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

* 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.

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 also shows Hong Kong's maritime boundaries.

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.

It is usually helpful to make a sketch map in the field, showing the size and location of the features of interest and to take photographs at the site.

After obtaining the map, which reveals the location of R ' lyeh and other secret places, Shrewsbury finally lets Alhazred return to his eternal rest.

Older avionics required a pilot or navigator to plot the intersection of signals on a paper map to determine an aircraft's location ; modern systems calculate the position automatically and display it to the flight crew on moving map displays.

A map of Gaul in the 1st century BC, showing the location of the Aedui tribe.

A map depicting the location of the Bosphorus ( red ) relative to the Dardanelles ( yellow ) and the Sea of Marmara.

* Ben Franklin Birthplace A historic site, link provides location and map.

A map dating 1669 showing the location of Multan, Pakistan.

However, the topography other than coastlines and major rivers is quite different, and the only apparent reference to the real world besides the map may be the Blood Wood, known as " Wyrm Wood " before the Scourge and similar in location and extent to the Chernobyl ( Ukrainian for " wormwood ") Zone of alienation.

This graph is planar ( it is important to note that we are talking about the graphs that have some limitations according to the map they are transformed from only ): it can be drawn in the plane without crossings by placing each vertex at an arbitrarily chosen location within the region to which it corresponds, and by drawing the edges as curves that lead without crossing within each region from the vertex location to each shared boundary point of the region.

In 1877 a map was published called Tiefenkarte des Grossen Ozeans by Petermann, which showed a Challenger Tief at the location of that sounding.

The location of this attack, probably because of the Maginot Line, was through the Belgian Ardennes forest ( sector 4 ) which is off the map to the left of Maginot Line sector 6 ( as marked ).

* Named entity recognition ( NER ): Given a stream of text, determine which items in the text map to proper names, such as people or places, and what the type of each such name is ( e. g. person, location, organization ).

Worldwide map services show very little detail of the islands, and are even of limited use to show the location of them with respect to each other and to other islands, because they are so small and far apart.

However, Mapquest zoom level 1 is a suitable map to see the location between Peru and New Zealand.

See also map showing location of the Pitcairn Islands with respect to other island groups and to continents

For the location with respect to French Polynesia, see the inset of: Image: French Polynesia map. jpg.

( not the Canary Islands, as long accepted ) as suggested by the location of the six dots labelled the " FORTUNATA " islands near the left extreme of the blue sea of Ptolemy's map here reproduced.

Using statistics collected from tens of thousands of coincidence events, a set of simultaneous equations for the total activity of each parcel of tissue along many LORs can be solved by a number of techniques, and, thus, a map of radioactivities as a function of location for parcels or bits of tissue ( also called voxels ) may be constructed and plotted.

In nearly every Zelda game, navigating a dungeon is aided by locating a map, which reveals its layout, and a magic compass, which reveals the location of significant items.

* Yahoo map showing jog from west to east for northerly traffic and indicating the approximate location of the original boundary line

An important reference point along a chromosome, which is a very long and compacted string of DNA and proteins, is the centromere ; the distance from a gene to the centromere is referred to as the gene's locus or map location.

* X is commonly used as a generic mark ( selecting an item on a form, indicating a location on a map, etc.