Later, his published letters were the basis of Waldseemüller's 1507 map, which is the first usage of America.

Thompson's 1814 map, his greatest achievement, was so accurate that 100 years later it was still the basis for many of the maps issued by the Canadian government.

Equally proficient in mathematics and geography as well as classical languages, he produced the first woodcut map of Silesia made on the basis of surveys and data collected from local inhabitants, which he published in 1561 under the title " Silesiae Typus " and dedicated to Nicolaus II.

However, in the absence of additional data ( such as a basis ), there is no given map from a space to its dual, and thus such an isomorphism requires a choice, and is " not natural ".

Many government and private publishers use the artwork ( especially the contour lines ) from existing topographic map sheets as the basis for their own specialized or updated topographic maps.

* The first geological map of Britain, much copied in his time, and the basis for all others.

* Karl Richard Lepsius, during the Prussian expedition of 1842, made a quick survey of the ruins and created a first detailed map that would serve as the basis for all future explorations and excavations.

In this case, the perturbation can still be performed ; however, one must be careful to work in a basis for the unperturbed states so that these map one-to-one to the perturbed states, rather than being a mixture.

Jedediah Smith's explorations were the main basis for accurate Pacific-West maps ; all the travels and discoveries of the trappers and fur traders since Ashley went into the map of the western United States he prepared in the winter of 1830 – 31.

Additional contexts could be handled by treating the segment map as a context cache and replacing out-of-date contexts on a least-recently-used basis.

The FAO soil map was a very simple classification system with units very broad, but was the first truly international system, and most soils could be accommodated on the basis of their field descriptions.

The Interim Agreement of 1995 became the basis for subsequent negotiations and agreements such as the Hebron Protocol of 1997 and the Wye River Memorandum of 1998 and it is a basis for the latter Road map for peace of 2002.

If it were possible to draw a map of the world on the basis of Weltanschauung, it would probably be seen to cross political borders — Weltanschauung is the product of political borders and common experiences of a people from a geographical region, environmental-climatic conditions, the economic resources available, socio-cultural systems, and the language family.

Similarly, it would probably almost coincide with a map of the world drawn on the basis of music across people.

The dérive would enable them to map out these forces, and these results could then be used as a basis upon which to build a system of unitary urbanism.

If V is a finite-dimensional vector space, then a linear map T: V → V is called diagonalizable if there exists a basis of V with respect to T which is represented by a diagonal matrix.

* A linear map T: V → V is diagonalizable if and only if the sum of the dimensions of its eigenspaces is equal to dim ( V ), which is the case if and only if there exists a basis of V consisting of eigenvectors of T. With respect to such a basis, T will be represented by a diagonal matrix.

symmetric bilinear form with orthonormal basis v < sub > i </ sub >, the map sending a lattice to its dual lattice gives an automorphism with square the identity, giving the permutation σ that sends each label to its negative modulo n. The image of the above homomorphism is generated by σ and τ and is isomorphic to the dihedral group D < sub > n </ sub > of order 2n ; when n = 3, it gives the whole of S < sub > 3 </ sub >.

Given a set S of matrices, each of which is diagonalizable, and any two of which commute, it is always possible to simultaneously diagonalize all of the elements of S. Equivalently, for any set S of mutually commuting semisimple linear transformations of a finite-dimensional vector space V there exists a basis of V consisting of simultaneous eigenvectors of all elements of S. Each of these common eigenvectors v ∈ V, defines a linear functional on the subalgebra U of End ( V ) generated by the set of endomorphisms S ; this functional is defined as the map which associates to each element of U its eigenvalue on the eigenvector v. This " generalized eigenvalue " is a prototype for the notion of a weight.

< ul >< li > Take an arbitrary set S and form the K-vector space with basis S. The elements of this vector space are those functions from S to K that map all but finitely many elements of S to zero ; we identify the element s of S with the function that maps s to 1 and all other elements of S to 0.

where the first map is the inclusion of " the " fiber F into the total space E and the second map is the fibration onto the basis B.

Let ( C, F ) be a concrete category ( i. e. F: C → Set is a faithful functor ), let X be a set ( called basis ), A ∈ C an object, and i: X → F ( A ) a map between sets ( called canonical injection ).

It is sex that obsesses them, sex that is at the basis of their aesthetic creed.

that is, on the basis of his own sinfulness and abject wretchedness, Piepsam becomes a prophet who in his ecstasy and in the name of God imprecates doom on Life -- not only the cyclist now, but the audience, the world, as well: `` all you light-headed breed ''.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

One of the obvious conclusions we can make on the basis of the last election, I suppose, is that we, the majority, were dissatisfied with Eisenhower conservatism.

But is the result new barnsful of tested knowledge on the basis of which we can with confidence solve our domestic and international problems??

The point is that the reactionary, for whatever motive, perceives himself to have been part or a partner of something that extended beyond himself, something which, consequently, he was not able to accept or reject on the basis of subjective preference.

That he read some of the books assigned to him with a studied carefulness is evident from his notes, which are often so full that they provide an unquestionable basis for the identification of reviews that were printed without his signature.

He assures us, early in the Poetics, that all art is `` imitation '' and that all imitation gives pleasure, but he distinguishes between art in general and poetic art on the basis of the means, manner, and the objects of the imitation.

And it is this, particularly the establishment of archaeology and place-name studies on a scientific basis, which are immediately pertinent to the Saxon Shore.

A court may strike down a law on the basis of an intuitive feeling that the law is inimical to the numerical majority.

Paradoxically the council is weakest in areas that register 4- and 5-to-1 in the party's favor, strongest where Democrats and Republicans compete on a fairly even basis.

The only hope which the public has for getting good teachers is to pay teachers on the basis of merit rather than tenure.

The purchase of compact ( economy ) cars is being made currently on a test basis.

To summarize, it may be said that there is no one prevailing practice in Rhode Island with respect to the taxation of movable property, that assessors would like to see an improvement, and of those who have an opinion, that assessment by the town of location is preferred on the basis of their present knowledge.

In the case of taxpaying corporate stockholders, the measure would be the lesser of the fair market value of the shares or Du Pont's tax basis for them, which is approximately $2.09 per share.

As was said in Gonzales, `` it is the Appeal Board which renders the selective service determination considered ' final ' in the courts, not to be overturned unless there is no basis in fact.

It is estimated that about 542,250 miles of forest development roads, and 80,000 miles of trails, constitute the system that will eventually be needed to obtain the maximum practicable yield and use of the wood, water, forage, and wildlife and recreation resources of the National Forests on a continuing basis.

With the existence of these many factors, some of them variable, it obviously has never been and is not now possible for the Commission to make assignments of AM stations on a case-to-case basis which will insure against any interference in any circumstances.

Essentially, the question presented for decision in the present Daytime Skywave proceeding is whether our decision ( in 1938-1939 ) to assign stations on the basis of daytime conditions from sunrise to sunset, is sound as a basis for AM allocations, or whether, in the light of later developments and new understanding, skywave transmission is of such significance during the hours immediately before sunset and after sunrise that this condition should be taken into account, and some stations required to afford protection to other stations during these hours.