WWDC26：2026 年 6 月 8 日至 12 日 (太平洋时间)

We give lower bounds on the growth rate of Dejean words, i.e. minimally repetitive words, over a k-letter alphabet, for k=5, 6, 7, 8, 9, 10. Put together with the known upper bounds, we estimate these growth rates with the precision of 0,005. As an consequence, we establish the exponential growth of the number of Dejean words over a k-letter alphabet, for k=5, 6, 7, 8, 9, 10.

The $α$--$α$ differential cross sections are analyzed in the optical model using a double--folded potential. With the knowledge of this potential bound and resonance--state properties of $α$--cluster states in $^{8}$Be and $^{12}$C as well as astrophysical S--factors of $^{4}$He($α$,$γ$)$^{8}$Be and $^{8}$Be($α$,$γ$)$^{12}$C are calculated. $Γ_γ$--widths and B(E2)--values are deduced.

The $α$--$α$ differential cross sections are analyzed in the optical model using a double--folded potential. With the knowledge of this potential bound and resonance--state properties of $α$--cluster states in $^{8}$Be and $^{12}$C as well as astrophysical S--factors of $^{4}$He($α$,$γ$)$^{8}$Be and $^{8}$Be($α$,$γ$)$^{12}$C are calculated. $Γ_γ$--widths and B(E2)--values are deduced.

The paper discusses Problems 8 and 88 posed by Stanislaw Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Section 5 of my paper "Estimates of functions of power bounded operators on Hilbert spaces", J. Operator Theory 7 (1982), 341-372. We discuss here some quantitative aspects of Problems 8 and 88 and give answers to open problems discussed in a recent paper by Pelczynski and Sukochev.