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Function in geometric group theory
theory, a length function is a function that assigns a number to each element of a group. A length function L : G → R+ on a group G is a function satisfying:
Length_function
Function with a repeating pattern
length of the interval over which a periodic function repeats is called its period. Any function that is not periodic is called aperiodic. A function
Periodic_function
Culler and Vogtmann constructed an embedding, via the translation length functions discussed below, of X n {\displaystyle X_{n}} into the infinite-dimensional
Outer_space_(mathematics)
Distance along a curve
continuously differentiable (i.e., the derivative is a continuous function) function. The length of the curve is given by the formula L ( f ) = ∫ a b | f ′ (
Arc_length
Mapping arbitrary data to fixed-size values
there are some hash functions that support variable-length output. The values returned by a hash function are called hash values, hash codes, (hash/message)
Hash_function
Fundamental trigonometric functions
intensity and day length, and average temperature variations throughout the year. They can be traced to the jyā and koṭi-jyā functions used in Indian astronomy
Sine_and_cosine
particular, a simple reflection has length one. The function l is then an integer-valued function of W; it is a length function of W. It follows immediately
Length of a Weyl group element
Length_of_a_Weyl_group_element
Geometric line segment whose endpoints lie on a circular arc
them. In the table below (where c is the chord length, and D the diameter of the circle) the chord function can be shown to satisfy many identities analogous
Chord_(geometry)
basic example of a string function is the length(string) function. This function returns the length of a string literal. e.g. length("hello world") would return
Comparison of programming languages (string functions)
Comparison_of_programming_languages_(string_functions)
Group theory function
element of the group) in terms of the length of that relation (see pp. 79–80 in ). The growth type of the Dehn function is a quasi-isometry invariant of a
Dehn_function
Sequence of characters, data type
string. This function is often named length, len, or size. For example, length("hello world") would return 11. Another common function is concatenation
String_(computer_science)
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Part of the mathematical subject of group theory
g\in G\mapsto \ell _{X}(g)} is called the hyperbolic length function or the translation length function for the action of G on X. For g ∈ G exactly one of
Bass–Serre_theory
Measure of a system's order
correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe how
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Concept in laser optics
In optics and especially laser science, the Rayleigh length or Rayleigh range, z R {\displaystyle z_{\mathrm {R} }} , is the distance along the propagation
Rayleigh_length
Theory of cryptography
sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce
Sponge_function
Let G {\displaystyle G} be a topological group. A length on G {\displaystyle G} is a continuous function l : G ↦ [ 0 , + ∞ [ {\displaystyle l:G\mapsto [0
Harish-Chandra's Schwartz space
Harish-Chandra's_Schwartz_space
Hash function that is suitable for use in cryptography
check (CRC) functions. Most cryptographic hash functions are designed to take a string of any length as input and produce a fixed-length hash value. A
Cryptographic_hash_function
Program function without side effects
In computer programming, a pure function is a function that has the following properties: the function return values are identical for identical arguments
Pure_function
distinguish the hard-core function value h(x) and uniformly random bits of length |h(x)| with negligible advantage over the length of x. A hard-core predicate
Hard-core_predicate
Cryptographic tool
output of a variable length. In this respect, a MGF can be viewed as a extendable-output function (XOF): it can accept input of any length and process it to
Mask_generation_function
Cryptographic primitive
cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output. The transformation is "one-way"
One-way_compression_function
Distance over which a propagating wave maintains a certain degree of coherence
analogous concept of the quantum coherence length of a wave function. In radio-band systems, the coherence length is approximated by L = c n Δ f ≈ λ 2 n Δ
Coherence_length
Mathematical functions
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied
Lemniscate_elliptic_functions
Method of building collision-resistant cryptographic hash functions
the length of the original message. This is called length padding or Merkle–Damgård strengthening. In the diagram, the one-way compression function is
Merkle–Damgård_construction
Continuous function that is not absolutely continuous
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in
Cantor_function
Computing concept
