In modern commentary, the columns ( called files ) are labeled by the letters a to h from left to right from the white player's point of view, and the rows ( called ranks ) by the numbers 1 to 8, with 1 being closest to the white player, thus providing a standard notation called algebraic chess notation.

However, the " h " is sometimes dropped for languages that don't support that method of notation ; for example, it is known as screen mode 13 in QuickBasic and its spinoffs.

Let X be any Lie algebra over K. Given a unital associative K-algebra U and a Lie algebra homomorphism: h: X → U < sub > L </ sub >, ( notation as above ) we say that U is the universal enveloping algebra of X if it satisfies the following universal property: for any unital associative K-algebra A and Lie algebra homomorphism f: X → A < sub > L </ sub > there exists a unique unital algebra homomorphism g: U → A such that: f (-) = g < sub > L </ sub > ( h (-)).

We express this relation by means of the notation ∠( h, k ) ≅ ( h ′, k ′) Every angle is congruent to itself ; that is, ∠( h, k ) ≅ ( h, k ) or ∠( h, k ) ≅ ( k, h )

In computational terms, this is a useful property, since the calculation can be performed in time ( where h is height and w is width ; see Big O notation ), as opposed to for a non-separable kernel.

MISE ( h ) = AMISE ( h ) + o ( 1 /( nh ) + h < sup > 4 </ sup >) where o is the little o notation.

gives that AMISE ( h ) = O ( n < sup >- 4 / 5 </ sup >), where O is the big o notation.

Given any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.

The CE / BCE notation has been adopted by numerous authors and publishers wishing to be

because it does not explicitly make use of religious titles for Jesus, such as " Christ " and Domin-(" Lord "), which are used in the BC / AD notation, nor does it give implicit expression to the Christian creed that Jesus was the Christ.

Among the reasons given by those who oppose the use of Common Era notation is that it is selective as other aspects of the Western calendar have origins in various belief systems ( e. g., January is named for Janus ), Style guides for academic texts on religion generally prefer BCE / CE to BC / AD.

Instead, these parsers just provide to the application the parsed FPI and / or URI associated to the notations found in the parsed SGML or XML document, and with a facility for a dictionary containing all notation names declared in the DTD ; these validating parsers will also check the uniqueness of notation name declarations, and will report a validation error if some notation names are used anywhere in the DTD or in the document body but not declared:

* if the application can't use any notation ( or if their FPI and / or URI are unknown or not supported in their local catalog ), these notations may be either ignored silently by the application or the application could signal an error ;

Many Asian civilizations distinguish between art / court / classical styles and " folk " music, though cultures that do not depend greatly upon notation and have much anonymous art music must distinguish the two in different ways from those suggested by western scholars.

An example of such a finite field is the ring Z / pZ, which is essentially the set of integers from 0 to p − 1 with integer addition and multiplication modulo p. It is also sometimes denoted Z < sub > p </ sub >, but within some areas of mathematics, particularly number theory, this may cause confusion because the same notation Z < sub > p </ sub > is used for the ring of p-adic integers.

This is analogous to the slash notation (/ a /, / b /) used for phonemes, and the square bracket notation used for phonetic transcriptions (, ).

Gosling aimed to implement a virtual machine and a language that had a familiar C / C ++ style of notation.

This dual declarative / procedural interpretation later became formalised in the Prolog notation

Pronunciation is shown as ( nēŏtˈnē ) and in IPA notation it is / niˈɒtni / as can be inferred from the Pronunciation Key .</ ref >, < i > Neoteny .</ i > ( 2012 ).

* Nine-eleven ( or 9 / 11 ) in the US date notation for September 11.

For positive a, the principal square root can also be written in exponent notation, as a < sup > 1 / 2 </ sup >.

Therefore, in a right-angled triangle, the two non-right angles total 90 ° ( π / 2 radians ), so each of these angles must be in the range of ( 0 °, 90 °) as expressed in interval notation.

* Z / Eves — A proof checker for the Z notation ( German site but all manuals in English )

The AD / BC notation does not use a year zero ; however, astronomical year numbering does use a minus sign, so " 2 BC " is equal to " year-1 ".

and for p > 2 it extends these basic operations in a way that happens to be expressible in Knuth's up-arrow notation as

Fortunately, faster methods have been developed which require only O ( p ( log p )< sup > 2 </ sup >) operations ( see big-O notation ).

The active ingredients are monocalcium aluminate CaAl < sub > 2 </ sub > O < sub > 4 </ sub > ( CaO · Al < sub > 2 </ sub > O < sub > 3 </ sub > or CA in Cement chemist notation, CCN ) and mayenite Ca < sub > 12 </ sub > Al < sub > 14 </ sub > O < sub > 33 </ sub > ( 12 CaO · 7 Al < sub > 2 </ sub > O < sub > 3 </ sub >, or C < sub > 12 </ sub > A < sub > 7 </ sub > in CCN ).

