Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations

In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are generated. An operational matrix concerning fractional integration of these wavelets is extracted. A numerical scheme is established based on these wavelets and their fractional integral matrix together with the collocation technique to solve fractional pantograph equations. The presented method reduces solving the problem under study into solving a system of algebraic equations. Several examples are provided to show the accuracy of the method.     

Thermodynamic Consistency Test of Vapor–liquid Equilibrium Data of Binary Systems Including Carbon Dioxide (CO 2 ) and Ionic Liquids Using the Generic Redlich–Kwong Equation of State

The thermodynamic consistency test of solubility P–T–x data for binary mixtures including carbon dioxide (CO2) + a room temperature ionic liquid has been investigated. Experimental solubility data taken from the open literature for 32 binary mixtures of CO2/RTILs contains 80 isotherms. The applied consistency test is based on the fundamental Gibbs–Duhem equation with use of the generic Redlich–Kwong (GRK) equation of state (EoS) coupled with the van der Waals–Berthelot (GRK/vdWB) mixing rule. The optimum parameters were obtained by minimizing the summation of per cent relative deviations between modeled and experimental data, based on the bubble pressure algorithm. Modeling was found acceptable for all isotherms, which demonstrated the usability of the GRK equation of state. Results of the thermodynamic consistency test showed that 36 of the isothermal data sets were thermodynamically consistent, 37 were not fully consistent, 6 were thermodynamically inconsistent and only one data set was found to need another model.     

Characterisation of decorations on Iranian (10th–13th century) lustreware

It has been recently shown that lustre decoration of Medieval and Renaissance pottery consists of silver and copper nanoparticles, dispersed within the glassy matrix of the ceramic glaze. Lustre surfaces show peculiar optical effects, such as metallic reflection and iridescence. Here we report the findings of a study on lustred glazes of several shards belonging to Iranian pottery of the 10th and 13th centuries, decorated on both sides. Two different glazes, depending on the side of the sample, have been identified. Different lustre chromatic effects are characterised by the relative presence of silver- and copper-metal nanoparticles dispersed in the glassy matrix. PACS 61.46.+w     

Morphology and Mechanical Properties of Polyamide 6/Acrylonitrile-Butadiene-Styrene Blends Containing Carbon Nanotubes

The blends of polyamide 6/acrylonitrile-butadiene-styrene (PA6/ABS), with added styrene-maleic acid copolymer (SMA) compatibilizer, were prepared through melt mixing in an internal mixer. The effects of blend composition and various process conditions, as well as the addition of multi-wall carbon nanotubes (MWCNTs) to the blends, on the morphology and mechanical properties were investigated. The morphology of the blends and blend nanocomposites were observed by scanning electron microscopy (SEM) and analyzed using an image analysis technique. The mechanical behavior of the blends was investigated by tensile and also impact testing. The results showed that the blend composition as well as the processing conditions significantly affected the morphology and mechanical properties of the PA6/ABS blends. Among the various compositions, the blend with 36?wt.% of ABS and 4?wt.% of SMA compatibilizer exhibited the best mechanical properties. Comparing various speeds and times of mixing, it was found that less mixing speed and longer mixing times resulted in the favorable morphology and conditions for achievement of the desired toughness for the polyamide 6. By adding different amounts of MWCNTs to the blends, it was found that the presence of the carbon nanotubes changed the viscosity of the resulting nanocomposite and thus changed the morphology. These nanocomposites also showed an improvement in mechanical properties. The MWCNTs acted as a second compatibilizer, resulting in a synergistic effect on the mechanical properties of the PA6/ABS blend nanocomposites.     

Investigation of Aqueous Diethanolamine Performance in Prediction of Hydrogen Sulfide and Carbonyl Sulfide Removal from Liquefied Propane

Journal of Solution Chemistry - Hydrogen sulfide and carbonyl sulfide represent undesirable impurities in a variety of industrial gas streams such as natural gas, liquefied natural gas and...     

A characterization of nonlinear Hölder seminorm preserving bijections

For a compact metric space (X, d) and \(\alpha \in (0,1)\), let \(\mathrm{Lip}^\alpha (X)\) be the linear space of all complex-valued functions f on X satisfying

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and \(\mathrm{lip}^\alpha (X)\) be the subspace of \(\mathrm{Lip}^\alpha (X)\) consisting of functions f with \(\lim \frac{f(x)-f(y)}{d^\alpha (x,y)} =0\) as \(d(x,y) \rightarrow 0\). In this paper, we give a characterization of a bijective map \(T:\mathrm{lip}^\alpha (X)\longrightarrow \mathrm{lip}^\alpha (Y)\), not necessarily linear, which is an isometry with respect to the Hölder seminorm \(L(\cdot )\). It is shown that there exist \(K_0>0\), a surjective map \(\Psi : Y \longrightarrow X\) with \(d^\alpha (y,z)= K_0 \, d^\alpha (\Psi (y),\Psi (z))\) for all \(y,z\in Y\), and a function \(\Lambda : \mathrm{lip}^\alpha (X) \longrightarrow {\mathbb {C}}\) (which is linear or real-linear if T is so) such that either

$$\begin{aligned} Tf(y)= T0(y)+\overline{\tau } K_0\, f(\Psi (y))+\Lambda (f)\quad (f\in \mathrm{lip}^\alpha (X), y\in Y) \end{aligned}$$

or

$$\begin{aligned} Tf(y)= T0(y)+\overline{\tau } K_0 \,\overline{f(\Psi (y))}+ \Lambda (f)\quad (f\in \mathrm{lip}^\alpha (X), y\in Y), \end{aligned}$$

where \(\tau =e^{i\theta }\) for some \(\theta \in [0,\pi )\).

     

An Efficient One-Pot Synthesis of 2,3-Dialkyl-1,1-Diethyl-1-(Acetylamino)-3-(1,1,1-Triphenylphosphanilidene)-1,1,2,3-Propanetetracarboxylates and Their Temperature-Dependent NMR Spectra

Abstract

Stable crystalline phosphorus ylides of 1,1-diethyl 2,3-dimethyl 1-(acetylamino)-3-(1,1,1-triphenylphosphanilidine)-1,1,2,3-propanetetracarboxylates were obtained in excellent yields from the 1:1:1 addition reaction between triphenylphosphine and dialkyl acetylenedicarboxylates in the presence of diethyl acetamidomalonate as a CH-acid. These stable ylides exist in solution as a mixture of two geometrical isomers (E and Z) as a result of restricted rotation around the carbon–carbon partial double bond resulting from conjugation of the ylide moiety with the adjacent carbonyl group on the nuclear magnetic resonance (NMR) time scale at ambient temperature. The dynamic effects in the ylide moieties were investigated by ¹H NMR spectra.

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