Some new common fixed point results for generalized contractive multi-valued non-self-mappings

In this work, we study some new common fixed point results for generalized contractive multi-valued non-self-mappings on complete metric spaces.     

Fuzzy pricing,marketing and service planning in a fuzzy inventory model: A geometric programming approach

In the real world markets, demand is influenced by different parameters. Recently, many researchers have been interested in integrated production and marketing planning strategies in inventory models where demand depends on different parameters such as price and/or marketing expenditure. The quality of services that are offered to customers of a product is one of the most important parameters that affects demand in the real markets and has not been considered in development of inventory models. On the other hand, the cost parameters in real inventory systems and other parameters such as price, marketing and service elasticity to demand are imprecise and uncertain in nature. So, the notion of fuzziness can be applied to cope with this uncertainty. In this paper, a new fuzzy profit maximization inventory model with shortages is proposed. The demand is considered as a power function of price, marketing expenditure and service expenditure. Furthermore, unit cost is determined as a power function of order quantity. Since the proposed model is in a fuzzy environment, a fuzzy decision should be made to meet the decision criteria, and the results should be fuzzy. Therefore, the proposed model is formulated and solved using geometric programming and fuzzy optimization techniques to derive an approximation of the results’ membership functions. The model is illustrated with a numerical example and finally a case study is provided for evaluation and validation of the results of model.     

One‐Pot stereoselective synthesis of trans‐4,5‐dialkoxy‐1,3‐bis (2‐pyrimidinyl)imidazolidines through a three‐component reaction

Stoichiometric reaction of 2‐aminopyrimidine with formaldehyde in the presence of formic acid catalyst in water gave N,N′‐bis(2‐pyrimidinyl)methanediamine ( 5 ). Subsequent cyclocondensation of 5 with glyoxal in alcohol (MeOH, EtOH, PrOH and i‐PrOH) under reflux conditions led to the formation of the corresponding 4,5‐dialkoxy‐1,3‐bis(2‐pyrimidinyl)imidazolidines ( 6a‐d ). 4,5‐Dihydroxy‐1,3‐bis(2‐pyrimidinyl) imidazolidine ( 6e ) was obtained when the reaction was carried out in acetonitrile. Based on ¹H NMR analysis, it was found that the trans‐dialkoxyimidazolidines ( 6 ) were selectively obtained in these cyclocondensation reactions.     

Synthesis of New 1,3‐bis(Heteroaryl)‐4,5‐imidazolidinediones Through Reaction of N,N′‐bis(Heteroaryl)methanediamines with Oxalyl Chloride

Reaction of N,N′‐bis(2‐pyridinyl, 3‐pyridinyl, 4‐pyridinyl, 2‐thiazolyl, 4‐nitrophenyl, and 2‐benzothiazolyl)methanediamines 1a–f with oxalyl chloride in dry dichloroethane in the presence of pyridine affords the corresponding 1,3‐bis (heteroaryl)‐4,5‐imidazolidinediones 3a–f in good to excellent yields. The essential role of pyridine in the reaction mixture is described, and reaction details as well as product characterization is discussed.     

Vitamin B1 as a metal-ion-free natural catalyst for sustainable quinoxaline ring condensation under sonochemical conditions

Abstract  

The role of vitamin B₁ as a catalyst is investigated for the quinoxaline ring condensation under various mild reaction conditions. The results revealed that the combination of vitamin B₁ and ultrasonic irradiation promotes the reaction more efficiently. The salient features of this environmentally benign method are fast conversions, excellent yields for a wide range of substrates, and the use of a low-cost, readily available, nontoxic, and metal-ion-free natural catalyst. The wide range of turnover frequency values (6–400 h⁻¹) shows that the reaction rate is highly dependent on the nature of the functional groups on the aromatic ring of substrates. Moreover, a plausible mechanism for the catalytic action of vitamin B₁ has been introduced.     

Radiation emission from the ＂Rhodotron-TT200＂ cavity

In this paper, the X-rays emitted from the Rhodotron-TT200 cavity have been studied in depth. We found that the Bremsstrahlung interaction is the only contribution of X-ray generation important to safety. The X-ray dose rate in the Rhodotron vault is calculated for normal conditions based on MCNP4C results. The presented calculation shows good agreement with the experimental measurements, which consequently confirms the reliability of the calculation for use in shielding design and other safety aspects.     

Rationalizing chain microstructure in the polyα-olefins synthesized by cationic AlCl3/H2O catalytic system

In this study, three middle range α-olefin monomers including 1-hexene, 1-octene, and 1-decene were oligomerized using conventional AlCl₃/H₂O catalytic system. Molecular weight and microstructure of the oligomers were analyzed by GPC and ¹HNMR, respectively. By ¹HNMR spectra, both internal (CHR=CHR′ and CHR=CR′R′′) and external (CH₂=CR′R′′) olefins containing di and tri-substituted C=C bonds were detected. After successful oligomerization, synthesized polyα-olefins underwent hydrogenation process using Pd(0)-Hal catalyst to yield synthetic oils of PHex, POct, and PDec, respectively and then completion of the hydrogenation was confirmed by ¹HNMR spectroscopy. The microstructure of the synthesized oligomers was rationalized using the ratio under the peak of CH?+?CH₂/CH₃ hydrogens (S1/S2) in ¹HNMR spectra and the degree of oligomerization obtained from M_n. According to the results, the best match between theoretical and real S1/S2 is obtained when considering double bond isomerization in the synthesized PAOs. By knowing PAO molecular weight, a relationship between monomer type and S1/S2 in the PAO homopolymers was detected. Our suggested methodology can be generalized to the unknown PAO homopolymers to unravel their monomer type by simple ¹HNMR and GPC analyses.     

Remarkable Oxygen‐Evolution Activity of a Perovskite Oxide from the Ca2−xSrxFe2O6−δ Series

Herein in we report the unprecedented catalytic activity of an iron‐based oxygen‐deficient perovskite for the oxygen‐evolution reaction (OER). The systematic trends in OER activity as a function of composition, defect‐order, and electrical conductivity have been demonstrated, leading to a methodical increase in OER catalytic activity: Ca₂Fe₂O_6?δ<CaSrFe₂O_6?δ<Sr₂Fe₂O_6?δ. Sr₂Fe₂O_6?δ also has the highest electrical conductivity and a unique type of defect‐order. In conventional experiments using glassy carbon electrode, Sr₂Fe₂O_6?δ shows better OER activity than the current state of the art catalysts, Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3?δ and RuO₂. It also offers a high intrinsic electrical conductivity, which allows it to act as a catalyst without the need for glassy carbon electrode or carbon powder. Pure disks of this material exhibit an outstanding activity for OER, without any additives or need for electrode preparation.