This theorem is similar to the theorem of Kakutani that there exists a circumscribing cube around any closed, bounded convex set in Af.

This is true of all components which have such a bounded support.

The tract is bounded by Island Ave., Dicks Ave., 61st St., and Eastwick Ave..

The Atlantic Ocean is bounded on the west by North and South America.

** A uniform space is compact if and only if it is complete and totally bounded.

The region is bounded by the Black Sea to the north, the Mediterranean Sea to the south and the Aegean Sea to the west.

The Anatolian peninsula, also called Asia Minor, is bounded by the Black Sea to the north, the Mediterranean Sea to the south, the Aegean Sea to the west, and the Sea of Marmara to the northwest, which separates Anatolia from Thrace in Europe.

Under this definition, Anatolia is bounded to the East by the Armenian Highland, and the Euphrates before that river bends to the southeast to enter Mesopotamia.

To the southeast, it is bounded by the ranges that separate it from the Orontes valley in Greater Syria and the Mesopotamian plain.

thus, as T decreases, ΔG and ΔH approach each other ( so long as ΔS is bounded ).

We now consider how the choice of description language affects the value of K, and show that the effect of changing the description language is bounded.

The South African plateau, as far as about 12 ° S, is bounded east, west and south by bands of high ground which fall steeply to the coasts.

It lies on Abadan Island ( long, 3 – 19 km or 2 – 12 miles wide, the island is bounded in the west by the Arvand waterway and to the east by the Bahmanshir outlet of the Karun River ), from the Persian Gulf, near the Iraqi-Iran border.

The ACT is bounded by the Goulburn-Cooma railway line in the east, the watershed of Naas Creek in the south, the watershed of the Cotter River in the west, and the watershed of the Molonglo River in the north-east.

The Arabian Sea ( Persian Sea ) is a region of the Indian Ocean bounded on on the north by Pakistan and Iran, on the south by northeastern Somalia, on the east by India and on the west by the Arabian Peninsula.

However, the recursion is bounded because in each recursive application either m decreases, or m remains the same and n decreases.

It is bounded by the Scandinavian Peninsula, the mainland of Europe, and the Danish islands.

The Black Sea is bounded by Europe, Anatolia and the Caucasus and is ultimately connected to the Atlantic Ocean via the Mediterranean and the Aegean Seas and various straits.

Since Bulgarian lev is anyway bounded to Euro Bulgaria is looking for more positive outcomes of the becoming a member of the Eurozone rather than risks.

In general, a linear mapping on a normed space is continuous if and only if it is bounded on the closed unit ball.

Note that the requirement that the maps be continuous is essential ; if X is infinite-dimensional, there exist linear maps which are not continuous, and therefore not bounded.

It is possible, although highly doubtful, that he killed none at all but merely let his reputation work for him by privately claiming every unsolved murder in the state.

The place is inhabited by several hundred warlike women who are anachronisms of the Twentieth Century -- stone age amazons who live in an all-female, matriarchal society which is self-sufficient ''.

since Bourbon whiskey, though of Kentucky origin, is at least as much favored by liberals in the North as by conservatives in the South.

In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.

But apart from racial problems, the old unreconstructed South -- to use the moderate words favored by Mr. Thomas Griffith -- finds itself unsympathetic to most of what is different about the civilization of the North.

The two main charges levelled against the Bourbons by liberals is that they are racists and social reactionaries.

It became the sole `` subject '' of `` international law '' ( a term which, it is pertinent to remember, was coined by Bentham ), a body of legal principle which by and large was made up of what Western nations could do in the world arena.

Ratified in the Republican Party victory in 1952, the Positive State is now evidenced by political campaigns being waged not on whether but on how much social legislation there should be.

He was, and is, with the RAND Corporation, a nonprofit pool of thinkers financed by the U.S. Air Force.

