Now let us imagine a wing of B-52's, on alert near their `` positive control ( or fail-safe ) points '', the spots on the map, many miles from Soviet territory, beyond which they are forbidden to fly without specific orders to proceed to their targets.

To find out, we traveled throughout that part of Laos still nominally controlled, in the daytime at least, by the Royal Lao Army: from Attopeu, the City of Buffalo Dung in the southeast, to Muong Sing, the City of Lions in the northwest, close to Communist China ( map, page 250 ).

Ethnographic map of Anatolia from 1911.

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

Celsius conducted many geographical measurements for the Swedish General map, and was one of earliest to note that much of Scandinavia is slowly rising above sea level, a continuous process which has been occurring since the melting of the ice from the latest ice age.

A map of Asia dating to 1570, entitled Asiae Nova Descriptio, from Ortelis's Theatrum labels the sea " Mar Maggior.

Brenner's team sliced worms into thousands of ultrathin sections and photographed every section under an electron microscope, then visually matched fibers from section to section, to map out every neuron and synapse in the entire body.

Because F ( x ) is a map from X ′ to K, it is an element of X ′′.

Parts of the Bantu area include languages from other language families ( see map ).

is a linear map from V to X, and for any v in V the map

is a linear map from W to X.

The admiral ordered Hood to establish the safest course into the harbour ; the British had no charts of the depth or shape of the bay except a rough sketch map Swiftsure had obtained from a merchant captain, an inaccurate British atlas on Zealous, and a 35-year old French map aboard Goliath.

The Nigeria-Cameroon border region on the coast from a 1963 map, with Bakassi peninsula in the middle

Satellite map of the San Francisco Bay Area from the U. S. Geological Survey.

A map of Federal Republic of Yugoslavia | Serbia and Montenegro from the 2000 edition of The World Factbook.

* Detailed map of Chad from www. izf. net

A map of Cambridge from 1873

Additional milieu were provided by Chaosium with the release of Dreamlands, a boxed supplement containing additional rules needed for playing within the Lovecraft Dreamlands, a large map and a scenario booklet, and Cthulhu By Gaslight, another boxed set which moved the action from the 1920s to the 1890s.

* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.

) In particular, every continuous bijective map from a compact space to a Hausdorff space is a homeomorphism.

A world map screenshot from the Amiga version of Civilization

Since the map d restricts to 0 on I < sub > x </ sub >< sup > 2 </ sup > ( the reader should verify this ), d descends to a map from I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup > to the dual of the tangent space, ( T < sub > x </ sub > M )< sup >*</ sup >.

There is a natural map F: X → X ′′ ( the dual of the dual

The map F: x → F ( x ) is thus a map X → X ′′.

Let V, W and X be three vector spaces over the same base field F. A bilinear map is a function

A map τ: X → X is said to be Σ-measurable if and only if, for every σ ∈ Σ, one has.

Combining the above, a map τ is said to be a measure-preserving transformation of X, if it is a map from X to itself, it is Σ-measurable, and is measure-preserving.

The canonical map ker: X ^ X → Con X, relates the monoid X ^ X of all functions on X and Con X. ker is surjective but not injective.

By definition a multilinear map is alternating if it vanishes whenever two of its arguments are equal.

* Orchestrate the elements of the map to best convey its message to its audience.

Yet those are all a typical passenger wishes to know, so the map fulfils its purpose.

" Robinson codified the mapmaker's understanding that a map must be designed foremost with consideration to the audience and its needs.

The intent of the map should be illustrated in a manner in which the percipient acknowledges its purpose in a timely fashion.

In order to convey the message of the map, the creator must design it in a manner which will aid the reader in the overall understanding of its purpose.

The quality of a map's design affects its reader's ability to extract information and to learn from the map.

A legend explains the pictorial language of the map, known as its symbology.

* It is essential for U to be simply connected for the function f to be globally invertible ( under the sole condition that its derivative is a bijective map at each point ).

The first map to delineate the island under its present name, Diego Garcia, is the World Map of Edward Wright ( London 1599 ), possibly as a result of misreading Dio ( or simply " D .") as Diego, and Gratia as Garcia.

The Taylor series of the map is F ( x ) = J · x + O ( x < sup > 2 </ sup >), so a change of coordinates h can only be expected to simplify F to its linear part

Indeed, the map of Barsaive and its neighboring regions established that most of the game takes place where the Ukraine and adjacent Russia are in our world.

Appearing with the term, and helping spread and sustain its popularity, was a political cartoon depicting a strange animal with claws, wings and a dragon-type head satirizing the map of the odd shaped district.

Power sets: The power set functor P: Set → Set maps each set to its power set and each function to the map which sends to its image.

Dual vector space: The map which assigns to every vector space its dual space and to every linear map its dual or transpose is a contravariant functor from the category of all vector spaces over a fixed field to itself.

Tangent and cotangent bundles: The map which sends every differentiable manifold to its tangent bundle and every smooth map to its derivative is a covariant functor from the category of differentiable manifolds to the category of vector bundles.

Likewise, the map which sends every differentiable manifold to its cotangent bundle and every smooth map to its pullback is a contravariant functor.