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.

Here, i is the complex number whose square is the real number − 1 and is identified with the point with coordinates ( 0, 1 ), so it is not the unit vector in the direction of the x-axis ( this confusion is just an unfortunate historical accident ).

Here are the point coordinates in the canonical system, whose origin is the center of the ellipse, whose-axis is the unit vector coinciding with the major axis, and whose-axis is the perpendicular vector coinciding with the minor axis.

Here is the Jones vector ( is the imaginary unit with ).

Here a rank 1 tensor ( matrix product of a column vector and a row vector ) is the same thing as a rank 1 matrix of the given size.

Here is the tensor derivative of the velocity vector, equal in Cartesian coordinates to the component by component gradient.

Here the random vector is the vector r of random returns on the individual assets, and the portfolio return p ( a random scalar ) is the inner product of the vector of random returns with a vector w of portfolio weights — the fractions of the portfolio placed in the respective assets.

Here is a-dimensional vector, is the known-dimensional mean vector, is the known covariance matrix and is the quantile function for probability of the chi-squared distribution with degrees of freedom.

Here the first three vectors are linearly independent ; but the fourth vector equals 9 times the first plus 5 times the second plus 4 times the third, so the four vectors together are linearly dependent.

Here the numerator is a symmetric matrix while the denominator is a number, the squared magnitude of v. This is a reflection in the hyperplane perpendicular to v ( negating any vector component parallel to v ).

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

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 is a known vector, and is an unknown vector of numbers x < sub > i </ sub > yet to be determined.

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 one considers a modification of the directional derivative by a certain linear operator, whose components are called the Christoffel symbols, which involves no derivatives on the vector field itself.

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

* 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 >

Apollonius's genius reaches its highest heights in Book v. Here he treats of normals as minimum and maximum straight lines drawn from given points to the curve ( independently of tangent properties ); discusses how many normals can be drawn from particular points ; finds their feet by construction ; and gives propositions that both determine the center of curvature at any point and lead at once to the Cartesian equation of the evolute of any conic.

Here is the tangent bundle of.

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, and are vectors in the tangent space ; that is,.

Here, as all three circles are tangent to each other at the same point, Descartes ' theorem does not apply.

Here is a linear transformation of the tangent space of the manifold ; it is linear in each argument.

Here describe the indices of coordinates of the submanifold while the functions encode the embedding into the higher-dimensional manifold whose tangent indices are denoted.

Here td ( X ) is the Todd genus of ( the tangent bundle of ) X.

Here it is tangent at (< sup > 16 </ sup >⁄< sub > 5 </ sub >, 0, < sup > 12 </ sup >⁄< sub > 5 </ sub >) and at (< sup >− 16 </ sup >⁄< sub > 5 </ sub >, 0, < sup >− 12 </ sup >⁄< sub > 5 </ sub >).

Here, is everywhere tangent to the world lines of our adapted observers, and these observers measure the energy density of the incoherent radiation to be.

Here, the timelike unit vector field is everywhere tangent to the world lines of observers who are comoving with the fluid elements, so the density and pressure just mentioned are those measured by comoving observers.

Here, the vector space is the tangent space at the given event, and thus isomorphic as a ( real ) inner product space to E < sup > 1, 3 </ sup >.

Here, the first vector is understood to be a timelike unit vector field ; this is everywhere tangent to the world lines of the corresponding family of adapted observers, whose motion is " aligned " with the electromagnetic field.