** In the category of Riemann surfaces, an automorphism is a bijective biholomorphic map ( also called a conformal map ), from a surface to itself.

For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies

The 1523 " Turin map " of the islands was the first to refer to them as Los Lagartos, meaning alligators or large lizards, By 1530 they were known as the Caymanes after the Carib word caimán for the marine crocodile, either the American or the Cuban crocodile, Crocodylus acutus or C. rhombifer, which also lived there.

If A is a fixed element of a ring ℜ, the first additional relation can also be interpreted as a Leibniz rule for the map given by B ↦.

" He also claimed, when considering all aspects of cartography, that " map design is perhaps the most complex.

Wyman also prototyped such a map for the Washington Metro, though ultimately the idea was rejected.

* ESP shows textual information about the enemy ; such as health, name and distance ; also information about weapons lying around the map, which could be missed without the hack.

They are diffeomorphic if there is an r times continuously differentiable bijective map between them whose inverse is also r times continuously differentiable.

It is also suggested that the Arabs, who reached Lakshadweep and Maldives around 900 AD, may have visited the Chagos, and that Zheng He may have sailed close in 1413 – 1415, since it is documented on a Ming Dynasty map.

Other attributes also set each map apart, for example, restrictions on the placement of initial settlements, whether tiles are distributed randomly, the number of victory points needed to win, and special victory point awards, usually for building on islands across the sea.

Furthermore, the pirate mechanics have also changed: the pirate moves through the middle of the map in a fixed path every turn, and attacks the owner of any nearby settlements.

When the evolution map Φ < sup > t </ sup > ( or the vector field it is derived from ) depends on a parameter μ, the structure of the phase space will also depend on this parameter.

Since all such bijections map an equivalence class onto itself, such bijections are also known as permutations.

By projective duality, an ellipse can be defined also as the envelope of all lines that connect corresponding points of two lines which are related by a projective map.

The Imperial cartographer Johann Friedrich Endersch completed a map of Warmia () in 1755 and also made a copper etching of the galley named " The City of Elbląg " ().

However, he also justified the expression he coined — " the map is not the territory " — by saying that " the denial of identification ( as in ' is not ') has opposite neuro-linguistic effects on the brain from the assertion of identity ( as in ' is ').

For example, in the map of the United States of America, Utah and Arizona are adjacent, but Utah and New Mexico, which only share a point that also belongs to Arizona and Colorado, are not.

This smaller map has the condition that if it can be colored with four colors, then the original map can also.

One can also consider the contravariant power set functor which sends to the map which

In areas of mathematics where one considers groups endowed with additional structure, a homomorphism sometimes means a map which respects not only the group structure ( as above ) but also the extra structure.

E. W. Gilbert's version ( 1958 ) of John Snow ( physician ) | John Snow's 1855 map of the Soho cholera outbreak showing the clusters of cholera cases in the London epidemic of 1854 While the basic elements of topography and theme existed previously in cartography, the John Snow map was unique, using cartographic methods not only to depict but also to analyze clusters of geographically dependent phenomena.

The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite dimensional ; Grothendieck's theorem shows that the higher direct images of coherent sheaves under a proper map are coherent ; this reduces to Serre's theorem over a one-point space.

The map shows both the Angeln and the Schwansen peninsulas

The base does not appear on public U. S. government maps ; the USGS topographic map for the area only shows the long-disused Groom Mine.

A map of Cyprus in the later Bronze Age ( such as is given by J. L. Myres and M. O. Richter in Catalogue of the Cyprus Museum ) shows more than 25 settlements in and about the Mesaorea district alone, of which one, that at Enkomi, near the site of Salamis, has yielded the richest Aegean treasure in precious metal found outside Mycenae.

The latest Ordnance Survey Ireland " Discovery Series " ( Third Edition 2005 ) 1: 50, 000 map of the Dublin Region, Sheet 50, shows the boundaries of the city and three surrounding counties of the region.

This map shows their relative distribution in various parts of Europe.

Information richness or a map that is multivariate shows relationships within the map.

This issue assumes more importance as the scale of the map gets smaller ( i. e. the map shows a larger area ) because the information shown on the map takes up more space on the ground.

This map of the world in 1914 shows the large colonial empires that powerful nations established across the globe

The Sebastian Cabot map ( Antwerp 1544 ) shows a number of islands to the south which may be the Mascarene Islands.

This electrostatic potential map shows how the oxygen atom has a more negative charge ( red ) than the positive ( blue ) hydrogen atoms of a water molecule.

The map at the beginning of this article shows the 32 traditional counties that were in place in Ireland by early 17th century.

A 1905 map shows the Khazar empire in 814.

This 1856 map shows slave states ( gray ), free states ( pink ), U. S. territories ( green ), and Kansas in center ( white ).

A map of the world in the years 1920 – 1945, which shows the League of Nations members during its history

As the map shows, the firestorm jumped natural firebreaks ( river channels ), as well as prepared firebreaks.

* Macbeth's Scotland on Google Maps This map shows some of the primary locations in Macbeth.

This map shows the boundary of 13th century Mongol Empire and location of today's Mongols in modern Mongolia, Russia, Central Asia n States and People's Republic of China | China.

The national Railroad Development Corporation map shows a proposed extension across the border to Chipata in Zambia.

The map also shows the 75th parallel north and 60th parallel north.