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In this paper, we presented the geometrical properties of Smarandache curves on 3-pseudo-spheres. These curves were examined in the context of the lightcone, de Sitter space, and anti-de Sitter space. By leveraging the curvature relationships between the null curve and its corresponding Smarandache curves, we established necessary and sufficient conditions. Additionally, we illustrated our main results through two examples.

ZnO particles (flower and pseudo sphere) were synthesized via precipitation route and characterized using X-ray diffraction (XRD), Scanning electron microscopy (SEM), Energy dispersive X-ray analysis (EDX), Fourier transform infra-red (FTIR) spectroscopy, Atomic force microscopy (AFM), Particle size analyzer and UV–visible techniques. The photocatalytic activities (PCA) of ZnO flower (uncalcined) and pseudo-sphere (calcined) were evaluated by degrading nonylphenol ethoxylate-9 (NP9EO) under UV and solar irradiation. The process variables i.e., catalyst dose, calcination temperature, H 2 O 2 concentration, pH and UV/solar light exposure were investigated and under optimum conditions of process variables, paper, textile and leather industries effluents were also treated. Calcination at high temperature affected the morphology of ZnO particles. Both ZnO flower and pseudo-sphere degraded NP9EO and pollutants in industrial wastewater efficiently under both UV and solar irradiation. Maximum NP9EO degradation was achieved at 2.5 g/L catalyst dose, high calcination temperature, 4% H 2 O 2 concentration, 6 pH, 110 UV exposure and 12 h solar light exposure. Results reveal that ZnO is efficient photo-catalyst and could be used under solar irradiation for photocatalytic application by tuning the band gap. [ABSTRACT FROM AUTHOR]

Abstract: We consider the one-parameter families of Gauss indicatrices on Lorentzian hypersurfaces in pseudo-spheres in semi-Euclidean 4-space with index 2 and give the types of singularities of the Lorentzian hypersurfaces by the contact theory. [Copyright &y& Elsevier]

Abstract: In this paper we define one-parameter families of Legendrian double fibrations in the products of pseudo-spheres in Lorentz–Minkowski space which are the extensions of four Legendrian double fibrations in the previous research (Izumiya, 2009 ). We show that these are contact diffeomorphic to each other. Moreover, we construct one-parameter families of new extrinsic differential geometries on spacelike hypersurfaces in these pseudo-spheres as applications of such extensions of the Legendrian double fibrations. [Copyright &y& Elsevier]