Use of the BAN logic often accompanies a security protocol notation formulation of a protocol and is sometimes given in papers.

Use of Leibnizian notation began to spread after this.

In the Unified Modeling Language, the relationships between all ( or a set of ) the use cases and actors are represented in a Use Case Diagram or diagrams, originally based upon Ivar Jacobson's Objectory notation.

Use of character delimiters which include a length component ( Declarative notation ) is comparatively rare but vastly reduces the overhead associated with locating the extent of each field.

* Experimental Investigation on the Use of Ion Current on SI Engines for Knock Detection, SAE Technical Paper n. 2009-01-2745, http :// dx. doi. org / 10. 4271 / 2009-01-2745, ISSN 0148-7191, Nov., 2009.

Use the binomial theorem to expand ( a + b )< sup > n + m − 1 </ sup > ( with commutativity assumed ):

# Use sieving to locate π ( B ) + 1 numbers a < sub > i </ sub > such that b < sub > i </ sub >=( a < sub > i </ sub >< sup > 2 </ sup > mod n ) is B-smooth.

**( 1981 ), " The Best Example of Semiosis and Its Use in Teaching Semiotics ", American Journal of Semiotics v. I, n. 1-2, pp. 47 – 83.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

One notation for a finite field is or F < sub > p < sup > n </ sup ></ sub >.

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

This would have been clearer if the notation a < sub > n </ sub > b had been used, instead of the common traditional notation.

The set of all congruence classes modulo n is denoted or ( the alternate notation is not recommended because of the possible confusion with the set of n-adic integers ).

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.

The notation E: t can be read as expression E has type t. For instance, the argument n is assigned type integer ( int ), and fac ( n: int ), the result of applying fac to the integer n, also has type integer.

( In big O notation: O ( 1 ) insertion time, O ( n ) pull time due to search.

In an alternate notation for block designs, an S ( t, k, n ) would be a t -( n, k, 1 ) design.

Depending on the value of n, we specify a sufficiently large positive integer k ( to meet our needs later ), and multiply both sides of the above equation by, where the notation will be used in this proof as shorthand for the integral:

However, it may be convenient for notation to consider n-ary functions, as for example multilinear maps ( which are not linear maps on the product space, if n ≠ 1 ).

However, with big-O notation the sequence can only exceed the bound in a finite prefix of the sequence, whereas the limit superior of a sequence like e < sup >- n </ sup > may actually be less than all elements of the sequence.

The set of injective functions from X to Y may be denoted Y < sup >< u > X </ u ></ sup > using a notation derived from that used for falling factorial powers, since if X and Y are finite sets with respectively m and n elements, the number of injections from X to Y is n < sup >< u > m </ u ></ sup > ( see the twelvefold way ).

where the product is over the distinct prime numbers dividing n. ( The notation is described in the article Arithmetical function.

This biproduct is often written A < sub > 1 </ sub > ⊕ ··· ⊕ A < sub > n </ sub >, borrowing the notation for the direct sum.

In modern notation, a ratio exists between quantities p and q if there exist integers m and n so that mp > q and nq > m.