The ternary heap does two steps in less time than the binary heap requires for three steps, which multiplies the index by a factor of 9 instead of the factor 8 of three binary steps.

This can be reduced somewhat by using a binary space partitioning tree to reduce the amount of time spent determining which patches are completely hidden from others in complex scenes ; but even so, the time spent to determine the form factor still typically scales as n log n. New methods include adaptive integration

For moderate volumes of values, insertions and deletions in a colored binary tree are faster compared to B-trees because colored trees don't attempt to maximize the fill factor of each horizontal cluster of nodes ( only the minimum fill factor is guaranteed in colored binary trees, limiting the number of splits or junctions of clusters ).

The angular resolution of the telescope is an important factor in the detection of visual binaries, and as better angular resolutions are applied to binary star observations increasing number of visual binaries will be detected.

X-ray bursters are one class of X-ray binary stars exhibiting periodic and rapid increases in luminosity ( typically a factor of 10 or greater ) peaked in the X-ray regime of the electromagnetic spectrum.

For example, consider a fixed-point type represented as a binary integer with b bits in two's complement format, with a scaling factor of 1 / 2 < sup > f </ sup > ( that is, the last f bits are fraction bits ): the minimum representable value is − 2 < sup > b-1 </ sup >/ 2 < sup > f </ sup > and the maximum value is ( 2 < sup > b-1 </ sup >- 1 )/ 2 < sup > f </ sup >.

Decimal fixed-point types have a scaling factor that is a power of ten ; for binary fixed-point types it is a power of two.

Gottman's 2002 paper makes no claims to accuracy in terms of binary classification, and is instead a regression analysis of a two factor model where skin conductance levels and oral history narratives encodings are the only two statistically significant variables.

By contrast, a breadth-first ( level-order ) traversal will traverse a binary tree of infinite depth without problem, and indeed will traverse any tree with bounded branching factor.

This relationship is used in engineering, for example to approximate a factor of two in power as 3 dB ( actual is 3. 0103 dB – see 3dB-point ), or to relate a kilobyte to a kibibyte ; see binary prefix.

" An all-optical switch based on a high Quality factor cylindrical resonator has been proposed that allows for fast binary switching at low power.

Additional information, including blocking factor, binary vs. text, maximum number of records may be specified.

An integral binary quadratic form is called primitive if a, b, and c have no common factor.

ITRON's popularity comes from many factors, but one factor is the notion of " loose standardization ": the API specification is at the source level, and does not specify binary API compatibility.

However, Gottman's 2002 paper makes no claims to accuracy in terms of binary classification, and is instead a regression analysis of a two factor model where skin conductance levels and oral history narratives encodings are the only two statistically significant variables.

In data compression, a universal code for integers is a prefix code that maps the positive integers onto binary codewords, with the additional property that whatever the true probability distribution on integers, as long as the distribution is monotonic ( i. e., p ( i ) ≥ p ( i + 1 ) for all positive i ), the expected lengths of the codewords are within a constant factor of the expected lengths that the optimal code for that probability distribution would have assigned.

He also only measured absolute ( binary ) characteristics, such as color, shape, and position of the offspring, rather than quantitative characteristics.

In information theory, one bit is typically defined as the uncertainty of a binary random variable that is 0 or 1 with equal probability, or the information that is gained when the value of such a variable becomes known.

In turn, one can also derive ordinary functions of one variable from a binary function.

Deneb Algedi is a Beta Lyrae variable star ( a type of eclipsing binary ).

UV Ceti is an unusual binary variable star.

* RS CVn is the prototype of a special class of binary stars of chromospherically active and optically variable components.

The special case of information entropy for a random variable with two outcomes is the binary entropy function, usually taken to the logarithmic base 2:

Mira is a binary star, consisting of the red giant Mira A along with Mira B. Mira A is also an oscillating variable star and was the first non-supernova variable star discovered, with the possible exception of Algol.

