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Page "Euclidean geometry" ¶ 83
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case and doubling
In one case, in the early 1940s, Don Flowers ' Modest Maidens was so admired by William Randolph Hearst that he lured Flowers away from the Associated Press and to King Features Syndicate by doubling the cartoonist's salary, and renamed the feature Glamor Girls to avoid legal action by the AP.
* Harvard-Kyoto: Uses upper and lower case and doubling of letters, to avoid the use of diacritics, and to restrict the range to 7-bit ASCII.
Finishing the basement can add significant floor space to a house ( doubling it in the case of a bungalow ) and is a major renovation project
The removed vertices and the new copy of the doubled vertex can then be added back as a single color class, showing that in this case the doubling step leaves the chromatic number unchanged.
Once they had witnessed nearly a doubling of the rate of LP activation, they knew this belief in that keeping cells intact was crucial to studying the effects of hormones was not necessarily true, at least in this case.
Alan Hart had decided to experiment with doubling the length of Doctor Who episodes, with season twenty-two comprising thirteen 45-minute episodes rather than twenty-six 25-minute ones as had previously been the case.
For example, an EV of 10 may be achieved with an aperture ( f-number ) of 2. 8 and a shutter speed of 1 / 125 s. The same exposure is achieved by doubling the aperture area to 2 and halving the exposure time to 1 / 250 s, or by halving the aperture area to 4 and doubling the exposure time to 1 / 60 s ; in each case the response of the film is expected to be the same.
The process of expanding a single track to double track is called duplication or doubling, unless the expansion is to restore what was previously double track, in which case it is called redoubling.
The annual production was about 100, 000 bags of shot a year, with the capacity of doubling that in case of war or other high demand.
Bokor Hill Station plays a prominent part of the movie, in this case doubling as a colonial French plantation.
Furthermore, in this case, we only need to use the same procedure to compute the addition, doubling or subtraction of points to get efficient results, as said above.

case and cube
NeXT's first workstation was officially named the NeXT Computer, although it was widely referred to as " the cube " because of its distinctive case, a 1 ft x 1 ft x 1 ft magnesium cube, an edict of Jobs ' designed by Apple IIc case designer Frogdesign.
In this case the ends of the string are fitted with a ball, cube or similar which stops the string from slipping out too easily.
The Hilbert cube shows that this is not the case.
While the latter is less obvious than the former for the general case, it is easily seen for the one-sixth of the unit cube formed by a face ( area 1 ) and the midpoint of the cube ( height 1 / 2 ).
In this case, the cube is classed as a simple magic cube.
This is not the case with the above definition for the cube.
As in the case of magic squares, a bimagic cube has the additional property of remaining a magic cube when all of the entries are squared, a trimagic cube remains a magic cube under both the operations of squaring the entries and of cubing the entries.
This is not the case with the above definition for the cube.
This is not the case with the original definition, which does not require that the planar and diagonal squares be a pandiagonal magic cube.
The ring of integers of K is spanned by 1 and the square root of d only in the second case, and in the first case there are such integers that lie at half the ' lattice points ' ( for example, when d = − 3, these are the Eisenstein integers, given by the complex cube roots of unity ).
** Hypercube, a cube < sup > d </ sup >, where d > 3 ( the word tesseract was used, especially in nineteenth and early twentieth century British semi-popular books on mathematics, to denote the special case d = 4
In the case of ICT4D, this three-dimensional interplay has been depicted as a cube.
In this case, the pyrite has dissolved away yielding a cube shape and residual gold.
As a special case, this can be used to solve the Delian problem: how much must the length of a cube be increased in order to double its volume?

