Divisibility of certain $$\ell $$ -regular partitions by 2

The Ramanujan Journal - For a positive integer $$\ell $$ , let $$b_{\ell }(n)$$ denote the number of $$\ell $$ -regular partitions of a nonnegative integer n. Motivated by some recent conjectures...     

Ultraviolet absorption and vibrational spectra of 2-fluoro-5-bromopyridine

The ultraviolet absorption spectrum in the range 340-185 nm in the vapour and solution phase has been measured for 2-fluoro-5-bromopyridine. Three fairly intense band systems identified as the pi* <-- pi transitions II, III and IV have been observed. A detailed vibronic analysis of the vapor and solution spectra is presented. The first system of bands is resolved into about sixty-two distinct vibronic bands in the vapour-phase spectrum. The 0,0 band is located at 35944 cm(-1). Two well-developed progressions, in which the excited state frequencies nu'25 (283 cm(-1)) and nu'19 (550 cm(-1)) are excited by several quanta, have been observed. The corresponding excited state vibrational and anharmonicity constants are found to be omega'i = 292 cm(-1), x'ii = 4.5 cm(-1) (i = 25) and omega'i = 563.8 cm(-1), x'ii = 6.9 cm(-1) (i = 19). The other two band systems show no vibronic structure, the band maxima being located at 48346 and 52701 cm(-1), respectively. The oscillator strength of the band systems in different solutions and the excited state dipole moments associated with the first two transitions have been determined by the solvent-shift method. The infrared spectrum in the region 4000-130 cm(-1) and the laser Raman spectrum of the molecule in the liquid state have been measured and a complete vibrational assignment of the observed frequencies is given. A correlation of the ground and excited state fundamental frequencies observed in the UV absorption spectrum with the Raman or infrared frequencies is presented.     

Reverse fragment based drug discovery approach via simple estimation of fragment contributions

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DNA interaction,cytotoxicity and molecular structure of cobalt complex of 4‐amino‐N‐(6‐chloropyridazin‐3‐yl)benzene sulfonamide in the presence of secondary ligand pyridine

Novel cobalt complex of 4‐amino‐N‐(6‐chloropyridazin‐3‐yl)benzene sulfonamide (sulfachloropyridazine) has been synthesized and characterized by elemental analysis, FT‐IR spectroscopy and magnetic susceptibility (VSM). Cobalt complex of Sulfachloropyridazine (Co‐SCP) crystallized in monoclinic space group P2₁/n with Z = 4. The structure is solved by direct method and refined to R = 0.099 for 4720 reflections with I ?4σ(I). The results of FT‐IR spectra suggest the binding of cobalt atom to the sulfonamide ligand which is in agreement with the crystal structure determination. In crystal structure, molecule is linked via, C‐H … π, C‐Cl … π and π … π intermolecular interactions. The computational studies like the optimization energy and root means square deviation compare with single crystal structure, frontier molecular orbital (Homo‐Lumo energy) and binding energy of the Co‐SCP has been carried out using DFT/B3LYP level of theory in gaseous phase. Hirshfeld surfaces and the 2D‐fingerprint analysis are performed to study the nature of interactions and their measurable contributions towards crystal packing. The interaction of the complex with DNA is investigated using viscosity measurement and absorption titration studies. The result shows the complex bind to DNA with intercalative mode with high DNA‐binding constant (K_b). Also, in vivo and in vitro cytotoxic studies are performed using S. pombe cells and brine shrimp lethality bioassay. DNA‐cleavage study shows better cleaving ability of the complex.     

Solvent-free silica gel mediated decarboxylation of C–O coupling products of β-diketones and β-oxo esters with malonyl peroxides

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An Anthracene-Based Metal-Organic Framework for Selective Photo-Reduction of Carbon Dioxide to Formic Acid Coupled with Water Oxidation

A Zr-based metal-organic framework has been synthesized and employed as a catalyst for photochemical carbon dioxide reduction coupled with water oxidation. The catalyst shows significant carbon dioxide reduction property with concomitant water oxidation. The catalyst has broad visible light as well as UV light absorption property, which is further confirmed from electronic absorption spectroscopy. Formic acid was the only reduced product from carbon dioxide with a turn-over frequency (TOF) of 0.69 h⁻¹ in addition to oxygen, which was produced with a TOF of 0.54 h⁻¹. No external photosensitizer is used and the ligand itself acts as the light harvester. The efficient and selective photochemical carbon dioxide reduction to formic acid with concomitant water oxidation using Zr-based MOF as catalyst is thus demonstrated here.