Here we define the distance in B ( X, M ) in terms of the distance in M as

Here, X is a set, and Σ is a sigma-algebra on X, so that the pair ( X, Σ ) is a measurable space.

Here is the center of the ellipse, and is the angle between the < math > X </ Math >- axis and the major axis of the ellipse.

Notable story arcs of this decade are " Revolution " ( 2000 ), " Eve of Destruction ," " E Is For Extinction " ( 2001 ), " Planet X ," " Here Comes Tomorrow ," " Gifted ," ( 2004 ) X-Men: Phoenix-Endsong, " House of M ," " Decimation " ( 2005 ), Deadly Genesis ( 2005 – 2006 ), " Endangered Species " ( 2007 ), " Messiah Complex " ( 2007 – 2008 ), " Divided We Stand " ( 2008 ), " Manifest Destiny " ( 2008 – 2009 ), X-Infernus, " Messiah War ," " Utopia ," " Nation X " and " Necrosha " ( 2009 ).

Here Mavrodes ' worry about X = " to make something its maker cannot lift " will no longer be a problem because " God does X " is not logically consistent.

Here C < sub > b </ sub >( X ) denotes the C *- algebra of all continuous bounded functions on X with sup-norm.

(" Here lies very high and powerful excellent prince Charles X by name king, by the grace of God, of France and of Navarre ")

The American Journal of Human Genetics released an article in 2007 stating " Here we show, by using 86 complete mitochondrial genomes, that all Indigenous American haplogroups, including Haplogroup X ( mtDNA ), were part of a single founding population.

Here A < sub > n </ sub > is the free abelian group or module whose generators are the n-dimensional oriented simplexes of X.

Here one starts with some covariant additive functor F and some module X.

Here the X < sub > i </ sub > are the generalized forces corresponding to the external variables x < sub > i </ sub >.

In 1999, DMX released his best-selling album ... And Then There Was X, which featured the hit single " Party Up ( Up in Here )".

Here Q < sub > Y | X </ sub >( y | x ), sometimes called a test channel, is the conditional probability density function ( PDF ) of the communication channel output ( compressed signal ) Y for a given input ( original signal ) X, and I < sub > Q </ sub >( Y ; X ) is the mutual information between Y and X defined as

Here, each vector Y < sub > j </ sub > of the f ' basis is a linear combination of the vectors X < sub > i </ sub > of the f basis, so that

Here Var ( X ) is the variance of X, defined as:

Here P represents the value of the stream in state P and Q the cost of operating the stage with conditions Q.

Here the left-hand side represents the true difference between the value of g at a and at, whereas the right-hand side represents the approximation determined by the derivative plus an error term.

Here each vertex ( or node ) represents a point of choice for a player.

Here represents the reflexive and transitive closure of the step relation meaning any number of consecutive steps ( zero, one or more ).

: Here Fe ()- E represents the iron center of the heme group attached to the enzyme.

Here the first '−' represents the binary subtraction operation, while the second '−' represents the unary negation of the 2.

Here, self-blame and self-contempt mean the application, towards ( a part of ) one's self, of exactly the same dynamic that blaming of, and contempt for, others represents when it is applied interpersonally.

Here is the time integral of voltage but whether or not that represents a physical quantity depends on the nature of the voltage source.

Here, dq < sub > k </ sub >/ T represents a very small exchange of heat energy at temperature T. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.

Here represents the states of no particles, the state of one particle, the states of two identical particles etc.

Here every symbol represents an unambiguous speech sound, but without going into any unnecessary detail.

( Here, the product is taken over all primes p ; in the following, a sum or product taken over p always represents a sum or product taken over a specified set of primes, unless noted otherwise.

Here it is usually coupled with connotation which is the second level of analysis, being what the denotation represents.

Here, represents the maximum rate achieved by the system, at maximum ( saturating ) substrate concentrations.

( Here α and β are real and i represents the imaginary unit.

Here, represents an empty tree, contains a piece of data, and organizes the data into branches.

Here, represents the state variable and represents the flux or flow of.

Here, represents a vector of states and represents the corresponding flux tensor.

Here, S ( P, Ei ) represents the similarity between the prototype and the ith exemplar, k is the subscript for the dimensions ( k

Here the ( pc )< sup > 2 </ sup > term represents the square of the Euclidean norm ( total vector length ) of the various momentum vectors in the system, which reduces to the square of the simple momentum magnitude, if only a single particle is considered.

Here, indexes i, j are related to the various components and not to the space coordinates.

Here V is called the representation space and the dimension of V is called the dimension of the representation.

Here the kets and columns are identified with the vectors of V and the bras and rows with the dual vectors or linear functionals of the dual space V < sup >*</ sup >, with conjugacy associated with duality.

Here Ip, 2ψ and 2χ are the spherical coordinates of the polarization state in the three-dimensional space of the last three Stokes parameters.

Here, G × G is viewed as a topological space by using the product topology.

Here, an " event " is a set of zero or more outcomes, i. e., a subset of the sample space.

Here, White has a long-term space advantage.

Here is my space!

Here y *( w ) denotes the value of the linear functional y * ( which is an element of the dual space of W ) when evaluated at the element w ∈ W. This scalar in turn is multiplied by x to give as the final result an element of the space V.

Here one is working with a vector space over the complex numbers.

Here, water partially fills a boiler barrel with a small volume left above to accommodate the steam ( steam space ).

Here is the operator which symmetrizes or antisymmetrizes a tensor, depending on whether the Hilbert space describes particles obeying bosonic or fermionic statistics.

Here + is addition either in the field or in the vector space, as appropriate ; and 0 is the additive identity in either.

Here the vectors are elements of a given vector space V over a field K, and the coefficients are scalars in K.

Here Kasparov played 8. d5 exd5 9. cxd5 a few times early in his career, increasing his space advantage further but falling behind in development.

Here the fiber over a point x in M is the set of all frames ( i. e. ordered bases ) for the tangent space T < sub > x </ sub > M.

:: Here, as in the classical theory V is a braided vector space of dimension n spanned by the E ´ s, and σ ( a so-called cocylce twist ) creates the nontrivial linking between E ´ s and F ´ s.

Here the space of global sections is often finite dimensional, but there may not be any non-vanishing global sections at a given point.

* The dimension of the – vector space is the same for all prime ideals of R .< ref > Here, is the residue field of the local ring .</ ref >

Here, S < sup > n </ sup > denotes the n-dimensional sphere in ( n + 1 )- dimensional space ( so the " ordinary " sphere is S < sup > 2 </ sup > and a circle is S < sup > 1 </ sup >).

In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here " increasing " means each is a proper subspace of the next ( see filtration ):