Evaluation Fibrations and Path-Components of the Mapping Space M( S ^n+k ,S ^n ) for 8 ≤ k ≤ 13, volume=65, url=https://umj.imath.kiev.ua/index.php/umj/article/view/2488, abstractNote=Let M( S ^m ,S ^n ) be the space of maps from the m-sphere S ^m into the n-sphere S ^n with m,n ≥ 1. We estimate the number of homotopy types of path-components M_α( S ^n+k ,S ^n ) and fiber homotopy types of the evaluation fibrations ω_α :M_α ( S ^n+k ,S ^n )→ S ^n for 8 ≤ k ≤ 13 and α π_n+k ( S ^n ) extending the results of [Mat. Stud. - 2009. - 31, № 2. -P. 189-194]. Further, the number of strong homotopy types of ω_α :M_α ( S ^n+k ,S ^n )→ S ^n for 8 ≤ k ≤ 13 is determined and some improvements of the results from [Mat. Stud. - 2009. - 31, № 2. - P. 189-194] are obtained., number=8, journal=Ukrains’kyi Matematychnyi Zhurnal, author=de, Melo Thiago and Golasinski, M., year=2013, month=Aug., pages=1023–1034