Zone diagrams in compact subsets of uniformly convex normed spaces

A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matoušek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and proved the existence and uniqueness of zone diagrams there. In the present paper we prove the existence of zone diagrams with respect to finitely many pairwise disjoint compact sites contained in a compact and convex subset of a uniformly convex normed space, provided that either the sites or the convex subset satisfy a certain mild condition. The proof is based on the Schauder fixed point theorem, the Curtis-Schori theorem regarding the Hilbert cube, and on recent results concerning the characterization of Voronoi cells as a collection of line segments and their geometric stability with respect to small changes of the corresponding sites. Along the way we obtain the continuity of the Dom mapping as well as interesting and apparently new properties of Voronoi cells.     

Metal complexes of novel Schiff base derived from iron sandwiched organometallic and 4‐nitro‐1,2‐phenylenediamine: Synthesis,characterization, DFT studies,antimicrobial activities and molecular docking

The condensation of 2‐acetylferrocene with 4‐nitro‐1,2‐phenylenediamine in a 1:1 molar ratio, resulting in formation of a novel bi‐dentate organometallic Schiff base ligand (L), (2‐(1‐((2‐amino‐5‐nitrophenyl)imino)ethyl)cyclopenta‐2,4‐dien‐1‐yl)(cyclopenta‐2,4‐dien‐1‐yl)iron. Also, its Cr(III), Mn(II), Fe(III), Co(II), Ni(II), Cu(II), Zn(II) and Cd(II) complexes have been synthesized. The stoichiometric ratios of the prepared compounds were estimated using elemental analysis (C, H, N, M), molar conductivity, FT‐IR, UV‐Vis, ¹H‐NMR, SEM and mass spectral analysis. Furthermore, their TG and DTG properties were studied. The geometrical structure of the complexes was found to be octahedral. From spectral analysis, the Schiff base coordinated to metal ions through the azomethine and amine groups. DFT‐based molecular orbital energy calculations of the synthesized ligand have been studied, in which the ligand was theoretically optimized. The Schiff base and its metal complexes have been screened for their antimicrobial activities against different bacterial and fungal species by using disc diffusion method. The anticancer activities of the ligand and its metal complexes have also been studied towards breast cancer (MCF‐7) and human normal melanocytes (HFB‐4) cell lines. Molecular docking was also used to identify the interaction between the Schiff base ligand and its Cd(II) complex with the active site of the receptors of breast cancer mutant oxidoreductase (PDB ID: 3HB5), crystal structure of Staphylococcus aureus (PDB ID: 3Q8U) and yeast‐specific serine/threonine protein phosphatase (PPZ1) of Candida albicans (PDB ID:5JPE).     

Effect of the ac field on a single-molecule magnet bridged between conducting leads

We study quantum spin-rotation effects for a single-molecule magnet bridged between two conducting leads in the ac and dc magnetic fields. The Landau-Zener dynamics induced by the magnetic field generates mechanical torque, making the molecule to oscillate. This mechanical motion of the molecule exhibits unique features that can be detected by measuring the electronic tunneling current through the molecule.     

Facile synthesis and optical properties of Co3O4 nanostructures by the microwave route

Cobalt oxide (Co₃O₄) nanoplatelet shape like nanostructures have been successfully synthesized through a simple microwave route for the first time using cobalt acetate, NaOH and citric acid at 200 °C for 30 min. The structure and morphology of as-prepared Co₃O₄ nanoplatelets are characterized by means of powder X-ray diffraction (XRD), Fourier transform infrared spectrum (FTIR), and scanning electron microscope (SEM). XRD measurements indicate that the product has a perfect crystalline cubic phase of Co₃O₄ with a lattice constant a=8.082 Å. The SEM images show that the obtained Co₃O₄ nanopowder consists of nanoplatelets with diameter 125 nm and thickness 20 nm. Energy-dispersive X-ray spectroscopy (EDS) show that the composition of Co₃O₄ is stoichiometric. Room temperature photoluminescence measurement is exhibited by a strong UV emission and a suppressed green emission, confirming the good optical properties for the as-prepared Co₃O₄ nanoplatelets.     

