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.

Here X represents the space of messages transmitted, and Y the space of messages received during a unit time over our channel.

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, on the hottest day, it is cool beneath the stone and fresh from the water flowing in the sluices at the bottom of the vaults.

Here in these little rooms -- or stages arched open to the sky and river -- they choose a few lines out of the hundreds they may know and sing them according to one of the modes into which Persian music is divided.

Here, on a desk, is a stack of pamphlets representing the efforts of some of the best men of the day to penetrate these questions.

Here, if anywhere, it is not wholly incontrovertible.

Here we may observe that at least one modern philosophy of history is built on the assumption that ideas are the primary objectives of the historian's research.

Here an important caveat is in order.

Here, then, is what Swift would have called a modest proposal by way of a beginning.

But this we know: Here is a great life that in every area of American politics gives the American people occasion for pride and that has invested the democratic process with the most decent qualities of honor, decency, and self-respect.

Here is a word of advice when you go shopping for your pansy seeds.

Here then is our problem: aircraft are vital to winning a war today because they can perform those missions which a missile is totally incapable of performing ; ;

Here is truly a `` Great Recording of the Century '', and its greatness is by no means diminished by the fact that it is not quite perfect.

Here is an original kedgeree recipe from the Family Club's kitchen:

Here is the promise of a vacation trip they can afford.

Here is where things stand today:

Here the Af distance is 2.44 Aj.

Here the pulmonary vein, as in type 2,, is noted to draw away from the bronchus, and to follow a more direct, independent course to the hilum ( figs. 23, 24 ).

Here the number of trials is a random variable, not a fixed number.

Here there is a specific preventive component which applies in a more generalized sense to any casework situation.

( Here an entry is a form plus the information that pertains to it.

Here again, in the written language it is possible to help the reader get his stresses right by using underlining or italics, but much of the time there is simply reliance on his understanding in the light of context.

Here is the best short explanation of the origins of the Cold War that has been written.

A different ontology arises if we need to attend to the electrodynamics in the device: Here signals propagate at finite speed and an object ( like a resistor ) that was previously viewed as a single component with an I / O behavior may now have to be thought of as an extended medium through which an electromagnetic wave flows.

Here, the are independently distributed error terms with zero mean and finite variance, which may not be the same for all.

Here C is either empty or Prikry generic over K ( so it has order type ω and is cofinal in κ ) and unique except up to a finite initial segment.

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

Here Z < sub > l </ sub > denotes the ℓ-adic integers, but the definition is by means of the system of ' constant ' sheaves with the finite coefficients Z / l < sup > k </ sup > Z.

Here the monodromy around the origin is finite.

In mathematics, an arithmetic group ( arithmetic subgroup ) in a linear algebraic group G defined over a number field K is a subgroup Γ of G ( K ) that is commensurable with G ( O ), where O is the ring of integers of K. Here two subgroups A and B of a group are commensurable when their intersection has finite index in each of them.

( Here F < sub > q </ sub > ⊂ K is the finite field of order q.

Here, the right hand side is clearly not convergent for any non-zero value of t. However, by truncating the series on the right to a finite number of terms, one may obtain a fairly good approximation to the value of for sufficiently small t. Substituting and noting that results in the asymptotic expansion given earlier in this article.

Here the prize-problem consists, especially, in a proof of the conjecture that the lowest excitations of a pure Yang – Mills theory ( i. e. without matter fields ) have a finite mass-gap with regard to the vacuum state.

Here the " objects " should be sets of finite measure ( or, in fact, just of finite outer measure ) for the notion of " dividing the volume in half " to make sense.

Here, as in the philosophy of history, there are three great moments, Oriental religion, which exaggerated the idea of the infinite, Greek religion, which gave undue importance to the finite, and Christianity, which represents the union of the infinite and the finite.

Here the trace formula is an extension of the Frobenius formula for the character of an induced representation of finite groups.

Here a modulus ( or ray divisor ) is a formal finite product of the valuations ( also called primes or places ) of K with positive integer exponents.

Here, is a finite and nonempty set and and are integers.

Here, gevurah implies God's essential power to contract and concentrate His infinite light and strength into the finite letters of Torah ( especially those engraved on the tablets of the covenant, the Ten Commandments ).

Here r < sub > i </ sub > is an element of R and g < sub > i </ sub > an element of G. The sums are finite, by definition of the group ring.