Therefore, phenological phases are used as indicators for detecting ecological impacts of climate change on flora and fauna such as plants, migratory birds or fishes and, consequently, on ecosystems reflecting the results of manifold combinations of environmental interactions [1].
In this section, we introduce some definitions and well-known results of Riemannian manifolds, which help us throughout the article.
In this section we recall some basic definitions and some basic results of Riemannian manifolds, for further study these materials are available in (cf. [15]).
We conduct various shape experiments and our new theoretical and algorithmic results alleviate the modeling difficulty of manifold splines, and hence, promote the widespread use of manifold splines in surface and solid modeling, geometric design, and reverse engineering.
In TSB 08-12-5 issued on June 16, Ford says that while some engine vibration is normal when driving, excessive vibration between 1,800 and 2,200 r.p.m. may be the result of trouble with the intake-manifold bracket, cylinder-head bracket and upper-intake-manifold bracket and bolts.
Findings show that bi-axial rotation of the vessel results in manifold increases of fluid velocity within the constructs, relative to uni-axial rotation about the X- and Z-axes, respectively.
Reconstruction results of PPCA and manifold PPCA are red and blue dots in the second and third rows, respectively.
As a result, the manifold is constructed in terms of temporal and dominant state variables.
Later on, Lyra [2] proposed a further modification of Riemannian geometry and removed non-integrability of length transfer by introducing a gauge function into the structure-less manifold as a result of which a displacement vector arise naturally.
