This explains the failure of the classical equipartition theorem for metals that eluded classical physicists in the late 19th century.

His generalization of the classical Riemann-Roch theorem launched the study of algebraic and topological K-theory.

Compactness in this more general situation plays an extremely important role in mathematical analysis, because many classical and important theorems of 19th century analysis, such as the extreme value theorem, are easily generalized to this situation.

This was solved by Aschbacher's classical involution theorem.

The theory of field extensions ( including Galois theory ) involves the roots of polynomials with coefficients in a field ; among other results, this theory leads to impossibility proofs for the classical problems of angle trisection and squaring the circle with a compass and straightedge, as well as a proof of the Abel – Ruffini theorem on the algebraic insolubility of quintic equations.

The Bohr – van Leeuwen theorem shows that magnetism cannot occur in purely classical solids.

The classical results about interpolation of operators are the Riesz – Thorin theorem and the Marcinkiewicz theorem.

The theorem partly resolves the small-divisor problem that arises in the perturbation theory of classical mechanics.

Examples of early theorems from classical model theory include Gödel's completeness theorem, the upward and downward Löwenheim – Skolem theorems, Vaught's two-cardinal theorem, Scott's isomorphism theorem, the omitting types theorem, and the Ryll-Nardzewski theorem.

An important step in the evolution of classical model theory occurred with the birth of stability theory ( through Morley's theorem on uncountably categorical theories and Shelah's classification program ), which developed a calculus of independence and rank based on syntactical conditions satisfied by theories.

Double negative elimination is a theorem of classical logic, but not of weaker logics such as intuitionistic logic and minimal logic.

There is a classical analogue to the quantum no-cloning theorem, which we might state as follows: given only the result of one flip of a ( possibly biased ) coin, we cannot simulate a second, independent toss of the same coin.

The proof of this statement uses the linearity of classical probability, and has exactly the same structure as the proof of the quantum no-cloning theorem.

* The no-cloning theorem prevents us from using classical error correction techniques on quantum states.

* Similarly, cloning would violate the no teleportation theorem, which says classical teleportation ( not to be confused with entanglement-assisted teleportation ) is impossible.

While crystals, according to the classical crystallographic restriction theorem, can possess only two, three, four, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders, for instance five-fold.

The postulate is justified in part, for classical systems, by Liouville's theorem ( Hamiltonian ), which shows that if the distribution of system points through accessible phase space is uniform at some time, it remains so at later times.

This modern form of Stokes ' theorem is a vast generalization of a classical result first discovered by Lord Kelvin, who communicated it to George Stokes in July 1850.

This classical Kelvin – Stokes theorem relates the surface integral of the curl of a vector field F over a surface Σ in Euclidean three-space to the line integral of the vector field over its boundary ∂ Σ:

Joseph Dongell stated that " open theism actually moves beyond classical Arminianism towards process theology.

* In episode 17, season 5 of " Family Guy ", entitled " It Takes a Village Idiot, and I Married One ", the Griffin family is wearing powdered wigs in their living room and Stewie Griffin begins playing several classical compositions, including those by Joseph Haydn and George Frideric Handel, when Peter Griffin, as Salieri, says " Play Peter Griffin ", alluding to the 1984 film Amadeus, when the disguised Salieri character requests that Mozart imitate his compositional style.

However, some classical rabbinical sources argue that Joseph identified himself for other reasons.

The 2011 contemporary classical concept album Troika is composed of new orchestral songs set to Russian, English, and French-language poetry by five multilingual Russian-born writers: Joseph Brodsky, Mikhail Lermontov, Vladimir Nabokov, Aleksandr Pushkin and Fyodor Tyutchev.

English Elizabethan and Stuart composers had often evolved their music from folk themes, the classical suite was based upon stylised folk-dances and Joseph Haydn's use of folk melodies is noted.

