In this work systems of sines $\sin \left(n+\beta \right)t,\, \, n=1,2, \ldots,$ and cosines $\cos \left(n-\beta \right)t,\, \, n=0,1,2, \ldots,$ are considered, where $\beta \in R-$is a real parameter. The subspace $M^{p,\alpha } \left(0,\pi \right)$ of the Morrey space $L^{p,\alpha } \left(0,\pi \right)$ in which continuous functions are dense is considered. Criterion   for the completeness, minimality and Basicity of these systems with respect to the parameter $\beta $  in the subspace  $M^{p,\alpha } \left(0,\pi \right)$, $1

Epoxies are generally cross-linked by the addition of a hardener, most of the time a diamine such as diamine diphenyl sulphone, oxydianiline or methylene diamine, and then thermocured. These formulations are quite often used, particularly in the aerospace industry for making structural materials, prepregs or composites. In this paper we have investigated the cross-linking reactions of a difunctional cycloaliphatic epoxide monomer 3,4-epoxycyclohexylmethyl-3', 4'-epoxycyclohexane carboxylate initiated by UV-irradiation and compared the kinetics with N,N-diglycidyl- 4-glycidyloxyaniline (a nitrogen-containing monomer with a functionality of three) and 4,4'-methylenebis (N,N-diglycidylaniline) (another nitrogen-containing monomer with a functionality of four). Kinetics is followed using a differential photocalorimetry (DPC) technique. Upon UV irradiation in the presence of cationic photoinitiator, the difunctional cycloaliphatic epoxide monomer shows an exotherm peak whereas for the latter two monomers, no exotherm peaks were observed from the sample as a result of exposure to the UV source. To explain the phenomenon observed, the effect of addition of two amines with wide difference in the Basicity of p-nitroaniline and pyridine, has been studied on the UV-curing of epoxy resins. It has been found that the presence of amines does retard the rate of photopolymerization and the extent of retardation is dependent on the Basicity of the amine. Of the two amines used, pyridine and p-nitroaniline, the former is a stronger inhibitor, because of the ready availability of the lone pair of electrons. The results explain the non-reactivity of nitrogencontaining epoxy monomers N,N-diglycidyl-4-glycidyloxyaniline and 4,4'-methylenebis (N,N-diglycidylaniline) to cationic polymerization upon exposure to UV-radiation.

Two approaches for metal ion incorporation were employed to introduce Ca2+into SBA-15; Direct Synthesis (DS) and Wet Impregnation (WI). The non-ionic template was removed by two different methods; calcination and solvent extraction. The obtained catalysts were characterized by means of X-Ray Powder Diffraction (XRD), Energy Dispersive X-ray (EDX), and FT-IR spectroscopy. The Basicity was determined by using Hammett indicators and benzoic acid titration. The effects of synthesis methods and organic template on Basicity and catalytic performance were studied in the transesterification of Canola oil with methanol.1H NMR was used to analyze the products. The best results were obtained using catalysts which prepared by wet impregnation method. Furthermore calcination is a better method of template removal. So calcined Ca/SBA-15 prepared by impregnation showed particularly the highest activity (conversion 84.2 %).Although this catalyst has a limited reusability in transesterification reaction.

In the present study, the effect of calcination temperature on the structure and performance of mesoporous CaO/TiO2– ZrO2 catalyst fabricated by sol– gel method used in the esterification reaction was assessed. Then, CaO/TiO2 catalyst was also synthesized via the same method to evaluate the effect of zirconia cations on its properties and activity. The samples were characterized by X-ray Diffraction (XRD), Fourier transmittance infra-red (FT-IR), Brunauer– Emmett– Teller (BET)– Barrett-Joyner-Halenda (BJH), scanning electron microscope (SEM) and transmission electron microscopy (TEM) analyses. Moreover, Hammett indicator method was utilized to assess the acidity and Basicity of the samples. It was found that zirconium was clearly incorporated in CaO/TiO2 lattice and transformed that from amorphous phase to crystalline structure. In addition, the Basicity and acidity of CaO/TiO2 was clearly increased by zirconia loading. Evaluation of the samples’ activity presented that CaO/TiO2 catalyst exhibit no activity in the esterification reaction, while all CaO/TiO2– ZrO2 catalysts showed high ability to convert oleic acid to its ester. Moreover, the catalyst calcined at 400 ° C showed the highest activity in the esterification reaction with desirable properties such as high crystallinity, acidity, Basicity and surface area along with well-distribution of particle size and pore size. The best catalyst converted around 90% of oleic acid to ester at optimized conditions of 150 ° C, 12: 1 molar ratio of methanol/oleic acid, 3 wt% of catalyst for 4 h of reaction time. Moreover, the sample was successfully used for five runs without significant reduction in activity that makes it a suitable choice as a catalyst for industrial applications.

In the present study, effect of inclusions characteristics changing on the formation of acicular ferritein submerged arc welding of API5l-X65 low alloy steel was investigated. Three different welding fluxes with different chemical composition and Basicity index of 0. 72, 0. 82 and 0. 99, and two different welding heat inputs of 1. 6 kJ / mm and 2. 4 kJ / mm were used to create inclusions with different characteristics such as chemical composition and size. The results indicate that inclusions acting as acicular ferrite nucleation sites and improvement of the microstructure and resulted mechanical properties, can be observed in welding conditions in which the welding flux with lowest Basicity index and higher welding heat input. Under these conditions, the percentage of inclusions with a high titanium oxide value and size range of 0. 5 to 1. 5 micrometers is increased, which increases the amount of acicular ferrite in the microstructure. However, in other welding conditions, formation of grain boundary ferrite reduces amount of acicular ferrite and weakens mechanical properties of weld metal compared to the base metal.

Sulfonamides are a class of pharmaceutical compounds included – SO2NH– group that show a variety of biological activities. Sulfacetamide is an N-acyl sulfonamide that has broad-spectrum antibiotic effects. The acid-base properties of these compounds are believed to play an important role in their biological activities. Therefore, calculation of its acidic-Basicity has a specific importance in predicting and justifying the pharmaceutical properties of this compound. In this study, the synthesis of sulfacetamide has been carried out from a new multi-steps method in presence of heterogeneous catalyst of nano zinc oxide and homogeneous base catalyst of magnesium hydroxide. The stage and overall yields are better and their reaction time is less than previous procedures. Using heterogeneous catalyst, recoverable nano zinc oxide and magnesium hydroxide in solvent-free condition is a new procedure for better synthesis of this compound. Also in this work, acidic-Basicity of sulfacetamide and its derivatives have been studied using high level ab initio calculations. The calculated values have been found in good agreement with experimental data. Therefore, predictions of pharmaceutical properties of these compounds are possible.