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In this paper, we define inhomogeneous Graph-Directed (GD) iterated function systems and show the existence of attractors for this new system. We also prove the existence of fractal invariant measures supported on the attractors constructed therein. Further, we establish some relations between homogeneous GD attractor and inhomogeneous GD attractor.

0.5Ba (Zr0.2Ti0.8)O3-0.5(Ba0.7Sr0.3)TiO3(BST-BZT) ceramic composition is known for exihibiting electrical properties. The present study brings out the prospective approach of utilizing well known BST-BZT ceramic composition for water cleaning application via piezocatalysis, photocatalysis and piezo-photocatalysis process. For this, BST-BZT ceramic composition was synthesized through solid state route reaction method and was characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). Methylene Blue (MB) a cationic dye was used as a representative organic pollutant, where the maximum degradation was observed in piezo-photocatalysis process (∼92%) followed by photocatalysis process (∼82%) and piezocatalysis process (∼65%) in 240 min. Furthermore, the degradation of MB dye was examined under solar light irradiation in order to assess the potential of the BST-BZT ceramic composition. A study on the BST-BZT ceramic composition's photocatalytic activity in an indoor setting was also conducted. Finally, the phytotoxicity level of “Vigna radiata” seeds was examined to determine the extent of MB dye breakdown and its subsequent usage.

An efficient, mild, and novel route is developed to synthesize sulfonylurea via the nickel-catalyzed tandem coupling of sulfonyl azide, isocyanide, and water in aqueous media. The sulfonyl azide is expected to act as a nitrene precursor, which upon reaction with isocyanide generates carbodiimide. Herein, water acts as a nucleophile and reacts with carbodiimide to deliver the product. The protocol uses an inexpensive nickel catalyst, environmentally friendly water (as the nucleophile), and room temperature and provides products in moderate to good yields.