In German, words starting with sch-( constituting the German phoneme ) would be intercalated between words with initial sca-and sci-( all incidentally loanwords ) instead of this graphic cluster appearing after the letter s, as though it were a single letter — a lexicographical policy which would be de rigueur in a dictionary of Albanian, i. e. dh -, ë -, gj -, ll -, rr -, th -, xh-and zh-( all representing phonemes and considered separate single letters ) would follow the letters d, e, g, l, n, r, t, x and z respectively.

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.

For given nonzero integers a and b there is a nonzero integer of minimal absolute value among all those of the form ax + by with x and y integers ; one can assume d > 0 by changing the signs of both s and t if necessary.

which serve to show that s = 0 is located at position 0 and s = ρπ / 2 at ρ, which agrees with the original expressions for x and y.

For example, uncompressed songs in CD format have a data rate of 16 bits / channel x 2 channels x 44. 1 kHz ≅ 1. 4 Mbit / s, whereas AAC files on an iPod are typically compressed to 128 kbit / s, yielding a compression ratio of 0. 09, for a data-rate savings of 0. 91, or 91 %.

* http :// www. amazon. com / s / ref = nb_sb_noss? url = search-alias % 3Dstripbooks & field-keywords = hostile + shores % 3A + A + year + and + a + day & x = 0 & y = 0

the bubble expansion period for an experimental ( x ) or a standard ( s ) charge.

If f is an element of G ( x, y ) then x is called the source of f, written s ( f ), and y the target of f ( written t ( f )).

More explicitly, the action groupoid is the set with source and target maps s ( g, x )

That is, the free variables of < tt > x </ tt > are just < tt > x </ tt >; the free variables of < tt > λx. t </ tt > are the free variables of < tt > t </ tt >, with < tt > x </ tt > removed, and the free variables of < tt > ts </ tt > are the union of the free variables of < tt > t </ tt > and < tt > s </ tt >.

For example, for every < tt > s </ tt > we have < tt >( λx. x ) s → x := s = s </ tt >, demonstrating that < tt > λx. x </ tt > really is the identity.

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.

Since p ( x ) is irreducible, this means that p ( x ) = k ( x − a ), for some k ∈ F

Because the characters were 8 x 12 pixels this meant that video resolutions of 512 x 192 pixels ( in 64x16 character mode ), or 640 x 300 pixels ( in 80x24 character mode ) were created, which was quite high for the time.

The " double width " mode of the TRS-80 was also supported, so 256 x 192 pixels ( in 32x16 character mode ), or 320 x 300 pixels ( in 40x24 character mode ) were also possible.

In general, if y = f ( x ), then it can be transformed into y = af ( b ( x − k )) + h. In the new transformed function, a is the factor that vertically stretches the function if it is greater than 1 or vertically compresses the function if it is less than 1, and for negative a values, the function is reflected in the x-axis.

As in so many programming languages, the operation ( V, x ) is often written V ← x ( or some similar notation ), and ( V ) is implied whenever a variable V is used in a context where a value is required.

* Ai ( x ), the Airy function, a special function in mathematics

For example, the graph contains the points ( 1, 1 ), ( 2, 0. 5 ), ( 5, 0. 2 ), ( 10, 0. 1 ), ... As the values of x become larger and larger, say 100, 1000, 10, 000 ..., putting them far to the right of the illustration, the corresponding values of y,. 01,. 001,. 0001, ..., become infinitesimal relative to the scale shown.

The oblique asymptote, for the function f ( x ), will be given by the equation y = mx + n.

Similarly, given any element y of Y, there is a function f < sub > y </ sub >, or f (·, y ), from X to Z, given by f < sub > y </ sub >( x ) := f ( x, y ).

( valid for any elements x, y of a commutative ring ),

In a 3-way ANOVA with factors x, y and z, the ANOVA

model includes terms for the main effects ( x, y, z ) and

Some adaptations of the Latin alphabet are augmented with ligatures, such as æ in Old English and Icelandic and Ȣ in Algonquian ; by borrowings from other alphabets, such as the thorn þ in Old English and Icelandic, which came from the Futhark runes ; and by modifying existing letters, such as the eth ð of Old English and Icelandic, which is a modified d. Other alphabets only use a subset of the Latin alphabet, such as Hawaiian, and Italian, which uses the letters j, k, x, y and w only in foreign words.

The aspect ratio is expressed as two numbers separated by a colon ( x: y ).

A common misunderstanding is that x and y represent actual length and height.

: When comparing the above illustration to the below text, please note that the above x: y aspect ratio values are shown as vertical orientation rectangles to better demonstrate visual differences, whereas the aspect ratio values of the text below are written as rotated horizontal orientation rectangles ( e. g. compare 3: 4 vertical orientation illustration to 4: 3 horizontal orientation text ).

Aspect ratios are mathematically expressed as x: y ( pronounced " x-to-y ") and x × y ( pronounced " x-by-y "), with the latter particularly used for pixel dimensions, such as 640 × 480.

The usual order relation ≤ on the real numbers is antisymmetric: if for two real numbers x and y both inequalities x ≤ y and y ≤ x hold then x and y must be equal.

where is the Gelfand representation of x defined as follows: is the continuous function from Δ ( A ) to C given by The spectrum of in the formula above, is the spectrum as element of the algebra C ( Δ ( A )) of complex continuous functions on the compact space Δ ( A ).

(* x x ))

Because the functions f ( g ( x )) and x are equal, their derivatives must be equal.

The derivative of x is the constant function with value 1, and the derivative of f ( g ( x )) is determined by the chain rule.

When g ( x ) equals g ( a ), then the difference quotient for is zero because f ( g ( x )) equals f ( g ( a )), and the above product is zero because it equals f ′( g ( a )) times zero.

The two factors are Q ( g ( x )) and.

: df < sub > x </ sub >( γ ′( 0 ))

x = ( c + ( c ^ 2-4 * k )^( 1 / 2 ))/( 2 * exp ( t *( c / 2-( c ^ 2-4 * k )^( 1 / 2 )/ 2 ))*( c ^ 2-4 * k )^( 1 / 2 )) -

: f ( f ( x )) = f ( x ).

"". join ( chr ( x ^ 0x36 ) for x in xrange ( 256 ))

For a probability density function f ( x ) with the cumulative distribution function F ( x ), the Lorenz curve L ( F ( x )) is given by:

For example, the axiom AC < sub > 11 </ sub > can be paraphrased to say that for any relation R on the set of real numbers, if you have proved that for each real number x there is a real number y such that R ( x, y ) holds, then there is actually a function F such that R ( x, F ( x )) holds for all real numbers.