case and impossibility
One proof of the impossibility of finding a planar embedding of K < sub > 3, 3 </ sub > uses a case analysis involving the Jordan curve theorem, in which one examines different possibilities for the locations of the vertices with respect to the 4-cycles of the graph and shows that they are all inconsistent with a planar embedding.
In opposition to this, the fetish represents the impossibility of pleasure with the body of the mother or the paternal body in the case of females.
Other cases that illustrate the case law for impossibility defences are People v. Lee Kong ( 1892 ), State v. Mitchell ( 1902 ) and United States v. Thomas ( 1962 ).
A replicator can create any inanimate matter, as long as the desired molecular structure is on file, but it cannot create antimatter, dilithium, latinum, or a living organism of any kind ; in the case of living organisms, non-canon works such as the Star Trek: the Next Generation Technical Manual state that, though the replicators use a form of transporter technology, it's at such a low resolution that creating living tissue is a physical impossibility.
Modern historians, though, keep in mind Suetonius, Tacitus and Cassius Dio's severe bias against Nero and the impossibility of them knowing private events, and hence recognize that Poppaea may have simply died due to fatal miscarriage complications or in childbirth ( in which case the second child also did not survive ).
This ordering is not only a well ordering, it also has the property that any monomial is preceded only by a finite number of other monomials ; this is not the case for lexicographic order, where all ( infinitely many ) powers of y are less than x ( that lexicographic order is nevertheless a well ordering is related to the impossibility to construct an infinite decreasing chain of monomials ).
This was also the case for the Swiss Army knife manufacturers especially Wenger S. A. Changing airport security regulations and the impossibility to carry pocket knives as carry on luggage diminished the sales of Swiss Army knives at duty free shops.
It provides the figure of vice president, who in case of physical or moral impossibility of the president, exercise the powers and prerogatives of the latter.
While talking about appealing against " reports ", the authors of the paper, according to lawyer Dmitry Bartenev, mistakenly identify reports with actions of experts ( or an expert institution ) and justify the impossibility of " parallel " examination and evaluation of actions of experts without regard for the scope of evaluated case.
In the former case, there is a trivial proof of impossibility — such an algorithm would need to map a finite large set of input onto a smaller set of output on a one-to-one basis.
The non-numerical preference relation were initially considered unsuitable for iterated revision because of the impossibility of reverting a revision by a number of other revisions, which is instead possible in the numerical case.
Azerbaijan, Kyrgyzstan, Turkistan and Bashkortostan should receive a territorial autonomy, Turks living along the Volga and the Crimean Turks should receive a cultural autonomy in the case of impossibility of territorial autonomy.
In the case of the EPR paradox, quantum entanglement appears to allow for the physical impossibility of information transmitted faster than the speed of light, violating special relativity.

case and construction
Locating the lowercase letters in columns 6 and 7 caused the characters to differ in bit pattern from the upper case by a single bit, which simplified case-insensitive character matching and the construction of keyboards and printers.
Because there is no canonical well-ordering of all sets, a construction that relies on a well-ordering may not produce a canonical result, even if a canonical result is desired ( as is often the case in category theory ).
Extremely large objects are normally shipped in sections and assembled onsite, but shipping an assembled unit reduced costs and avoided reliance on construction labor at the delivery site ( which in this case was still recovering from Hurricane Katrina ).
With their careful constructionand in the case of Easy Street and The Immigrant, their social commentary — these films are considered by Chaplin scholars to be among his finest work.
A typical application is furnished by the Arzelà – Ascoli theorem and in particular the Peano existence theorem, in which one is able to conclude the existence of a function with some required properties as a limiting case of some more elementary construction.
The same type of construction works in the general case of congruence equations.
Before beginning the construction, the vertex figure ABCD is obtained by cutting each connected edge at ( in this case ) its midpoint.
The case helped halt the construction of a power plant on Storm King Mountain in New York State.
However, there could still be an even more complex flash-back construction in American films in the case of W. S. Van Dyke ' sThe Lady of the Dugout ( 1918 ).
Placing the modifying noun in the genitive case is one way to indicate that two nouns are related in a genitive construction.
Modern English typically does not morphologically mark nouns for a genitive case in order to indicate a genitive construction ; instead, it uses either the
Early Italian instruments, on the other hand, were so light in construction that they were treated rather like a violin: kept for storage in a protective outer case, and played after taking it out of its case and placing it on a table.
# We apply this construction to the case when the manifold M is the underlying space of a Lie group G, with G acting on G = M by left translations L < sub > g </ sub >( h ) = gh.
( Diophantus also resorts to what could be called a special case of a secant construction.
In categorical terms, this is a special case of a ( co ) filtered limit construction.
In 1888, during the construction of the new building, workers discovered the dismembered torso of a female ; the case, known as the " Whitehall Mystery ", has never been solved.
In the case of extremely mountainous terrain, railway engineers opted for the more economical narrow gauge construction.
Ideon's article also mentioned the fact that Meri himself had shown concern for the condition of the then Soviet-era construction ( in one memorable case Meri, having arrived from Japan, led the group of journalists that were expecting him, to the airport's toilets to do the interview there, in order to point out the shoddy condition of the facilities ).
(" Screen " in this case refers to electrical " screening " or shielding, not physical construction: all " grid " electrodes in between the cathode and plate are " screens " of some sort rather than solid electrodes since they must allow for the passage of electrons directly from the cathode to the plate ).
One such application, ccsNet, was tested in a case study funded by the Federal Transportation Administration ( FTA ) in which the efficacy of configuration management was measured through comparing the approximately 80 % complete construction of the Los Angeles County Metropolitan Transit Agency ( LACMTA ) 1st and 2nd segments of the Red Line, a $ 5. 3 billion rail construction project.
The Jones matrix in each case may therefore be written with the convenient construction
Most Lithuanian nouns can take the illative ending, indicating that from the descriptive point of view the illative still can be treated as a case in Lithuanian, although since the beginning of the 20th century it isn't included in the lists of standard Lithuanian cases in most grammars and textbooks and the prepositional construction į + accusative is more frequently used today to denote direction.

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