Another set of methods is the aromatization of cyclohexanes and other aliphatic rings: reagents are catalysts used in hydrogenation such as platinum, palladium and nickel ( reverse hydrogenation ), quinones and the elements sulfur and selenium.

Therefore rings and Z-algebras are equivalent concepts, in the same way that abelian groups and Z-modules are equivalent.

In organic chemistry, compounds composed of carbon and hydrogen are divided into two classes: aromatic compounds, which contain benzene or similar rings of atoms, and aliphatic compounds (; G. aleiphar, fat, oil ), which do not contain those rings.

In aliphatic compounds, carbon atoms can be joined together in straight chains, branched chains, or non-aromatic rings ( in which case they are called alicyclic ).

Four rings of gold are to be attached to its four feet — two on each side — and through these rings staves of shittim-wood overlaid with gold for carrying the Ark are to be inserted ; and these are not to be removed.

For bridged alkenes, the Bredt's rule states that a double bond cannot be placed at the bridgehead of a bridged ring system, unless the rings are large enough.

His plot thoroughly unraveled, Pseudolus appears to be in deep trouble — but Erronius, completing his third circuit of the Roman hills, shows up fortuitously to discover that Miles Gloriosus and Philia are wearing matching rings which mark them as his long-lost children.

The ascending chain condition ( ACC ) and descending chain condition ( DCC ) are finiteness properties satisfied by some algebraic structures, most importantly, ideals in certain commutative rings.

Minsk has a digital metropolitan network ; waiting lists for telephones are long ; fixed line penetration is improving although rural areas continue to be undeserved ; intercity-Belarus has developed fibre-optic backbone system presently serving at least 13 major cities ( 1998 ); Belarus's fibre optics form synchronous digital hierarchy rings through other countries ' systems ; an inadequate analogue system remains operational.

Binary operations are the keystone of algebraic structures studied in abstract algebra: they form part of groups, monoids, semigroups, rings, and more.

This ring has the property that a · a = a for all a in A ; rings with this property are called Boolean rings.

The categories of Boolean rings and Boolean algebras are equivalent.

There are four gearing options: two-speed hub gear integrated with chain ring, up to 3 chain rings, up to 11 sprockets, hub gear built in to rear wheel ( 3-speed to 14-speed ).

The most common options are either a rear hub or multiple chain rings combined with multiple sprockets ( other combinations of options are possible but less common ).

** β-Lactams containing thiazolidine rings are named penams.

** β-Lactams containing pyrrolidine rings are named carbapenams.

Thomson theorized that multiple electrons revolved in orbit-like rings within a positively charged jelly-like substance, and between the electron's discovery and 1909, this " plum pudding model " was the most widely accepted explanation of atomic structure.

Galileo used smaismrmilmepoetaleumibunenugttauiras for Altissimum planetam tergeminum observavi (" I have observed the most distant planet to have a triple form ") for discovering the rings of Saturn in 1610.

Several patterns of linking the rings together have been known since ancient times, with the most common being the 4-to-1 pattern ( where each ring is linked with four others ).

Among the most plunderable portables from the Etruscan tombs of Etruria are the finely engraved gemstones set in patterned gold to form circular or ovoid pieces intended to go on finger rings.

Turret presses, most commonly of the " C " type, are similar to single stage presses, but permit mounting all of the dies for one cartridge ( or sometimes two cartridges ) simultaneously, with each die being installed and correctly locked in position with lock rings onto the press at the same time.

There are several patterns of clutch used to support the top cymbal, but the most common uses a knurled collar that is part threaded below the cymbal, and a pair of knurled rings above it.

The distinction is used most often for sets that support both binary operations, such as rings.

Lifting is most important when, the Jacobson radical of R. Yet another characterization of semiperfect rings is that they are semilocal rings whose idempotents lift modulo J ( R ).

If the hardware provides multiple rings or CPU modes, the microkernel is the only software executing at the most privileged level ( generally referred to as supervisor or kernel mode ).

The most stable rings contain five or six carbon atoms, but large rings ( macrocycles ) and smaller rings are common.

