If we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have

In an " extended model " which includes hot dark matter in the form of neutrinos, then if the " physical baryon density " Ω < sub > b </ sub > h < sup > 2 </ sup > is estimated at about 0. 023 ( this is different from the ' baryon density ' Ω < sub > b </ sub > expressed as a fraction of the total matter / energy density, which as noted above is about 0. 046 ), and the corresponding cold dark matter density Ω < sub > c </ sub > h < sup > 2 </ sup > is about 0. 11, the corresponding neutrino density Ω < sub > v </ sub > h < sup > 2 </ sup > is estimated to be less than 0. 0062.

where I < sub > v </ sub >( λ ) is the luminous intensity in candelas, I < sub > e </ sub >( λ ) is the radiant intensity in W / sr and is the standard luminosity function.

If a source emits a known luminous intensity I < sub > v </ sub > ( in candelas ) in a well-defined cone, the total luminous flux Φ < sub > v </ sub > in lumens is given by

: Φ < sub > v </ sub > = I < sub > v </ sub > 2π ( 1-cos ( A / 2 )),

Retrieved at < http :// books. google. com / books? id = NztlWQeXf2IC & printsec = frontcover & dq = zhou + enlai & hl = en & ei = wBkuTdKyB4H_8AaJucigAQ & sa = X & oi = book_result & ct = result & resnum = 2 & ved = 0CCsQ6AEwAQ # v = onepage & q & f = false > on March 12, 2011. p. 38 </ ref > More liberal estimates regarding the White Terror in China, estimate it took millions of lives, most of them in the rural areas.

( v < sub > 0 </ sub >, v < sub > 1 </ sub >, – v < sub > 0 </ sub >, – v < sub > 1 </ sub >, v < sub > 0 </ sub >, v < sub > 1 </ sub >, v < sub > 0 </ sub >, v < sub > 1 </ sub >) = ( 1, – 1, – 1, 1, 1, – 1, 1, – 1 ).

A " common law system " is a legal system that gives great precedential weight to common law ,< ref > Washington Probate, " Estate Planning & Probate Glossary ", Washington ( State ) Probate, s. v.

One example of this ( from the Queen's Bench in England ) is Doyle v Olby ( Ironmongers ) Ltd 2 QB 158, the claimant appealed ( successfully ) on the basis that, although he won in the court below, the lower court had applied the wrong measure of damages and he had not been fully recompensated.

It was the mutual bond and obligation between monarch and subjects, whereby subjects are called his liege subjects, because they are bound to obey and serve him ; and he is called their liege lord, because he should maintain and defend them ( Ex parte Anderson ( 1861 ) 3 El & El 487 ; 121 ER 525 ; China Navigation Co v Attorney-General ( 1932 ) 48 TLR 375 ; Attorney-General v Nissan 1 All ER 629 ; Oppenheimer v Cattermole 3 All ER 1106 ).

Where territory is occupied in the course of hostilities by an enemy's force, even if the annexation of the occupied country is proclaimed by the enemy, there can be no change of allegiance during the progress of hostilities on the part of a citizen of the occupied country ( R v Vermaak ( 1900 ) 21 NLR 204 ( South Africa )).

Allegiance is owed both to the Sovereign as a natural person and to the Sovereign in the political capacity ( Re Stepney Election Petition, Isaacson v Durant ( 1886 ) 17 QBD 54 ( per Lord Coleridge CJ )).

A natural-born subject owes allegiance wherever they may be, so that where territory is occupied in the course of hostilities by an enemy's force, even if the annexation of the occupied country is proclaimed by the enemy, there can be no change of allegiance during the progress of hostilities on the part of a citizen of the occupied country ( R v Vermaak ( 1900 ) 21 NLR 204 ( South Africa )).

In the Euclidean plane, the angle θ between two vectors u and v is related to their dot product and their lengths by the formula

Access Now v. Southwest Airlines was a case where the District Court decided that the website of Southwest Airlines was not in violation of the Americans with Disability Act because the ADA is concerned with things with a physical existence and thus cannot be applied to cyberspace.

There is no distinction made in Scotland between assault and battery ( which is not a term used in Scots law ), although, as in England and Wales, assault can be occasioned without a physical attack on another's person, as demonstrated in Atkinson v. HM Advocate wherein the accused was found guilty of assaulting a shop assistant by simply jumping over a counter wearing a ski mask.

His chief work is a Historia Francorum, or Libri v de Gestis Francorum, which deals with the history of the Franks from the earliest times to 653, and was continued by other writers until the middle of the twelfth century.

