam will be encountered. Eventually HOAG originated beam will become a pure Gaussian beam after propagating an excessive distance in the turbulent medium.     

The enantiomeric recognition of chiral organic ammonium salts by chiral pyridino-macrocycles bearing aminoalcohol subunits

Pyridine-based macrocycles were prepared by treating 2,6-bis[[2′6′-bis(bromomethyl)-4′-methylphenoxy]methyl]pyridine 3 with the appropriate chiral aminoalcohols. The enantiomeric recognition of these macrocycles bearing aminoalcohol subunits of the pyridinocrown type ligand was evaluated for chiral organic ammonium salts by UV titration. The important differences were observed in the K_a values of (R)-Am2 and (S)-Am2 for (S,S,S)-1, (S,S,S)-2 and (S,S,S)-3 hosts, K_S/K_R = 5.0, K_S/K_R = 2.4 and K_S/K_R = 5.0, respectively. There seems to be a general tendency for hosts to recognise (S)-enantiomers for both Am1 and Am2.     

Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere

It is shown that a general shaped laser beam will eventually approach a Gaussian average intensity profile after propagation in turbulent atmosphere. In our formulation, source field at the exit plane of the laser is taken as the product of arbitrary functions of source transverse coordinates with Gaussian exponential modulations. Following the expansion of the arbitrary functions in terms of Hermite polynomials, the average receiver intensity expression is derived using the extended Huygens-Fresnel principle and the conditions for the intensity profile to assume a Gaussian shape are stated. The results are illustrated by simulating various source field distributions.     

Flow and structure development behavior of bar soaps containing synthetic detergent

Many bar soaps are processed using continuous processing technologies, including single and twin screw extrusion. However, in spite of the industrial importance of the extrusion-based processing of bar soaps the rheological behavior of bar soaps is poorly understood. Here, the shear viscosity and the formation of gross surface irregularities upon extrusion of the bar soap were investigated using steady torsional, rectangular slit, and capillary flows. Furthermore, the structure development aspects were investigated using wide-angle X-ray diffraction and scanning electron microscopy. It is revealed that the flow and deformation behavior of bar soaps is complicated by the ubiquitous presence of wall slip, viscoplasticity, gross surface irregularities, and various structuring aspects. The orientation of crystallites and the shear stress dependent fracture of a crystalline component of the formulation at the wall during flow were identified as some of the contributing effects to the development of the structure of the bar soap during flow and deformation.     

Thermal and kinetic analysis of uranium salts

Thermal decomposition of U(C₂O₄)₂·6H₂O was studied using TG method in nitrogen, air, and oxygen atmospheres. The decomposition proceeded in five stages. The first three stages were dehydration reactions and corresponded to removal of four, one, and one mole water, respectively. Anhydrous salt decomposed to oxide products in two stages. The decomposition products in nitrogen atmosphere were different from those in air and oxygen atmospheres. In nitrogen atmosphere UO_1.5(CO₃)_0.5 was the first product and U₂O₅ was the second product, while these in air and oxygen atmospheres were UO(CO₃) and UO₃, respectively. The second decomposition products were not stable and converted to stable oxides (nitrogen: UO₂, air–oxygen: U₃O₈). The kinetics of each reaction was investigated with using Kissinger–Akahira–Sunose and Flynn–Wall–Ozawa methods. These methods were combined with modeling equations for thermodynamic functions, the effective models were investigated and thermodynamic values were calculated.