# notation

## Definitions

• WordNet 3.6
• n notation the activity of representing something by a special system of marks or characters
• n notation a comment or instruction (usually added) "his notes were appended at the end of the article","he added a short notation to the address on the envelope"
• n notation a technical system of symbols used to represent special things
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Webster's Revised Unabridged Dictionary
• Interesting fact: Irving Berlin has never learned to read music or to write it. He hums or sings his songs to a secretary, who takes them down in musical notation.
• Notation Any particular system of characters, symbols, or abbreviated expressions used in art or science, to express briefly technical facts, quantities, etc.
• Notation Literal or etymological signification. "“Conscience” is a Latin word, and, according to the very notation of it, imports a double or joint knowledge."
• Notation The act or practice of recording anything by marks, figures, or characters.
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Century Dictionary and Cyclopedia
• n notation The act of noting, in any sense.
• n notation A system of written signs of things and relations (not of significant sounds or letters), used in place of language on account of its superior clearness and brevity. Notations are employed to advantage in every branch of mathematics, in logic, in astronomy, in chemistry, in music, in proofreading, etc. Thus, (1 /i) means that in the expression 1 / i all the whole numbers from 1 to n inclusive are to be successively substituted for i and the resulting values added together to give the quantity denoted by the expression. When the limits are not indicated, the lower one is to be understood as constant, and generally zero, and the upper one as one less than the actual value of the variable. For example, if we write ϲ (2 x + 1) = x, this signifies In like manner, δ is used to signify the difference, or the amount by which the quantity written after it would be increased by increasing the variable by unity. The variable may be indicated by a subjacent letter; thus, δxx = (x + 1) —x; but δyx = x + 1 —xy = (x— 1) xy. The product of two quantities is denoted by writing them in their order, either directly, or with an interposed cross or dot (.); thus, 3 x a = 3. a = 3 a. A quotient is usually denoted by one of the signs ÷ or: or /, with the dividend before it and the divisor after it, or by a horizontal line with the dividend above and the divisor below. A continued product is also written with 11, just as a summation is written with ϲ ; but when the limits are not indicated, the lower one is constant, and generally unity, and the upper one the actual value of the variable. A positive whole number with the mark of admiration (!) after it denotes the continued product of all numbers from 1 up to that number inclusive; thus, 4! = 24. Instead of the mark of admiration, a right-angled line beneath and at the left of the number is sometimes used: as, A power of a quantity is denoted by writing the exponent to the right and above the base; thus. x = x. x. x. This notation is extended to symbols of operation. Thus, δu = δδ u; and δ— u = ϲ u, because u = δδ— u = δ u. If the exponent is included in parentheses, the quantity denoted is the continued product of a number of factors equal to the exponent, one factor being the base, and the others the results of successive subtractions of 1 from the base; thus, x () = x (x— 1) (x—2). A root is denoted either by a fractional exponent, or by the sign √ written before the base, with the index above and to the left; thus, If the index is omitted, it is understood to be 2. One of the most important parts of algebraical notation is the use of parentheses, ( ), square brackets, [ ], braces, and vincula or horizontal lines above the expressions, to signify that the symbols so included are to be treated as signifying one quantity. Thus, (3 + 2) x 5 = 25, but 3 + (2 x 5) = 13. Functions are usually denoted by operative symbols, especially f, F, φ, Φ, written before the variable, the latter being often inclosed in parentheses. If there are several variables, these are inclosed in one parenthesis and separated by commas, as F (x, y). Various special functions have special abbreviations, as log for logarithm, sin for sine, cos for cosine, tan for tangent, cot for cotangent, sec for secant, cosec for cosecant, vsin for versed sine, sinh for hyperbolic sine, am for amplitude, sn for sine of the amplitude, cn for cosine of the amplitude, etc. (For the special notation of matrices, determinants, graphs, and groups, see those words.) A differential is expressed by d before the function, and a partial differential is now generally written with δ instead of d; the variable is indicated, if necessary, by a subjacent letter. A variation is expressed by a δ before the varying quantity. A differential coefficient is most frequently expressed fractionally as a ratio of differentials, or by etc., written before the function. But the capital D is often used: thus, Dxxy = yx— 1, and Dxxy = log x. x. Differentiation relatively to the time is frequently expressed by accents: thus, s′ = Dts′ and s′ = Dts′ . Dots over the letters are also used instead of the accents, this being the original fluxional notation of Newton. The differential coefficients of a function are frequently denoted by accents attached to the operational symbols: thus, f″x = Dxfx. A number of other differential operations are indicated by special operational symbols, as for Laplace's operator. The integral of an expression is written with the sign f, introduced by Leibnitz, before the differential. The limits of a definite integral are written above and below this sign. Besides these notations, there are many others peculiar to different branches of mathematics. Two systems of arithmetical notation are now in use, the Roman and the Arabic. The Roman system is employed for numbering books and their parts, in monumental inscriptions, and in marking timber and other objects with the chisel. A large number in this system is written as follows: As many thousands as possible being taken from the number (without a negative remainder), an M is written for every thousand; five hundred is then taken, if possible, and D is written for it; as many hundreds as possible are next taken, and a C written for each; fifty is next taken, if possible, and L is written for it; as many tens as possible are next taken, and an X written for each; five is then taken, if possible, and V is written for it; and finally an I is written for every unit remaining. But usually instead of IIII is written IV; in place of VIIII, IX; in place of XXXX, XL; in place of LXXXX, XC, etc. Anciently, there were other extensions of this system. The Arabic notation consists in the use of the Arabic figures and decimal places. See Arabic and decimal.
• n notation Etymological signification; etymology.
• n notation In music, the act, process, or result of indicating musical facts by written or printed characters. As a process and a science, musical notation is a branch of semiotics or semiiography in general. Notation is also used as a collective term for all the signs for musical facts taken together. Notation, whether regarded as a science or as a body of visible characters, may be divided into notation of pitch, of duration, of force, of style, etc. The various historic systems of notation are more particular about pitch than about the other matters.
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Chambers's Twentieth Century Dictionary
• n Notation nō-tā′shun the act or practice of recording by marks or symbols: a system of signs or symbols
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## Quotations

