Convex hull of powers of a complex number,trinomial equations and the Farey sequence

The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set of points where the color changes is investigated here. It is observed that there is a connection between this fractal set and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation.     

Sol-gel approach to in situ creation of high pH-resistant surface-bonded organic-inorganic hybrid zirconia coating for capillary microextraction (in-tube SPME)

A novel zirconia-based hybrid organic-inorganic sol-gel coating was developed for capillary microextraction (CME) (in-tube SPME). High degree of chemical inertness inherent in zirconia makes it very difficult to covalently bind a suitable organic ligand to its surface. In the present work, this problem was addressed from a sol-gel chemistry point of view. Principles of sol-gel chemistry were employed to chemically bind a hydroxy-terminated silicone polymer (polydimethyldiphenylsiloxane, PDMDPS) to a sol-gel zirconia network in the course of its evolution from a highly reactive alkoxide precursor undergoing controlled hydrolytic polycondensation reactions. A fused silica capillary was filled with a properly designed sol solution to allow for the sol-gel reactions to take place within the capillary for a predetermined period of time (typically 15-30 min). In the course of this process, a layer of the evolving hybrid organic-inorganic sol-gel polymer got chemically anchored to the silanol groups on the capillary inner walls via condensation reaction. At the end of this in-capillary residence time, the unbonded part of the sol solution was expelled from the capillary under helium pressure, leaving behind a chemically bonded sol-gel zirconia-PDMDPS coating on the inner walls. Polycyclic aromatic hydrocarbons, ketones, and aldehydes were efficiently extracted and preconcentrated from dilute aqueous samples using sol-gel zirconia-PDMDPS coated capillaries followed by thermal desorption and GC analysis of the extracted solutes. The newly developed sol-gel hybrid zirconia coatings demonstrated excellent pH stability, and retained the extraction characteristics intact even after continuous rinsing with a 0.1 M NaOH solution for 24 h. To our knowledge, this is the first report on the use of a sol-gel zirconia-based hybrid organic-inorganic coating as an extraction medium in solid phase microextraction (SPME).     

Highly oxygenated triterpenes from the roots of Atropa acuminata

Two new oleanane triterpenes; 2alpha,3alpha,24-trihydroxyolean-12-ene-28,30-dioic acid ([structure: see text]) and 2alpha,3alpha,24,28-tetrahydroxyolean-12-ene ([structure: see text]) have been isolated from the roots of Atropa acuminata. Anti-oxidant p-hydroxyphenethyl trans-ferulate ([structure: see text]), beta-sitosterol-3-O-beta-D-glucopyranoside ([structure: see text]) and oleanolic acid ([structure: see text]) have also been reported for the first time from this species. The structures were determined by spectroscopic studies including 2D-NMR.     

Silver(I)‐N‐heterocyclic carbene complexes of bis‐imidazol‐2‐ylidenes having different aromatic‐spacers: synthesis,crystal structure,and in vitro antimicrobial and anticancer studies

A series of Ag(I) complexes ( 6 , 7 , 8 , 9 ) derived from imidazol‐2‐ylidenes was synthesized by reacting Ag₂O with an o‐, m‐, p‐xylyl or 1,3,5‐triazine‐linked imidazolium salts ( 1 , 2 , 3 , 4 ) and then characterizing these using various spectro‐analytical techniques. Additionally, triazine‐linked bis‐imidazolium salt 5 was characterized using the single‐crystal X‐ray diffraction method. Complexes 6–9 were formed from the N‐heterocyclic carbene ligand precursors 1–3 as PF₆^‐ salts in good yields. Conversely, salt 5 does not form Ag(I) complex even under various reaction conditions. Using ampicillin as a standard, complexes 6–9 were tested against bacteria strains Escherichia coli and Staphylococcus aureus as Gram‐negative and Gram‐positive bacteria, respectively, showing potent antimicrobial activities against the tested bacteria even at minimum inhibition concentration and bacterial concentration levels. Furthermore, the potential anticancer activities of the reported complexes were evaluated against the human colorectal cancer (HCT 116) cell lines, using 5‐fluorouracil as a standard drug. The highest anticancer activities were observed for complex 8 with an IC₅₀ value of 3.4 μm , whereas the lowest was observed for complex 9 with an IC₅₀ value of 18.1 μm . Copyright © 2013 John Wiley & Sons, Ltd.     

Taguchi orthogonal design assisted immobilization of Candida rugosa lipase onto nanocellulose-silica reinforced polyethersulfone membrane: physicochemical characterization and operational stability

Cellulose - A greener processing route to replace the current environmentally-unfriendly esterification technique to produce biofuels such as pentyl valerate (PeVa) was explored. This study...