They are huge areas which have been swept by winds for so many centuries that there is no soil left, but only deep bare ridges fifty or sixty yards apart with ravines between them thirty or forty feet deep and the only thing that moves is a scuttling layer of sand.

It is softened by the saltbush and the bluebush, has a peaceful quality, the hills roll softly.

On Fridays, the day when many Persians relax with poetry, talk, and a samovar, people do not, it is true, stream into Chehel Sotun -- a pavilion and garden built by Shah Abbas 2, in the seventeenth century -- but they do retire into hundreds of pavilions throughout the city and up the river valley, which are smaller, more humble copies of the former.

Poetry in Persian life is far more than a common ground on which -- in a society deeply fissured by antagonisms -- all may stand.

Nostalgic Yankee readers of Erskine Caldwell are today informed by proud Georgians that Tobacco Road is buried beneath a four-lane super highway, over which travel each day suburbanite businessmen more concerned with the Dow-Jones average than with the cotton crop.

All but the most rabid of Confederate flag wavers admit that the Old Southern tradition is defunct in actuality and sigh that its passing was accompanied by the disappearance of many genteel and aristocratic traditions of the reputedly languid ante-bellum way of life.

Westbrook further bemoans the Southern writers' creation of an unreal image of their homeland, which is too readily assimilated by both foreign readers and visiting Yankees: `` Our northerner is suspicious of all this crass evidence ( of urbanization ) presented to his senses.

As his disciples boast, even though his emphasis is elsewhere, Faulkner does show his awareness of the changing order of the South quite keenly, as can be proven by a quick recalling of his Sartoris and Snopes families.

The unit of form is determined subjectively: `` the Heart, by the way of the Breath, to the Line ''.

Even the knowledge that she was losing another boy, as a mother always does when a marriage is made, did not prevent her from having the first carefree, dreamless sleep that she had known since they dropped down the canyon and into Bear Valley, way, way back there when they were crossing those other mountains.

I seized the rack and made a western-style flying-mount just in time, one of my knees mercifully landing on my duffel bag -- and merely wrecking my camera, I was to discover later -- my other knee landing on the slivery truck floor boards and -- but this is no medical report.

It is these other differences between North and South -- other, that is, than those which concern discrimination or social welfare -- which I chiefly discuss herein.

To him, law is the command of the sovereign ( the English monarch ) who personifies the power of the nation, while sovereignty is the power to make law -- i.e., to prevail over internal groups and to be free from the commands of other sovereigns in other nations.

Already accidental war is a silent guest at the discussions within the Kennedy Administration about the urgency of disarmament and nearly all other questions of national security.

The one apparent connection between the two is a score of buildings which somehow or other have survived and which naturally enough are called `` historical monuments ''.

The other variables include the dancer who is to perform the movement and the length of time he is to take in its performance.

For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.

In fact the accumulation of the hardware of destruction is day by day increasing our fear of each other.

One is not more true than the other.

Though sex in some form or other enters into all human activity and it was a good thing that Freud emphasized this aspect of human nature, it is fantastic to explain everything in terms of sex.

As Lipton puts it: `` The Eros is felt in the magic circle of marijuana with far greater force, as a unifying principle in human relationships, than at any other time except, perhaps, in the mutual metaphysical orgasms.

it is a spectacle absolutely painful, an epiphany of the suffering flesh unredeemed by spirit, untouched by any spirit other than abasement and humiliation.

But the highroad, according to the description of its traffic, belongs to life as it is lived in unawareness of death, while the way to the churchyard belongs to some other sort of life: a suffering form, an existence wholly comprised in the awareness of death.

Neither is primary experience understood according to the attitude of modern empiricism in which nothing is thought to be received other than signals of sensory qualities producing their responses in the appropriate sense organs.

Whitehead contends that the human way of understanding existence as a unity of interlocking and interdependent processes which constitute each other and which cause each other to be and not to be is possible only because the basic form of such an understanding, for all its vagueness and tendency to mistake the detail, is initially given in the way man feels the world.