• Elias Canetti
“The process of writing has something infinite about it. Even though it is interrupted each night, it is one single notation.”

## Etymology

Webster's Revised Unabridged Dictionary
L. notatio, a marking, observing, etymology, fr. notare, to mark, nota, a mark: cf. F. notation,. See 5th Note
Chambers's Twentieth Century Dictionary
L.,—notāre, -ātum, to mark.

## Usage

### In literature:

Scholar Phelps waited patiently until I'd made the notation.
"Highways in Hiding" by George Oliver Smith
Careful notations of the temperature should be made during the first week.
"The Mother and Her Child" by William S. Sadler
There were no notations but his own.
"Ten From Infinity" by Paul W. Fairman
Hunc et sectiones adhibuisse notat Pindarus Pyth.
"The Iliad of Homer (1873)" by Homer
He was also surprised to find that "many have their Grain yet in the Field," a notation for the 26th of July.
"The Fair Play Settlers of the West Branch Valley, 1769-1784" by George D. Wolf
"The Shadow World" by Hamlin Garland
This is the third dimension of color, and must be included in our notation.
"A Color Notation" by Albert H. Munsell
If possible a convenient notation should be adopted.
"Manual of Military Training" by James A. Moss
I'll mail this original application to the proper place with a notation that you've left.
"Where the Souls of Men are Calling" by Credo Harris
Roman notation table, how taught, 428.
"Popular Education" by Ira Mayhew
Before a child knows anything of notation or a keyboard, it sings.
"Great Pianists on Piano Playing" by James Francis Cooke
In some cases the notation varied according to the purpose of the calculation.
"A History of Art in Chaldæa & Assyria, v. 1" by Georges Perrot
But each time he would rouse himself from the chair to pencil new notations on the pads of paper that littered his desk.
"Empire" by Clifford Donald Simak
He pulled out some memorandum slips from his pocket and made some notations.
"Ted Marsh on an Important Mission" by Elmer Sherwood
He seemed to be making a mental notation of every move that Peter made, for future reference.
"Peter the Brazen" by George F. Worts
Again it could be a mere notation.
"Whispering Wires" by Henry Leverage
There is a complete edition in modern notation by T.L.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 4" by Various
The notation of this mass of MSS.
"Encyclopaedia Britannica, 11th Edition, Volume 3, Slice 7" by Various
The notation read, 'The Green Parrot, Tuesday at 9:15.
"Saboteurs on the River" by Mildred A. Wirt
The notations were still present wherever I looked.
"Palos of the Dog Star Pack" by J. U. Giesy
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### In poetry:

Vous estes ma morte et ma vye,
I preye you for your curteisie
Amate,
Cestes maundes jeo vous pry
In youre herte stedefastly Notate.
"Lines from Love Letters" by Anonymous British

