Sentence examples for focus of order from inspiring English sources

Actually, when the degenerate singular point of system (1.2) δ 1 = δ 2 = 0 is a fine focus of order nine, its infinity is at most a fine focus of order three; when the infinity of system (1.2) δ 1 = δ 2 = 0 is a fine focus of order seven, its degenerate singular point is at most a fine focus of order three.

They proved that nine limit cycles could bifurcate from the origin when the origin is a weak focus of order eight.

For the succession function in (13), if v2(2π) = v3(2π) = · · · = v2k(2π) = 0 and v2k+1(2π) ≠ 0, then the origin is called the fine focus or weak focus of order k, and the quantity of v2k+1(2π) is called the k th focal value at the origin on center manifold of system (8) or (2), k = 1, 2,.... Remark 1.

Further, Theorem 3.1.3 in [15] yields that if the origin of system (3.4)(mid_{delta =varepsilon =0}) is a weak focus of order m, then, when (0<delta,varepsilon ll 1), (3.4) has at most m limit cycles in a neighborhood of the origin.

Next we will prove that the third-order nilpotent singular O ( 0, 0 ) is at most a weak focus of order five, moreover, based on this conclusion, the perturbed system of (1.2) can produce five limit cycles enclosing an elementary node at the origin.

Further, Theorem 3.1.3 in [15] shows that if the origin of system (4.3)(|_{delta=varepsison=0}) is a weak focus of order m, then, when (0<delta,varepsilonll1), (4.3) has at most m limit cycles in a neighborhood of the origin.

But then that's true in our society overall, where the notion of service to the poor that is the focus of the order he helped start seems as quaint as friars in cassocks.

The origin is a weakened focus of maximum order eight for system (1.3).

Although the synchronization algorithm can tolerate changes in focus of the order of 50 μm in our particular optical configuration, the brightfield focus should ideally be maintained at a constant depth in the sample – especially when acquiring 3D datasets over several hundred μm – in order to maintain good synchronization.

But there are stylistic date stamps as well: the soft focus, the out-of-order edits, the reverse zooms, the song "Los Angeles," by Warren Marley.

Only the first order beam is used, and the other orders are predominantly rejected by using an order-sorting aperture, which is placed between the focus of the first-order beam (the location of the sample) and the zone plate.