Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.     

Influence of Polarity and Activation Energy in Microwave–Assisted Organic Synthesis (MAOS)

The aim of this work was to determine the parameters that have decisive roles in microwave-assisted reactions and to develop a model, using computational chemistry, to predict a priori the type of reactions that can be improved under microwaves. For this purpose, a computational study was carried out on a variety of reactions, which have been reported to be improved under microwave irradiation. This comprises six types of reactions. The outcomes obtained in this study indicate that the most influential parameters are activation energy, enthalpy, and the polarity of all the species that participate. In addition to this, in most cases, slower reacting systems observe a much greater improvement under microwave irradiation. Furthermore, for these reactions, the presence of a polar component in the reaction (solvent, reagent, susceptor, etc.) is necessary for strong coupling with the electromagnetic radiation. We also quantified that an activation energy of 20–30 kcal mol⁻¹ and a polarity (μ) between 7–20 D of the species involved in the process is required to obtain significant improvements under microwave irradiation.     

Synthesis,spectral investigation and development of tetrahedral copper(II) complexes as artificial metallonucleases and antimalarial agents

Seven new copper(II) complexes of type [Cu(A)(L)]?H₂O (A = sparfloxacin, ciprofloxacin, levofloxacin, gatifloxacin, pefloxacin, ofloxacin, norfloxacin; L = 5‐[(3‐chlorophenyl)diazenyl]‐4‐hydroxy‐1,3‐thiazole‐2(3H)‐thione) were synthesized and characterized using elemental and thermogravimetric analyses, and electronic, electron paramagnetic resonance (EPR), Fourier transform infrared and liquid chromatography–mass spectroscopies. Tetrahedral geometry around copper is assigned in all complexes using EPR and electronic spectral analyses. All complexes were investigated for their interaction with herring sperm DNA utilizing absorption titration (K_b = 1.27–3.13 × 10⁵ M^?1) and hydrodynamic volume measurement studies. The studies suggest the classical intercalative mode of DNA binding. The cleavage reaction on pUC19 DNA was monitored by agarose gel electrophoresis. The results indicate that the Cu(II) complexes can more effectively promote the cleavage of plasmid DNA. The superoxide dismutase mimic activity of the complexes was evaluated by nitroblue tetrazolium assay, and the complexes catalysed the dismutation of superoxide at pH = 7.8 with IC₅₀ values in the range 0.597–0.900 μM. The complexes were screened for their in vitro antibacterial activity against five pathogenic bacteria. All the complexes are good cytotoxic agents and show LC₅₀ values ranging from 5.559 to 11.912 µg ml^?1. All newly synthesized Cu(II) complexes were also evaluated for their in vitro antimalarial activity against Plasmodium falciparum strain (IC₅₀ = 0.62–2.0 µg ml^?1). Copyright © 2015 John Wiley & Sons, Ltd.