On the structure ofn-point sets

Letn be an integer greater than one. Our main result, called the “Structure Theorem” is that a set that containsn−1 disjoint continua that are cut by a single line cannot be ann-point set, that is, a set that meets every line in preciselyn points. This theorem unifies and significantly improves upon a number of known theorems. The second part of the paper is devoted to several theorems that address the question when a set that meets every line in at mostn points can be extended to ann-point set. These theorems also highlight the sharpness of the Structure Theorem.     

Development of temporal spectroscopic properties for Xerogel matrices doped with Rhodamine 6G dye

The solid host of a laser dye modifies its spectroscopic properties with respect to its liquid host. During the Sol-Gel process the dye molecules suffer from changing their environment. Two parameters affect this matter, the change in the concentration due to the evaporation of the solvent (drying) and the caging of dye molecules inside the pores or attachment to the silica network. Rhodamine 6G absorption and fluorescence spectra with different concentrations, during Sol-Gel time processing, have been studied. Both, absorption and fluorescence spectra of the dye in the solid host, for different concentrations, show a blue-shift relative to its liquid phase.     

A magnetic study of the ThCr2Si2-type RPd2Ge2 (R=Pr, Nd) compounds. Magnetic structure of PrPd2Ge2 from powder neutron diffraction

The magnetic properties of the PrPd₂Ge₂ and NdPd₂Ge₂ compounds have been investigated by magnetic measurements, specific heat measurements and neutron diffraction experiments. The PrPd₂Ge₂ compound orders antiferromagnetically below T_N=5.0(2) with an original modulated magnetic structure characterized by a magnetic cell three times larger than the chemical one by tripling of the c parameter. The palladium atom is non magnetic and the Pr moments are parallel to the c-axis with a value of ≈2.0 μ_B at 2 K. The specific heat measurements clearly detect a low temperature transition for the NdPd₂Ge₂ compound, interpreted as a Nd sublattice antiferromagnetic ordering below 1.3(2) K.     

An Accurate In Vitro Model of the E. coli Envelope

Gram‐negative bacteria are an increasingly serious source of antibiotic‐resistant infections, partly owing to their characteristic protective envelope. This complex, 20 nm thick barrier includes a highly impermeable, asymmetric bilayer outer membrane (OM), which plays a pivotal role in resisting antibacterial chemotherapy. Nevertheless, the OM molecular structure and its dynamics are poorly understood because the structure is difficult to recreate or study in vitro. The successful formation and characterization of a fully asymmetric model envelope using Langmuir–Blodgett and Langmuir–Schaefer methods is now reported. Neutron reflectivity and isotopic labeling confirmed the expected structure and asymmetry and showed that experiments with antibacterial proteins reproduced published in vivo behavior. By closely recreating natural OM behavior, this model provides a much needed robust system for antibiotic development.     

Identification,control strategies,and analytical approaches for the determination of potential genotoxic impurities in pharmaceuticals: A comprehensive review

Potential genotoxic impurities in pharmaceuticals at trace levels are of increasing concern to both pharmaceutical industries and regulatory agencies due to their possibility for human carcinogenesis. Molecular functional groups that render starting materials and synthetic intermediates as reactive building blocks for small molecules may also be responsible for their genotoxicity. Determination of these genotoxic impurities at trace levels requires highly sensitive and selective analytical methodologies, which poses tremendous challenges on analytical communities in pharmaceutical research and development. Experimental guidance for the analytical determination of some important classes of genotoxic impurities is still unavailable in the literature. Therefore, the present review explores the structural alerts of commonly encountered potential genotoxic impurities, draft guidance of various regulatory authorities in order to control the level of impurities in drug substances and to assess their toxicity. This review also describes the analytical considerations for the determination of potential genotoxic impurities at trace levels and finally few case studies are also discussed for the determination of some important classes of potential genotoxic impurities. It is the authors’ intention to provide a complete strategy that helps analytical scientists for the analysis of such potential genotoxic impurities in pharmaceuticals.     

Synthesis,Spectroscopy, Semi‐empirical and Biological Activities of Organotin(IV) Complexes with o‐Isopropyl Carbonodithioic Acid

New organotin(IV) complexes have been synthesized by treating potassium o‐isopropyl carbonodithioate with R₂SnCl₂/R₃SnCl in 1 : 2/1 : 1 M/L ratio. All complexes have been characterized by IR and NMR (¹H, ¹³C) spectroscopy. IR results shows that ligand acts as bidentate which is also confirmed by semi‐empirical study. NMR data reveals four coordinated geometry in solution. Computed positive heat of formation shows that complex 5 is thermodynamically unstable. UV/visible spectroscopy was used to assess the mode of interaction and binding of the complexes with DNA which shows that complex 5 exhibits higher binding constant as compared to complex 3 . In protein kinase inhibition assay, compound 3 was found most active, while other biological activities shows that triorganotin(IV) complexes are biologically more active as compared to diorganotin(IV) complexes.     

Biological evaluations and spectroscopic characterizations of 3-(4-ethoxyphenyl)-2-methylacrylate based organotin(IV) carboxylates derivatives

Six new organotin(IV) carboxylates, [Me₂SnL₂] (1), [n-Bu₂SnL₂] (2), [n-Oct₂SnL₂] (3), [Me₃SnL] (4), [n-Bu₃SnL] (5) and [Ph₃SnL] (6), where L = 3-(4-ethoxyphenyl)-2-methylacrylate, have been synthesized and characterized by FT-IR, NMR spectroscopy and elemental analyses. The synthesized compounds were tested for in vitro antibacterial and antifungal activities. The complexes 4–6 demonstrated higher activity than the complexes 1–3. UV-Vis absorption spectroscopy indicated that the ligand and its complexes interacted with DNA via partial intercalation as well as minor groove binding.

     

Homobimetallic organotin(IV) complexes with succinohydrazide Schiff base: Synthesis,spectroscopic characterization,and biological screening

Russian Journal of General Chemistry - Six new bis-diorganotin(IV) complexes, [(Me2Sn)2L] (1), [(Et2Sn)2L] (2), [(n-Bu2Sn)2L] (3), [(Ph2Sn)2L] (4), [(n-Oct2Sn)2L] (5), and [(tert-C4H9)2Sn)2L] (6),...     

Local commensurability graphs of solvable groups

The commensurability index between two subgroups A,B of a group G is [A:A∩B][B:A∩B]. This gives a notion of distance among finite index subgroups of G, which is encoded in the p-local commensurability graphs of G. We show that for any metabelian group, any component of the p-local commensurabilty graph of G has diameter bounded above by 4. However, no universal upper bound on diameters of components exists for the class of finite solvable groups. In the appendix we give a complete classification of components for upper triangular matrix groups in GL(2,𝔽_q).