On the representation of integers as sums of an odd number of squares

In a recent work, S. Cooper (J. Number Theory 103:135–162, [1988]) conjectured a formula for r _2k+1(p ²), the number of ways p ² can be expressed as a sum of 2k+1 squares. Inspired by this conjecture, we obtain an explicit formula for r _2k+1(n ²),n≥1. Dedicated to Srinivasa Ramanujan.     

Synthesis,DNA binding,and antimicrobial studies of novel metal complexes containing a pyrazolone derivative Schiff base

A novel series of Co(II), Ni(II), Cu(II), Zn(II), and VO(IV) complexes has been synthesized from the Schiff base derived from 4-[(3,4-dimethoxybenzylidene)amino]-1,5-dimethyl-2-phenyl-1,2-dihydropyrazol-3-one and 1,2-diaminobenzene. Structural features were determined by analytical and spectral techniques. Binding of synthesized complexes with calf thymus DNA (CT DNA) was studied by spectroscopic methods and viscosity measurements. Experimental results indicate that the complexes are able to form adducts with DNA and to distort the double helix by changing the base stacking. Lower DNA affinity of the VO(IV) complex is caused by the change of coordination geometry by the vanadyl ion resulting in a somewhat unfavorable configuration for the DNA binding. Oxidative DNA cleavage activities of the complexes were studied with supercoiled (SC) pUC19 DNA using gel electrophoresis; the mechanism studies revealed that the hydroxyl radical is likely to be the reactive species responsible for the cleavage of pUC19 DNA by the synthesized complexes. The in vitro antimicrobial screening effects of the investigated compounds were monitored by the disc diffusion method. The synthesized Schiff base complexes exhibit higher antimicrobial activity than the respective free Schiff base.     

Acridinedione-functionalized gold nanoparticles and model for the binding of 1,3-dithiol linked acridinedione on gold clusters

The design and synthesis of 1,3-dithiol linked acridinedione functionalized gold nanoparticles (ADDDT-GNP) is described. ADDDT-GNP was characterized by transmission electron microscopy (TEM), Fourier transform infrared (FT-IR), UV-vis, steady-state and time-resolved fluorescence techniques. Conformational analysis of 1,3-dithiol ligands using density functional theory (DFT) reveals that they can cap on gold clusters through 1,2-capping mode, in which the two sulfur atoms of the dithiol bind covalently with two adjacent gold atoms on the surface of the cluster. The present study shows that three conformers of the ligand can cap in the 1,2-mode of capping. The triexponential fluorescence decay observed in the capped nanogold complex with fluorophore-labeled 1,3-dithiol may originate from the three conformers of the complex in the 1,2-capping mode.     

Kinetics and adsorption equilibrium in the system aqueous solution of copper ions—granulated activated carbon

The feasibility of using granulated activated carbon for adsorption removal of copper from aqueous solution was studied. The influence of pH, amount of the adsorbent, contact time, and copper concentration on adsorption of copper was investigated. The single-component equilibrium data on copper adsorption were analyzed using the Langmuir, Freundlich, Redlich—Peterson, Temkin, and Toth adsorption isotherms. The adsorption process was followed by two simplified kinetic models including pseudo-first- and pseudo-second-order equations. Kinetic parameters, rate constants, equilibrium sorption capacities, and the corresponding correlation coefficients were calculated and examined for each kinetic model. It was shown that copper adsorption can be described by the pseudo-second-order equation.     

Percolation-enhanced generation of terahertz pulses by optical rectification on ultrathin gold films

Emission of pulses of electromagnetic radiation in the terahertz range is observed when ultrathin gold films on glass are illuminated with femtosecond near-IR laser pulses. A distinct maximum is observed in the emitted terahertz amplitude from films of average thickness just above the percolation threshold. Our measurements suggest that the emission is through a second-order nonlinear optical rectification process, enhanced by the excitation of localized surface plasmon hot spots on the percolated metal film.     

5,5-Diaryldipyrromethanes: syntheses and anion binding properties

A two-step synthesis of 5,5-diaryldipyrromethanes in good yields is described. The adopted synthetic strategy can be used to tune the substituent at the meso-carbon very easily by choosing the Grignard reagent of interest. Further, the influence of the incorporation of various diaryl units at the meso-carbon atom in the inherent anion binding affinities of the dipyrromethanes through hydrogen bonding was discussed.     

A Facile Photochemical Synthesis of 12H-Benzothiazolo [2,3-b]Quinazolin-12-Ones

The photochemical synthesis of 12H-benzothiazolo [2,3-b]quinazolin-12-ones (4) by the irradiation of 2-thioquinazolinediones 1 and disulphide 5 are described.