The Etymologicum Magnum presents a medieval learned pseudo-etymology, explaining Aphrodite as derived from the compound habrodiaitos (" she who lives delicately " from habros + diaita ) explaining the alternation between b and ph as a " familiar " characteristic of Greek " obvious from the Macedonians ".

S ( a, b )=( nc + me / m + n, nd + mf / m + n )

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.

Binary operations are often written using infix notation such as a * b, a + b, a · b or ( by juxtaposition with no symbol ) ab rather than by functional notation of the form f ( a, b ).

Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

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.

Now the remainder of dividing either a or b by d is also of the form ax + by since it is obtained by subtracting a multiple of from a or b, and on the other hand it has to be strictly smaller in absolute value than d. This leaves 0 as only possibility for such a remainder, so d divides a and b exactly.

If c is another common divisor of a and b, then c also divides as + bt

: r = ( 2 < sup >( n-m )</ sup >+ 1 )< sup > 2 </ sup > × 2 < sup > m + n </ sup > − 1,

: Ba + 2 ROH → Ba ( OR )< sub > 2 </ sub > + H < sub > 2 </ sub >↑ ( R is an alkyl or a hydrogen atom )

It is the coefficient of the x < sup > k </ sup > term in the polynomial expansion of the binomial power ( 1 + x )< sup > n </ sup >.

This is related to binomials for the following reason: if we write ( x + y )< sup > n </ sup > as a product

However, as 1 + ( k + 1 ) x + kx < sup > 2 </ sup > ≥ 1 + ( k + 1 ) x ( since kx < sup > 2 </ sup > ≥ 0 ), it follows that ( 1 + x )< sup > k + 1 </ sup > ≥ 1 + ( k + 1 ) x, which means the statement is true for r = k + 1 as required.

This may be proved using the inequality ( 1 + 1 / k )< sup > k </ sup > < e.

Harvey writes that the asymptotic time complexity of this algorithm is O ( n < sup > 2 </ sup > log ( n )< sup > 2 + eps </ sup >) and claims that this implementation is significantly faster than implementations based on other methods.

The equation of a circle is ( x − a )< sup > 2 </ sup > + ( y − b )< sup > 2 </ sup > = r < sup > 2 </ sup > where a and b are the coordinates of the center ( a, b ) and r is the radius.

: 2 Dy ( s ) + 6 H < sub > 2 </ sub > O ( l ) → 2 Dy ( OH )< sub > 3 </ sub > ( aq ) + 3 H < sub > 2 </ sub > ( g )

Integrating + 1. 7 ms / d / cy and centering the resulting parabola on the year 1820 yields ( to a first approximation ) 31 ×(( Year − 1820 )/ 100 )< sup > 2 </ sup > seconds for ΔT.

As in the continuous case, the change of coordinates x → x + ( 1 − A )< sup > – 1 </ sup > b removes the term b from the equation.

: 2 Eu + 6 H < sub > 2 </ sub > O → 2 Eu ( OH )< sub > 3 </ sub > + 3 H < sub > 2 </ sub >

: H < sub > 2 </ sub > O ( l ) + H < sub > 2 </ sub > O ( l ) H < sub > 3 </ sub > O < sup >+</ sup >( aq ) + OH < sup >−</ sup >( aq )

# H < sub > 3 </ sub > O < sup >+</ sup >( aq ) + Cl < sup >−</ sup >( aq ) + NH < sub > 3 </ sub > → Cl < sup >−</ sup >( aq ) + NH < sub > 4 </ sub >< sup >+</ sup >( aq )

With the formula C < sub > n </ sub > H < sub > 2n + 2 </ sub >, Alkanes belong to a homologous series of organic compounds in which the members differ by a constant relative molecular mass of 14.

: Precise instructions ( in language understood by " the computer ") for a fast, efficient, " good " process that specifies the " moves " of " the computer " ( machine or human, equipped with the necessary internally contained information and capabilities ) to find, decode, and then process arbitrary input integers / symbols m and n, symbols + and =

: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.

An important class of alcohols are the simple acyclic alcohols, the general formula for which is C < sub > n </ sub > H < sub > 2n + 1 </ sub > OH.

