Titanium (Ti), as a hard tissue implant, is facing a big challenge for rapid and stable osseointegration owing to its intrinsic bio-inertness. Meanwile, surface-related infection is also a serious threat. In this study, large-scale quasi-vertically aligned sodium titanate nanowire (SNW) arrayed coatings incorporated with bioactive Cu2+ ions were fabricated through a compound process involving acid etching, hydrothermal treatment (HT), and ion exchange (IE). A novel coating based on sustained ion release and a shape-preserving design is successfully obtained. Cu2+ substituted Na+ in sodium titanate lattice to generate Cu-doped SNW (CNW), which maintains the micro-structure and phase components of the original SNW, and can be efficiently released from the structure by immersing them in physiological saline (PS) solutions, ensuring superior long-term structural stability. The synergistic effects of the acid etching, bidirectional cogrowth, and solution-strengthening mechanisms endow the coating with higher bonding strengths. In vitro antibacterial tests demonstrated that the CNW coatings exhibited effective good antibacterial properties against both Gram-positive and Gram-negative bacteria based on the continuous slow release of copper ions. This is an exciting attempt to achieve topographic, hydrophilic, and antibacterial activation of metal implants, demonstrating a paradigm for the activation of coatings without dissolution and providing new insights into insoluble ceramic-coated implants with high bonding strengths.

In this paper, we introduce a new family of generalized Bernstein operators based on q integers, called ( α , q ) -Bernstein operators, denoted by T n , q , α ( f ) . We investigate a Kovovkin-type approximation theorem, and obtain the rate of convergence of T n , q , α ( f ) to any continuous functions f. The main results are the identification of several shape-preserving properties of these operators, including their monotonicity- and convexity-preserving properties with respect to f ( x ) . We also obtain the monotonicity with n and q of T n , q , α ( f ) .