In this paper, we construct two classes of planar polynomial Hamiltonian systems having a center at the origin, and obtain lower bounds for number critical periods these systems. For potential degree n, provide bound n?2 periods, acquire n2/2+n?5/2 when n is odd n2/2?2 even periods. To best our knowledge, are new, moreover latter one twice existing results up to dominant term.

The aim of this study was to identify the morphological configuration of youth athletes from professional soccer clubs and to verify their differences according to the tactical position on the field. Overall, 67 male players aged 15 to 17 years were evaluated. The examined anthropometric measurements included body mass, body height, skinfolds (triceps, subscapular, supraspinal and medial calf),...

We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article is to show that for a principal fibre bundle over paracompact manifolds, there is a principal fibre bundle isomorphism between pull-backs obtained from homoto...

Hemlock forests of the northeastern United States are declining due to the invasive hemlock woolly adelgid (HWA) (Adelges tsugae). Hardwood species replace these forests, which affects soil properties that may influence other communities, such as red-backed salamanders (red-backs) (Plethodon cinereus). This study examined the effects of HWA invasion on soil properties and how this affects red-b...