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

n + 1

n + 1

n + 1

mean + delta / n

Two results which follow from the axiom are that " no set is an element of itself ," and that " there is no infinite sequence ( a < sub > n </ sub >) such that a < sub > i + 1 </ sub > is an element of a < sub > i </ sub > for all i. "

For example, if the sorted list to which we apply binary search has n elements, and we can guarantee that each lookup of an element in the list can be done in unit time, then at most log < sub > 2 </ sub > n + 1 time units are needed to return an answer.

The numbers of AD / CE years are not changed and are written with either no sign or a positive sign ; thus in general n AD / CE is simply n or + n.

:: A ( m, n ) = hyper ( 2, m, n + 3 ) − 3.

# HCl ( benzene ) + NH < sub > 3 </ sub >( benzene ) → NH < sub > 4 </ sub > Cl ( s )

# HCl ( g ) + NH < sub > 3 </ sub >( g ) → NH < sub > 4 </ sub > Cl ( s )

Alphabets: < span style =" background-color: lightblue ; color: white ;"> Armenian alphabet | Armenian </ span >, < span style =" background-color :# 008080 ; color: white ;"> Cyrillic | < font color =" white "> Cyrillic </ font color > </ span >, < span style =" background-color: brown ; color: white ;"> Georgian alphabet | < font color =" white "> Georgian </ font color > </ span >, < span style =" background-color :# 0000FF ; color: white ;"> Greek alphabet | < font color =" white "> Greek </ font color > </ span >, < span style =" background-color :# AAAAAA ; color: black ;"> Latin script | Latin </ span >, < span style =" background-color :# CCFF99 ; color: black ;"> Latin ( and Arabic script | Arabic ) </ span >, < span style =" background-color: cyan ; color: black ;"> Latin and Cyrillic </ span > Abjads: Arabic script | < span style =" background-color: green ; color: white ;"> Arabic </ span >, < span style =" background-color :# 00ff7f ; color: black ;"> Hebrew alphabet | Hebrew </ span > Abugidas: < span style =" background-color :# FFC000 ; color: black ;"> Indic scripts | North Indic </ span >, < span style =" background-color: orange ; color: black ;"> Indic scripts | South Indic </ span >, < span style =" background-color :# 66FF00 ; color: white ;"> Ge ' ez script | Ge ' ez </ span >, < span style =" background-color: olive ; color: white ;"> < font color =" white "> Tāna </ font > </ span >, < span style =" background-color :# FFFF80 ; color: black ;"> Canadian Aboriginal syllabics | Canadian Syllabic and Latin </ span > Logographic + syllabic: < span style =" background-color: red ; color: white ;"> Pure logographic </ span >, < span style =" background-color :# DC143C ; color: white ;"> Mixed logographic and syllabaries </ span >, < span style =" background-color :# FF00FF ; color: black ;"> Featural-alphabetic syllabary + limited logographic </ span >, < span style =" background-color :# 800080 ; color: white ;"> Featural-alphabetic syllabary </ span >

The number of neutrons, N, is known as the neutron number of the atom ; thus, A = Z + N. Since protons and neutrons have approximately the same mass ( and the mass of the electrons is negligible for many purposes ), and the mass defect is usually very small compared to the mass, the atomic mass of an atom is roughly equal to A.

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.

Karpov defeated Lev Polugaevsky by the score of + 3 = 5 in the first Candidates ' match, earning the right to face former champion Boris Spassky in the semifinal round.

Spassky won the first game as Black in good style, but tenacious, aggressive play from Karpov secured him overall victory by + 4 − 1 = 6.

Adventists believe that the body + the breath of God = a living soul.

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.

Stephen Cohn, http :// books. google. com / books? id = wRCJwgmfhzYC & pg = PA161 & lpg = PA161 & dq = the + fall + of + absalom + rilke & source = bl & ots = E2J7SyG2cS & sig = sKxj2GkktYN_73QMiFTMtMG6fcA & hl = en & sa = X & ei =-- FaUNiGOO6B0AGt1YHACg & ved = 0CDcQ6AEwAw # v = onepage & q = the % 20fall % 20of % 20absalom % 20rilke & f = false ).