Volume fraction

In chemistry, the volume fraction φ_i is defined as the volume of a constituent V_i divided by the volume of all constituents of the mixture V prior to mixing:

Being dimensionless, its unit is 1; it is expressed as a number, e.g., 0.18. It is the same concept as volume percent (vol%) except that the latter is expressed with a denominator of 100, e.g., 18%.

The volume fraction coincides with the volume concentration in ideal solutions where the volumes of the constituents are additive (the volume of the solution is equal to the sum of the volumes of its ingredients).

The sum of all volume fractions of a mixture is equal to 1:

The volume fraction (percentage by volume, vol%) is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and mole fraction (percentage by moles, mol%) are others.

Volume percent

Volume percent is a common expression of a solution's concentration. It is the volume fraction expressed with a denominator of 100, and thus is defined as:

Vol. 4 (Black Sabbath album)

Vol. 4 is the fourth studio album by English heavy metal band Black Sabbath, released in September 1972. It was the first album by Black Sabbath not produced by Rodger Bain; guitarist Tony Iommi assumed production duties. Patrick Meehan, the band's then-manager, was listed as co-producer, though his actual involvement in the album's production was minimal at best.

Recording

In June 1972, Black Sabbath reconvened in Los Angeles to begin work on their fourth album at the Record Plant Studios. The recording process was plagued with problems, many due to substance abuse issues. In the studio, the band regularly had large speaker boxes full of cocaine delivered. While struggling to record the song "Cornucopia" after "sitting in the middle of the room, just doing drugs",Bill Ward feared that he was about to be fired from the band. "I hated the song, there were some patterns that were just horrible", Ward said. "I nailed it in the end, but the reaction I got was the cold shoulder from everybody. It was like 'Well, just go home, you're not being of any use right now.' I felt like I'd blown it, I was about to get fired". According to the book How Black Was Our Sabbath, Bill Ward "was always a drinker, but rarely appeared drunk. Retrospectively, that might have been a danger sign. Now, his self-control was clearly slipping." Iommi claims in his autobiography that Ward almost died after a prank-gone-wrong during recording of the album. The Bel Air mansion the band was renting belonged to John DuPont of the DuPont chemical company and the band found several spray cans of gold DuPont paint in a room of the house; finding Ward naked and unconscious after drinking heavily, they proceeded to cover the drummer in gold paint from head to toe.

Volume 4

Volume Four, Volume 4, or Volume IV may refer to:

Music

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Quasigroup

In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that they need not be associative.

A quasigroup with an identity element is called a loop.

Definitions

There are at least two equivalent formal definitions of quasigroup. One defines a quasigroup as a set with one binary operation, and the other, from universal algebra, defines a quasigroup as having three primitive operations. We begin with the first definition.

A quasigroup (Q, ∗) is a set, Q, with a binary operation, ∗, (that is, a magma), obeying the Latin square property. This states that, for each a and b in Q, there exist unique elements x and y in Q such that both

hold. (In other words: Each element of the set occurs exactly once in each row and exactly once in each column of the quasigroup's multiplication table, or Cayley table. This property ensures that the Cayley table of a finite quasigroup is a Latin square.)

Loop (knot)

In reference to knots, loop may refer to:

References

Loop (inlet)

The Loop or Darss Canal (Darßer Kanal) was an inlet of the sea between the lagoon known as the Saaler Bodden and the Baltic Sea near Ahrenshoop on the German coast. It formed the northern boundary of the region of Fischland. Originally the Loop was the northern estuarine branch of the River Recknitz.

The old inlet ran between the present villages of Ahrenshoop and Althagen. The Loop was roughly two metres deep and had posts for mooring boats and barges. Its navigability was frequently curtailed by storms and silting up. Today only a small ditch remains on the former Mecklenburg-Pomeranian border, which runs alongside a main road, the so-called Grenzweg ("border way").

The cartographer and court astronomer at the Mecklenburg court, Tilemann Stella, described the Loop thus: "Between the village of Oldenhagen [Althagen] and the Arnshope [Ahrenshoop], the waters of the Ribnitz river and lake break through into the salty sea. Beyond the beach is a large pile of rock and bricks at the place by the beach; that was the customs post, located 3 or 4 ruthen [50 metres] into the salty sea. Beyond that, forty or fifty posts stood in the salt sea, at the end of which was a large pile of rocks on which the fort stood."