Many symphonies are tonal works in four movements with the first in sonata form, which is often described by music theorists as the structure of a " classical " symphony, although many symphonies by the acknowledged classical masters of the form, Joseph Haydn, Wolfgang Amadeus Mozart, and Ludwig van Beethoven do not conform to this model.

* American — Craton, John: Pierrot and Pierrette a. k. a. Le Mime solitaire ( 2009 ; ballet ); Muller, Jennifer ( head of three-member Works Dance Company, New York ): Pierrot ( 1986 ; music and scenario by Thea Musgrave below under # Western classical | Western classical: Instrumental ); Russillo, Joseph ( works mainly in France ): Pierrot ( 1975 ; ballet ).

Aufstieg und Niedergang der römischen Welt, for example, began in 1972 as a Festschrift to commemorate the 75th birthday of Joseph Vogt, a German classical historian.

When he was 11 or 12, he was adopted by Joseph W. Clokey, a classical music composer and organist who taught music at Pomona College in Claremont, California.

Featured participants included Nuria Schoenberg ( daughter of Arnold Schoenberg and widow of Luigi Nono ), musicologist James Harrison, the opera conductor Roberto Abbado, violinist Ivry Gitlis, composers Salvatore Sciarrino, Lorenzo Ferrero, and Andrea Liberovici, poet Edoardo Sanguineti, popular singer-songwriters Teresa De Sio, Gianna Nannini, and Gino Paoli, rock and jazz artists Peppe Servalo and Peppe D ' Argenzio of the Piccola Orchestra Avion Travel, and administrators Anna Cammarano ( director of classical music at RAI Trade ), Gennaro di Benedetto ( superintendent of the Teatro Carlo Felice in Genoa ), and Joseph Hussek ( director of the artistic programme at the Salzburg Festival ).

Joseph Justus Scaliger (; August 5, 1540, Agen – January 21, 1609, Leiden ) was a French religious leader and scholar, known for expanding the notion of classical history from Greek and Ancient Roman history to include Persian, Babylonian, Jewish and Ancient Egyptian history.

" In 2012, Orchestra Nova San Diego premiered " Surf ", a symphonic homage to surf music, the ocean and surfing, by classical composer Joseph Waters.

It arose from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, but can be formulated without recourse to Lagrangian mechanics using symplectic spaces ( see Mathematical formalism, below ).

The concept of a Lagrangian was introduced in a reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, known as Lagrangian mechanics.

according to some classical rabbinical sources, Jacob suspected that Judah had killed Joseph, especially, according to the Midrash Tanhuma, when Judah was the one who had brought the blood stained coat to Jacob.

Even if Judah had been trying to save Joseph, the classical rabbinical sources still regard him negatively for it ; these sources argue that, as the leader of the brothers, Judah should have made more effort, and carried Joseph home to Jacob on his ( Judah's ) own shoulders.

The earlier theory, stated by Joseph Fullonton in his History of Raymond, published 1875, is that the name was chosen as " a new and classical one.

It was sharply criticised for its obscenity by contemporary authors Joseph Hall and John Davies of Hereford, though Nashe had tried to pre-empt criticism by placing it in the tradition of classical erotica: " Yet Ovid's wanton muse did not offend ".

Joseph Alessi is a world-renowned, primarily classical, trombonist ; he is the current Principal Trombone of the New York Philharmonic Orchestra and an active soloist, teacher / clinician and recording artist.

Later, he had arguments with the classical scholar Joseph Juste Scaliger.

In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics.

This yields a master equation which is a special case of a more general setting called the Lindblad equation that is the quantum equivalent of the classical Liouville equation.

In mathematics and its applications, a classical Sturm – Liouville equation, named after Jacques Charles François Sturm ( 1803 – 1855 ) and Joseph Liouville ( 1809 – 1882 ), is a real second-order linear differential equation of the form

In the classical theory of Hamiltonian dynamical systems, there is the notion of Liouville integrability.