Bit length or bit width is the number of binary digits, called bits, necessary to represent an unsigned integer as a binary number. Formally, the bit length
Bit-length
Cryptographic hash function
how the Skein function intertwines the input, similar to a skein of yarn. Skein was designed to natively support arbitrary, variable-length outputs, so
Skein_(hash_function)
2015 password-based key derivation function
return Hash(C, tagLength) Argon2 makes use of a hash function capable of producing digests up to 232 bytes long. This hash function is internally built
Argon2
Cryptographic hash function
to length extension, indifferentiability from a random oracle, etc. BLAKE2 removes addition of constants to message words from BLAKE round function, changes
BLAKE_(hash_function)
Computer communications authentication algorithm
Thus the algorithm provides better immunity against length extension attacks. An iterative hash function (one that uses the Merkle–Damgård construction) breaks
HMAC
Attack against cryptographical hash functions
function before their payload (in this case, a 0x80 followed by a number of 0x00s and a message length, 0x228 = 552 = (14+55)*8, which is the length of
Length_extension_attack
Tables comparing general and technical information for common hashes
of BLAKE2b's message length counter is 128-bit, but it counts message length in bytes, not in bits like the other hash functions in the comparison. It
Comparison of cryptographic hash functions
Comparison_of_cryptographic_hash_functions
The group algebra of a group with a length function is a filtered algebra. Filtration (mathematics) Length function Abe, Eiichi (1980). Hopf Algebras.
Filtered_algebra
Constant describing the distance a membrane potential passively travels along a neuron
In neurobiology, the length constant (λ) is a mathematical constant used to quantify the distance that a graded electric potential will travel along a
Length_constant
Password cracking dataset
is a precomputed table for caching the outputs of a cryptographic hash function, usually for cracking password hashes. Passwords are typically stored not
Rainbow_table
Hyperbolic analogues of trigonometric functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just
Hyperbolic_functions
Topics referred to by the same term
Primitive recursive function, a function which can be computed with loops of bounded length Another name for computable function Recurrence relation,
Recursive_function
Linear combination of indicator functions of real intervals
mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals
Step_function
Extension of the Luhn algorithm
{ return codePoints.length; } function codePointFromCharacter(character) { return codePoints.indexOf(character); } function characterFromCodePoint(codePoint)
Luhn_mod_N_algorithm
Extension of the factorial function
gamma function, denoted by Γ {\displaystyle \Gamma } (capital Greek letter gamma), is the most common extension of the factorial function to complex
Gamma_function
Russian cryptographic hash function
hash function, determined by user. Σ := 0 {\displaystyle \Sigma :=0} — Control sum L := 0 {\displaystyle L:=0} — Message length Compression function of
GOST_(hash_function)
In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member
Integer-valued_function
Type of data structure
there is no need to pass the length to the Process function. type Vals_Type is array (Positive range <>) of Float; function Read_And_Process (N : Integer)
Variable-length_array
involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified
List of trigonometric identities
List_of_trigonometric_identities
Period of a day in which a location experiences natural illumination
about half of the Earth is facing the Sun and experiencing daytime. The length of daytime varies with latitude and changes over the course of the year
Daytime
Key derivation function
Password, Salt, c, dkLen) where: PRF is a pseudorandom function of two parameters with output length hLen (e.g., a keyed HMAC) Password is the master password
PBKDF2
Measure of electrostatic effect and how far it persists
and electrolytes, the Debye length λ D {\displaystyle \lambda _{\text{D}}} (Debye radius or Debye–Hückel screening length), is a measure of a charge carrier's
Debye_length
In algebra, integer associated to a module
In algebra, the length of a module over a ring R {\displaystyle R} is a generalization of the dimension of a vector space which measures its size. page
Length_of_a_module
Function with unusual fractal properties
2676} The question-mark function reverses this process: it translates the continued-fraction of a given real number into a run-length encoded binary sequence
Minkowski's question-mark function
Minkowski's_question-mark_function
Outer automorphism group of a free group on n generators
path in X. The length of the word is then the minimal length of a path in the free homotopy class of that closed path. Such a length function is constant
Out(Fn)
Arbitrary-precision calculator supporting interactive and scripted use
library. The scale() function for determining the precision (as with the scale variable) of its argument and the length() function for determining the
