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With the increasing demand for bone implant therapy, titanium alloy has been widely used in the biomedical field. However, various potential applications of titanium alloy implants are easily hampered by their biological inertia. In fact, the interaction of the implant with tissue is critical to the success of the implant. Thus, the implant surface is modified before implantation frequently, which can not only improve the mechanical properties of the implant, but also polish up bioactivity and osseoconductivity on a cellular level. This paper aims at reviewing titanium surface modification techniques for biomedical applications. Additionally, several other significant aspects are described in detail in this article, for example, micromorphology, microstructure evolution that determines mechanical properties, as well as a number of issues concerning about practical application of biomedical implants.

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We introduce the concept of interval harmonically convex functions. By using two different classes of convexity, we get some further refinements for interval fractional Hermite-Hadamard type inequalities. Also, some examples are presented. MSC: 26D15; 26E25; 26A33

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