For example, the open interval ( 0, 1 ) does not have a least element: if x is in ( 0, 1 ), then so is x / 2, and x / 2 is always strictly smaller than x.

As an example, the field of real numbers is not algebraically closed, because the polynomial equation x < sup > 2 </ sup > + 1 = 0 has no solution in real numbers, even though all its coefficients ( 1 and 0 ) are real.

Also, no finite field F is algebraically closed, because if a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > n </ sub > are the elements of F, then the polynomial ( x − a < sub > 1 </ sub >)( x − a < sub > 2 </ sub >) ··· ( x − a < sub > n </ sub >) + 1

Here, < sub > n </ sub > denotes the sample mean of the first n samples ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >), s < sup > 2 </ sup >< sub > n </ sub > their sample variance, and σ < sup > 2 </ sup >< sub > n </ sub > their population variance.

In more general sense, each column is treated as a polynomial over GF ( 2 < sup > 8 </ sup >) and is then multiplied modulo x < sup > 4 </ sup >+ 1 with a fixed polynomial c ( x ) = 0x03 · x < sup > 3 </ sup > + x < sup > 2 </ sup > + x + 0x02.

For example, the analysis of the debris at the testing site of the first U. S. hydrogen bomb, Ivy Mike, ( 1 November 1952, Enewetak Atoll ), revealed high concentrations of various actinides including americium ; due to military secrecy, this result was published only in 1956.

It hit number 1 in the UK singles chart in April 1972, spending 24 weeks total on the charts, topped the RPM national singles chart in Canada for three weeks, and rose as high as number 11 in the U. S. It is also a controversial instrumental, as it combined pipes with a military band.

He reprised resolutions for constitutional amendments to provide for 1 ) the direct election of the president, rather than by the electoral college, 2 ) the direct election of U. S. Senators, rather than by state legislatures and 3 ) the limiting of judges ' terms to twelve years.

* 2005 – Hurricane Katrina devastates much of the U. S. Gulf Coast from Louisiana to the Florida Panhandle, killing more than 1, 836 and causing over $ 80 billion in damage.

The U. S. survey acre is about 4, 046. 872 609 874 252 square metres ; its exact value ( m < sup > 2 </ sup >) is based on an inch defined by 1 metre = 39. 37 inches exactly, as established by the Mendenhall Order.

ASU Online was ranked # 1 in online Student Services and Technology by U. S. News and World Report.

On March 2, the circular formally filing the organization and capitalization ( at $ 1, 400, 000, 000 — 4 % of U. S. national wealth at the time ) of the United States Steel Corporation actually completed the contract.

* 1974 – Vietnam War: the U. S. Congress places a $ 1 billion dollar limit on military aid to South Vietnam.

A court case allowing the União do Vegetal to import and use the tea for religious purposes in the United States, Gonzales v. O Centro Espirita Beneficente Uniao do Vegetal, was heard by the U. S. Supreme Court on November 1, 2005 ; the decision, released February 21, 2006, allows the UDV to use the tea in its ceremonies pursuant to the Religious Freedom Restoration Act.

The U. S. welcomed Brunei Darussalam's full independence from the United Kingdom on January 1, 1984, and opened an embassy in Bandar Seri Begawan on that date.

Category: U. S. Route 1

In 2009, the North Carolina Department of Transportation began widening 1. 1 miles of U. S. 421 ( King Street ) to a four to six-lane divided highway with a raised concrete median from U. S. 321 ( Hardin Street ) to east of N. C. 194 ( Jefferson Road ), including a new entrance and exit to the new Watauga High School, at a cost of $ 16. 2 million.

The 2003 All-Star Game had the same U. S. viewership as 2002 ( 9. 5 rating ; 17 share ) and the ratings declined in 2004 ( 8. 8 rating ; 15 share ) and 2005 ( 8. 1 rating ; 14 share ).

