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 nearby astronomical objects ( such as stars in our galaxy ) luminosity distance D < sub > L </ sub > is almost identical to the real distance to the object, because spacetime within our galaxy is almost Euclidean.

For much more distant objects the Euclidean approximation is not valid, and General Relativity must be taken into account when calculating the luminosity distance of an object.

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 a meteor, the standard distance for measurement of magnitudes is at an altitude of at the observer's zenith.

For example, using Cartesian coordinates on the plane, the distance between two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >) is defined by the formula

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

For example, in AC power lines, the waves of electromagnetic energy propagate through the space between the wires, moving from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance.

For example, it should not matter whether one measures the distance between the Great Pyramids of Giza by laser rangefinding, by satellite imaging, or with a meter stick-in all three cases, the answer should be approximately the same.

The completion of M can be constructed as a set of equivalence classes of Cauchy sequences in M. For any two Cauchy sequences ( x < sub > n </ sub >)< sub > n </ sub > and ( y < sub > n </ sub >)< sub > n </ sub > in M, we may define their distance as

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance.

For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.

For example, if we suppose at t = 0 the extension is a unit distance ( x = 1 ), and the particle is not moving ( dx / dt = 0 ).

For example, Innova Discs divides their discs into Distance Drivers and Fairway Drivers, with a fairway driver being somewhere between a distance driver and a mid-range disc.

For light, we can often neglect one direction if the diffracting object extends in that direction over a distance far greater than the wavelength.

For example, if two slits are separated by 0. 5mm (), and are illuminated with a 0. 6μm wavelength laser (), then at a distance of 1m (), the spacing of the fringes will be 1. 2mm.

For example, there are usually no trade tariffs or import quotas ; there are usually no delays as goods pass from one part of the country to another ( other than those that distance imposes ); there are usually no differences of taxation and regulation.

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 instance, if a vehicle travels a certain distance at a speed x ( e. g. 60 kilometres per hour ) and then the same distance again at a speed y ( e. g. 40 kilometres per hour ), then its average speed is the harmonic mean of x and y ( 48 kilometres per hour ), and its total travel time is the same as if it had traveled the whole distance at that average speed.

The penalty for this is noticeable in the big, bold, brilliant, but brassy piano sounds in Melody And Percussion For Two Pianos ( SP-44007 ).

For example, Bhutan has abolished the death penalty, but Thailand still retains it, although Buddhism is the official religion in both.

For example, systems that depend heavily on immutable objects such as many functional programming languages can suffer an efficiency penalty due to frequent copies.

For example, when programming in C, there will be a performance penalty for including a call to an expensive function inside a loop, even if the function call could be moved outside of the loop without changing the results of the program.

For summary conviction offences that fall under the jurisdiction of the federal government ( which includes all criminal law ), section 787 of the Criminal Code of Canada specifies that, unless another punishment is provided for by law, the maximum penalty for a summary conviction offence is a sentence of 6 months of imprisonment, a fine of $ 5, 000 or both.

For the head to head round, the remaining two players are each required to answer five questions each in a penalty shootout format.

For example, although federal law classifies both cocaine and amphetamines as " Schedule II " drugs, the penalty for possession of cocaine is greater than the penalty for possession of amphetamines because cocaine, unlike amphetamines, is classified as a narcotic.

For each penalty, unless the rules have been changed appropriately, the penalty card is given with the declaration of the rule violated.

For extreme misconduct by one team, the umpire may award five penalty runs to the other team.

For his role in the shooting, Floyd Allen received the death penalty, and was electrocuted in 1913.

For example: a threat of violence can change the likely costs and benefits of different actions ; so can a financial penalty in a ' voluntarily agreed ' contract, or indeed a friendly offer.

For this, Gower was fined £ 1000, a penalty that could have been steeper had he released the water bombs he had also prepared.

For example, photographs of nooses in a South African execution chamber opened to the public after abolishment of the death penalty, showed double nooses.

For the following and final year the weight penalty was reduced and works backed Hasemi returned with another privateer R32 that crashed in the race, while Hasemi retired with engine failure.

For example, a poll of over 1, 800 Americans showed that about 40 % would support the death penalty for child rape.

For example, U. S. rules impose a 20 % penalty where the adjustment exceeds USD 5 million, increased to 40 % of the additional tax where the adjustment exceeds USD 20 million.

