Is cyclic ether oxidised by periodic acid?
Cyclic ethers usually do not get oxidized by periodic acid. However, epoxides would do only if they were acidified first or use acidified periodic acid in the reaction (Ref.1). In general, acidified periodic acid has been used as a qualitative test for the presence of epoxide moiety in organic compounds (Ref.1). The procedure is a modification of the qualitative test for  glycols (Ref.2). Hence, epoxide must be converted to 1,2-diols first by acid and oxidation by periodic acid must be followed. The test is described as follows:


  Exactly 2 drops of concentrated nitric acid is added to 2 ml. of a 0.5% solution of periodic acid, and 1 or 2 drops of the unknown is added. Water-insoluble unknowns should first be dissolved in 2 ml. of dioxane or acetic acid. The mixture is shaken and 1 or 2 drops of 5% silver nitrate is added at room temperature. A positive test is the appearance of a white precipitate of silver iodate which usually forms immediately, but may require up to 5 minutes for complete precipitation. In all cases a blank should be run for comparison. The test is negative for simple aldehydes, ketones, and alcohols.


References:


R. Fuchs, R. C. Waters, C. A. Vanderwerf, “General Qualitative Test for Epoxides,” Anal. Chem. 1952, 24(9), 1514 (https://doi.org/10.1021/ac60069a047).
R. L. Shriner, R. C. Fuson, Identification of Organic Compounds; 3rd ed., John Wiley &amp; Sons: New York, NY, 1948, pp. 115-116.