A Differential Calculus on the Z<Subscript>3</Subscript>-graded Quantum Group GL<Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(2)

In this work, we introduce Z₃-graded quantum group GL\({_q(2,{\mathbb C})}\) with the help of Z₃-graded quantum plane and a Z₃-graded bicovariant differential calculus on the Z₃-graded quantum group GL _q (2). The corresponding Z₃-graded quantum Lie superalgebra is obtained.     

Novel phthalocyanines bearing four 4-phenyloxyacetic acid functionalities

Metal-free (2) and Co(II), Zn(II), Ni(II), Cu(II) metallophthalocyanines (2a–d) with four 4-phenyloxyacetic acid groups on the periphery were prepared by cyclotetramerization of new p-(3,4-dicyanophenoxy)phenylacetic acid (1) and the corresponding divalent metal salts. Further reactions of these products with thionylchloride and then benzylamine in tetrahydrofuran, and octanol in pyridine gave amide (3, 3a–d) and ester (4, 4a–d) derivatives, respectively. The new compounds have been characterized by elemental analyses, IR, UV–Vis, mass and ¹H NMR spectroscopy. The redox properties of compounds 2 and 2a–d were identified by cyclic voltammetry.     

Analysis of underivatized cellodextrin oligosaccharides by capillary electrophoresis with direct photochemically induced UV‐detection

This work focuses on the development of a CE method allowing, for the first time, the simultaneous separation of the underivatized first seven cellodextrin oligomers (glucose, cellobiose, cellotriose, cellotetraose, cellopentaose, cellohexaose, and celloheptaose), with a view to analyze the hydrolysates obtained after partial acid depolymerization of nitrocellulose, and eight carbohydrates (ribose, xylose, fructose, mannose, galactose, maltose, lactose, and sucrose), which might be potential interfering compounds in explosives samples. Separation was achieved with a highly alkaline BGE containing sodium chloride and direct mid‐UV‐absorbance detection was performed after photo‐oxidation in the detection window. EOF was reversed to speed up the analysis using a dynamic capillary coating by hexadimethrine bromide. A central composite design was carried out to determine the effects of BGE conductivity and sodium hydroxide concentration on resolutions between neighboring peaks, and analysis time. A desirability analysis on modeled responses was applied to maximize resolutions and to minimize analysis time. The simultaneous analysis in 20 min total runtime of the 15 carbohydrates plus internal reference (naphthalene sulfonate) was carried out at 25°C with a BGE composed of 77.4 mM NaOH and 183 mM NaCl to adjust the conductivity at the optimum value. Finally, the resolution robustness was checked. This new method should also be of interest to monitor food and nonfood crop products.     

On asymptotically equivalent difference sequences with respect to a modulus function

This paper presents new definitions which are a natural combination of the definition for asymptotically equivalence and Δ ^m -lacunary strongly summable with respect to a modulus f. Using this definitions we have proved the (f, Δ ^m )-asymptotically equivalence and Δ ^m -lacunary statistical asymptotically equivalence analogues of theorems of Tripathy and Et (Stud Univ Babe?-Bolyai Math (1):119–130, 2005) and Çolak’s theorems (Filomat 17:9–14, 2003).     

The prime dicompletion of a di-uniformity on a plain texture

Working within a plain texture (S,S), the authors construct a completion of a dicovering uniformity υ on (S,S) in terms of prime S-filters. In case υ is separated, a separated completion is then obtained using the T₀-quotient, and it is shown that this construction produces a reflector. For a totally bounded di-uniformity it is verified that these constructions lead to dicompactifications of the uniform ditopology. A condition is given under which complementation is preserved on passing to these completions, and an example on the real texture (R,R,ρ) is presented.     

Cloud-point extraction of rhodamine 6G by using Triton X-100 as the non-ionic surfactant

Cloud-point extraction (CPE) using the non-ionic surfactant Triton X-100 was used successfully to remove a highly toxic dye, rhodamine 6G (R6G), from water and wastewater. The effects of different analytical parameters such as pH, concentration of Triton X-100 (TX-100) and salts, equilibrium temperature, and incubation time on the efficiency of the extraction of R6G were studied in detail, and optimum conditions for dye extraction were obtained. Thermodynamic parameters including changes in Gibbs free energy, enthalpy, and entropy were also calculated, and these parameters indicated that the CPE of R6G was feasible, spontaneous, and endothermic in the temperature range of 75-95 degrees C. The equilibrium solubilization capacity of TX-100 was found to be 1.10 mmol/mol by using Langmuir isotherm models. No significant interference effects were observed in the presence of phenol and its derivatives, some acidic and basic dyes and most of the anions and cations. It was concluded that the CPE process described in this paper can be an alternative technique for removal of dyes and other pollutants from waters and wastewaters.     