The flag most frequently associated with the pope is the yellow and white flag of Vatican City, with the arms of the Holy See ( blazoned: " Gules, two keys in saltire or and argent, interlacing in the rings or, beneath a tiara argent, crowned or ") on the right-hand side ( the " fly ") in the white half of the flag ( the left-hand side — the " hoist "— is yellow ).

The most notable planetary rings known in the Solar System are those around Saturn, but the other three gas giants of the Solar System ( Jupiter, Uranus and Neptune ) also possess ring systems of their own.

A characteristic of most trunk pistons, particularly for diesel engines, is that they have a groove for an oil ring below the gudgeon pin, not just the rings between the gudgeon pin and crown.

While he has two championship rings with the 1999 – 2000 Yankees, Clemens has also been on the losing end of four World Series ( 1986 Red Sox, 2001 and 2003 Yankees, and 2005 Astros ), which is tied with Tom Glavine and John Smoltz ( who were both on the Braves when they lost the ' 91, ' 92, ' 96 and ' 99 World Series ) for the most among active players.

In addition, tracks did not need to be perfect rings, but could be sectioned so that sectors could be staggered across overlapping offset tracks, the most extreme version being known as spiral tracking.

In its most basic form the rings are tatted with a length of plain thread between them, as in single shuttle tatting.

The most common symbol of Unitarian Universalism is the flaming chalice, often framed by two overlapping rings that many interpret as representing Unitarianism and Universalism ( the symbol has no official interpretation ).

The most important feature of Zeppelin's design was a rigid light-alloy skeleton, made of rings and longitudinal girders.

These tetrahedra sometimes occur as isolated SiO < sub > 4 </ sub >< sup > 4 -</ sup > centres, but most commonly, the tetrahedra are joined together in various ways, such as pairs ( Si < sub > 2 </ sub > O < sub > 7 </ sub >< sup > 6 -</ sup >) and rings ( Si < sub > 6 </ sub > O < sub > 18 </ sub >< sup > 12 -</ sup >).

A piece of cloth, a wallet, gel, or fitted rings made of mylar are common objects.

Gifts were often exchanged, especially rings: a gold coin broken in half between the couple was also common.

The body wore ecclesiatical vestments common for Boniface's lifetime: long stockings covered legs and thighs, and it was garbed also with the maniple, soutain, and pontifical habit made of black silk, as well as stole, chasuble, rings, and bejeweled gloves.

Ashley notes that it was once common for sailors ' wedding rings, where gold wire was wrought to incorporate the " true lovers " knot such that resultant ring would comprise two tori: each flexible to move about the other ; yet nevertheless inseparable.

The most common method is to measure lamellar growth rings in bones and teeth — each ring corresponds to a change in growth rate which typically occurs once a year between dry and wet seasons.

The most common props are balls or beanbags, rings, clubs, oranges, apples, and special bounce balls.

To achieve these goals, Boehm adapted a system of axle-mounted keys with a series of " open rings " ( called brille, German for " eyeglasses ", as they resembled the type of eyeglass frames common during the 19th century ) that were fitted around other tone holes, such that the closure of one tone hole by a finger would also close a key placed over a second hole.

Engagement rings didn't become standard in the West until the end of the 19th century, and diamond rings didn't become common until the 1930s.

Wedding rings amongst men were more common during World War II, as the men overseas wore their rings in reminder of their wives and families back home.

The three phyla share four characters in common — chitinous cuticle, rings of scalids on the introvert, flosculi, and two rings of introvert retracts.

It may also have been associated with the Holy Trinity, as in the three hares motif, representing the " One in Three and Three in One " of which the triangle or three interlocking shapes such as rings are common symbols.

Preset aperture controls have taken several forms ; the most common has been the use of essentially two lens aperture rings, with one ring setting the aperture and the other serving as a limit stop when switching to working aperture.

These molecules, composed primarily of fused rings of carbon ( either neutral or in an ionized state ), are said to be the most common class of carbon compound in the galaxy.