Closed paths of light trapped in a closed Fermat curve

Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the curve varies, including a generalization to non integer powers.     

Polymer complexes. LXX. Synthesis,spectroscopic studies,thermal properties and antimicrobial activity of metal(II) polymer complexes

The monomer 3‐allyl‐5‐(phenylazo)‐2‐thioxothiazolidine‐4‐one (HL) was prepared by the reaction of allyl rhodanine with aniline through diazo‐coupling reaction. Reaction of HL with Ni(II) or Co(II) salts gave polymer complexes ( 1 – 8 ) with general stoichiometries [M(HL)(Cl)₂(OH₂)₂]_n, [M(HL)(O₂SO₂)(OH₂)₂]_n, [M(L)(O₂NO)(H₂O)₂]_n and [M(L)(O₂CCH₃)(H₂O)₂]_n (where M = Ni(II) or Co(II)). The structures of the polymer complexes were identified using elemental analysis, infrared and electronic spectra, molar conductance, magnetic susceptibility, X‐ray diffraction and thermogravimetric analysis. The interaction between the polymer complexes and calf thymus DNA showed a hypochromism effect. HL and its polymer complexes were tested against bacterial and fungal species. Co(II) polymer complex 2 is the most effective against Klebsiella pneumoniae and is more active than penicillin. The results showed that Ni(II) polymer complex 5 is a good antibacterial agent against Staphylococcus aureus and Pseudomonas aeruginosa. Molecular docking was used to predict the binding between the monomer with the receptors of prostate cancer (PDB code: 2Q7L Hormone) and breast cancer (PDB code: 1JNX Gene regulation). Coats–Redfern and Horowitz–Metzger methods were applied for calculating the thermodynamic parameters of HL and its polymer complexes. The thermal activation energy of decomposition for HL is higher than that for the polymer complexes.     

Microsoft Excel as a supplement in a high school statistics course

This study was conducted in the spring of 2002 at Arlington High School in a Probability and Statistics course for junior and senior level students. Two sections of the class were compared with respect to the use/non-use of EXCEL in the course. The experimental group (the one using EXCEL) outperformed the control group on five of the six teacher-created unit tests and on both of the criterion referenced assessments used by the district; however, the differences were not statistically significant at the 0.05 level. Furthermore, the experimental group expressed very positive feelings towards the use of the software in a survey administered at the conclusion of the course.     

Synthetic studies towards zetekitoxin AB: preparation of 4,5-epi-11-hydroxy-saxitoxinol

A concise synthesis of 4,5-epi-11-hydroxy-saxitoxinol utilizing d-ribose to direct an asymmetric Mannich reaction. This approach allows many modes of reactivity, which can be used to access various analogs of saxitoxin.     

Polymer complexes. LXXVI. Synthesis,characterization, CT‐DNA binding,molecular docking and thermal studies of sulfoxine polymer complexes

Novel polymer complexes of 8‐hydroxyquinoline‐5‐sulfonic acid hydrate ( H ₂ L ) with Cu²⁺, Co²⁺ and Ni²⁺ chloride were prepared and characterized. Microanalysis, magnetic susceptibility, IR spectra, electron spin resonance, mass spectra, X‐ray, molar conductance, thermal, and UV–Vis spectra studies have been used to confirm the structure of the prepared polymer complexes. The molecular and electronic structures of the hydrogen bond conformers for ligand ( H ₂ L ) were optimized theoretically and the quantum chemical parameters were calculated. On the basis of elemental and IR data, the chemical structure of metal chelates commensurate that the tri‐dentate (H₂L) coordinate to metal chlorides through oxygen atom of phenolic OH and oxygen atom of SO₃‐H group by replacing H atoms and nitrogen of the quinoline ring. The magnetic studies suggested the octahedral geometrical structure for all produced polymer complexes with general formula {[ML (OH₂)₃] .xH₂O}_n (M = Cu²⁺, x = 1.; Co²⁺, x = 2 and Ni²⁺, x = 2) in molar ratio (1:1). Coats–Redfern and Horowitz–Metzger methods have been used for calculating the activation thermodynamic parameters of the thermal decomposition for H ₂ L and its polymer complexes. The interaction between H ₂ L and its transition metal complexes with the calf thymus DNA (CT‐DNA) was determined by UV–Vis spectra. Binding efficiency between H ₂ L with the receptors of the prostate cancer (PDB code 2Q7L Hormone) and the breast cancer (PDB code 1JNX Gene regulation) was studied by molecular docking. The inhibition behaviour of H ₂ L against the corrosion of carbon steel / HCl (2 M) solution was studied by weight loss, Tafel polarisation, electrochemical impedance spectroscopy (EIS) and electrochemical frequency modulation (EFM) techniques. The adsorption isotherm was found to be Friendlish isotherm. The morphology of inhibited carbon steel? s surface was studied using scanning electron microscope (SEM) and energy dispersive X‐ray spectroscopy (EDS).     

Synthesis,characterization of Schiff base metal complexes and their biological investigation

A new Schiff base ligand named (E)‐2‐(((3‐aminophenyl)imino)methyl)phenol (HL) was prepared through condensation reaction of m‐phenylenediamine and 2‐hydroxybenzaldehyde in 1:1 molar ratio. The new ligand was characterized by elemental analysis and spectral techniques. The coordination behavior of a series of transition metal ions named Cr (III), Mn (II), Fe (III), Co (II), Ni (II), Cu (II), Zn (II) and Cd (II) with the newly prepared Schiff base ligand (HL) is reported. The nature of bonding and the stereochemistry of the complexes have been deduced from elemental analyses, IR, UV–Vis, ¹H NMR, mass, electronic spectra, magnetic susceptibility and conductivity measurements and further their thermal stability was confirmed by thermogravimetric analysis (TG). From IR spectra, it was observed that the ligand is a neutral tridentate ligand coordinates to the metal ions through protonated phenolic oxygen, azomethine nitrogen and nitrogen atom of NH₂ group. The existence, the number and the position of the water molecules was studied by thermal analysis. The molecular structures of the Schiff base ligand (HL) and its metal complexes were optimized theoretically and the quantum chemical parameters were calculated. The synthesized ligand and its complexes were screened for antimicrobial activities against bacterial species (Staphylococcus aureus and Bacillis subtilis, (gram positive bacteria)), (Salmonella SP., Escherichia coli and Pseudomonas aeruginosa, (gram negative bacteria)) and fungi (Aspergillus fumigatus and Candida albicans). The complexes were found to possess high biological activities against different organisms. Molecular docking was used to predict the efficiency of binding between Schiff base ligand (HL) and both receptors of Escherichia coli (3 T88) and Staphylococcus aureus (3Q8U). The receptor of Escherichia coli (3 T88) showed best interaction with Schiff base ligand (HL) compared to receptor of Staphylococcus aureu (3Q8U).