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Page "Birthday problem" ¶ 23
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The sum, difference, product and quotient of two algebraic numbers is again algebraic ( this fact can be demonstrated using the resultant ), and the algebraic numbers therefore form a field, sometimes denoted by A ( which may also denote the adele ring ) or < span style =" text-decoration: overline ;"> Q </ span >.
" text-decoration: overline "> 2 </ span > is irrational.
The following nomina sacra are written in abbreviated forms: < span style =" text-decoration: overline "> ΘΣ </ span > < span style =" text-decoration: overline "> ΚΣ </ span > < span style =" text-decoration: overline "> ΙΣ </ span > < span style =" text-decoration: overline "> ΧΣ </ span > < span style =" text-decoration: overline "> ΠΝΑ </ span > < span style =" text-decoration: overline "> ΠΝΙΚΟΣ </ span > < span style =" text-decoration: overline "> ΥΣ </ span > < span style =" text-decoration: overline "> ΑΝΟΣ </ span > < span style =" text-decoration: overline "> ΟΥΟΣ </ span > < span style =" text-decoration: overline "> ΔΑΔ </ span > < span style =" text-decoration: overline "> ΙΛΗΜ </ span > < span style =" text-decoration: overline "> ΙΣΡΛ </ span > < span style =" text-decoration: overline "> ΜΗΡ </ span > < span style =" text-decoration: overline "> ΠΗΡ </ span > < span style =" text-decoration: overline "> ΣΩΡ </ span >.

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According to the pigeonhole principle, < u style =" text-decoration: overline "> p </ u >( n ) is zero when n > 365.

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It is common, especially in engineering applications, to represent the ideal gas constant by the symbol R. In such cases, the universal gas constant is usually given a different symbol such as < u style =" font-style: italic ; text-decoration: overline "> R </ u > to distinguish it.
In order to derive Charles's law from kinetic theory, it is necessary to have a microscopic definition of temperature: this can be conveniently taken as the temperature being proportional to the average kinetic energy of the gas molecules, < u style =" font-style: italic ; text-decoration: overline "> E </ u >< sub > k </ sub >:
where C is the number density of the gas and < u style =" text-decoration: overline "> u </ u > is the mean speed of the molecules ( not the root mean square speed, although the two are related ).

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If the observed data X < sub > 1 </ sub >, ..., X < sub > n </ sub > are ( i ) uncorrelated, ( ii ) have a common mean μ, and ( iii ) have a common variance σ < sup > 2 </ sup >, then the sample average < span style =" text-decoration: overline "> X </ span > has mean μ and variance σ < sup > 2 </ sup > / n. If our null hypothesis is that the mean value of the population is a given number μ < sub > 0 </ sub >, we can use < span style =" text-decoration: overline "> X </ span > − μ < sub > 0 </ sub > as a test-statistic, rejecting the null hypothesis if < span style =" text-decoration: overline "> X </ span > − μ < sub > 0 </ sub > is large.
To calculate the standardized statistic Z = (< span style =" text-decoration: overline "> X </ span > − μ < sub > 0 </ sub >) / s, we need to either know or have an approximate value for σ < sup > 2 </ sup >, from which we can calculate s < sup > 2 </ sup > = σ < sup > 2 </ sup > / n. In some applications, σ < sup > 2 </ sup > is known, but this is uncommon.
In the above example, a connection with classical Galois theory can be seen by regarding as the profinite Galois group Gal (< span style =" text-decoration: overline "> F </ span >/ F ) of the algebraic closure < span style =" text-decoration: overline "> F </ span > of any finite field F, over F. That is, the automorphisms of < span style =" text-decoration: overline "> F </ span > fixing F are described by the inverse limit, as we take larger and larger finite splitting fields over F. The connection with geometry can be seen when we look at covering spaces of the unit disk in the complex plane with the origin removed: the finite covering realised by the z < sup > n </ sup > map of the disk, thought of by means of a complex number variable z, corresponds to the subgroup n. Z of the fundamental group of the punctured disk.
The nomina sacra are abbreviated in an unusual way: for Ἰησοῦς ( Jesus ), for Ἰησοῦ ( of Jesus ), for Χριστὸς ( Christ ), for Χριστοῦ ( of Christ ), < span style =" text-decoration: overline "> ΠΑP </ span > for Πατήρ ( Father ), and < span style =" text-decoration: overline "> ΣTH </ span > for Σταυρωθῇ ( crucify ).< ref group =" n "> Πατήρ usually was abbreviated to < span style =" text-decoration: overline "> ΠHP </ span >, Σταυρωθῇ to < span style =" text-decoration: overline "> ΣTΘH </ span >.

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For instance, " F ", "< span style =" font-weight: bold "> F </ span >", "< span style =" font-style: italic "> F </ span >", "< span style =" text-decoration: underline "> F </ span >", "< span style =" color: red "> F </ span >", and "< span style =" font-family: Courier "> F </ span >" are all different glyphs, but use the same character.

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The second step occurs when the values stored in Q and < span style =" text-decoration: overline ;"> Q </ span > are transferred to the bit lines by leaving BL at its precharged value and discharging < span style =" text-decoration: overline ;"> BL </ span > through M < sub > 1 </ sub > and M < sub > 5 </ sub > to a logical 0 ( i. e. eventually discharging through the transistor M < sub > 1 </ sub > as it is turned on because the Q is logically set to 1 ).
In the original X-bar theory, the two respective types of entity are called noun phrase ( NP ) and N-bar (< span style =" text-decoration: overline "> N </ span >, N ′).
" text-decoration: overline "> x </ span > and < span style =" text-decoration: overline "> y </ span > are the sample means of X and Y, and s < sub > x </ sub > and s < sub > y </ sub > are the sample standard deviations of X and Y.
Certain structures are represented by < span style =" text-decoration: overline "> X </ span > ( an X with a bar over it ).
Other ways of writing the Philippine Peso sign are " PHP ", " PhP ", " P ", or "< span style =" text-decoration: line-through ;"> P </ span >" ( strike-through or double-strike-through uppercase P ), which is still the most common method, however font support for the Unicode Peso sign has been around for some time.

