Multiplicative scrambler / descrambler is defined similarly by a polynomial ( for the scrambler on the picture it is ), which is also a transfer function of the descrambler.

Multiplicative constants in the amount of time used do not change the power of DTIME classes ; a constant multiplicative speedup can always be obtained by increasing the number of states in the finite state control.

* Multiplicative inverse, a set of numbers which when multiplied yield the multiplicative identity, 1

Multiplicative scramblers ( also known as feed-through ) are called so because they perform a multiplication of the input signal by the scrambler's transfer function in Z-space.

* Multiplicative scramblers lead to error multiplication during descrambling ( i. e. a single bit error at the descrambler's input will result into w errors at its output, where w equals the number of the scrambler's feedback taps ).

The residue classes ( mod n ) that are coprime to n form a group under multiplication ( see the article Multiplicative group of integers modulo n for details.

Multiplicative characters are linearly independent, i. e. if are different characters on a group G then from it follows that.

# REDIRECT Multiplicative group

In November 1944, David Hawkins and Ulam addressed this point in a report entitled " Theory of Multiplicative Processes I ", whose last page gives some suggestions pertinent to bomb design.

Multiplicative inverses can be defined over many mathematical domains as well as numbers.

Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions.

* Eliminative and Multiplicative Materialism by Albert P. Carpenter

These include Bayesian Networks, clustering models, latent semantic models such as singular value decomposition, probabilistic latent semantic analysis, Multiple Multiplicative Factor, Latent Dirichlet allocation and markov decision process based models.

* Multiplicative composition denies the structural rules of weakening and contraction.

A Fast Algorithm for Computing Multiplicative Inverses in GF ( 2 < sup > m </ sup >) Using Normal Bases.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

An abugida ( from Ge ‘ ez አቡጊዳ ’ äbugida ), also called an alphasyllabary, is a segmental writing system in which consonant – vowel sequences are written as a unit: each unit is based on a consonant letter, and vowel notation is secondary.

The same notation is used with sets to denote cardinality ; the meaning depends on context.

In mathematical notation, this is:

In X-ray notation, the principal quantum number is given a letter associated with it.

The numeral system employed, known as algorism, is positional decimal notation.

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.

( b ) illustrates the same process using spectroscopic notation,. The Auger effect () is a physical phenomenon in which the filling of an inner-shell vacancy of an atom is accompanied by the emission of an electron from the same atom.

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 ).

Either approach is adequate for most uses, provided that one attends to the necessary changes in language, notation, and the definitions of concepts like restrictions, composition, inverse relation, and so on.

In quantum mechanics, Bra-ket notation is a standard notation for describing quantum states, composed of angle brackets and vertical bars.

The notation was introduced in 1939 by Paul Dirac and is also known as Dirac notation, though the notation has precursors in Grassmann's use of the notation for his inner products nearly 100 years previously.

Bra-ket notation is widespread in quantum mechanics: almost every phenomenon that is explained using quantum mechanics — including a large portion of modern physics — is usually explained with the help of bra-ket 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.

Additive notation is typically used when numerical addition or a commutative operation other than multiplication interprets the group operation ;

In scientific notation, the given number is scaled by a power of 10 so that it lies within a certain range — typically between 1 and 10, with the radix point appearing immediately after the first digit.

Scorewriting, or notation software typically lacks advanced sequencing tools, and is optimized for the creation of a neat, professional printout designed for live instrumentalists.

In a notation " β-th element " where β can also be an infinite ordinal, it will typically count from zero.

On the other hand, such systems are in practice less flexible than Hungarian notation, typically defining only a few different types — the lack of adequate easy-to-remember symbols obstructs more extensive use.

Rather than a property of the instrument, the transposition is a convention of music notation — however, instruments whose music is typically notated in this way are called transposing instruments.

When used in the first sense, recursion is an example of iteration, but typically using a recursive notation, which is typically not the case for iteration.

It typically ranges between the F below middle C ( F < sub > 3 </ sub > in scientific pitch notation ) to the second G above middle C ( G < sub > 5 </ sub >), although at the extremes some voices can reach the E below middle C ( E < sub > 3 </ sub >) or the second B above middle C ( B < sub > 5 </ sub >).

— the medium of sheet music typically is paper ( or, in earlier times, parchment ), although the access to musical notation in recent years includes also presentation on computer screens.

There are four common ways of notating or representing chords in western music other than conventional staff notation ; Roman numerals ; figured bass much used in the Baroque era ; macro symbols, sometimes used in modern musicology, and various systems of symbols and notations such as are typically found in the lead sheets, fake books and chord charts used in popular music to lay out the harmonic groundplan of a piece so that the musician may improvise, " jam ", " vamp ", " busk " or " head arrange " a part.

Despite this seemingly innocuous change in the name and notation, coproducts can be and typically are dramatically different from products.

In a typical large integer implementation, each integer is represented as a sequence of digits in positional notation, with the base or radix set to some ( typically large ) value b ; for this example we use b = 10000, so that each digit corresponds to a group of four decimal digits ( in a computer implementation, b would typically be a power of 2 instead ).

Multitrack sequencer software and scorewriters typically employ different methods for the input and display of music notation.

Unlike many programming languages, pipelines have a very small amount of notation, limited to stage separators ( typically ""), pipeline separators ( typically "" or ""), and label separators ("").

Such systems typically allow a sighted or visually impaired user to enter music into a computerized music notation program.

John French then transcribed this pattern, typically only a measure or two long, into musical notation.

In numerical computation, mathematical style pseudocode is sometimes called pidgin code, for example pidgin ALGOL ( the origin of the concept ), pidgin Fortran, pidgin BASIC, pidgin Pascal, and pidgin C. It is a compact and often informal notation that blends syntax taken from a conventional programming language with mathematical notation, typically using set theory and matrix operations, and perhaps also natural language descriptions.

The theory examinations are taken by pupils of all instruments and typically cover areas such as musical notation, construction of scales and composition.

Molecule editors typically support reading and writing at least one file format or line notation.