For example N = 4 Super Yang Mills Theory requires an SU ( N ) gauge group.

For example, the Lie algebra of SU ( n ) is written as.

For a Yang – Mills theory these inequivalent sectors can be ( in an appropriate gauge ) classified by the third homotopy group of SU ( 2 ) ( whose group manifold is the 3-sphere ).

For urban combat ISU-122's were utilized as assault guns, but with a lower efficiency in comparison to the SU / ISU-152.

For example, in the mid 1980s Bernard de Wit and Hermann Nicolai found an alternate theory in D = 11 Supergravity with Local SU ( 8 ) Invariance.

For SU ( 3 ), the color charge gauge group of QCD, the theory is therefore asymptotically free if there are 16 or fewer flavors of quarks.

For SU ( 3 )

For example, the N-dimensional fundamental representation of SU ( N ) for N greater than two is a complex representation whose complex conjugate is often called the antifundamental representation.

For example, in 1965 the 4. 2-litre with triple SU carburettors fitted to the US-specification E-Type was rated at SAE gross whereas by 1969, now with twin Zenith-Stromberg carburettors, this had fallen to SAE gross.

For example, projective representations of the 3-dimensional rotation group, which is the special orthogonal group SO ( 3 ), are ordinary representations of the special unitary group SU ( 2 ).

For an SU ( 2 ) gauge theory, neglecting, we have the following equations for the gauge field and the Higgs field in the gauge A < sub > 0 </ sub >

* For SU ( 2 ) gauge theory in D dimensions, the maximum Abelian subgroup is a U ( 1 ) subgroup.

* For SU ( 3 ) gauge theory in D dimensions, the maximum Abelian subgroup is a U ( 1 )× U ( 1 ) subgroup.

For an SU ( 2 ) theory the leading order chiral Lagrangian is given by

For example, if one wishes to compute an observable to, then one must compute the contact terms that come from the Lagrangian ( this is different for an SU ( 2 ) vs. SU ( 3 ) theory ) at tree-level and the one-loop contributions from the Lagrangian.

For example, in the case of G = SU ( 3 )-the strong nuclear interaction-the winner must prove that glueballs have a lower mass bound, and thus cannot be arbitrarily light.

For example, the importance of the Regulus 2, a very promising aerodynamic ship-to-surface missile designed to be launched by surfaced submarines, was greatly diminished by the successful acceleration of the much more advanced Polaris ballistic missile launched by submerged submarines.

For the prevention or treatment of the early stages of shipping fever complex, increase feeding level to 0.5 to 2 grams per head per day.

For prevention of foamy bloat, feed at a rate of 0.5 to 2 milligrams per head per day in mineral or salt or feed.

For example, arrow 17 in Figure 3 portrays the proximal radial epiphysis for boy 34, whereas the same epiphysis for girl 2 is portrayed by arrow 18 in Figure 4.

For an experiment to qualify as a binomial experiment, it must have four properties: ( 1 ) there must be a fixed number of trials, ( 2 ) each trial must result in a `` success '' or a `` failure '' ( a binomial trial ), ( 3 ) all trials must have identical probabilities of success, ( 4 ) the trials must be independent of each other.

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 instance, see Example 2 of Section 5-5, on red cards in hands of 5.

For Yokuts, I tabulated these 71 items in five columns, according as they were expressed by 1, 2, 3, 4, and more than 4 stems.

For Athabascan, with a greater range of stems, the first two of five corresponding columns were identical, 1 and 2 stems ; ;

For instance, there have been two Presidential Commissions on higher education since World War 2.

For these crimes he was sentenced to be hanged in public on Friday, December 2, 1859.

For hundreds of years, the evidence available consisted of ( 1 ) the captain's fragmentary journal, ( 2 ) a highly prejudiced account by one of the survivors, ( 3 ) a note found in a dead man's desk on board, and ( 4 ) several second-hand reports.

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 easy viewing, the middle 2 beads on each wire ( the 5th and 6th bead ) usually are of a different colour from the other eight beads.

For example, the open interval ( 0, 1 ) does not have a least element: if x is in ( 0, 1 ), then so is x / 2, and x / 2 is always strictly smaller than x.

For example, if an author is paid a modest advance of $ 2000. 00, and their royalty rate is 10 % of a book priced at $ 20. 00-that is, $ 2. 00 per book-the book will need to sell 1000 copies before any further payment will be made.

For example, the orbital 1s < sup > 2 </ sup > ( pronounced " one ess two ") has two electrons and is the lowest energy level ( n

For some elements, allotropes have different molecular formulae which can persist in different phases – for example, two allotropes of oxygen ( dioxygen, O < sub > 2 </ sub > and ozone, O < sub > 3 </ sub >), can both exist in the solid, liquid and gaseous states.

For instance, iron changes from a body-centered cubic structure ( ferrite ) to a face-centered cubic structure ( austenite ) above 906 ° C, and tin undergoes a transformation known as tin pest from a metallic phase to a semiconductor phase below 13. 2 ° C.

Many who side with this view disagree that Luke portrays Christianity or the Roman Empire as harmless and thus reject the apologetic view because “ Acts does not present Christians as politically harmless or law abiding for there are a large number of public controversies concerning Christianity, particularly featuring Paul .” For example, to support this view Cassidy references how Paul is accused of going against the Emperor because he is “ saying that there is another king named Jesus .” ( Acts 17: 7 ) Furthermore, there are multiple examples of Paul ’ s preaching causing uprisings in various cities ( Acts 14: 2 ; 14: 19 ; 16: 19-23 ; 17: 5 ; 17: 13-14 ; 19: 28-40 ; 21: 27 ).

For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.

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 example, if the sorted list to which we apply binary search has n elements, and we can guarantee that each lookup of an element in the list can be done in unit time, then at most log < sub > 2 </ sub > n + 1 time units are needed to return an answer.

For this reason, they are often called mechanical gauges in modern language.

For list see: List of broad gauges, by gauge and country

** For gauges on a car dashboard, see Dashboard items

For the most part the TAR would not change national gauges ; mechanized facilities would be built to move shipping containers from train to train at the breaks of gauge.

For example the cockpit of RAH-66 " Comanche " does not have analog dials or gauges at all.

For this reason McLeod gauges continue to be used as a calibration standard for electronic gauges.

For track gauges