Sentence examples for without regularity from inspiring English sources

However, the theorems in [19, 20] deal with solutions of the linear equation under some regularity conditions, for example, the continuity, convexity, differentiability, analyticity and so on, while Theorem 2.1 deals with the general solution of (1.7) without regularity conditions.

It is scary to be without control and routines, but the truth is you are without regularity.

The main part of the ensemble is a long visual field painted in somber tones and punctuated with glistening metal spoons, arranged without regularity but with internal vertical symmetry, synchronized as they are by a powerful guiding force, gravity.

In the various cells, there exists red-shift or blue-shift without obvious regularity.

Besides, without any regularity assumptions, our method can deal with asymmetric and several other failure cases of existing approaches.

The contact resistance presented a fluctuation without obvious regularity, concentrating in the region of 25 and 50 mΩ.

Surprisingly, performance in a random visual search, without any regularity, was better than performance in a mixed design search that contained a beneficial regularity.

In all three cases it is straightforward to use the Axiom of Choice to show that there are sets of reals without the regularity property.

The contact resistance was majorly concentrated in the region of 25 and 50 mΩ, and a relative fluctuation without obvious regularity could be found.

This estimate is known to hold for smooth strongly pseudoconvex domains and also for convex ones (without any regularity assumption, see [23]).

To form metal catalytic layers on a silicon substrate with or without pattern regularity, physical deposition techniques in vacuum such as focused ion beam deposition [3], sputtering [2, 4, 5], conventional vacuum vapor deposition [6], and electron beam evaporation [7] are generally used.