* Birkhoff's HSP theorem, concerning the closure operations of homomorphism, subalgebra and product

Garrett Birkhoff proved equivalent the two definitions of variety given above, a result of fundamental importance to universal algebra and known as Birkhoff's theorem or as the HSP theorem.

* Birkhoff's Theorem on ScienceWorld

Doob's approach to probability was evident in his first probability paper, in which he proved theorems related to the law of large numbers, using a probabilistic interpretation of Birkhoff's ergodic theorem.

Birkhoff's theorem has the consequence that any pulsating star which remains spherically symmetric cannot generate gravitational waves ( as the region exterior to the star must remain static ).

Jørg Tofte Jebsen ( 1888-1922 ) was a Norwegian physicist who discovered and published an important theorem concerning general relativity which is now known as Birkhoff's theorem.

Birkhoff's representation theorem for distributive lattices states that every finite distributive lattice is isomorphic to the lattice of lower sets of the poset of its join-prime ( equivalently: join-irreducible ) elements.

In fact, the static assumption is stronger than required, as Birkhoff's theorem states that any spherically symmetric vacuum solution of Einstein's field equations is stationary ; then one obtains the Schwarzschild solution.

In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat.

In the period between 1935 and 1950, most papers were written along the lines suggested by Birkhoff's papers, dealing with free algebras, congruence and subalgebra lattices, and homomorphism theorems.

According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.

According to Birkhoff's theorem, the Schwarzschild solution is the most general spherically symmetric, vacuum solution of the Einstein field equations.

Another case of Stone duality is Birkhoff's representation theorem stating a duality between finite partial orders and finite distributive lattices.

Applying Birkhoff's theorem, this is sufficient to tell us that the groups form a variety, and so it should be defined by a collection of identities.

For pseudovarieties, there is no general finitary counterpart to Birkhoff's theorem but in many cases the introduction of a more complex notion of equations allows similar results to be derived ..

The intuitive idea of Birkhoff's theorem is that a spherically symmetric gravitational field should be produced by some massive object at the origin ; if there were another concentration of mass-energy somewhere else, this would disturb the spherical symmetry, so we can expect the solution to represent an isolated object.

Then Birkhoff's theorem says that the exterior geometry must be Schwarzschild ; the only effect of the pulsation is to change the location of the stellar surface.

Another interesting consequence of Birkhoff's theorem is that for a spherically symmetric thin shell, the interior solution must be given by the Minkowski metric ; in other words, the gravitational field must vanish inside a spherically symmetric shell.

It is known ( see Birkhoff's theorem ) that any spherically symmetric solution of the vacuum field equations is necessarily isometric to a subset of the maximally extended Schwarzschild solution.

Conversely, every distributive lattice is isomorphic to a ring of sets ; in the case of finite distributive lattices, this is Birkhoff's representation theorem and the sets may be taken as the lower sets of a partially ordered set.

George D. Birkhoff's 1927 book already takes a modern approach to dynamical systems.

* Birkhoff's axioms: Birkhoff proposed four postulates for Euclidean geometry that can be confirmed experimentally with scale and protractor.

From 1936 to 1939, after following up on Birkhoff's suggestion, Ulam spent summers in Poland and academic years at Harvard University in Cambridge, MA.

In his 1951 review of Birkhoff's book, the mathematician James J. Stoker sharply criticizes the first chapter of the book:

In the second and revised edition of Birkhoff's Hydrodynamics in 1960, the above two statements no longer appear.

In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry sometimes referred to as Birkhoff's axioms.

Birkhoff's theorem can be generalized: any spherically symmetric solution of the Einstein / Maxwell field equations must be stationary and asymptotically flat, so the exterior geometry of a spherically symmetric charged star must be given by the Reissner-Nordström electrovacuum.

* Johansen, Nils Voje ; and Ravndal, Finn On the discovery of Birkhoff's theorem version of September 6, 2005.

In the past, HSP also has been classified as type I or type II on the basis of the patient's age at the onset of symptoms, which influences the amount of spasticity versus weakness.

Furthermore, there may be significant clinical variability within a given family in which all subjects have the same HSP gene mutation ; between families with the same genetic type of HSP ; and between families with different genetic types of HSP.

The HSP, along with other modern Croatian parties ( such as Croatian Pure Party of Rights ), claims legacy of the Party of Rights which was founded in 1861 and existed until 1929.

The ruling HDZ cooperated with the HSP until the fall of Vukovar, after which the leaders of the HSP and HOS were imprisoned for " terrorist activities " and " obstruction of democratically elected government ".

There are other diseases associated with glomerular IgA deposits, the most common being Henoch-Schönlein purpura ( HSP ), which is considered by many to be a systemic form of IgA nephropathy.

A heat shock protein ( HSP ) is a one of group of proteins which increase their expression when the cells which contain them are exposed to high temperatures.

For instance, Jeffrey E. Young, founder of the increasingly applied Schema Therapy, although never having been critical of HSP writers or writings, links high sensitivity, or as he calls it, the " highly empathic temperament " with the Self Sacrifice Schema ( Young, 2003, pp. 246 – 251 ), which in turn is almost always related to the Emotional Deprivation Schema.

In 1991, he joined the Croatian Party of Right ( HSP ), which was renewed year earlier.

In the 1995 election, HSP won 4. 8 % of vote, but after a recount, 5. 01 % was claimed to be official result, which meant that HSP remained represented in Parliament.

Host Signal Processing ( HSP ) is a term used in computing to describe hardware such as a modem or printer which is emulated ( to various degrees ) in software.

Heat shock proteins ( HSP ) are a class of functionally related proteins involved in the folding and unfolding of other proteins.

It is simple to see that the class of algebras satisfying some set of equations will be closed under the HSP operations.

Proving the converse — classes of algebras closed under the HSP operations must be equational — is much harder.