Synthesis and physical properties of mixed Co3O4/CoO nanorods by microwave hydrothermal technique

A mixture of crystalline Co₃O₄/CoO nanorods with non-uniform dense distribution has been successfully synthesized by microwave hydrothermal technique. The synthesized nanorods have been characterized by several techniques such as X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), energy-dispersive X-ray spectroscopy (EDX), and Fourier transforms infrared spectroscopy (FT-IR). The results showed that the as synthesized specimens contained mixed crystalline Co₃O₄/CoO nanorods with an average length of around 80 nm and an average diameter of 42 nm. UV–Vis spectrum of the nanorods exhibited a strong UV emission. The band energy gap of the product was 1.79 eV which lies between the energy gap of CoO and that for Co₃O₄. The obtained carrier concentration is of the order 4.32 × 10²⁷ m⁻³ and the dielectric constant is found to be 4.89. The electrical conductivity increases with increasing temperature and behaves as a semiconducting material with an activation energy of a bout 0.26 eV. This makes the as synthesized mixed Co₃O₄/CoO nanorods very useful for supercapacitor devices application. Magnetic hysteresis loops at room temperature of the as synthesized mixed oxides (Co₃O₄/CoO) nanorods exhibit typical soft magnetic behavior.     

Labeling and biodistribution of 99mTc-7-bromo-1,4-dihydro-4-oxo-quinolin-3-carboxylic acid complex

7-Bromo-1,4-dihydro-4-oxo-quinolin-3-carboxylic acid (BDOQCA), was synthesized with a yield of 93% and well characterized. The obtained compound was investigated to label with one of the most important radioactive isotopes (technetium-99m). Effect of BDOQCA concentration, stannous chloride dihydrates (SnCl₂.2H₂O) concentration, pH and reaction time on the percent labeling yield of ^99mTc-BDOQCA complex was studied in details. ^99mTc-BDOQCA complex was obtained at a maximum yield of 97.3% by mixing 2.5 mg of BDOQCA with 25 μg SnCl₂.2H₂O at pH 6 and 30 min reaction time and the formed complex was stable for a time up to 8 h with a maximum yield of 97.3%. Biodistribution studies in mice were carried out using experimentally induced infection in the left thigh using E. coli. Both thighs of the mice were dissected and counted to evaluate the ratio of bacterial infected thigh/contralateral thigh. Higher uptake in the infected thigh was observed after 2 h of IV administration of ^99mTc-BDOQCA complex (T/NT = 7.6 ± 0.6%) than that of the commercially available ^99mTc-ciprofloxacin complex (T/NT = 3.8 ± 1%). The in vitro binding and biodistribution of ^99mTc-BDOQCA complex in the septic and aseptic inflammation bearing mice showed that, ^99mTc-BDOQCA complex is a promising agent for infection imaging and can differentiate between infected and inflamed muscle.     

Synthesis of new 2-pyridinone and thiazole derivatives containing coumarin moiety

Coumarin has shown considerable therapeutic potency because of its versatile biological prosperities. Also, pyridines have been adopted in medicinal chemistry as potent ring. Moreover, several investigations reported the potency of thiazole-containing compounds. So, during this research, new functionalized 2-pyridinone and thiazole derivatives bearing coumarin moiety were aimed to synthesize. Many trials to obtain the 6-amino-2-oxo-pyridine-3,5-dicarbonitriles through the condensation of cyanoacetohydrazone of 3-acetyl coumarin with 2-(arylidene)malononitriles were carried out using different reaction conditions. In all cases, the reaction gave none of the corresponding 2-pyridinone derivatives except the reaction with 2-(benzylidene)-malononitrile afforded product in few yield. Moreover, the reaction of another cyanoacetanilide with the 2-(arylidene)-malononitrile afforded the unexpected arylidene derivatives rather than the expected pyridin-2-one derivatives. Finally, new thiazoles bearing coumarin moiety were synthesized using 3-acetylcoumarin N-(2,4-dimethoxyphenyl)-thiosemicarbazone. Cyclization of thiosemicarbazone derivative with ethyl 2-chloroacetate, chloroacetone or phenacyl bromide afforded in high yields the corresponding derivatives of thiazolidin-4-one, 4-methylthiazole or 4-phenylthiazole, respectively.     

Castor Oil Based Organogels: I. Synthesis,Swelling, and Network Parameters

Linear and branched polyesters were prepared by transesterification of methyl recinoleate without or with diethylene glycol, trimethylol propane or pentaerithirtol for different durations. Molecular weight of the synthesized polyesters were determined using gel permeation chromatography and hydroxyl number. Their chemical structure were characterized by FTIR. Crosslinked polyesters were prepared using different weight ratios of trimethylolpropane triacrylate in presence of benzoyl peroxide initiator. These organogels were characterized through soluble fraction and toluene sorption capacity. Swelling kinetics and network parameters including polymer solvent interaction, effective and theoretical crosslink densities, average molecular weight between crosslinks and modulus of elasticity were determined.