Here the group B is a Borel subgroup and N is the normalizer of a maximal torus contained in B.

Let V be a smooth vector field on a smooth manifold M. There is a unique maximal flow D → M whose infinitesimal generator is V. Here D ⊆ R × M is the flow domain.

Here I is the maximal open interval of R for which the geodesic is defined.

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

( Here a subset S of R is located if, whenever x < y are real numbers, either there exists an element s of S such that x < s, or y is an upper bound of S .)

Given a homogeneous prime ideal P of, let X be a subset of P < sup > n </ sup >( k ) consisting of all roots of polynomials in P .< ref > The definition makes sense since if and only if for any nonzero λ in k .</ ref > Here we show X admits a structure of variety by showing locally it is an affine variety.

Here is a nonempty closed subset of, is a random vector whose probability distribution is supported on a set, and.

Here, denotes the set of bounded analytic functions, whenever U is an open subset of the complex plane.

Here general position means that no subset of n + 1 of these points lies in a hyperplane ( a projective subspace of dimension n − 1 ).

Here the set of ideles ( correctly, idèles ) consists of the invertible adeles ; but the topology on the idele group is not their topology as a subset of the adeles.

Here a non-trivial coordinate subspace means a linear subspace spanned by any proper subset of basis vectors.

Here a cut is a subset U of A < sup >+</ sup > ( the non-zero elements of A ) such that if q is in U and p ≤ q then p is in U, and is called regular if whenever p is not in U there is some r ≤ p such that U has no elements ≤ r.

Defeasibility as an anytime algorithm: Here, it is assumed that calculating arguments takes time, and at any given time, based on a subset of the potentially constructible arguments, a conclusion is defeasibly justified.

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, too, she talked low, quirking her head at one or another of the places, most often at Izaak's armchair which faced her across the long table.

Here the New York Central Railroad, one of the Nation's most important carriers, has alone lost 47.6 percent of its passengers since 1949.

Here the problem is essentially one of defining the word `` filling ''.

Here is one of the loveliest fountains in Rome, the Fontana delle Tartarughe or `` Fountain of the Tortoises ''.

Here I was accompanied by Mrs. Okamoto ( Fumio's mother ), her son, Mr. Washizu ( a prospective student with whom I have been corresponding for more than a year ), and Mr. Nishima, one of the science teachers.

`` Here, this will help '', suggested Helva, substituting a magnifying device in one extension and holding it over the picture.

Here, the lord Krishna says that just as a man discards his old clothes and wears new ones ; similarly the soul discards the old body and takes on a new one.

A case has been made out for borrowings of many place-names and even misremembered rhymes such as " Here we go looby-loo ... " – chiefly from one of the Luba varieties – in the USA.

Here we are before you in our guilt, though because of it not one of us can stand in your presence.

In 1953, Lancaster played one of his best remembered roles with Deborah Kerr in From Here to Eternity.

Here, in a supposedly smooth step from one room to another, the Tramp loses his hat in one room, but it is instantly back on his head as he enters the next room.

Here, the difference between the two notions of program mentioned in the last paragraph becomes clear ; one is easily recognized by some grammar, while the other requires arbitrary computation to recognize.

Here, one loops through each of the primitives, determines which pixels in the image it affects, and modifies those pixels accordingly.

Here, the paintings were often done in one sitting and the paints were applied wet-on-wet ;

Borgia was originally buried in a marble tomb beneath the altar of the Church of Santa Maria in Viana with an inscription " Here lies in little earth one who was feared by all, who held peace and war in his hand.

Here f ′ ( a ) is one of several common notations for the derivative ( see below ).

Here the superscript is one of the two musical isomorphisms, and is the Hodge dual.

Here the nymphs came to converse with Dryope, who had become a priestess of the temple, but one day Apollo again returned in the form of a serpent and coiled around her while she stood by a spring.

Here Oscan, Greek, and Latin languages were in contact with one another ; according to Aulus Gellius 17. 17. 1, Ennius referred to this heritage by saying he had " three hearts " ( Quintus Ennius tria corda habere sese dicebat, quod loqui Graece et Osce et Latine sciret ).

He famously put the point into dramatic relief with his 1939 essay " Proof of an External World ", in which he gave a common sense argument against scepticism by raising his right hand and saying " Here is one hand ," and then raising his left and saying " And here is another ," then concluding that there are at least two external objects in the world, and therefore that he knows ( by this argument ) that an external world exists.

( In addition to fueling Moore's own work, the " Here is one hand " argument also deeply influenced Wittgenstein, who spent his last years working out a new approach to Moore's argument in the remarks that were published posthumously as On Certainty.

Here, then, is my frank avowal for any one who cares to require it.