Sentence examples for any dimensional from inspiring English sources

For space-based telescopes, the mirror substrates often require materials with expansion coefficients close to zero, in order to avoid any dimensional changes due to temperature fluctuations.

As the presented formulations are dimensionless, they are applicable in any dimensional system.

However, no significant differences were observed in any dimensional or mechanical properties of the repair tissues across seeding densities at each evaluation time.

Since the wear of teeth determines their stability and lifetime in relation to the physiological load, an ultrasonic survey of any dimensional changes of the enamel layer and especially of the dentin wall thickness may be very helpful.

This work discusses the second-order generalization of previous research on matrix differential equations dealing with the construction of approximate solutions for the initial problem Y″(x)="f x,Y x),Y′(x)) using matrix-cubic splines without any dimensional increase.

The two problems can be extended to the problems in any dimensional space.

Let (tilde{X}subset X) be any finite dimensional subspace.

Let X ˜ ⊂ X be any finite dimensional subspace.

Let (widetilde{E}subset E) be any finite dimensional subspace.

Under the assumptions of Lemma 3.7, for any finite dimensional subspace.

In any finite dimensional subspace X ⊂ W 0 2, p , all norms are equivalent.