Calcium sulfoaluminate cements are made from clinkers that include ye ' elimite ( Ca < sub > 4 </ sub >( AlO < sub > 2 </ sub >)< sub > 6 </ sub > SO < sub > 4 </ sub > or C < sub > 4 </ sub > A < sub > 3 </ sub > in Cement chemist's notation ) as a primary phase.

Note that pure application of this method may provide only a partial ordering on the strings, since different strings can represent the same number ( as with " 2 " and " 2. 0 ", or when scientific notation is used, " 2e3 " and " 2000 ").

In this system, the number ten may be written as " A ", " T " or " X ", and the number eleven as " B " or " E " ( another common notation, introduced by Sir Isaac Pitman, is to use a rotated " 2 " for ten and a reversed " 3 " for eleven ).

Historically, several number bases have been used for representing floating-point numbers, with base 2 ( binary ) being the most common, followed by base 10 ( decimal ), and other less common varieties, such as base 16 ( hexadecimal notation ), as well as some exotic ones like 3 ( see Setun ).

In modern notation the first is CO ( carbon monoxide ) and the second is CO < sub > 2 </ sub > ( carbon dioxide ).

This notation can also be used for quantities that are surrounded by parentheses ( e. g. 5 ( 2 ) or ( 5 )( 2 ) for five times two ).

The expression for adding the numbers 1 and 2 is, in prefix notation, written "+ 1 2 " rather than " 1 + 2 ".

Despite the name, reverse Polish notation is not exactly the reverse of Polish notation, for the operands of non-commutative operations are still written in the conventional order ( e. g. "/ 6 3 " in Polish notation and " 6 3 /" in reverse Polish both evaluating to 2, whereas " 3 6 /" in reverse Polish notation would evaluate to ½ ).

The use case notation from Objectory and the component notation from Booch were integrated with the rest of the notation, but the semantic integration was relatively weak in UML 1. 1, and was not really fixed until the UML 2. 0 major revision.

Decimal notation often refers to a base-10 positional notation such as the Hindu-Arabic numeral system ; however, it can also be used more generally to refer to non-positional systems such as Roman or Chinese numerals which are also based on powers of ten.

The description " Polish " refers to the nationality of logician Jan Łukasiewicz, who invented ( prefix ) Polish notation in the 1920s.

The term SMILES refers to a line notation for encoding molecular structures and specific instances should strictly be called SMILES strings.

However, because the hook appeared on the eighth note ( or quaver ) in the later white notation, the modern French term croche refers to an eighth note.

The sordino of this notation refers to the felt dampers, each of which stops the sound of a note's strings when the note is not being played.

The terminology is usually abbreviated to .< ref > The notation "- dimensional " is to clarify the dimension of all manifolds in question, otherwise it is unclear whether a " 5-dimensional cobordism " refers to a 5-dimensional cobordism between 4-dimensional manifolds or a 6-dimensional cobordism between 5-dimensional manifolds .</ ref > and are called cobordant if such a cobordism exists.

The 7: 15 chapter and verse notation refers to July 15, 2003, the day when America Online shut down its Netscape browser division and the Mozilla Foundation was launched.

The 8: 20 chapter and verse notation refers to August 20, 2006, when the first internal email was sent mentioning the possibility of developing the next Netscape Navigator in house.

Here, O refers to Big O notation.

* International Phonetic Alphabet, a system of phonetic notation ; " API " refers to the French name for the system, Alphabet phonétique international

The notation AR ( p ) refers to the autoregressive model of order p. The AR ( p ) model is written

The notation MA ( q ) refers to the moving average model of order q:

The notation ARMA ( p, q ) refers to the model with p autoregressive terms and q moving-average terms.

The notation ARMAX ( p, q, b ) refers to the model with p autoregressive terms, q moving average terms and b exogenous inputs terms.

where the notation refers to the flow of net investment, which is the difference between gross investment and depreciation.

Resolutions of 1080i60 or 1080i50 often refers to 1080i / 30 or 1080i / 25 in EBU notation.

The system defines not only detailed subject classifications, but also an algebraic notation for referring to the intersection of several subjects ; for example, the notation < nowiki >" 31 :( 485 )"</ nowiki > refers to the statistics of mining and metallurgy in Sweden.

In the Whyte notation the number designates the number of wheels rather than the number of axles, thus the final 2 in the Mikado's 2-8-2 refers to two wheels ( one axle ) while the Northern type's 4-8-4 designation refers to four wheels ( two axles ).

In Whyte notation, 2-4-4-2 refers to a railroad steam locomotive that has two leading wheels followed by four coupled driving wheels, a second set of four coupled driving wheels, and two trailing wheels.

In the sport of cricket, a bowling analysis ( sometimes shortened to just analysis, especially in the phrase innings analysis ) usually refers to a notation summarising a bowler's performance in terms of overs bowled, how many of those overs are maidens ( i. e. with no runs conceded ), total runs conceded and number of wickets taken.

Gray & Tall's notion of procept improved upon the existing literature by noting that mathematical notation is often ambiguous as to whether it refers to process or object.