Bc_(programming_language)
Study of curves from a differential point of view
of the parametric curve. Similarly, the length of the curve from γ(a) to γ(t) can be expressed as a function of t, with s : [a, b] → [0, ℓ] defined as
Differentiable_curve
Branch of mathematics studying functions of a complex variable
holomorphic functions, which are differentiable functions of a complex variable. In contrast with a differentiable real function, a holomorphic function is always
Complex_analysis
Form of lossless data compression
consecutive repeating characters (run length). Store the character and its run length. Imports and helper functions from itertools import repeat, compress
Run-length_encoding
Topics referred to by the same term
term chord function may refer to: Diatonic function – in music, the role of a chord in relation to a diatonic key; In mathematics, the length of a chord
Chord_function
Class of periodic mathematical functions
the arc length of an ellipse. Important elliptic functions are Jacobi elliptic functions and the Weierstrass ℘ {\displaystyle \wp } -function. Further
Elliptic_function
In typography, width of a block of typeset text
line. Line length is determined by typographic parameters based on a formal grid and template with several goals in mind: balance and function for fit and
Line_length
Parametrizes complex structures on a surface
{\displaystyle x} of the length function associated to (the homotopy class of) α {\displaystyle \alpha } is then: ℓ α ( x ) = Length ( α x ) . {\displaystyle
Teichmüller_space
Password-based key derivation function
bcrypt is a password-hashing function designed by Niels Provos and David Mazières. It is based on the Blowfish cipher and presented at USENIX in 1999.
Bcrypt
Description of continuous random distribution
probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given
Probability_density_function
Message-digest hashing algorithm
widely used hash function producing a 128-bit hash value. MD5 was designed by Ronald Rivest in 1991 to replace an earlier hash function MD4, and was specified
MD5
Named container for a particular type of data
multiple types. For example, a function named length may determine the length of a list. Such a length function may be parametric polymorphic by including
Variable (high-level programming language)
Variable_(high-level_programming_language)
Software programming optimization technique
input under consideration. Let the return value of the function RuleAcceptsSomeInput be the length of the input accepted by Rule, or 0 if that rule does
Memoization
{\displaystyle \mathbb {P} } is the set of prime numbers. The Selberg zeta-function uses the lengths of simple closed geodesics instead of the prime numbers. If Γ
Selberg_zeta_function
Largest known protein in human muscles
humans is encoded by the TTN gene. The protein, which is over 1 μm in length, functions as a molecular spring that is responsible for the passive elasticity
Titin
Type of metric space
group (written additively) and d {\displaystyle d} is generated by a length function ‖ ⋅ ‖ {\displaystyle \|\cdot \|} (so that d ( x , y ) = ‖ x − y ‖ {\displaystyle
Ultrametric_space
Key derivation function based on an HMAC
with r {\displaystyle r} as the key (all zeros up to length of the underlying extractor hash function, if not provided) and the I K M {\displaystyle \mathrm
HKDF
Mathematical finite graph-associated function
mathematics, the Ihara zeta function is a zeta function associated with a finite graph. It closely resembles the Selberg zeta function, and is used to relate
Ihara_zeta_function
Cryptographic hash function
arbitrary-length message and compresses it down to a fixed bit-length (either 224, 256, 384 or 512 bits). The hash functions for the different output lengths are
Fugue_(hash_function)
Function used in computer cryptography
function "lossy" (not one-to-one) to have a one-way function. In particular, the function that outputs the string of n zeros on any input of length n
One-way_function
Mathematical functions
mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use:
Inverse_hyperbolic_functions
functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions
List of mathematical functions
List_of_mathematical_functions
Comparative measure of electrostatic and thermal energy
The Bjerrum length (after Danish chemist Niels Bjerrum 1879–1958 ) is the separation at which the electrostatic interaction between two elementary charges
Bjerrum_length
Concept in quantum mechanics
The scattering length in quantum mechanics describes low-energy scattering. For potentials that decay faster than 1 / r 3 {\displaystyle 1/r^{3}} as r
Scattering_length
Mathematical formula for the number of Young tableaux
\cdots (\lambda _{1}+k-1)!}}.} Hook lengths can also be used to give a product representation to the generating function for the number of reverse plane partitions
Hook_length_formula
Unique element of maximal length in a finite Coxeter group
Coxeter element, a different distinguished element Coxeter number Length function (Humphreys 1992, pp. 15–16, Section 1.8: Simple transitivity and the
