Sentence examples for of equal dimension from inspiring English sources

Let G1and G2be connected, simply connected, nilpotent Lie groups of equal dimension.

[[13], Theorem 3.1] Let G1, G2be oriented, connected, simply connected, nilpotent Lie groups of equal dimension.

Let M1 and M2 be oriented, closed, connected manifolds of equal dimension.

[[14], Theorem 4.9] Let M1and M2be closed oriented infra-nilmanifolds of equal dimension and f, g : M1 → M2continuous maps.

Let f, g : M1 → M2 be continuous maps between closed oriented manifolds M1, M2 of equal dimension.

Let M1and M2be orientable infra-nilmanifolds of equal dimension modeled on connected, simply connected, nilpotent Lie groups G1and G1andpectively.

The two types are of equal dimensions: span length=10.1 m, upper flange width=150 cm, column height=4.65 m.

Compared to unreinforced pipes of equal dimensions, a 47-times reduction in the effective strain rate was observed with a 50° reinforcement angle.

One of them wore, covering head and shoulders, a giant penis fashioned out of finely woven straw, appropriately painted, erect, and pointing forward; the other figure wore a similarly fashioned and painted vulva of equal dimensions, elliptical and vertical.

We compare two sensors that consist of 195 μm × 195 μm resonators, where all of the resonator features are of equal dimensions, but one's substrate is partially removed (suspended architecture) and the other's is not (planar architecture).

This weighted average (for each Red, Green, and Blue) is between 0 and 255, and is calculated using the formula below where: x represents a pixel in the newly-resolved image, i represents a pixel in user's provided image, and X represents the subset of all pixels i that are contained in rectangle x when the new and old images are scaled to be of equal dimensions and superimposed.