For an example of its use, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyze neutron activation to develop discrete measurements within vast samples.

For example, an 8-bit CPU deals with a range of numbers that can be represented by eight binary digits ( each digit having two possible values ), that is, 2 < sup > 8 </ sup > or 256 discrete numbers.

For the study of the mechanical behavior of solids and fluids these are assumed to be continuous bodies, which means that the matter fills the entire region of space it occupies, despite the fact that matter is made of atoms, has voids, and is discrete.

For example, the real line equipped with the discrete topology is closed and bounded but not compact, as the collection of all singleton points of the space is an open cover which admits no finite subcover.

For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by

For example, when a laboratory apparatus was developed that could reliably fire one electron at a time through the double slit, the emergence of an interference pattern suggested that each electron was interfering with itself, and therefore in some sense the electron had to be going through both slits at once — an idea that contradicts our everyday experience of discrete objects.

For real inputs, the real part of is none other than the discrete Hartley transform, which is also involutary.

For elliptic-curve-based protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible.

For more than 40 years, Paul Ekman has supported the view that emotions are discrete, measurable, and physiologically distinct.

For example, JPEG compression uses a variant of the Fourier transformation ( discrete cosine transform ) of small square pieces of a digital image.

For periodic functions, both the Fourier transform and the DTFT comprise only a discrete set of frequency components ( Fourier series ), and the transforms diverge at those frequencies.

For a discrete probability function f ( y ), let y < sub > i </ sub >, i = 1 to n, be the points with non-zero probabilities indexed in increasing order ( y < sub > i </ sub > < y < sub > i + 1 </ sub >).

For a population of discrete values, or for a continuous population density, the th-quantile is the data value where the cumulative distribution function crosses.

( For comparison, a terabyte of digital information stores only 2 < sup > 43 </ sup > discrete on / off values.

For instance, it is known from quantum mechanics that certain aspects of electromagnetism involve discrete particles — photons — rather than continuous fields.

For n independent and identically distributed discrete random variables X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > with cumulative distribution function G ( x ) and probability mass function g ( x ) the range of the X < sub > i </ sub > is the range of a sample of size n from a population with distribution function G ( x ).

For Leibniz, then, space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete.

For example, if J is a discrete category, the components of the unit are the diagonal morphisms δ: N → N < sup > J </ sup >.

For discrete devices, for example, there are three standards: JEDEC JESD370B in United States, Pro Electron in Europe and Japanese Industrial Standards ( JIS ) in Japan.

For example, the product of the unit circle ( with its usual topology ) and the real line with the discrete topology is a locally compact group with the product topology and Haar measure on this group is not inner regular for the closed subset

For the definition of the likelihood function, one has to distinguish between discrete and continuous probability distributions.

For an observation from the discrete component, the probability can either be written down directly or treated within the above context by saying that the probability of getting an observation in an interval that does contain a discrete component ( of being in interval j which contains discrete component k ) is approximately

For example, the abstract concept of number springs from the experience of counting discrete objects.

For example, localized osteoporosis can occur after prolonged immobilization of a fractured limb in a cast.

For example, the Chicxulub Crater, which was caused by an impact that has been implicated in the extinction of the dinosaurs, was localized to Central America by analyzing ejecta in the Cretaceous – Paleogene boundary, and then physically proven to exist using seismic maps from oil exploration.

For example, the electrons in a CRT display have a De Broglie wavelength of about 10 < sup >− 13 </ sup > m. To prevent the wave function for such a particle being spread over all space, de Broglie proposed using wave packets to represent particles that are localized in space.

For the wavepacket ( right ), ψ is localized and the particle can be found within some confined region of space.

For example, a localized source such as an antenna produces a field that is approximately a plane wave far from the antenna in its far-field region.

For Turkish youth who didn ’ t identify with Germany as a homeland, localized German hip hop still did not appeal to them nor function as a medium of self-expression.

For the very reason that his presence is common and universal he is not localized to the same extent as his fellow-deities, and, while always enumerated in a list of the great gods, his place in the systematized pantheon is more or less vague.

" For the masses of insurgents, this Virgin represented an intense and highly localized religious sensibility.

For reasons not yet understood in detail, sometimes these structures lose stability, leading to coronal mass ejections into interplanetary space, or flares, caused by sudden localized release of magnetic energy driving copious emission of ultraviolet and X-ray radiation as well as energetic particles.

For crystals, these regions of localized plasticity are called shear bands.

For localized movement, cytoplasmic streaming within cells and slow diffusion of ions and molecules between cells are utilized.

For example, in the era before chemotherapy, long term survival for patients with localized osteosarcoma was only approximately 20 %, but now has risen to 60-70 %.

For localized tumors, the surgical procedure is much less extensive than the types of surgery used to treat pancreatic adenocarcinoma.

For instance, abdominal pain and tenderness may be very localized, mimicking acute appendicitis.

In practice, this is usually the maximally-localized set, in which the Wannier function is localized around the point R and rapidly goes to zero away from R. For the one-dimensional case, it has been proved by Kohn that there is always a unique choice that gives these properties ( subject to certain symmetries ).

For more specific regions, the most frequently replicated positive correlations appear localized in the lateral and medial frontal lobe cortex.

*" Reach For The Stars on Channel 4 " ( 1981 – 1982 ; localized version of CBS ad campaign )

For nanoparticles, localized surface plasmon oscillations can give rise to the intense colors of suspensions or sols containing the nanoparticles.

For Libet, some unifying process or phenomenon likely mediates the transformation of localized, particularized neuronal representations into our unified conscious experience.

For example, studies of chemotypes in Greenland, Iceland, Norway, England, Scotland, and Ireland show that chemotypes span those countries rather than being geographically localized.

For example, if a differential equation is known to have some simple, localized solutions, and the solutions are a function of a single parameter, that parameter can take the conceptual role of time.