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Algebraically, a map is anticonformal if at every point the Jacobian is a scalar times an orthogonal matrix with negative determinant: in two dimensions the Jacobian must be a scalar times a reflection at every point.
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Algebraically and is
; Algebraically closed field: A field F is algebraically closed if every polynomial in F has a root in F ; equivalently: every polynomial in F is a product of linear factors.
Algebraically, a lattice is a set with two associative, commutative idempotent binary operations linked by corresponding absorption laws.
Algebraically it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions.
Algebraically, the projectivization of this vector space is Proj of its symmetric algebra, that is,
Algebraically and if
; Algebraically independent elements: Elements of an extension field of F are algebraically independent over F if they don't satisfy any non-zero polynomial equation with coefficients in F.
Algebraically and with
Algebraically compact modules share many other properties with injective objects because of the following: there exists an embedding of R-Mod into a Grothendieck category G under which the algebraically compact R-modules precisely correspond to the injective objects in G.
Algebraically and be
Algebraically, these units can be thought of as the squares of the corresponding length units.
Algebraically, let a + b be the circumference of a circle, divided into a longer arc of length a and a smaller arc of length b such that
Algebraically and .
Algebraically, this means that the standard MV-algebra generates the variety of all MV-algebras.
map and is
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.
Korzybski is remembered as the author of the dictum: " The map is not the territory ".
This was expressed by Korzybski's most famous premise, " the map is not the territory ".
* The map is not the territory
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
** On every infinite-dimensional topological vector space there is a discontinuous linear map.
** In the category of Riemann surfaces, an automorphism is a bijective biholomorphic map ( also called a conformal map ), from a surface to itself.
Later, his published letters were the basis of Waldseemüller's 1507 map, which is the first usage of America.
" " Giving Directions " is the term for thinking and projecting an anatomically ideal map of how one's body may be used effortlessly.
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 is oriented with south at the top.
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.
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.
The associator is a trilinear map given by
By definition a multilinear map is alternating if it vanishes whenever two of its arguments are equal.
More precisely, a binary operation on a non-empty set S is a map which sends elements of the Cartesian product S × S to S:
Furthermore, a map f: A → B is a homomorphism of Boolean algebras if and only if it is a homomorphism of Boolean rings.
There is a natural map F: X → X ′′ ( the dual of the dual
Because F ( x ) is a map from X ′ to K, it is an element of X ′′.
The map F: x → F ( x ) is thus a map X → X ′′.
map and anticonformal
The circle inversion map is anticonformal, which means that at every point it preserves angles and reverses orientation ( a map is called conformal if it preserves oriented angles ).
1 /|| x ||< sup > 4 </ sup >, and additionally det ( J ) is negative ; hence the inversive map is anticonformal.
The complex analytic inverse map is conformal and its conjugate, circle inversion, is anticonformal.
map and if
Begin the examination of a site with a good map and aerial photos if possible.
Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula
In other words, if we hold the first entry of the bilinear map fixed, while letting the second entry vary, the result is a linear operator, and similarly if we hold the second entry fixed.
Even if the technology to map out every neuron in the brain in real-time were available, and it were known when each neuron was firing, it would still be impossible to know how a particular firing of neurons translates into the observed behavior.
A bounded linear map, π: A → B, between C *- algebras A and B is called a *- homomorphism if
Given two manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both
Two manifolds M and N are diffeomorphic ( symbol usually being ) if there is a smooth bijective map f from M to N with a smooth inverse.
They are diffeomorphic if there is an r times continuously differentiable bijective map between them whose inverse is also r times continuously differentiable.
Model example: if U and V are two connected open subsets of R < sup > n </ sup > such that V is simply connected, a differentiable map f: U → V is a diffeomorphism if it is proper and if
The board starts off with a portion of the map left blank: when players expand into the blank region, terrain hexes are drawn at random from a supply and placed in the empty space, and, if a land hex is " discovered ", a number token may be assigned.
For example, if u < sub > 1 </ sub > is an eigenvector of A, with a real eigenvalue smaller than one, then the straight lines given by the points along α u < sub > 1 </ sub >, with α ∈ R, is an invariant curve of the map.
A map τ: X → X is said to be Σ-measurable if and only if, for every σ ∈ Σ, one has.
A map τ is said to preserve the measure 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.
This smaller map has the condition that if it can be colored with four colors, then the original map can also.
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