Enumerate the reactions of $D$-glucose which cannot be explained by its open chain structure.

(N/A) $(1)$ Aldehydes typically give $2, 4-DNP$ test,Schiff's test,and react with $NaHSO_3$ to form hydrogen sulphite addition products. However,$D$-glucose does not undergo these reactions.
$(2)$ The pentaacetate of $D$-glucose does not react with hydroxylamine $(NH_2OH)$. This indicates that a free $-CHO$ group is absent in the cyclic structure of glucose.
$(3)$ $D$-glucose exists in two crystalline forms,$\alpha$ and $\beta$. The $\alpha$-form $(m.p. = 419 \ K)$ crystallises from a concentrated solution at $303 \ K$,while the $\beta$-form $(m.p. = 423 \ K)$ crystallises from a hot saturated aqueous solution at $371 \ K$. This isomerism cannot be explained by the open chain structure.