W Ursae Majoris is the prototype of a class of contact binary variable stars, and ranges between 7. 75 < sup > m </ sup > and 8. 48 < sup > m </ sup >.

In a continuously variable slope delta ( CVSD ) modulation converter, the mean proportion of binary " 1 " digits at the converter output in which each " 1 " indicates a run of a specified number of consecutive bits of the same polarity in the digital output signal.

Several types of astrophysical objects emit, fluoresce, or reflect X-rays, from galaxy clusters, through black holes in active galactic nuclei ( AGN ) to galactic objects such as supernova remnants, stars, and binary stars containing a white dwarf ( cataclysmic variable stars and super soft X-ray sources ), neutron star or black hole ( X-ray binaries ).

* The luminous blue variable Eta Carinae has recently been determined to be a binary star system.

A binary symmetric channel with crossover probability p denoted by, is a channel with binary input and binary output and probability of error p ; that is, if X is the transmitted random variable and Y the received variable, then the channel is characterized by the conditional probabilities

Cygnus X-1 belongs to a high-mass X-ray binary system about from the Sun that includes a blue supergiant variable star designated HDE 226868 which it orbits at about 0. 2 AU, or 20 % of the distance from the Earth to the Sun.

It is currently classified as a luminous blue variable ( LBV ) binary star due to peculiarities in its pattern of brightening and dimming.

Being variable word length decimal, as opposed to fixed-word-length pure binary, made it an especially attractive first computer to learn on — and hundreds of thousands of students had their first experiences with a computer on the IBM 1620.

* KUI 93AB, an eclipsing binary of Algol variable type

* Fixed point numbers were variable length, stored in either binary ( 1 to 64 bits ) or decimal ( 1 to 16 digits ) and either unsigned format or sign / magnitude format.

A special form of the LLN ( for a binary random variable ) was first proved by Jacob Bernoulli.

In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in X

The redesigned AIM for Mac is a full universal binary Cocoa API application that supports both Tiger and Leopard – Mac OS X 10. 4. 8 ( and above ) or Mac OS X 10. 5. 3 ( and above ).

A binary relation R is usually defined as an ordered triple ( X, Y, G ) where X and Y are arbitrary sets ( or classes ), and G is a subset of the Cartesian product X × Y.

Set-theoretically, one may represent a binary function as a subset of the Cartesian product X × Y × Z, where ( x, y, z ) belongs to the subset if and only if f ( x, y ) = z.

Conversely, a subset R defines a binary function if and only if, for any x in X and y in Y, there exists a unique z in Z such that ( x, y, z ) belongs to R.

Alternatively, a binary function may be interpreted as simply a function from X × Y to Z.

A binary operation is a binary function where the sets X, Y, and Z are all equal ; binary operations are often used to define algebraic structures.

In linear algebra, a bilinear transformation is a binary function where the sets X, Y, and Z are all vector spaces and the derived functions f < sup > x </ sup > and f < sub > y </ sub > are all linear transformations.

A bilinear transformation, like any binary function, can be interpreted as a function from X × Y to Z, but this function in general won't be linear.

* The Intel versions of Mac OS X from versions 10. 4 ( Tiger ) to 10. 6 ( Snow Leopard ) have Rosetta, a binary translation program that allows applications meant for use on PowerPC Macs to run on Apple systems that use Intel processors.

This yields a convenient way of generating an equivalence relation: given any binary relation R on X, the equivalence relation generated by R is the smallest equivalence relation containing R. Concretely, R generates the equivalence relation a ~ b if and only if there exist elements x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub > in X such that a

If G is a group and X is a set, then a ( left ) group action of G on X is a binary operator:

If one object consists of a set X with a binary relation R and the other object consists of a set Y with a binary relation S then an isomorphism from X to Y is a bijective function such that:

Suppose that on these sets X and Y, there are two binary operations and that happen to constitute the groups ( X ,) and ( Y ,).