A new approach for the derivation of bounds for the Jensen difference

There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory.     

Furo- and thieno-fused 1,3-diazepine-4,6-diones

We report the first preparation of furo- and thieno-fused 1,3-diazepine-4,6-dione derivatives starting from ethyl 2-(2-methoxy-2-oxoethyl)-3-furancarboxylate and -thiophencarboxylate. The ester functionalities connected to the hetero-ring were converted regiospecifically into the desired amides. The ester groups attached to the methylene unit were converted into isocyanates via Curtius rearrangement. The ring-closure reaction was performed in the presence of lithium bis(trimethylsilyl)amide at room temperature to give furo- and thieno-fused diazepinone derivatives.     

Palladium(II) complexes bearing N‐alkylpiperidoimidazolin‐2‐ylidene derivatives: Effect of alkyl chain length of ligands on catalytic activity

A series of piperidoimidazolinium salts which differ in the chain lengths (butyl, octyl, dodecyl, octadecyl) and their Pd–N‐heterocyclic carbene complexes with pyridine were synthesized and characterized using elemental analysis and spectroscopic methods. The effects of these ligands on catalyst activation and the performance of the complexes were studied in Suzuki–Miyaura reactions of arylboronic acid with aryl chlorides. The complex with the ligand having the longest chain length was found to be most active. The results demonstrated that the length of the alkyl chain of the piperidoimidazolin‐2‐ylidene controlled the dispersion and composition of the nanoparticles and it affected the catalytic activity. The impact of alkyl chain length of piperidoimidazolin‐2‐ylidene on the Suzuki–Miyaura reactions of arylboronic acid with aryl halides was systematically investigated.     

Sonochemical synthesis and electrochemical characterization of α-nickel hydroxide: precursor effects

Sonochemical degradation of urea was employed to synthesize alpha-nickel hydroxide from different nickel salts. Utilization of ultrasound yielded products with properties significantly different than the products obtained by thermal degradation of urea. The effect of intercalating chloride, nitrate, acetate, and sulfate anions on morphology and electrochemical performance was studied. The sulfate-intercalated sample had the smallest interlayer spacing when obtained by the sonochemical method, contradicting all the previous thermal synthesis results. The specific capacitance trend also differed from the literature values, and the value for the sulfate-intercalated sample was larger than that of acetate- and nitrate-intercalated samples. Ultrasonic synthesis increased the specific capacitance of the sulfate-intercalated sample significantly. This sample was also the most reversible and had the highest charge efficiency.     

Synthesis of thio- and furan-fused heterocycles: furopyranone,furopyrrolone, and thienopyrrolone derivatives

We report herein the synthesis of a novel class of compounds, ethyl 4-oxo-4H-furo[3,2-c]pyran-6-yl carbonate, (7E)-7-[(dimethylamino)methylene]-4H-furo[3,2-c]pyran-4,6(7H)-dione, 5-oxo-N-phenyl-2,5-dihydro-4H-furo[3,2-b]pyrrole-4-carboxamide, and 5-oxo-N-phenyl-5,6-dihydro-4H-thieno[3,2-b]pyrrole-4-carboxamide starting from the corresponding acid derivatives. Intramolecular cyclization in the presence of thionyl chloride formed the target fused ring systems. Additional transformation was seen in the cyclization of furan-fused heterocycle. A mechanism was proposed based on experimental and computational findings.     

A Comparison of Four Different Electrode Matrices on the Performance of Amperometric Hydrogen Peroxide (Bio)Sensors

A comparison of the analytical performances of four different (bio)sensor designs in H₂O₂ determination is discussed. The (bio)sensor designs developed were based on the use of (i) multiwalled carbon nanotubes (MWCNT), zinc oxide nanoparticles (ZnONP), prussian blue (PB); (ii) MWCNT, ZnONP, PB and ionic liquid (IL); (iii) MWCNT, ZnONP and horseradish peroxidase (HRP) and (iv) MWCNT, ZnONP, HRP and IL modified glassy carbon electrode (GCE). A performance comparison of (bio)sensors showed that the one based on HRP/IL-MWCNT-ZnONP/GCE showed the best analytical characteristics with a linear dynamic range of 9.99×10⁻⁸–7.55×10⁻⁴ M, detection limit of 1.37×10⁻⁸ M and sensitivity of 17.00 μA mM⁻¹.     

One-pot preparation and uranyl adsorption properties of hierarchically porous zirconium titanium oxide beads using phase separation processes to vary macropore morphology

A simple and engineering friendly one-step process has been used to prepare zirconium titanium mixed oxide beads with porosity on multiple length scales. In this facile synthesis, the bead diameter and the macroporosity can be conveniently controlled through minor alterations in the synthesis conditions. The precursor solution consisted of poly(acrylonitrile) dissolved in dimethyl sulfoxide to which was added block copolymer Pluronic F127 and metal alkoxides. The millimeter-sized spheres were fabricated with differing macropore dimensions and morphology through dropwise addition of the precursor solution into a gelation bath consisting of water (H(2)O beads) or liquid nitrogen (LN(2) beads). The inorganic beads obtained after calcination (550 °C in air) had surface areas of 140 and 128 m(2) g(-1), respectively, and had varied pore architectures. The H(2)O-derived beads had much larger macropores (5.7 μm) and smaller mesopores (6.3 nm) compared with the LN(2)-derived beads (0.8 μm and 24 nm, respectively). Pluronic F127 was an important addition to the precursor solution, as it resulted in increased surface area, pore volume, and compressive yield point. From nonambient XRD analysis, it was concluded that the zirconium and titanium were homogeneously mixed within the oxide. The beads were analyzed for surface accessibility and adsorption rate by monitoring the uptake of uranyl species from solution. The macropore diameter and morphology greatly impacted surface accessibility. Beads with larger macropores reached adsorption equilibrium much faster than the beads with a more tortuous macropore network.