Longest element of a Coxeter group
Longest_element_of_a_Coxeter_group
checksum. Hash function security summary Secure Hash Algorithms NIST hash function competition Key derivation functions (category) "Hash functions". www.azillionmonkeys
List_of_hash_functions
Fast-growing function
with maximal length. The function SSCG ( k ) {\displaystyle {\text{SSCG}}(k)} denotes that length for simple subcubic graphs. The function SCG ( k ) {\displaystyle
Friedman's_SSCG_function
Mass per unit length
the rod as having a varying mass (one that varies as a function of position along the length of the rod, l {\displaystyle l} ), we can write: m = m (
Linear_density
Smooth and compactly supported function
serve as a bump function. When b < c the plateau has positive length; when b = c it degenerates to a single point, but the function is still smooth.
Bump_function
Form of computer memory allocation
fixed length local to the currently active functions. Programmers may further choose to explicitly use the stack to store local data of variable length. If
Stack-based_memory_allocation
Measurement of the human penis
Human penis size varies on a number of measures, including length and circumference when flaccid and erect. Besides the natural variability of human penises
Human_penis_size
Inverse functions of sin, cos, tan, etc.
correspond to an arc whose length is rθ, where r is the radius of the circle. Thus in the unit circle, the cosine of x function is both the arc and the angle
Inverse trigonometric functions
Inverse_trigonometric_functions
Function for correlating hair cells with auditory neurons
scaled to the appropriate cochlear spiral lengths and audible frequency ranges. Moreover, the Greenwood function provides the mathematical basis for cochlear
Greenwood_function
Stationary exercise machine
this study support the claims made regarding the changeable stride length function feature on some newer ellipticals. While procedures differ slightly
Elliptical_trainer
Key elements of Extensible Stylesheet Language Transformations (XSLT)
semantics of XSLT 1.0 W3C XSLT 2.0 recommendation XSLT Elements Reference - by W3Schools "XSLT Reference". "XSLT 1.0: Function contains". "Example 16:1".
XSLT_elements
Programming paradigm based on applying and composing functions
are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that
Functional_programming
Collection of hash functions
hashing function. uint32_t jenkins_one_at_a_time_hash(const uint8_t* key, size_t length) { size_t i = 0; uint32_t hash = 0; while (i != length) { hash
Jenkins_hash_function
Measure of algorithmic complexity
the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language)
Kolmogorov_complexity
Use of functions that call themselves
recursion in small cases, and arm's-length recursion is a special case of this. A wrapper function is a function that is directly called but does not
Recursion_(computer_science)
Function definition that is not bound to an identifier
anonymous function (function literal, lambda function, or block) is a function definition that is not bound to an identifier. Anonymous functions are often
Anonymous_function
Function that counts distinct factors of a string
generally, the complexity function of a formal language (a set of finite strings) counts the number of distinct words of given length. Let u be a (possibly
Complexity_function
Computer programming function
In many programming languages, map is a higher-order function that applies a given function to each element of a collection, e.g. a list or set, returning
Map_(higher-order_function)
Growth curve model
case of the generalised logistic function. The growth curve is used to model mean length from age in animals. The function is commonly applied in ecology
Von_Bertalanffy_function
Transfer length method (a.k.a. Transmission line measurement)
the measured resistance values in dependence of the gap length together with the fitting function corresponding to the determined coefficients A {\displaystyle
Transfer_length_method
Functions such that f(–x) equals f(x) or –f(x)
In mathematics, an even function is a real function such that f ( − x ) = f ( x ) {\displaystyle f(-x)=f(x)} for every x {\displaystyle x} in its domain
Even_and_odd_functions
Cryptographic hash function
cryptography, Whirlpool (sometimes styled WHIRLPOOL) is a cryptographic hash function. It was designed by Vincent Rijmen (co-creator of the Advanced Encryption
Whirlpool_(hash_function)
Parameter of some vertical wind profile equations
Counehan, J. (August 1971). "Wind tunnel determination of the roughness length as a function of the fetch and the roughness density of three-dimensional roughness
Roughness_length
Mapping function
In mathematics, an additive set function is a function μ \mu mapping sets to numbers, with the property that its value on a union of two disjoint sets
Sigma-additive_set_function
travel, tourism, insurance
LENGTH FUNCTION
LENGTH FUNCTION
Boy/Male
Hindu
Written
Male
Scottish
Scottish surname transferred to forename use, derived from the name of a river of Celtic origin, LEITH means "flowing water."
