Solution

In chemistry, a solution is a homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. The solution more or less takes on the characteristics of the solvent including its phase, and the solvent is commonly the major fraction of the mixture. The concentration of a solute in a solution is a measure of how much of that solute is dissolved in the solvent, with regard to how much solvent is present.

Characteristics

Types

Homogeneous means that the components of the mixture form a single phase. The properties of the mixture (such as concentration, temperature, and density) can be uniformly distributed through the volume but only in absence of diffusion phenomena or after their completion. Usually, the substance present in the greatest amount is considered the solvent. Solvents can be gases, liquids or solids. One or more components present in the solution other than the solvent are called solutes. The solution has the same physical state as the solvent.

Solution (band)

Solution were a Dutch progressive rock band that existed from 1970 to 1983, during which time they released six studio albums and one live album. They incorporated jazz, rock, pop and soul influences, becoming more commercial on their fifth and sixth albums.

History

Their first eponymous LP comprised mainly instrumental pieces, complex yet repetitive in structure, with bassist Peter van der Sande singing on one track. He was succeeded by Guus Willemse around the time of its release, and immediately the band began recording more vocal songs; three of the tracks on second album Divergence featured lyrics.

The third album Cordon Bleu (1975) was released on Elton John's own label named The Rocket Record Company, as was its follow-up Fully Interlocking (1977). Both albums were produced by John's producer Gus Dudgeon, and featured a crisper sound and more concise songwriting.

Despite some criticism for a more commercial direction, the next two albums, ...It's Only Just Begun... (1980) and Runaway (1982) continued this trend. The two title tracks from these albums became hit singles in Europe.

Equation solving

In mathematics, to solve an equation is to find what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an equation (two expressions related by equality). When searching a solution, one or more free variables are designated as unknowns. A solution is an assignment of expressions to the unknown variables that makes the equality in the equation true. In other words, a solution is an expression or a collection of expressions (one for each unknown) such that, when substituted for the unknowns, the equation becomes an identity. A problem of solving an equation may be numeric or symbolic. Solving an equation numerically means that only numbers represented literately (not as a combination of variables), are admitted as solutions. Solving an equation symbolically means that expressions that may contain known variables or possibly also variables not in the original equation are admitted as solutions.

Logic

Logic (from the Ancient Greek: λογική, logike) is the branch of philosophy concerned with the use and study of valid reasoning. The study of logic also features prominently in mathematics and computer science.

Logic was studied in several ancient civilizations, including Greece, India, and China. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Hindus, Buddhists and Jains.

Logic is often divided into three parts: inductive reasoning, abductive reasoning, and deductive reasoning.

The study of logic

The concept of logical form is central to logic. The validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic.

Ω-logic

In set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin (1999) as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure . Just as the axiom of projective determinacy yields a canonical theory of , he sought to find axioms that would give a canonical theory for the larger structure. The theory he developed involves a controversial argument that the continuum hypothesis is false.

Woodin's Ω-conjecture asserts that if there is a proper class of Woodin cardinals (for technical reasons, most results in the theory are most easily stated under this assumption), then Ω-logic satisfies an analogue of the completeness theorem. From this conjecture, it can be shown that, if there is any single axiom which is comprehensive over (in Ω-logic), it must imply that the continuum is not . Woodin also isolated a specific axiom, a variation of Martin's maximum, which states that any Ω-consistent (over ) sentence is true; this axiom implies that the continuum is .

Logic (song)

"Logic" is a song by Australian band Operator Please. It is the first single released from the band's second album, Gloves. The song's official release was on 16 February 2010.

Release

The song first appeared on the band's official MySpace page on 15 January 2010. Around the same time a download offer was added to the band's official website where you could sign up to a mailing list which would send you a free download link on 8 February. The song went on to be officially released on the iTunes Store eight days later, and was released on 7" vinyl on 12 March. It is notable that new member Chris Holland contributes backing vocals to "Logic".

Music video

In early February, the band filmed the video for "Logic". The video premiered on 13 February on Video Hits. It is predominantly a performance-based video and features effects reminiscent of the artwork for the album.

Track listings