For galaxies ( which are of course themselves much larger than 10 parsecs, and whose overall brightness cannot be directly observed from relatively short distances ) the absolute magnitude is defined by reference to the apparent brightness of a point-like or star-like source of the same total luminosity as the galaxy, as it would appear if observed at the standard 10 parsecs distance.

For very large distances, cosmological redshift complicates the relation between absolute and apparent magnitude, and an additional k correction might be required.

For objects at very great distances ( outside our galaxy ) the luminosity distance D < sub > L </ sub > must be used instead of d ( in parsecs ).

For large and elaborate arrangements, special blockages ( also known as firebreaks ) are employed at regular distances to prevent a premature toppling from undoing more than a section of the dominoes while still being able to be removed without damage.

For any point P on the minor arc BC of the circumcircle of an equilateral triangle ABC, with distances q and t from B and C respectively, and with the intersection of PA and BC being at a distance y from point P, we have that y is half the harmonic mean of q and t.

For distances of greater than 100 kilometers, either amplifiers or regenerators need to be deployed.

For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods.

For point masses the gravitational energy decreases without limit as they approach zero separation, and it is convenient and conventional to take the potential energy as zero when they are an infinite distance apart, and then negative ( since it decreases from zero ) for smaller finite distances.

For a regular n-gon inscribed in a unit-radius circle, the product of the distances from a given vertex to all other vertices equals n.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:

For radial distances from the center which are much greater than the Schwarzschild radius, the accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton's theory of gravity.

For the nearest planetary nebulae, it is possible to determine distances by measuring their expansion parallax.

For an antenna that is small compared to the wavelength in question, the intermediate-field region is considered to exist at all distances between 0. 1 wavelength and 1. 0 wavelength from the antenna.

For power transmission at distances greater than a few kilometres see high-voltage cable, power cables and HVDC.

For example, if the vertices of the graph represent cities and edge path costs represent driving distances between pairs of cities connected by a direct road, Dijkstra's algorithm can be used to find the shortest route between one city and all other cities.

# For the current node, consider all of its unvisited neighbors and calculate their tentative distances.

For shorter distances, the higher cost of DC conversion equipment compared to an AC system may still be warranted, due to other benefits of direct current links.

For short distances and light, small shipments a van or pickup truck may be used.

For example, migratory animals that travel vast distances ( such as the Arctic Tern ) typically have a locomotion mechanism that costs very little energy per unit distance, whereas non-migratory animals that must frequently move quickly to escape predators ( such as frogs ) are likely to have costly but very fast locomotion.

For longer distances, the use of a DVI booster is recommended to mitigate signal degradation.

For the topic of approximating a function by a sum of others using an objective function based on squared distances, see least squares ( function approximation ).

For shorter distances, cheaper balanced pair cables were used for various systems including Bell System K-and N-Carrier.

For instance, the MQ-9 Reaper, a U. S. drone plane used for domestic operations by the Department of Homeland Security, carries cameras that are capable of identifying an object the size of a milk carton from altitudes of 60, 000 feet, and has forward-looking infrared devices that can detect the heat from a human body at distances of up to 60 kilometers.

For distances greater than 1 &# 160 ; m from the head, however, the HRTF can be said to attenuate inversely with range.

For a given subject magnification ( and thus different camera – subject distances ), longer lenses appear to compress distance ; wider lenses appear to expand the distance between objects.

For example Connecticut applies the following standard to review unpreserved claims: 1. the record is adequate to review the alleged claim of error ; 2. the claim is of constitutional magnitude alleging the violation of a fundamental right ; 3. the alleged constitutional violation clearly exists and clearly deprived the defendant of a fair trial ; 4. if subject to harmless error analysis, the state has failed to demonstrate harmlessness of the alleged constitutional violation beyond a reasonable doubt.

For society at large, and / or for individuals beyond the audience?

For example, one definition of bandwidth could be the range of frequencies beyond which the frequency function is zero.

( For example, if there are two empty positions between the jumping piece and the piece being jumped, the jumping piece lands leaving exactly two empty positions immediately beyond the jumped piece.

For example, to purify ethanol beyond 95 %, a drying agent or a ( desiccant such as potassium carbonate ) can be added to convert the soluble water into insoluble water of crystallization.

For Robert Price " docetism ", together with " encratism ", " Gnosticism ", and " adoptionism " has been employed " far beyond what historically descriptive usage would allow ".

For the sake of the example ( and this is a gross simplification ), let's assume that he values this particular risk at 5 % per annum ( we could perform a more precise probabilistic analysis of the risk, but that is beyond the scope of this article ).

For Lacan, ' The traversing of fantasy involves the subject's assumption of a new position with respect to the Other as language and the Other as desire ... a utopian moment beyond neurosis '.

For this, and several other acts to safeguard the public funds, Cleveland's reputation as an honest politician began to spread beyond Erie County.

For example, Adeline is reading the illegible manuscripts she found in her bedchamber ’ s secret passage in the abbey when she hears a chilling noise from beyond her doorway.

For example, a six-year-old child who passed all the tasks usually passed by six-year-olds — but nothing beyond — would have a mental age that exactly matched his chronological age, 6. 0.

The prophecies of doom concerning the fall of both the House of Jeroboam and the northern kingdom as a whole (" For the Lord shall smite Israel ..., and he shall root up Israel out of this good land, which he gave to their fathers, and shall scatter them beyond the river ") might have been composed retroactively, after the events described had already come to pass ( this position is a secular or non-literal approach to scripture ).

For example, in highly emotional cases, such as child rape, the jury may be tempted to convict based on personal feelings rather than on conviction beyond reasonable doubt.

For instance, it was understood to mean " the science of the world beyond nature ( phusis in Greek )," that is, the science of the immaterial.

For this reason, muonium is an ideal system for studying bound-state QED and also for searching for physics beyond the standard model.

For numbers beyond this, the torso, legs and toes may be used, or one might count back up the other arm and back down the first, depending on the people.

For pleasure alone he climbed Mount Ventoux, which rises to more than six thousand feet, beyond Vaucluse.

For further functionality beyond this goal, many libraries have been created to work on top of SDL.

For example, in the O. J. Simpson murder trial, the jury was not convinced beyond reasonable doubt that O. J. Simpson had committed the crime of murder ; but in a later civil trial, the jury in that case felt that there was sufficient evidence to meet the standard of preponderance of the evidence required to prove the tort of wrongful death.

For generalized or extended thermodynamics, the definition of the quantity known as the entropy of a small local region is in terms beyond those of classical thermodynamics ; in particular, flow rates are admitted into the definition of the entropy of a small local region.

For a long time, no one searched for other TNOs as it was generally believed that Pluto was the only major object beyond Neptune.

For frequencies extending beyond the VHF band, cores made from non-conductive magnetic ceramic materials called ferrites are common.

For most of us God is totally beyond the comprehension of mere finite beings such as ourselves, there may be exceptions.

For scheduling and advertising purposes some of these branches are further divided into sections such as the case with the Montauk Branch, which is known as the Babylon Branch service in the electrified portion of the line between Jamaica and Babylon, while the diesel service beyond Babylon to Montauk is referred to as the Montauk Branch service.

For Tillich, a symbol always " points beyond itself " to something that is unquantifiable and mysterious.