Boy/Male
Hindu
Computer
Female
Romanian
Pet form of Romanian Ileana, possibly LENUTA means "torch."
Boy/Male
Hindu
Male
English
Variant spelling of English unisex Lee, LEIGH means "meadow."Â
Boy/Male
Hindu
Boy/Male
Hindu
Female
Swedish
Feminine form of Swedish Bengt, BENGTA means "blessed."Â
Boy/Male
Hindu
Boy/Male
Hindu, Indian
Bright
Male
English
Variant spelling of English Kenneth, KENITH means both "born of fire" and "comely; finely made."
Surname or Lastname
English
English : habitational name from any of the numerous places (in at least sixteen counties, but especially Leigh in Lancashire) named either with the nominative case of Old English lēah ‘woodland clearing’ (see Lee) or with lēage, a late dative form of this word (see Lye).
Girl/Female
Christian, Indian
Nice and General
Boy/Male
British, English, Kenyan
Handsome
Girl/Female
Latin
Mild.
Girl/Female
Latin
Mild.
Girl/Female
Danish, Finnish, German, Swedish
Blessed
Boy/Male
Hindu, Indian
Tiger
Male
Swedish
Modern form of Swedish Benkt, BENGT means "blessed."Â
LENGTH FUNCTION
LENGTH FUNCTION
LENGTH FUNCTION
LENGTH FUNCTION
LENGTH FUNCTION
LENGTH FUNCTION
LENGTH FUNCTION
n.
A measure of length in the metric system; one tenth of a meter, equal to 3.937 inches.
adv.
In a lengthy manner; at great length or extent.
a.
The quality or state of being long, in space or time; extent; duration; as, some sea birds are remarkable for the length of their wings; he was tired by the length of the sermon, and the length of his walk.
a.
Ten feet in length.
a.
Detail or amplification; unfolding; continuance as, to pursue a subject to a great length.
adv.
At full length; lengthwise.
v. t.
To lengthen.
a.
The longest, or longer, dimension of any object, in distinction from breadth or width; extent of anything from end to end; the longest line which can be drawn through a body, parallel to its sides; as, the length of a church, or of a ship; the length of a rope or line.
a.
Distance.
adv.
By the length; in a line with the length; lengthwise.
n.
Length.
n.
The tenth part of annual produce, income, increase, or the like; a tithe.
a.
Extended in length; tiresome.
a. & adv.
Slow; in slow time; slowly; -- rarely written lente.
a.
A portion of space or of time considered as measured by its length; -- often in the plural.
a.
Of half the whole or ordinary length, as a picture.
a.
A single piece or subdivision of a series, or of a number of long pieces which may be connected together; as, a length of pipe; a length of fence.
v. t.
To extent in length; to make longer in extent or duration; as, to lengthen a line or a road; to lengthen life; -- sometimes followed by out.
superl.
Having length; rather long or too long; prolix; not brief; -- said chiefly of discourses, writings, and the like.
a.
See Lento.
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