( For groups of low 2-rank the proof of this breaks down, because theorems such as the signalizer functor theorem only work for groups with elementary abelian subgroups of rank at least 3.

For contributions to the unification of the weak and electromagnetic interaction between elementary particles, Abdus Salam, Sheldon Glashow and Steven Weinberg were awarded the Nobel Prize in Physics in 1979.

For polynomials of degree four and smaller there are explicit formulae for the roots ( the formulae are elementary functions ).

For mathematical purposes, elementary particles are normally treated as point particles, although some particle theories such as string theory posit a physical dimension.

For a more elementary discussion of Galois groups in terms of permutation groups, see the article on Galois theory.

For example, " the right to remain silent " means little to a deaf individual and the word " constitutional " may not be understood by people with only an elementary education.

For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences ; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science ; they are used in calculus and numerical analysis to approximate other functions.

For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical Coulomb potential.

For large numbers the Poisson distribution approaches a normal distribution, typically making shot noise in actual observations indistinguishable from true Gaussian noise except when the elementary events ( photons, electrons, etc.

For experimental evidence suggesting that one-day-old babies can do elementary arithmetic, see Brian Butterworth.

For example, in conventional electrical units, the values of the Josephson constant K < sub > J </ sub > and von Klitzing constant R < sub > K </ sub > are exact defined values ( written K < sub > J-90 </ sub > and R < sub > K-90 </ sub >), and it follows that the elementary charge is also an exact defined value in this unit system.

For example, one possible proposed redefinition is " the ampere ... is such that the value of the elementary charge e ( charge on a proton ) is exactly 1. 602176487 × 10 < sup >− 19 </ sup > coulomb " This proposal is not yet accepted as part of the SI system: The SI definitions are unlikely to change until at least 2015.

For 25 years, he worked on theories about elementary particles, played a role in the discovery of the quark, and researched the analytic and high-energy properties of Feynman integrals and the foundations of S-Matrix theory.

For example, an elementary problem in ring theory is how to turn a rng ( which is like a ring that might not have a multiplicative identity ) into a ring.

For some elementary operations, such as multiplication, such an abstraction does not lose any precision: to get the sign of a product, it is sufficient to know the sign of the operands.

For instance,, where 1, and ab are the elementary polynomials of degree 0, 1 and 2 in two variables.

For this reason, people will often distinguish the meanings of the two terms in this context, using " image " for the abstract categorical concept and " range " for the elementary function-theoretic concept.

For example, Philippe learned physics and mathematics from Joseph Sauveur ; and from Étienne Loulié he learned musical notation, elementary musical theory, plus the basics of playing the viol and the recorder.

For example, from elementary calculus, we know that a necessary condition for a local minimum or a maximum of a differentiable function is a vanishing first derivative ( that is, the first derivative is becoming zero ).

For mostly reasons of economic viability, several prior establishments have been closed over the years, including a bar ( The Red Barn ), pizza parlor ( Chuck's Pizza ), hardware store ( Hillman's True Value ), movie rental, bowling alley ( due to arson ), and the local elementary school ( Richard B. Lynch ).

For elementary school, the area is served by the Los Nietos School District and the Whittier City School District.

For grade school education, Wilmette is served by Wilmette Public Schools District 39 which includes elementary schools ( grades K – 4 ) Central, Harper, McKenzie, and Romona, Highcrest Middle School ( grades 5 & 6 ), and Wilmette Junior High School ( grades 7 & 8 ).

For the 2011-2012 School Year, the Accountability Status for all 7 original elementary schools and the high school was " In Good Standing ", while the middle school was " In Need Of Improvement ( Year 1 ) Basic ".

For its dependents, the base has three schools operated by Minot Public Schools: two elementary ( Dakota & North Plains ) and a middle school ( Memorial ).

For the most part, this discussion will be confined to results obtained since the introduction of the reference standard.

For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.

For example, the introduction of FM stereo transmission allowed backward compatibility since new FM radio receivers could receive monaural signals generated by old transmitters.

For a conversational introduction to these ideas, see John Baez, ' A Tale of n-categories ' ( 1996 ).

For a better high-level introduction to Cyclone, the reasoning behind Cyclone and the source of these lists, see this paper.

For 1991, Holden updated the Statesman and Caprice with a range of improvements, including the introduction of four-wheel anti-lock brakes ( ABS ), although a rear-wheel system had been standard on the Statesman Caprice from March 1976.

For four of the trips a photography book was made by Pao, each with an introduction written by Palin.

: a.: For example, writing in his introduction to Sun Tzu's Art of War, B. H. Liddell Hart stated that " Civilization might have been spared much of the damage suffered in the world wars of this century if the influence of Clausewitz's monumental tome On War, which molded European military thought in the era preceding the First World War, had been blended with and balanced by a knowledge of Sun Tzu's exposition on The Art of War.

For example, peroxisome-less mutants can restore peroxisomes upon introduction of the wild-type gene.

For Gorbachev, demokratizatsiya originally meant the introduction of multi-candidate ( but not multiparty ) elections for local Communist Party ( CPSU ) positions and Soviets.

For many years these processes were used almost exclusively for transparencies ( in slide projectors and similar devices ), but color prints became popular with the introduction of the Chromogenic negative, which is the most-used system in the C-41 process.

For an introduction to the economic analysis of property law, see Shavell ( 2004 ), and Cooter and Ulen ( 2003 ).

In November 2001 Dahl and Nygaard were awarded the IEEE John von Neumann Medal by the Institute of Electrical and Electronic Engineers " For the introduction of the concepts underlying object-oriented programming through the design and implementation of SIMULA 67 ".

For example, he favors the introduction of education vouchers as a prelude to privatization of the school system, and the decentralization of the police as a similar first step toward privatized defense.

It involves a great departure from the methods of political action established in this country, where reforms, and especially financial reforms, have always been considerate and even tender ... I do not yet see the ground on which it can be justly held that any one description of property should be more heavily burdened than others, unless moral and social grounds can be shown first: but in this case the reasons drawn from those sources seem rather to verge in the opposite direction, for real property has more of presumptive connection with the discharge of duty that that which is ranked as personal ... the aspect of the measure is not satisfactory to a man of my traditions ( and these traditions lie near the roots of my being )... For the sudden introduction of such change there is I think no precedent in the history of this country.

Tork, once free from Don Kirshner's restrictions, in 1967, contributed some of the most memorable and catchy instrumental flourishes, such as the piano introduction to " Daydream Believer " and the banjo part on " You Told Me ", as well as exploring occasional songwriting with the likes of " For Pete's Sake " and " Lady's Baby ".

For New Zealand, the ecologically disastrous effects of the introduction of possums can be described as similar to that of the introduction of rabbits and cane toads in Australia.

For many years after their introduction, vacuum cleaners remained a luxury item, but after World War II, they became common among the middle classes.

For 20 years prior to the first introduction of the bill in 1857, there was a political movement calling for the creation of agriculture colleges.

For comparison: the PCI bus, which was available in systems at the time of the RiscPC's introduction, is over 20 times faster ( e. g. the transfer of 650 MB would take 2 minutes, compared to 5 seconds via PCI ).

For many years after the introduction of cannon the powder was introduced into the bore by means of a scoop-shaped ladle fixed to the end of a long stave.

For instance he divided the Pauline epistles ( including the Epistle to the Hebrews ) into a series of texts on their theological points and wrote an introduction to each section.

For most of the show's history, the usual order of the show is the introduction followed by a Johnson Wax plug by Harlow then his introduction to Section 1 of the script ( usually 11 minutes ).