* 1905 – The Supreme Court of the United States decides Lochner v. New York which holds that the " right to free contract " is implicit in the due process clause of the Fourteenth Amendment of the United States Constitution.

In the 2006 case before the United States Court of Appeals for the Fifth Circuit, Ballard v. Burton, Judge Carl E. Stewart writing for the Court held that an Alford guilty plea is a " variation of an ordinary guilty plea ".

* 1818 – The case of Ashford v Thornton ends, with Abraham Thornton allowed to go free rather than face a retrial for murder, after his demand for trial by battle is upheld.

* 2000 – United States v. Microsoft: Microsoft is ruled to have violated United States antitrust laws by keeping " an oppressive thumb " on its competitors.

* 2010 – California's Proposition 8, the ballot initiative prohibiting same-sex marriage passed by the state's voters in 2008, is overturned by Judge Vaughn Walker in the case Perry v. Schwarzenegger.

In terms of ultra vires actions in the broad sense, a reviewing court may set aside an administrative decision if it is unreasonable ( under Canadian law, following the rejection of the " Patently Unreasonable " standard by the Supreme Court in Dunsmuir v. New Brunswick ), Wednesbury unreasonable ( under British law ), or arbitrary and capricious ( under U. S. Administrative Procedure Act and New York State law ).

According to the special theory of relativity, the aberration looks as a transform of the celestial sphere due to different frames of reference and is virtually a special case of velocity addition, namely one of the light beam and frames ' relative velocity v. The formula from relativistic aberration can be simplified to

There is also a U. S. Supreme Court case that predates the dictionary, Jackson ex dem Bradford v. Huntington, that uses the phrase " black letter " in the same sense as black letter law: " It is seldom that a case in our time savors so much of the black letter, but the course of decisions in New York renders it unavailable.

Part of the Gaelic lexicon, this spelling suggests a Germanic ( Saxon ) origin, as the ' w ' is most likely pronounced as a ' v '.

The deletion of historical final schwas ( weak vowels ) at the end of words such as give and have phonemicized / v /, but the now-silent ⟨ e ⟩ remained at the end of most / v /- final words.

Words spelled with final ⟨ v ⟩ such as rev and Slav remain comparatively rare.

The power delegated to the federal government was significantly expanded by the Supreme Court decision in McCulloch v. Maryland ( 1819 ), amendments to the Constitution following the Civil War, and by some later amendments — as well as the overall claim of the Civil War, that the states were legally subject to the final dictates of the federal government.

In the final ruling of Kitzmiller v. Dover Area School District, Judge Jones specifically singled out Behe and irreducible complexity:

v: final velocity

* Final Judgment in U. S. v. Microsoft ( injunction including final settlement terms approved by the court ) ( note that the copy posted on the district court's web site is actually an earlier version that the court declined to approve ).

The KL10 emulation supports v. 442 of the KL10 microcode, which enables it to run the final versions of both TOPS-10 and TOPS-20.

The KS10 emulation supports both ITS v. 262 microcode for the final version of KS10 ITS and DEC v. 130 microcode for the final versions of KS TOPS-10 and TOPS-20.

The court case was titled Courtesy Sandwich Shop v. Port of New York Authority and the final appeal was lost by the small business owners in November 1963 " for want of a substantial federal question ".

The presidential authority to commission officers would have a large impact on the 1803 case Marbury v. Madison, where outgoing Federalist President John Adams feverishly signed many commissions to the judiciary on his final day in office, hoping to, as incoming Democratic-Republican President Thomas Jefferson put it, " into the judiciary as a stronghold.

Grace made his final first-class appearance on 20 – 22 April 1908 for the Gentlemen of England v Surrey at The Oval, where, opening the innings, he scored 15 and 25.

where v is the final velocity, which is hence given by

: v < sub > b </ sub > is the final velocity of the second object after impact

where v is the final velocity, which is hence given by

where r < sub > 0 </ sub > and v < sub > 0 </ sub > are the particle's initial position and velocity, r, v, a are the final position ( displacement ), velocity and acceleration of the particle after the time interval.

Some observers have suggested that the Supreme Court saw RFRA as a threat to the Court's institutional power and an incursion on its role as final arbiter of the meaning of the Constitution, because that statute was aimed specifically at overturning the Employment Division v. Smith decision.

* Microsoft has announced that it is to make some concessions towards the proposed final settlement of the United States v. Microsoft case, ahead of the judge's verdict.