Sentence examples for autonomous planar from inspiring English sources

From (2.4), system (2.1) becomes the following real autonomous planar system: d x d t = y + μ x 2 + ∑ i + 2 j = 3 ∞ a i j x i y j = X ( x, y ), d y d t = − 2 x 3 + 2 μ x y + ∑ i + 2 j = 4 ∞ b i j x i y j = Y ( x, y ).

From (2.4), system (2.1) becomes the following real autonomous planar system d x d t = y + μ x 2 + ∑ i + 2 j = 3 ∞ a i j x i y i = X ( x, y ), d y d t = - 2 x 3 + 2 μ x y + ∑ i + 2 j = 4 ∞ b i j x i y j = Y ( x, y ).

The origin of a system is a third-order monodromic critical point if and only if the system can be written in the following form of a real autonomous planar system: begin{aligned} &frac{dx}{dt}=y+mu x^{2}+ sum_{i+2j=3}^{n} a_{ij}x^{i}y^{j}=X x,y), &frac{dy}{dt}=-2x^{3}+2mu xy+sum_{i+2j=4}^{n} b_{ij}x^{i}y^{j}=Y x,y). end{aligned} (2.1).

These observations suggest that PD-oriented cell boundaries have a greater tendency to disassemble than those oriented at other angles, and that this is an autonomous, planar polarized feature of wing epithelial cells.

We have discovered that cell-autonomous planar polarized T1 transitions occur early, during the first phase of the process.

Our data also provide strong evidence for the hypothesis that Fz receptors that cannot stably recruit Dsh, but still localize to cell junctions, can participate in only non-cell-autonomous planar polarity signaling (Amonlirdviman et al. 2005).

Similarly, there is still only sparse evidence for the suggestion that receptors that localize to the membrane but fail to recruit Dsh always show a deficit in only cell-autonomous planar polarity function.

Similarly, a mutation in the KTxxxW motif of Drosophila Fz that blocks Dsh binding also results in a protein that is deficient only in cell-autonomous planar polarity activity (Wu et al. 2008; Wu and Mlodzik 2008).

Taken together these results suggest that it may be a general property of Fz receptors that they need to bind to Dsh to mediate cell-autonomous planar polarity activity, but not to pass polarity information to neighboring cells (Amonlirdviman et al. 2005).

Bifurcation theory for finitely smooth planar autonomous differential systems was considered in [11].

The stabilization and trajectory tracking problems of autonomous airship's planar motion are studied.