The song was the # 1 hit in the U. S. for the five weeks encompassing March 1966, the # 1 hit on the Hot 100's end of the year chart for 1966, and the No. 21 song of 1960s, despite the later unpopularity of the Vietnam War and the competing " California Dreaming ", sharply dividing the popular music market.

As it turned out, neither of the originally-proposed UK-designed warheads were actually fitted, being superseded by Red Snow, an Anglicised variant of the U. S. W-28 thermonuclear warhead of 1. 1 Mt yield.

An agreement with Western Union required that U. S. company to route messages in a specified ratio of 3: 1, with three telegraphic messages transmitted to Canadian National for every message transmitted to Canadian Pacific.

Other examples include magnetized ferromagnets, which break rotational symmetry, and more exotic states such as the ground state of a BCS superconductor, that breaks U ( 1 ) rotational symmetry.

The U. S. State Department-funded Yale Cambodian Genocide Project estimates approximately 1. 7 million.

Since the U. S .- Chile Free Trade Agreement went into effect on January 1, 2004, U. S .- Chilean trade has increased by 154 %.

`` Even when the islands were under German mandate before World War 1,, Europeans gave Eromonga a wide berth.

Regardless of rights and wrongs, a population and an area appropriate to a pre-World-War- 1 great power have been, following conquest, ruled against their will by a neighboring people, and have had imposed upon them social and economic controls they dislike.

Soon he was playing in the Cologne Municipal Orchestra, and during World War 1,, when musicians were scarce, he joined the opera orchestra as well.

It will be shown that the objectives of the cooperative people in an organization determine the type of network required, because the type of network functions according to the characteristics of the messages enumerated in Table 1.

However, for convenience we will stick to the idea that information can be classified according to Table 1.

As shown in Figure 1, there is a connection for communication between every pair of points.

All four types of message listed in Table 1 are permitted, although decorum and cocktail tradition require holding the commands to a minimum, while exclamations having complimentary intonations are more than customarily encouraged.

Of types of message listed in Table 1, commands and statements are the only ones sent through the vertical network shown in Figure 3.

He points out that from the time of Jackson on through World War 1,, evangelical Protestantism was a dominant influence in the social and political life of America.

The dispatch must have been sent after sundown on September 1.

There was the Neapolitan, Ribas, a capable conniver whose father had been a blacksmith but who had fawned his way up the ladder of Catherine's and Potemkin's favor till he was now a brigadier ( and would one day be the daggerman designated to do in Czar Paul 1,, after traveling all the way to Naples to procure just the right stiletto ).

Four ecclesiastical questions were presented by the General Court to Gorton: `` 1.

The Secretary of War gave his assent after studying the history of the draft in the American Civil War as well as the British volunteer system in World War 1.

In later years Josephus Daniels was to claim that World War 1, was the first in American history in which there was great concern for both the health and morals of our soldiers.

In spite of this catastrophe the final mortality figure from disease in the American Army during World War 1, was 15 per 1,000 per year, contrasted with 110 per 1,000 per year in the Mexican War, and 65 in the American Civil War.

Sturley quoted Quiney as having written on November 1 that if he had `` more monei presente much might be done to obtaine our Charter enlargd, ij faires more, with tole of corne, bestes, and sheepe, and a matter of more valewe then all that ''.

Adrian Quiney wrote to his son Richard on October 29 and again perhaps the next day, since the bearer of the letter, the bailiff, was expected to reach London on November 1.

If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.

According to The Chicago Tribune News Service, State Atty. Gen. Stanley Mosk of California has devised a series of questions which the joiner might well ask about any organization seeking his money and his name: 1.

February's volume was 1 per cent above January's for the first pickup since last October, although it's still 1.5 per cent off from February 1960.

The new City Charter, which should get a Yes vote as Question No. 1 on Nov. 7, would not make a good Mayor out of a bad one.

A three-day confinement week, with a month's vacation and shorter hours all around could be an ultimate demand from cell occupants of the nation, with fringe benefits including: 1.

`` Wagon Train '' is reported the No. 1 TV show.

For example: 1.

1.