Seán

Seán or Seaghán (in its pre-1950s Irish form) is an Irish language masculine given name. It is an Irish borrowing of the Norman French Jehan (see Jean). Anglicisations of the name include Séan, Sean, Shane, Shayne, Shaine, Shon (Japanese), Shaun, Shawn and Seann. The name Shane comes from the Ulster English pronunciation of the name, whereas the names Shaun, Shawn, or Sean come from the way it is pronounced in Munster, Leinster, and Connacht.

Origin

The name originated in the Irish language. It is an adaption of the Anglo-Norman name Johan/John. In 1066, the Norman duke, William the Conqueror conquered England, where the Norman French name Jahan / Johan (pronounced [dʒɛˈan]) came to be pronounced Jean, and spelled John. The Norman from the Welsh Marches, with the Norman King of England's mandate invaded parts of Leinster and Munster in the 1170s. The Irish nobility in these areas were replaced by Norman nobles, some of whom bore the Norman French name Johan or the Anglicised name John. The Irish adapted the name to their own pronunciation and spelling, producing the name Seán. Sean is commonly pronounced Shawn (Seán), but in the northern parts of Ireland (owing to a northern dialect), it is pronounced "Shan", "Shen" or "Shayn" (Séan, with the accent on the e instead of the a), thus leading to the variant Shane.

Halland County

Halland County (Hallands län) is a county (län) on the western coast of Sweden. It corresponds roughly to the cultural and historical province of Halland. The capital is Halmstad.

It borders the counties of Västra Götaland, Jönköping, Kronoberg, Skåne and the sea of the Kattegat.

Heraldry

The County of Halland inherited its coat of arms from the province of Halland. When it is shown with a royal crown it represents the County Administrative Board.

Province

Counties mainly serve administrative purposes in Sweden. The culture and history of the area is to be found in its provincial counterpart Halland. The county was designed with virtually the same boundaries as the province. The major exception is a part of Hylte Municipality, which belongs to the province of Småland.

Administration

The main aim of the County Administrative Board is to fulfil the goals set in national politics by the Riksdag and the Government, to coordinate the interests and promote the development of the county, to establish regional goals and safeguard the due process of law in the handling of each case. The County Administrative Board is a Government Agency headed by a governor. See List of Halland Governors.

Euclidean group

In mathematics, the Euclidean group E(n), also known as ISO(n) or similar, is the symmetry group of n-dimensional Euclidean space. Its elements, the isometries associated with the Euclidean metric, are called Euclidean motions.

These groups are among the oldest and most studied, at least in the cases of dimension 2 and 3 – implicitly, long before the concept of group was invented.

Overview

Dimensionality

The number of degrees of freedom for E(n) is n(n + 1)/2, which gives 3 in case n = 2, and 6 for n = 3. Of these, n can be attributed to available translational symmetry, and the remaining n(n − 1)/2 to rotational symmetry.

Direct and indirect isometries

There is a subgroup E⁺(n) of the direct isometries, i.e., isometries preserving orientation, also called rigid motions; they are the moves of a rigid body in n-dimensional space. These include the translations, and the rotations, which together generate E⁺(n). E⁺(n) is also called a special Euclidean group, and denoted SE(n).

The others are the indirect isometries, also called opposite isometries. The subgroup E⁺(n) is of index 2. In other words, the indirect isometries form a single coset of E⁺(n). Given any indirect isometry, for example a given reflection R that reverses orientation, all indirect isometries are given as DR, where D is a direct isometry.