### In news:

In weeks to come, Nick Varney will continue his travelogue to include various notations aimed to educate you on the ways not to do things when sailing the Alaskan Marine Highway to the Aleutians , or anywhere else for that matter.
You will find the text and musical notation for each item in PDF format.
We have all heard the phrase "let's compare apples to apples," which is exactly what a standardized glaze notation offers potters.
Although there are other competitors, the notation software market, for the most part, is dominated by its two 800-pound gorillas: Avid Sibelius and MakeMusic Finale.
These programs are perpetually locked in a never-ending arms race to be the most feature-rich notation application.
Maria Grandy, a ballet teacher and coach long associated with the Joffrey Ballet and the chairwoman of the Dance Notation Bureau, died on Friday at Memorial Sloan-Kettering Cancer Center.
A notation on the US Patent Office Web site indicates that the Eolas patent on Web browsers is under reconsideration.
Music Notation Essentials Distributed by Alfred Music Publishing.
As you can see, this form of notation is more economical than using ties all the time because there are fewer items on the page to read.
The above check has the notation "Mike Miller" in the subject line.
A quick notation of the food & sugar content can be a great tool to see how quickly and frequently you are consuming sugar.
So field notations in all their variety interest me – the journals of explorers, the notebooks of artists, and the diaries of scientists.
Professional wine tasters make notations about different wines during the Top Taster Blind Wine Tasting Competition, a Flavor .
A notation regarding the total time needed to complete the individual lessons .
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### In science:

Notation: In the rest of the paper, we drop the notational dependence on N and H , and write simply X , B , T , ∆t for XH,N , BN , TN , ∆tN etc. when no confusion can arise.
A random walk approximation to fractional Brownian motion
In order to compare their notation with the notation used here, in the following all tensors from Mukohyama and Hayward will have a + or a − attached to them.
Dynamical surface gravity
Using our general deﬁnition of derivative with new notation, let us express the interaction when L = 3n using the notation ∆(S,T ) .
Derivative of functions over lattices as a basis for the notion of interaction between attributes
Also note that we have stuck with i notation for clarity in the arguments to come, even though we are assuming the GCH and so ℵ notation would be equivalent.
Large Cardinals and Definable Well-Orderings of the Universe
We recall that the notation and operative hypotheses were established at the end of the previous section in Notation 5.6.
Minimal connected simple groups of finite Morley rank with strongly embedded subgroups
Recall the notation P (δ) introduced in the second paragraph of Section 3 (this notation is distinct from P δ and emphasizes that the sequence (δ) is constant).
A random walk on Z with drift driven by its occupation time at zero
Remark: Our notation ℓ(z) is not totally fair, but in line with other traditional ﬁeld theory notation.
LERW as an example of off-critical SLEs
Notation 1 For convenience we introduce a short notation for the volume of the annulus; v = v (x, r, R) = V (x, R) − V (x, r).
Random walks on graphs with volume and time doubling
We use the notation C [ℓ + m, ℓ, k ] (for a sake of simplicity, sometimes we will use the notation C instead) to de ﬁne this new random network code de ﬁned by vector subspaces in the ambient space W of dimension ℓ + m, such that for any V ∈ C , dim(V ) = ℓ, and for any V ∈ C and U ∈ C , dim(U ∩ V ) ≤ k − 1.
Recursive Code Construction for Random Networks
Notations: • In order to avoid the use of too many notations, we shall deﬁne the binary operation ✷∨ on the set of probability measures on the real line with the same symbol as the operation ✷∨ on the set of cumulative distribution functions.
A matrix interpolation between classical and free max operations: I. The univariate case
The notation used in this chapter is consistent with the notation in the previous chapters.
Limiting distributions and large deviations for random walks in random environments
This notation may look unnatural, but it wil l help simplify notation later in the paper.
Intersection exponents for biased random walks on discrete cylinders
Consequently, we alternate frequently between additive notation and multiplicative notation; the meaning will be clear from the context.
Generating varieties for affine Grassmannians
Deﬁnitions and Notation Let us ﬁrst deﬁne the notation used throughout the paper, also summarized in Table I.
Optimal Filtering of Malicious IP Sources
Note that every node in the LCP-tree is a candidate preﬁx p/l; for brevity of notation, we will use interchangeably the notation p/l and its shorter version p.
Optimal Filtering of Malicious IP Sources
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