We do not index (X k, U k ) by t but note that these variables may contain time-varying elements.
The differential equations for the fields may contain also time derivative operator ∂ t in addition to the exterior derivative, and there may be additions of fields.
The lead concentration in crystal glassware is often 25 30%; it has been shown that wine kept in lead crystal glass containers for a long time may contain a considerable amount of lead.
Relative to the smoke from a single cigarette, the toxicant content of the smoke from a waterpipe use episode may contain up to 1.2 times the amount of nicotine, 8 times the CO, 3 times the nitric oxides, 4 15 times the acrolein, 6 31 times the formaldehyde, and 3 245 times the various PAHs.
For instance, a metadata for a text file may contain the date and time the document was created.
Parboiled rice may contain two to four times as much thiamine (vitamin B1) and niacin as milled raw rice, and losses in cooking may also be reduced.
Soil gases obtained above the zone of water saturation may contain 10 to 40 times as much carbon dioxide as the free atmosphere, and in some cases carbon dioxide has been shown to make up 30 percent of the soil gases as opposed to 0.03 percent of the free atmosphere.
It is common that external registration gives significantly larger errors than scanner-derived and internal registration errors (Pfeifer et al. 2007), because the point clouds at different times may contain large amount of different features that are natively different.
A cirrhotic liver may contain up to six times more collagen than that of a healthy liver [ 6- 8, 11].
Consider a particular edge u→v in P with the corresponding k-mer v sampled x times (some may contain errors).
