* Spin group, in mathematics, a particular double cover of the special orthogonal group SO ( n )

The most typical type of spinor, the Dirac spinor, is an element of the fundamental representation of the complexified Clifford algebra, into which the spin group Spin ( p, q ) may be embedded.

In this construction the representation of the Clifford algebra Cℓ ( V, g ), the Lie algebra so ( V, g ), and the Spin group Spin ( V, g ), all depend on the choice of the orthonormal basis and the choice of the gamma matrices.

Thus it is sometimes advantageous, or even necessary, to work with a covering group of SO ( n ), the spin group, Spin ( n ).

For n > 2, Spin ( n ) is simply connected, and thus the universal covering group for SO ( n ).

By far the most famous example of a spin group is Spin ( 3 ), which is nothing but SU ( 2 ), or the group of unit quaternions.

The dicyclic group is a binary polyhedral group — it is one of the classes of subgroups of the Pin group Pin < sub >−</ sub >( 2 ), which is a subgroup of the Spin group Spin ( 3 ) — and in this context is known as the binary dihedral group.

The universal cover of SO ( 3 ) is a Lie group called Spin ( 3 ).

Topologically, SO ( 3 ) is the real projective space RP < sup > 3 </ sup >, with fundamental group Z / 2, and only ( non-trivial ) covering space the hypersphere S < sup > 3 </ sup >, which is the group Spin ( 3 ), and represented by the unit quaternions.

At the University of Washington Medical School, the electronics group has developed the `` Respiratory Gas Analyzer '' shown in Fig. 3.

The actinide series derives its name from the group 3 element actinium.

In 1990, she also joined the group Hi-Tek 3 who were heard on the Teenage Mutant Ninja Turtles movie soundtrack.

The percentage of fluent speakers turns out to be even higher if those under 16 are also taken into account, given that the proportion of bilinguals is particularly high in this age group ( 76. 7 % of those aged between 10 and 14 and 72. 4 % of those aged 5 – 9 ): 37. 5 % of the population aged 6 and above in the whole Basque Autonomous Community, 25. 0 % in Álava, 31. 3 % in Biscay and 53. 3 % in Gipuzkoa.

At ambient conditions, berkelium assumes its most stable α form which has a hexagonal symmetry, space group P6 < sub > 3 </ sub >/ mmc, lattice parameters of 341 pm and 1107 pm.

One is an amino group, — NH < sub > 2 </ sub >, and one is a carboxylic acid group, — COOH ( although these exist as — NH < sub > 3 </ sub >< sup >+</ sup > and — COO < sup >−</ sup > under physiologic conditions ).

His goal in the 3 – 1 group win over Argentina was his 25th for England in just 38 appearances, but his individual success could not be replicated by that of the team, which was eliminated in the quarter final by Brazil, who went on to win the tournament.

: Subgroup 2f was added because these are serine-based carbapenemases, in contrast to the zinc-based carbapenemases included in group 3

Thus, the molecular formula of ethanol may be written in a paper in conformational, three-dimensional, full two-dimensional ( indicating every bond with no three-dimensional directions ), compressed two-dimensional ( CH < sub > 3 </ sub >– CH < sub > 2 </ sub >– OH ), separating the functional group from another part of the molecule ( C < sub > 2 </ sub > H < sub > 5 </ sub > OH ), or by its atomic constituents ( C < sub > 2 </ sub > H < sub > 6 </ sub > O ), according to what is discussed.

Berg communicated with his followers through more than 3, 000 published letters written over 24 years, referred to as " Mo Letters " by members of the group.

Salt-like carbides are composed of highly electropositive elements such as the alkali metals, alkaline earths, and group 3 metals including scandium, yttrium and lanthanum.

The asymmetric ends of DNA strands are called the 5 ′ ( five prime ) and 3 ′ ( three prime ) ends, with the 5 ' end having a terminal phosphate group and the 3 ' end a terminal hydroxyl group.

Then it took 3 to 6 millions of years for the crown group to differentiate in Mid Cretaceous.

* Comedy Band The Barron Knights ' 1978 UK # 3 hit single A Taste Of Aggro, a medley of parodies, included a version of The Smurf Song featuring, in place of the Smurfs, a group of bank robbers from Catford who have escaped from Dartmoor Prison.

For this group, + 4 and + 3 states are also known for the heavier members and dubnium may also form these reducing oxidation states.

The results have indicated the formation of typical group 5 halides and oxyhalides, namely DbCl < sub > 5 </ sub >, DbBr < sub > 5 </ sub >, DbOCl < sub > 3 </ sub > and DbOBr < sub > 3 </ sub >.

All known DNA replication systems require a free 3 ' OH group before synthesis can be initiated ( Important note: DNA is read in 3 ' to 5 ' direction whereas a new strand is synthesised in the 5 ' to 3 ' direction-this is entirely logical but is often confused ).

The content is not the same, however: rather than individual security, it is the security and continuing existence of an `` ideological group '' -- those in the `` free world '' -- that is basic.

Historically, however, the concept is one that has been of marked benefit to the people of the Western civilizational group.

The music director of the Pittsburgh Symphony Orchestra, William Steinberg, has molded his group into a prominent musical organization, which is his life.

With the group of boys it is different.

Nothing is more revealing of the way of life and literary aspirations of this group than their attitude toward sex.

This group is secularist and their program tends to be technological.

But the problem is one which gives us the measure of a man, rather than a group of men, whether a group of doctors, a group of party members assembled at a dinner to give their opinion, or the masses of the voters.

The group conducting the review is not holding formal hearings.

After allowing for group exposures, it is apparent that other factors must be considered if we are to comprehend fanaticism.

At Sounion there is a group of beautiful columns, the ruins of a temple to Poseidon, of particular interest at that time, as active reconstruction was in progress.

He is uncompromising in assigning guilt to the man who finds it necessary to inflict or permit injury to one individual or group for the sake of a larger good.

In the main stream of historical thinking is a group of scholars, H.M. Chadwick, R.H. Hodgkin, Sir Frank Stenton et al. who are in varying degrees sceptical of the native traditions of the conquest but who defend the catastrophic type of invasion suggested by them.

Although Patchen has given previous evidence of an interest in jazz, the musical group that he works with, the Chamber Jazz Sextet, is often ignored by jazz critics.

Patchen's musicians are outsiders in established jazz circles, and Patchen himself has remained outside the San Francisco poetry group, maintaining a self-imposed isolation, even though his conversion to poetry-and-jazz is not as extreme or as sudden as it may first appear.

Gov. Dalton's New Commerce and Industry Commission is moving to create a nine-state regional group in a collective effort to attract new industry.

Fortunately, there is a nursery school which he has been able to attend, with a group of normal children.

Perhaps Khrushchev is in a more difficult position than any since 1957, when the `` anti-party group '' nearly liquidated him.

When the fate of the individual is visited on the group, then ( the warm sweet butter dripped from her raised trembling fork and she pushed her head forward belligerently ), ah, then the true bitterness of existence could be tasted.

Mr. Claude is a specialist in torso development and he has long favored the now-famous Weider Push-Pull Super-Set technique in which one exercise of the Super-Set is a pressing or `` pushing '' movement which accents one sector of a muscle group in a specific way, followed by a `` pulling '' exercise which works the opposing sector of the same muscle group.