An attic space above insulation makes a house easier to cool.

At the very first, then, Brumidi was required, by the classically pyramidal shape of his central group, to fill in the triangular space above the seated girl on Liberty's right, before starting on the allegorical figures themselves.

Above them, the sky was the black of space, or the almost equal black of the winter sky above Minneapolis, seen against neon-lit snow.

In a complex inner product space, the expression for the cosine above may give non-real values, so it is replaced with

Usually, the train floor is at a level above the bogies, but the floor of the car may be lower between bogies, such as for a double decker train to increase interior space while staying within height restrictions, or in easy-access, stepless-entry, low-floor trains.

If in the above we relax Banach space to normed space the analogous structure is called a normed algebra.

where is the Gelfand representation of x defined as follows: is the continuous function from Δ ( A ) to C given by The spectrum of in the formula above, is the spectrum as element of the algebra C ( Δ ( A )) of complex continuous functions on the compact space Δ ( A ).

Much of the dark space between stars, as seen in the sky of the image above, is due to the human eye's low light sensitivity.

* The extreme value theorem: a continuous real-valued function on a nonempty compact space is bounded above and attains its supremum.

In each of the above cases, the functor sends each space to its tangent bundle and it sends each function to its derivative.

They are continuous through all concealed spaces ( e. g., above a ceiling ), but are not required to extend through concealed spaces if the construction assembly forming the bottom of the space has a fire resistance rating at least equal of the fire barrier wall.

Though easy to understand, the implementation of the algorithm used above is impractical in languages and environments where stack space is severely constrained ( e. g. Java applets ).

Note: The above definition of group velocity is only useful for wavepackets, which is a pulse that is localized in both real space and frequency space.

Heaven was a physical place far above the Earth in a " dark area " of space where there were no stars, basically beyond the Universe.

Also, the tree tops are shrouded in swirling fog, providing the common " negative space " mentioned above in East Asian Art.

Steam just above atmospheric pressure ( all that the boiler could stand ) was introduced into the lower half of the cylinder beneath the piston during the gravity-induced upstroke ; the steam was then condensed by a jet of cold water injected into the steam space to produce a partial vacuum ; the pressure differential between the atmosphere and the vacuum on either side of the piston displaced it downwards into the cylinder, raising the opposite end of a rocking beam to which was attached a gang of gravity-actuated reciprocating force pumps housed in the mineshaft.

The interior of the city hall is large and spacious ; windows in the ceiling above the eighth floor fill the main space with light.

Since the energy-momentum tensor T < sub > μν </ sub > is normally understood to be due to concentrations of matter in four-dimensional space, the above result is interpreted as saying that four-dimensional matter is induced from geometry in five-dimensional space.

And over it is cast the glamour, enhanced beyond all reckoning in the dream, of the remote in time and space – that visionary presence of a vague and gorgeous and mysterious Past which brooded, as Coleridge read, above the inscrutable Nile, and domed pavilions in Cashmere, and the vanished stateliness of Xanadu.

The Klein bottle can be seen as a fiber bundle over S < sup > 1 </ sup > as follows: one takes the square ( modulo the edge identifying equivalence relation ) from above to be E, the total space, while the base space B is given by the unit interval in y, modulo 1 ~ 0.

This elevates the abdominal wall above the internal organs like a dome to create a working and viewing space.

The height was only measured up to the cornice line, making any living space contained in a mansard roof exempt.

The vestibule is separated by a tripartite screen, with an arched central opening flanked above the cornice by bull's-eye openings in which baroque vases stand, from a grand Stair Hall that projects from the south block to accommodate a grand stair that sweeps forward through a heart-shaped opening into the floor space and divides at a landing to return in matched recurving flights to the upper floor.

The summit is small and frequently has a pronounced cornice, reducing usable space.

But there is hope, for Conservation Commissioner Bontempo has tagged the sanctuary as the kind of place the state hopes to include in its program to double its park space.

In general, such apartments afford more protection than smaller buildings because their walls are thick and there is more space.

Since there is a continual loss of micrometeoritic material in space because of the radiation effects, there must be a continual replenishment: otherwise, micrometeorites would have disappeared from interplanetary space.

Of course, if there is a dust blanket around the Earth, the fluxes in interplanetary space should be less than the figures given here.

Second, even if the characteristic polynomial factors completely over F into a product of polynomials of degree 1, there may not be enough characteristic vectors for T to span the space V.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

that is, there is, in the true sense, only a visual space ''.

to this he glued and fitted other pieces of paper and four taut strings, thus creating a sequence of flat surfaces in real and sculptural space to which there clung only the vestige of a picture plane.

One is led to speculate as to why the empty space was there, left for our century to finish.

You may ask what else there is, and the answer is nothing -- nothing but empty space.

Maggie was looking much happier already, clearing a space on the table and chattering about how she could put up a typewriter right there, and be brushing up on her typing so Eugenia wouldn't be ashamed of it.

** On every infinite-dimensional topological vector space there is a discontinuous linear map.

Between the two countries, there are political disputes over several aspects of political control over the Aegean space, including the size of territorial waters, air control and the delimitation of economic rights to the continental shelf.

Early mathematicians regarded axiomatic geometry as a model of physical space, and obviously there could only be one such model.

His report of life there covers a wide range of topics, such as marriage in heaven ( where all angels are married ), children in heaven ( where they are raised by angel parents ), time and space in heaven ( there are none ), the after-death awakening process in the World of Spirits ( a place halfway between Heaven and Hell and where people first wake up after death ), the allowance of a free will choice between Heaven or Hell ( as opposed to being sent to either one by God ), the eternity of Hell ( one could leave but would never want to ), and that all angels or devils were once people on earth.

By the beginning of World War II, many towns and cities had built space, and there were numerous qualified pilots available.

Since there are infinitely many vectors in the basis, this is an infinite-dimensional Hilbert space.

Since a maximal ideal in A is closed, is a Banach algebra that is a field, and it follows from the Gelfand-Mazur theorem that there is a bijection between the set of all maximal ideals of A and the set Δ ( A ) of all nonzero homomorphisms from A to C. The set Δ ( A ) is called the " structure space " or " character space " of A, and its members " characters.

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

This has to be planned in advance as if there is no such space partners have to bid a usually unmakeable slam contract.