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.

The notation travelled from France to Britain, where it became standard, although at least one journal did not change from using to until 1896.

A production rule in is formalized mathematically as a pair, where is a non-terminal and is a string of variables and nonterminals ; rather than using ordered pair notation, production rules are usually written using an arrow operator with as its left hand side and as its right hand side:

where the notation ρ is used to describe the distance of the path from the origin instead of R to emphasize that this distance is not fixed, but varies with time.

The common notation for the divergence ∇· F is a convenient mnemonic, where the dot denotes an operation reminiscent of the dot product: take the components of ∇ ( see del ), apply them to the components of F, and sum the results.

However multiple external entities may be referenced ( in a space-separated list of names ) in attributes declared with type ENTITIES, and where each named external entity is also declared with its own notation ).

Other notational traditions do exist ; Italian solo music is typically written at the sounding pitch, and the " old " German method sounded an octave below where notation except in the treble clef, where the music was written at pitch.

Other types of notation are used in algebraic expressions when the required formatting is not available, or can not be implied, such as where only letters and symbols are available.

In RPN, the operator is placed after its operands, as opposed to the more common infix notation where the operator is placed between its operands.

Another notation is GF ( p < sup > n </ sup >), where the letters " GF " stand for " Galois field ".

where is the representation of the wavefunction in Dirac notation, and is the Kronecker delta function.

One of the binary numbers to be multiplied is represented as a trivial polynomial, where, ( using the above notation ): a < sub > i </ sub >

Tabulature notation ( often abbreviated as " tab ") is a method of writing melodies by indicating where the notes are played on the instrument, rather than by indicating the pitches with circles and note heads printed on a staff, as with standard notation.

One of the advantages of tab is that it can be easier for performers without formal training to learn, because the notation directly indicates where to play the note.

Examples of ideograms include wayfinding signs, such as in airports and other environments where many people may not be familiar with the language of the place they are in, as well as Arabic numerals and formal languages ( mathematical notation, logic, UML ), which are used worldwide regardless of how they are pronounced in different languages.

An alternative representation uses degrees and minutes, where parts of a minute are expressed in decimal notation with a fraction, thus: 23 ° 27. 500 ′ E. Degrees may also be expressed as a decimal fraction: 23. 45833 ° E. For calculations, the angular measure may be converted to radians, so longitude may also be expressed in this manner as a signed fraction of π ( pi ), or an unsigned fraction of 2π.

The notation is used, because it is the factor ring of by the ideal containing all integers divisible by n, where is the singleton set.

In 1252, Safi al-Din al-Urmawi developed a form of musical notation, where rhythms were represented by geometric representation.

for some positive constant a, where O (…) is the big O notation.

The programming language is augmented with natural language description details, where convenient, or with compact mathematical notation.

Prefix notation has seen wide application in Lisp s-expressions, where the brackets are required due to the arithmetic operators having variable arity.

where a sum over μ is performed according to the rules of Einstein notation.

Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide and conquer algorithms, data structures, randomized algorithms, best, worst and average case analysis, time-space tradeoffs, and upper and lower bounds.

The numerical value of K < sub > a </ sub > is equal to the concentration of the products divided by the concentration of the reactants, where the reactant is the acid ( HA ) and the products are the conjugate base and H < sup >+</ sup >.

Because the range of possible values for K < sub > a </ sub > spans many orders of magnitude, a more manageable constant, pK < sub > a </ sub > is more frequently used, where pK < sub > a </ sub >

functions as real combinations of spherical harmonics Y < sub > lm </ sub >( θ, φ ) ( where l and m are quantum numbers ).

Within a shell where n is some integer n < sub > 0 </ sub >, ranges across all ( integer ) values satisfying the relation.

It lacks the NH < sub > 2 </ sub > group because of the cyclization of the side-chain and is known as an imino acid ; it falls under the category of special structured amino acids .</ ref > where R is an organic substituent known as a " side-chain "); often the term " amino acid " is used to refer specifically to these.

½ ( pKa < sub > 1 </ sub > + pKa < sub > R </ sub >), where pKa < sub > R </ sub > is the side-chain pKa.

where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E ( k ), and a < sub > k </ sub > denotes the corresponding annihilation operators.

where E < sub > 0 </ sub > is an infinite negative constant.

where p is a program in L < sub > 2 </ sub >.

He also offers a conversion table ( see Cohen, 1988, p. 283 ) for eta squared ( η < sup > 2 </ sup >) where 0. 0099 constitutes a small effect, 0. 0588 a medium effect and 0. 1379 a large effect.

Reactions of acids are often generalized in the form HA H < sup >+</ sup > + A < sup >−</ sup >, where HA represents the acid and A < sup >−</ sup > is the conjugate base.

## < tt > SubBytes </ tt >— a non-linear substitution step where each byte is replaced with another according to a lookup table.

## < tt > ShiftRows </ tt >— a transposition step where each row of the state is shifted cyclically a certain number of steps.

The < tt > MixColumns </ tt > function takes four bytes as input and outputs four bytes, where each input byte affects all four output bytes.

where the cohomology classes c < sub > i </ sub > are the Chern classes of E, and lie in the cohomology group H < sup > 2i </ sup >( X ).

where n < sup > c </ sup > denotes the charge conjugate state, i. e., the antiparticle.

The Battle of Qarqar is mentioned in extra-biblical records, and was perhaps at Apamea where Shalmaneser III of Assyria fought a great confederation of princes from Cilicia, Northern Syria, Israel, Ammon, and the tribes of the Syrian desert ( 853 BC ), including Ahab ( A-ha-ab-bu < sup > mat </ sup >) ( Adad -' idri ).

where n < sub > d </ sub >, n < sub > F </ sub > and n < sub > C </ sub > are the refractive indices of the material at the wavelengths of the Fraunhofer d -, F-and C-spectral lines ( 587. 6 nm, 486. 1 nm and 656. 3 nm respectively ).

where k < sub > B </ sub > is Boltzmann's constant, T is the temperature, R is the resistance, and is the bandwidth of the frequency.

After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

auxiliary regression is TR < sup > 2 </ sup >, where T is the sample size and R < sup > 2 </ sup > is the coefficient of determination.