On Descartes’ rule for polynomials with two variations of signs

Lithuanian Mathematical Journal - For sequences of d + 1 signs + and ? beginning with a + and having exactly two variations of sign, we give some sufficient conditions for the (non)existence...     

Green synthetic investigation and spectral characterization of some spiro pyrazolidine-based heterocycles with potential biological activity

A green, rapid, and efficient methodology is developed for the synthesis of 1-phenyl-3,5-pyrazolidinedione ( 3 ) by the reaction of malonic acid with phenyl hydrazine in the presence of phosphorous oxychloride under solvent-free conditions. The later compound 3 was used as a versatile precursor for green synthesis of chalcone derivatives ( 4a-h ) and spiroheterocyclic compounds ( 5a-h ) with good to excellent isolated yields. The chemical structures of the synthesized compounds were elucidated on the basis of elemental and spectral analyses.