For several months, the demand of the public for vengeance increased, so that Mallory feared that he would face the death penalty if convicted.

For Roth IRAs with only contributed funds the basis can be withdrawn before age 59½ without penalty ( or tax ) on a first in first out basis, and a penalty would apply only on any growth ( the taxable amount ) that was taken out before 59½ where an exception didn't apply.

For the year 2006 Mercedes-Benz draw $ 30. 3 million penalty for violating fuel economy standards.

For most of his NHL career, he has studiously avoided drawing penalties, although the introduction of many new rules in 2005 – 06 saw him rack up his career high ( 50 ) in penalty minutes.

For example, a negative case for the resolution " Resolved: A just society ought not use the death penalty as form of punishment " could have a value of justice, a value criterion of crime deterrence, and then contentions that demonstrate that the death penalty serves as a uniquely powerful deterrent ( which would require statistical and possibly psychological evidence.

For three straight years, Tom Horn patrolled the southern Wyoming pastures, and how many men he killed after Lewis and Powell ( if he killed Lewis and Powell ) will never be known.

William Wimsatt and Cleanth Brooks, it seems to me, have a penetrating insight into the way in which this control is effected: `` For if we say poetry is to talk of beauty and love ( and yet not aim at exciting erotic emotion or even an emotion of Platonic esteem ) and if it is to talk of anger and murder ( and yet not aim at arousing anger and indignation ) -- then it may be that the poetic way of dealing with these emotions will not be any kind of intensification, compounding, or magnification, or any direct assault upon the affections at all.

For if Serenissimus made the sign of the Cross with his right hand, and meant it, with his left he beckoned lewdly to any lady who happened to catch his eye.

For here if anywhere in contemporary literature is a major effort to counterbalance Existentialism and restore some of its former lustre to the tarnished image of the species Man, or, as Malraux himself puts it, `` to make men conscious of the grandeur they ignore in themselves ''.

For the sad truth is that while one might write well without having read Bartleby The Scrivener, one is more likely, to write well if one has `` read it, and much else.

`` For if ye forgive men their trespasses, your heavenly Father will also forgive you: but if ye forgive not men their trespasses, neither will your Father forgive -- your trespasses ''.

For a while there was such shrill girlish commotion I couldn't have made myself heard if I'd had the equivalent of the message to Garcia.

For instance -- what about all those people Harold Rhodes went toward unhesitatingly, as if this were the one moment they would ever have together, their one chance of knowing each other??

For those communities which have financial difficulties in effecting adjustments, there are a number of alternatives any one of which alone, or in combination with others, would minimize if not even eliminate the problem.

For, if so, the path leads through a complex process of parliamentary diplomacy which adds still another dimension to the problem.

For some unusual photographic subjects, if your vacation takes you nearby, try these events: the 600-mile auto race in Charlotte, N.C.,, on May 27 ; ;

For me, these will belong more completely to their surroundings if they are conceived in this early stage, though I freely admit that I do not hesitate to add or eliminate figures on the full sheet when it serves my final purpose.

For example, the marksman gets 5 shots, but we take his score to be the number of shots before his first bull's-eye, that is, 0, 1, 2, 3, 4 ( or 5, if he gets no bull's-eye ).

For if it did, the plane of L and l' would contain two generators of Af, which is impossible.

For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.

For instance, the following statement was rated low in compulsivity, `` She's naturally quite neat about things, but it doesn't bother her at all if her room gets messy.

For such an industry, it is only `` safe '' to raise its price if such an increase is manifestly `` justified '' by rising costs ( due to rising wages, etc. ).

For example, property `` used in the trade or business '' of a transferor corporation, as defined in section 1231, presumably would not retain its special status following a non-taxable reorganization if it is not so used in the business of the acquiring corporation.

For if the small group notion involves the implicit claim that the phenomena of sociological investigations are of atomic or subatomic proportions, the philosopher needs to know the extent to which such entities are valid.

For the same reason, the output fiber plate is planoconcave, its exposed flat side permitting contact photography if a permanent record is desired.

For example, if you are a reasonably well-adjusted person, there are certain ways that are reasonable and appropriate for addressing your mother.

For we must number here not only the names of Bushnell, Clarke, and Rauschenbusch, not to mention those of `` the Chicago School '' and Macintosh, but those of the brothers Niebuhr and ( if America may claim him!!

For every criterion which defines what something is, at the same time proclaims -- implicitly if not openly -- what that something is not.