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ZusammenfassungRational Parameterization of Quadrics and their Offsets. In this paper, we study two problems related to quadrics. One is the representation of triangular and quadrangular patches on qnadrics: a necessary and sufficient condition is given for triangular patches on quadrics to be representable as rational quadratic triangular B6zier surfaces. The other is the rationality of the offsets to quadrics: the offsets of regular quadrics are shown to be rational and the algorithms are given for computing their rational parameterizations.Rationale Parametrisierung yon Quadriken und ihren Parallelfliiehen. Die Arbeit studiert zwei mit Quadriken in Zusammenhang stehenden Probleme. Einerseits werden quadratische BEzier Dreiecke auf Quadriken gekennzeichnet. Andererseits wird gezeigt, dag die Parallelfl~ichen regulS.rer Fliichen zweiter Ordnung stets rational sind, und es werden Algorithmen zur Berechnung der rationalen Parametrisierung angegeben.

Early infection and peri‐implantitis after implant restoration are major reasons for dental implant failure. Implant‐associated infections are majorly attributed to biofilm formation. In this study, co‐incorporated zinc‐ (Zn‐) and strontium‐ (Sr‐) nanorod coating on sandblasted and acid‐etched (SLA) titanium (SLA‐Zn/Sr) was fabricated by hydrothermal synthesis. It was aimed at promoting osteogenesis while inhibiting biofilm formation. The nanorod‐like particles (φ 30–50 nm) were found to be evenly formed on SLA‐Zn/Sr (Zn: 1.49 ± 0.16 wt%; Sr: 21.69 ± 2.74 wt%) that was composed of well‐crystallized ZnTiO3 and SrTiO3 phases. With a sufficient interface bonding strength (42.00 ± 3.00 MPa), SLA‐Zn/Sr enhanced the corrosion resistance property of titanium. Besides, SLA‐Zn/Sr promoted the cellular initial adhesion, proliferation and osteogenic differentiation of rBMSCs in vitro while inhibiting the adhesion of Staphylococcus aureus and Porphyromonas gingivalis . In addition, through down‐regulating icaA gene expression, this novel surface reduced the secretion of polysaccharide intercellular adhesion (reduced by 87.9% compared to SLActive) to suppress the S. aureus biofilm formation. We, therefore, propose a new chemical modification on titanium for multifunctional implant material development. Due to the Zn/Sr co‐doping in coating, material properties, early osteogenic effect and antibacterial ability of titanium can be simultaneously enhanced, which has the potential to be applied in dental implantation in the future.