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is and bounded
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.

is and by
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 ''.

is and Asia
And, after becoming the right-hand man of Enver Pasha, he is sent by the latter to pave the way for a new Turkish Empire embracing `` the union of all Turks throughout Central Asia from Adrianople to the Chinese oases on the Silk Trade Route ''.
Central Asia is sunk in a somnolence from which nothing can awaken it ; ;
One such event is the landing in Europe itself, when the mingled familiarity and strangeness of the Occident, after the blank immensities of Asia, shocks the returning traveller into a realization of the infinite possibilities of human life.
`` The President says '', the translator came in, `` that the reason he asked you where you were going is because he hoped you would be visiting other areas in Southeast Asia, and that everywhere you went, you would seek the answer to your question.
It is generally conceded that the Formosan air force is the best by far in Asia, and the army the best trained.
Most immediately relevant to these episodes in Goa, Katanga and Ghana, as to the Suez-Hungary crisis before them, is the belief that the main theater of the world drama is the underdeveloped region of Asia, Africa and Latin America.
You remember the words of President Kennedy a week or so ago, when someone asked him when he was in Canada, and Dean Rusk was in Europe, and Vice President Johnson was in Asia, `` Who is running the store ''??
Then the editorial added prophetically: `` how far they may reach in Asia is yet undetermined, but they fall far short of our dreams of the war conferences ''.
It is not developing an awareness of the new kind of missionary strategy that is called for as young churches emerge in Asia and Africa.
Indonesia is one of the twenty under-developed countries of Asia, Africa and Latin America that are receiving Soviet aid.
As a result, the West is in a poor bargaining position at the current Geneva negotiations on Laos, and South Vietnam and other nations in Southeast Asia are under increased pressure.
`` The important thing from now on '', he said, `` is not to mourn the past but to seize the future opportunity to prevent the loss in northern Viet Nam from leading to the extension of Communism throughout Southeast Asia ''.
The Kennedy hope is that, at the conference or through bilateral talks, the low-wage textile-producing countries in Asia and Europe will see that `` dumping '' practices cause friction all around and may result in import quotas.
Although I have emphasized the barriers which an aroused nationalism has raised against relations between Christians and non-Christians in Asia, the fact is that this development has also widened the gulf between certain Afro-Asian religions themselves.
The god seems to be related to Appaliunas, a tutelary god of Wilusa ( Troy ) in Asia Minor, but the word is not complete.
The abacus ( plural abaci or abacuses ), also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes.
The abacus was in use centuries before the adoption of the written modern numeral system and is still widely used by merchants, traders and clerks in Asia, Africa, and elsewhere.
Most alphabetic scripts of India and Eastern Asia are descended from the Brahmi script, which is often believed to be a descendant of Aramaic.
This organization is used in Southeast Asia, Tibet, Korean hangul, and even Japanese kana, which is not an alphabet.
Asia Minor ( from, Mikrá Asía, small Asia ) is a geographical location at the westernmost protrusion of Asia, also called Anatolia, and corresponds to the western two thirds of the Asian part of Turkey.

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