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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 Northern
The Bourbon economic philosophy, moreover, is not very different from that of Northern conservatives.
Obviously, such a Northern tourist's purpose is somewhat akin to a child's experience with Disneyland: he wants to see a world of make-believe.
Most of these would be in the Northern Hemisphere, where the fallout is concentrating.
Still existing on a `` Northern Union '' telegraph form is a typical peremptory message from Peru grocer J. J. Hapgood to Burton and Graves' store in Manchester -- `` Get and send by stage four pounds best Porterhouse or serloin stake, for Mrs. Hapgood send six sweet oranges ''.
Today Northern Vietnam is overtly Communist ; ;
This is not due to any policy of discrimination on the part of the Northern universities.
and that they can ignore what is happening in Northern cities because what is happening in Little Rock or Birmingham is worse.
In England, Wales, Northern Ireland and Australia, arraignment is the first of eleven stages in a criminal trial, and involves the clerk of the court reading out the indictment.
The region north of this circle is known as the Arctic, and the zone just to the south is called the Northern Temperate Zone.
While strong forms of the various dialects are not normally fully comprehensible to Northern Germans, communication is much easier in Bavaria, especially rural areas, where Bavarian dialect still predominates as the mother tongue.
The town's name is attested as Aisincurt in 1175, derived from a Germanic masculine name Aizo, Aizino and the early Northern French word curt ' farm with a courtyard ' ( Late Latin cortem ).
April ( ) is commonly associated with the season of spring in the Northern hemisphere and autumn in the Southern hemisphere, where it is the seasonal equivalent to October in the Northern hemisphere and vice versa.
* Liberation Day in Italy-April 25 is a National Holiday that celebrates the end of the Nazi Germany occupation in the Northern Italy.
In the Southern Hemisphere, August is the seasonal equivalent of February in the Northern Hemisphere.
* 461 – Majorian is arrested near Tortona ( Northern Italy ) and deposed by the Suebian general Ricimer as puppet emperor.
The Northern Hemisphere is considered to be halfway through its summer and the Southern Hemisphere halfway through its winter on this day.
The Battle of Qarqar is mentioned in extra-biblical records, and was perhaps at Apamea where Shalmaneser III of Assyria fought a great confederation of princes from Cilicia, Northern Syria, Israel, Ammon, and the tribes of the Syrian desert ( 853 BC ), including Ahab ( A-ha-ab-bu < sup > mat </ sup >) ( Adad -' idri ).
under secction 7 ( 1 )( a ), but that section has been superseded by section 66 ( 1 ) of the Police ( Northern Ireland ) Act 1998 ( c. 32 ) which now provides that it is an offence for a person to, amongst other things, assault a constable in the execution of his duty, or a person assisting a constable in the execution of his duty.
Stuart is assigned command of all the cavalry of the Confederate Army of Northern Virginia.

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