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* 1 pica = exactly 0. 1660 inch ( versus 0. 166 < font style =" text-decoration: overline "> 6 </ font >
exactly 0. 013 8 < font style =" text-decoration: overline "> 3 </ font > inch
" text-decoration: overline "> 6 </ font > mm.
4. 2 < font style =" text-decoration: overline "> 33 </ font > mm.
0. 352 < font style =" text-decoration: overline "> 7 </ font > mm.
Access to the cell is enabled by the word line ( WL in figure ) which controls the two access transistors M < sub > 5 </ sub > and M < sub > 6 </ sub > which, in turn, control whether the cell should be connected to the bit lines: < span style =" text-decoration: overline ;"> BL </ span > and BL.
On the BL side, the transistors M < sub > 4 </ sub > and M < sub > 6 </ sub > pull the bit line toward V < sub > DD </ sub >, a logical 1 ( i. e. eventually being charged by the transistor M < sub > 4 </ sub > as it is turned on because < span style =" text-decoration: overline ;"> Q </ span > is logically set to 0 ).
If the content of the memory was a 0, the opposite would happen and < span style =" text-decoration: overline ;"> BL </ span > would be pulled toward 1 and BL toward 0.
Then these BL and < span style =" text-decoration: overline ;"> BL </ span > will have a small difference of delta between them and then these lines reach a sense amplifier, which will sense which line has higher voltage and thus will tell whether there was 1 stored or 0.
If we wish to write a 0, we would apply a 0 to the bit lines, i. e. setting < span style =" text-decoration: overline ;"> BL </ span > to 1 and BL to 0.

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The number of distinct semi-meanders of order n is the semi-meandric number < u > M </ u >< sub > n </ sub > ( usually denoted with an overline instead of an underline ).

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for all i and j, where a < sub > i, j </ sub > is the i, j-th entry of A, and the overline denotes complex conjugation.

overline and .
Moreover ( and more embarrassingly, although this is essentially trivial ), mathematicians usually write the dual entity not at the first place, as the physicists do, but at the second one, and they don't use the *- symbol, but an overline ( which the physicists reserve to averages ) to denote conjugate-complex numbers, i. e. for scalar products mathematicians usually write
The overline is a typographical symbol similar to the macron, used in a number of ways in mathematics and science.
( Where the overline over " a + bi " refers to the complex conjugate.

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Under Ambrose's major influence, emperors Gratian, Valentinian II and Theodosius I carried on a persecution of Paganism .< ref name = " MacMullen1984p100 "> MacMullen ( 1984 ) p. 100: ‘ The law of June 391, issued by Theodosius [...] was issued from Milan and represented the will of its bishop, Ambrose ; for Theodosius — recently excommunicated by Ambrose, penitent, and very much under his influence < sup > 43 </ sup > — was no natural zealot.
After the indecisive < ref name =" British historian Townsend Miller "> British historian Townsend Miller: “ But, if the outcome of < nowiki > battle of </ nowiki > Toro, militarily, is debatable, there is no doubt whatsoever as to its enormous psychological and political effects ” in The battle of Toro, 1476, in History Today, volume 14, 1964, p. 270 </ ref > Battle of Toro in 1476 against King Ferdinand II of Aragon, the husband of Isabella I of Castile, he went to France to obtain the assistance of Louis XI, but finding himself deceived by the French monarch, he returned to Portugal in 1477 in very low spirits.
The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:
Immediately prior to insertion, the clinician will perform a pelvic exam to determine the position of the uterus .< ref name =" Dean 2011 "> p. 150: Mechanism of action Although the precise mechanism of action is not known, currently available IUCs work primarily by preventing sperm from fertilizing ova .< sup > 26 </ sup > IUCs are not abortifacients: they do not interrupt an implanted pregnancy .< sup > 27 </ sup > Pregnancy is prevented by a combination of the " foreign body effect " of the plastic or metal frame and the specific action of the medication ( copper or levonorgestrel ) that is released.
* Emergency contraceptive pills ( ECPs )— sometimes simply referred to as emergency contraceptives ( ECs ) or the " morning-after pill "— are drugs intended to disrupt ovulation or fertilization, which are steps necessary for pregnancy ( contraceptives ).< ref name =" Trussell 2011 "> p. 121: Mechanism of actionCopper-releasing IUCsWhen used as a regular or emergency method of contraception, copper-releasing IUCs act primarily to prevent fertilization.
< p class =" robots-nocontent "> excluded content </ p >
"< ref >"< span dir =" ltr "> The secret lore of Egypt: its impact on the West </ span >", Erik Hornung, p. 73-75, Cornell University Press, 2001, ISBN 0-8014-3847-0 </ ref >
< span dir =" ltr "> Baptism and Resurrection: Studies in Pauline Theology Against Its Graeco-Roman Background </ span >", A. J. M. Wedderburn, p. 199, Mohr Siebeck, 1987, ISBN 3-16-145192-9 </ ref >
SIP employs design elements similar to the HTTP request / response transaction model .< ref name =" ws_209 "> William Stallings, p. 209
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