Crossword clues for invariant
invariant
The Collaborative International Dictionary
Invariant \In*va"ri*ant\, n. (Math.)
An invariable quantity; specifically, a function of the
coefficients of one or more forms, which remains unaltered,
when these undergo suitable linear transformations.
--J. J.
Sylvester.
Douglas Harper's Etymology Dictionary
Wiktionary
a. 1 not varying; constant 2 (context mathematics English) Unaffected by a specified operation (especially by a transformation) 3 (context computing programming English) Neither covariant nor contravariant. n. An invariant quantity, function etc.
WordNet
adj. unaffected by a designated operation or transformation
persistent in occurrence and unvarying in nature; "maintained a constant temperature"; "a constant beat"; "principles of unvarying validity"; "a steady breeze" [syn: changeless, constant, steady, unvarying]
Wikipedia
Invariant and invariance may refer to:
In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually indicated by the context in which the term is used. For example, the area of a triangle is an invariant with respect to isometries of the Euclidean plane. The phrases "invariant under" and "invariant to" a transformation are both used. More generally, an invariant with respect to an equivalence relation is a property that is constant on each equivalence class.
Invariants are used in diverse areas of mathematics such as geometry, topology and algebra. Some important classes of transformations are defined by an invariant they leave unchanged, for example conformal maps are defined as transformations of the plane that preserve angles. The discovery of invariants is an important step in the process of classifying mathematical objects.
In mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation.
Invariance does not imply not varying. Instead, it pertains to a condition where there is no variation of the system under observation, and the only applicable condition is the instantaneous condition. Invariance pertains to now . Now(+1), to a condition where all variations are solely due the internal variables, with no external aspects imparting nor removing energy (Newton´s law of motion: a system in motion continues in motion, unless an external force imparts or removes energy). That condition is met by using the partial derivative function, ∂f(internal)xf(external) and presuming/setting f(external)=constant, leading to ∂f(external)=1 using the chain rule. Obviously, this is a model used solely for calculations, and not a reality. Reality is, that at all and every instance, energy is both removed and added to any system in observation.
In computer science, an invariant is a condition that can be relied upon to be true during execution of a program, or during some portion of it. It is a logical assertion that is held to always be true during a certain phase of execution. For example, a loop invariant is a condition that is true at the beginning and end of every execution of a loop.
Usage examples of "invariant".
If the brain were not, most of the time, invariant, unmoved by experience, we would be unable to survive, as indeed the fates of Funes and Shereskevskii attest.
These ratios are intrinsically pitch translation invariant, so the significance of consonant ratios explains both how pitch translation invariance is achieved, and also why it exists as a precise frequency scaling.
Intensity will be pitch translation invariant, for similar reasons to those that cause invariance of intensity in other maps.
It has robust translation invariance, because it is invariant under any transformation that is monotonic.
In that case, a Neptunian Warlock made a Noumenal Recording, but then gave himself the brain structure of an Invariant.
Sennec was of the Invariant neuroform, a highly integrated unicameral nervous system.
On the one hand, we have mechanism, repetition, inertia, constants, and invariants: the play of the material world, from the point of view of quantity, offers us the aspect of an immense transformation without gain or loss, a homogeneous transformation tending to maintain in itself an exact equivalence between the departure and arrival point.
The being was modeled along unemotional Invariant lines, perhaps to render it immune from Hortator pressure.
In some ways, he was the most powerful Hortator here, because the special psychological uniformity of the Invariants, the so-called Protocols of Sanity, ensured that all the populations of the Cities in Space would follow his lead.
Any computation that starts with absolute pitch values and results in a pitch translation invariant output will still be pitch translation invariant if the input values are first reduced to a value modulo octaves.
These ratios are intrinsically pitch translation invariant, so the significance of consonant ratios explains both how pitch translation invariance is achieved, and also why it exists as a precise frequency scaling.
In a very analogous manner, comparisons of ratios between pairs of time durations are required to achieve time scaling invariant perception of rhythm.
Following a similar methodology as for pitch translation invariance, play different rhythms at different tempos, and look for cortical maps whose response is time scaling invariant.
Glynn had thin hair and an invariant three-day growth of gray stubble and diverticulitis that made him stoop somewhat over, and remaining physique-type issues from a load of bricks falling on his head from a Workers Comp scam gone rye that included crossed eyes that Lenz overheard the veiled girl Joe L.
A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them.