Synthesis and properties of crown ether functionalized coumarin substituted zinc phthalocyanine

The novel 6,7-[15-crown-5]-3-[p-(2,3-dicyanophenoxy)phenyl]coumarin (1) and its non-peripherally substituted zinc phthalocyanine complex (2) have been prepared and characterized by elemental analysis, ¹H NMR (for compound 1), MALDI-TOF, FT-IR and UV-Vis spectral data. Fluorescence intensity changes of compound 1 have been determined by addition of Na⁺ or K⁺ ions at 25 °C in THF. The effects of the chromenone crown ether substituent of the phthalocyanine molecule on the photophysical (fluorescence quantum yield and lifetime) and photochemical (singlet oxygen generation and photodegradation) properties were also investigated. The fluorescence of the zinc phthalocyanine complex is effectively quenched by addition of 1,4-benzoquinone (BQ).     

Analysis and Review of Chemical Reactions and Transport Processes in Pulsed Electrical Discharge Plasma Formed Directly in Liquid Water

Electrical discharges formed directly in liquid water include three general cases where (a) streamer-like plasma channels form in, but do not span, the electrode gap, (b) spark discharges produce transient plasma channels that span the electrode gap, and (c) arc discharges form plasma channels with relatively longer life times. Other factors including the input energy (from <1?J/pulse to >1?kJ/pulse) as well as solution properties and the rates of energy delivery affect the nature of the discharge channels. An understanding of the formation of chemical species, including the highly reactive hydroxyl radical and more stable molecular species such as hydrogen and hydrogen peroxide, in such plasma requires determination of temporal and spatial variations of temperature, pressure, plasma volume, and electrical characteristics including current, voltage (electric field), and plasma conductivity. In spark and arc discharges analysis of the physical processes has focused on hydrodynamic and thermal characterization, while only a limited amount of work has connected these physical processes to chemical reactions. On the other hand, the most successful model of the chemical reactions in streamer-like discharges relies on simple assumptions concerning the temperature and pressure in the plasma channels, while analysis of the physical processes is more limited. This paper reviews the literature on the mathematical modeling of electrical discharges in liquid water spanning the range from streamer-like to spark and arc discharges, and compares the properties and processes in these electrical discharges to those in electron beam radiolysis and ultrasound.     

Influence of ro-vibrational and isotope effects on the dynamics of the C(3 P)+ OD(X 2Π) → CO(X 1 Σ+) + D(2 S) reaction

The C(³ P)+OD(X ²Π) reaction has been studied by means of quantum mechanical real wave packet (RWP) and quasiclassical trajectory (QCT) methodologies on the ground potential energy surface of Zanchet et al. [J. Phys. Chem. A 110, 12017 (2006)]. Initial state selected total reaction probabilities at J?=?0 total angular momentum have been calculated for a wide range of collision energies. Product state-resolved integral cross-sections at selected collision energies and excitation functions have been determined from the RWP calculations using the J-shifting approximation and from QCT calculations. State-specific and thermal rate coefficients have been calculated using both methodologies up to 500 K. The effect of reagent rotational excitation on the dynamics for the C(³ P)+OH(X ²Π) and C(³ P)+OD(X ²Π) reactions has been investigated and interesting discrepancies between the QCT and RWP results have been found. The RWP results are found to be in an overall good agreement with the corresponding QCT results, although the QCT integral cross-section and rate coefficients are slightly smaller than those obtained from the RWP calculations.     

Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions

In this paper we establish a complete local theory for the energy-critical nonlinear wave equation (NLW) in high dimensions ? × ? ^d with d ≥ 6. We prove the stability of solutions under the weak condition that the perturbation of the linear flow is small in certain space-time norms. As a by-product of our stability analysis, we also prove local well-posedness of solutions for which we only assume the smallness of the linear evolution. These results provide essential technical tools that can be applied towards obtaining the extension to high dimensions of the analysis of Kenig and Merle [17 Kenig , C.E. , Merle , F. ( 2008 ). Global well-posedness, scattering and blow-up for the energy critical focusing non-linear wave equation . Acta Math. 201 : 147 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]] of the dynamics of the focusing (NLW) below the energy threshold. By employing refined paraproduct estimates we also prove unconditional uniqueness of solutions for d ≥ 6 in the natural energy class. This extends an earlier result by Planchon [26 Planchon , F. ( 2003 ). On uniqueness for semilinear wave equations . Math. Z. 244 : 587 – 599 .[Web of Science ®] , [Google Scholar]].