Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.     

Comparative Study of the Synthetic Approaches and Biological Activities of the Bioisosteres of 1,3,4-Oxadiazoles and 1,3,4-Thiadiazoles over the Past Decade

The bioisosteres of 1,3,4-oxadiazoles and 1,3,4-thiadiazoles are well-known pharmacophores for many medicinally important drugs. Throughout the past 10 years, 1,3,4-oxa-/thiadiazole nuclei have been very attractive to researchers for drug design, synthesis, and the study of their potential activity towards a variety of diseases, including microbial and viral infections, cancer, diabetes, pain, and inflammation. This work is an up-to-date comparative study that identifies the differences between 1,3,4-thiadiazoles and 1,3,4-oxadiazoles concerning their methods of synthesis from different classes of starting compounds under various reaction conditions, as well as their biological activities and structure–activity relationship.     

Smart Biopolymer-Based Nanocomposite Materials Containing pH-Sensing Colorimetric Indicators for Food Freshness Monitoring

Nanocomposite biopolymer materials containing colorimetric pH-responsive indicators were prepared from gelatin and chitosan nanofibers. Plant-based extracts from barberry and saffron, which both contained anthocyanins, were used as pH indicators. Incorporation of the anthocyanins into the biopolymer films increased their mechanical, water-barrier, and light-screening properties. Infrared spectroscopy and scanning electron microscopy analysis indicated that a uniform biopolymer matrix was formed, with the anthocyanins distributed evenly throughout them. The anthocyanins in the composite films changed color in response to alterations in pH or ammonia gas levels, which was used to monitor changes in the freshness of packaged fish during storage. The anthocyanins also exhibited antioxidant and antimicrobial activity, which meant that they could also be used to slow down the degradation of the fish. Thus, natural anthocyanins could be used as both freshness indicators and preservatives in biopolymer-based nanocomposite packaging materials. These novel materials may therefore be useful alternatives to synthetic plastics for some food packaging applications, thereby improving the environmental friendliness and sustainability of the food supply.     

Cobalt-promoted MoS2 nanosheets: A promising novel diesel hydrodesulfurization catalyst

MoS₂ has been commonly used as a catalyst in hydrodesulfurization (HDS) of petroleum cuts in crude oil refineries. In this study, the synthesis of unsupported MoS₂ and Co-promoted MoS₂ nanosheets produced from molybdenum oxide and thiourea is reported. The synthesized samples were characterized by using x-ray fluorescence, x-ray diffraction, Brunauer–Emmett–Teller (BET), temperature-programmed reduction, thermal gravimetric analysis, and transmission electron microscopy methods, and then they were utilized for HDS of diesel through a fixed-bed catalytic reactor. Results indicated that a cobalt promoter affected both the number and the performance of active sites of the molybdenum sulfides, and the activity of the promoted MoS₂ catalyst was consistently higher than that of the MoS₂ catalyst. More significantly, the activity of the promoted catalyst was slightly declined during 48 h continuous HDS reaction, which indicated the stability of this catalyst. Additionally, during 12 h of test run, the HDS activity of the promoted catalyst was about 60% higher than MoS₂ one.     

Large-Signal Performance of the Serially Cascaded Electroabsorption Modulator

Large signal analysis of the serially cascaded electroabsorption modulator driven by a multisinusoidal RF signal is presented. The special case of a two-tone equal-amplitude RF signal is considered in detail, and the results are compared with previously published results.     

Large Signal Analysis of Multiquantum Well Electroabsorption Modulators

Large signal analysis of the multiple-quantum-well electroabsorption modulators driven by a mutisinusoidal RF signal is presented. The special case of a two-tone equal-amplitude RF signal is considered in detail and the results are compared with previously published results.     

Amalgamation property for the class of basic algebras and some of its natural subclasses

We study Basic algebra, the algebraic structure associated with basic propositional calculus, and some of its natural extensions. Among other things, we prove the amalgamation property for the class of Basic algebras, faithful Basic algebras and linear faithful Basic algebras. We also show that a faithful theory has the interpolation property if and only if its correspondence class of algebras has the amalgamation property.     

On the linear Lindenbaum algebra of Basic Propositional Logic

We study the linear Lindenbaum algebra of Basic Propositional Calculus, called linear basic algebra. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of 3-aminoisoxazolmethylnaphthols via one-pot three-component reaction under solvent-free conditions

A one-pot three-component condensation reaction of 3-amino-5-methylisoxazole, aryl aldehyde and 2-naphthol to afford the corresponding 3-amino isoxazolmethylnaphthols in good to excellent yields. The remarkable features of this new procedure are high conversions, clean reaction condition, short reaction time, nonhazardous and environmentally friendly reaction condition, inexpensive and easily commercially availability of the catalyst and simple work-up procedures.     

A metal organic framework prepared from benzene-1,3,5-tricarboxylic acid and copper(II), and functionalized with various polysulfides as a sorbent for selective sorption of trace amounts of heavy metal ions

Novel composites were obtained via direct assembly of polysulfides (S_x^2?, X?=?3, 4, 6) on the surface of a metal organic framework (MOF; type benzene-1,3,5-tricarboxylic/Cu(II). They are referred to as S_x-MOFs and were used for highly selective and efficient extraction of ultra-trace amounts of heavy metal ions from aqueous solutions. The structure of the S_x-MOFs was characterized by Raman spectroscopy, FT-IR, X-ray diffraction, and scanning electron microscopy. The Raman spectra of S_x-MOF is similar to the bare MOF and shows the MOFs structure to be well retained after S_x functionalization. The selective interaction of S_x with soft metal ions and the high surface area of MOFs resulted in excellent affinity and selectivity for ions such as Hg(II). The S_x-MOFs of type S₄-MOF had the highest distribution coefficient K_d value (~10⁷) and best extraction recovery (~100%) for Hg(II). The S₄-MOF also has high selectivity in the following order: Hg(II) >?>?Pb(II)?>?Zn(II)?>?Ni(II)?>?Co(II). The binding process of the metals occurs via M–S bonding. The ions were quantified by inductively coupled plasma optical emission spectrometry (ICP-OES). The detection limit for Hg(II) is 0.13 μg L^?1. The S₄-MOF was applied to the extraction of trace metal ions from natural and contaminated waters and data were compared with other sorbets. The results revealed that S₄-MOF is an excellent adsorbent for sorption of heavy metal ions even in the presence of the relatively high concentration of other ions.

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Graphical abstract A composite was synthesized via direct assembly of polysulfides (S_x^2?, X?=?3, 4, 6) on surface of the metal organic framework (S_x-MOF) and was used for selective and efficient extraction of ultra-trace amounts of heavy metal ions from aqueous solutions.