Northumberland 1542 and Hexhamshire in 1572. Islandshire, Bedlingtonshire and Norhamshire were incorporated into Northumberland in 1844. Tynemouth and other settlements in North Tyneside were transferred to Tyne and Wear in 1974 under the Local Government Act 1972. Lying on the Anglo-Scottish border, Northumberland has been the site of a number of battles. The county is noted for its undeveloped landscape of high moorland, now largely protected as the Northumberland National Park. Northumberland is the least densely populated county in England, with only 62 people per square kilometre. Northumberland originally meant 'the land of the people living north of the River Humber'.
Densely defined operator of "X" and takes values in "Y", written "T" : dom("T") ⊆ "X" → "Y". Sometimes this is abbreviated as "T" : "X" → "Y" when the context makes it clear that "X" might not be the set-theoretic domain of "T". Densely defined operator In mathematics – specifically, in operator theory – a densely defined operator or partially defined operator is a type of partially defined function. In a topological sense, it is a linear operator that is defined "almost everywhere". Densely defined operators often arise in functional analysis as operations that one would like to apply to a larger