These theorems are also equivalent to the unitary condition below.

These experiments are used to prove, verify, and reinforce laws and theorems such as Ohm's law, Kirchhoff's laws, etc.

These assumptions are the elementary theorems of the particular theory, and can be thought of as the axioms of that field.

These two theorems are very different from each other ; the first one has a very simple proof and is very counterintuitive, while the proof of the second one is very technical but the result is not at all surprising.

" These theorems along with their alternative postulates, such as Playfair's axiom, played an important role in the later development of non-Euclidean geometry.

These include theorems about compactness of certain spaces such as the Banach – Alaoglu theorem on the compactness of the unit ball of the dual space of a normed vector space, and the Arzelà – Ascoli theorem characterizing the sequences of functions in which every subsequence has a uniformly convergent subsequence.

These theorems, strictly speaking, prove that there is at least one non-spacelike geodesic that is only finitely extendible into the past but there are cases in which the conditions of these theorems obtain in such a way that all past-directed spacetime paths terminate at a singularity.

These expressions are called axioms, in the case of those previously supposed to be true, or theorems, in the case of those derived.

These theorems apply to inviscid flows and flows where the influence of viscous forces is small and can be ignored.

These theorems have many important applications.

These concepts are dealt with by Norton's and Thévenin's theorems.

These equivalences immediately yield the Bott periodicity theorems.

These properties are essentially weaker versions of strong and supercompact cardinals, consistent with V = L. Many theorems related to these cardinals have generalizations to their unfoldable or strongly unfoldable counterparts.

These results are not equivalent theorems ; the Knaster – Tarski theorem is a much stronger result than what is used in denotational semantics.

These theorems provide a way to calculate limit loads without having to solve the boundary value problem in continuum mechanics.

These thinkers seem to have maintained a modified observational standpoint for the introduction of natural numbers, for the principle of complete induction < nowiki ></ nowiki > For these, even for such theorems as were deduced by means of classical logic, they postulated an existence and exactness independent of language and logic and regarded its non-contradictority as certain, even without logical proof.

These theorems illuminated the way that first-order logic behaves and established its finitary nature.

These convergence theorems can often be used to prove existence of harmonic functions having particular properties.

These appear as theorems VI and XI, respectively, in the paper.

These theorems can be proven using the orthogonality property.

These cases could be enunciated separately, were in a manner intermediate between theorems and problems, and were called " porisms.

These are colloquially known as the going-up and going-down theorems.

These theorems may be considered as simplifications of the Boltzmann result.

These higher stakes contests also opened up the door to reality television contests such as Survivor and Big Brother, in which contestants win large sums of money for outlasting their peers in a given environment.

These often opened with the show's main title logo within the teaser scene ; from season four onward, the show began using an anthropomorphic version of the logo in the opening scenes, using various animations.

These thinkers opened up the way for the deconstruction of the subject as a core-concept of metaphysics.

These policies abolished and prohibited monopolies and opened once closed and privileged unions, associations, and guilds, which he saw as impediments to commerce.

These routes were never opened.

These ports, when opened by detonation of shaped charges, reduced the chamber pressure so abruptly that the interior flame was blown out.

On that episode, Simon opened the show performing " Still Crazy After All These Years " in a turkey outfit, since Thanksgiving was the following week.

The pilot episode ( where it was originally called I'm Sorry, They're At It Again ) opened with Graeme Garden and Jo Kendall singing the words of " Three Blind Mice " to the tune of " Ol ' Man River " followed by Bill Oddie and Tim Brooke-Taylor performing the lyrics of " Sing a Song of Sixpence " to the melody of " These Foolish Things ".

These only release steam when the pan is opened, or as a safety precaution if the heat source is not reduced enough when the pan reaches the required cooking pressure.

These are further sanctified by the recent additions to the architectural excellence of buildings, a fusion of the traditional and modern architecture which are mostly post 1962, after Thimphu became the Capital of Bhutan and opened up for tourism under various Five Year Developmental Plans.

These new designs opened an economic door for contractors, engineers, architects, and investors, providing vast amounts of real estate space on minimal plots of land.

These actions violated Octavius ' right of sacrosanctity and worried Tiberius ' supporters, and so instead of moving to depose him, Tiberius commenced to use his veto on daily ceremonial rites in which Tribunes were asked if they would allow for key public buildings, for example the markets and the temples, to be opened.

These two new facilities opened in 2009.

These features were retained in the design despite the fact that by the time the station opened the 1921 Railway Act had been passed which spelt the end of the L & SWR as an independent concern.

These programmes are opened to applicants having completed their undergraduate studies at other institutions.

These lands were opened to non-Indian settlement on April 22, 1889.

These fifteen galleries — which opened in November 2001 — contain around 4, 000 items.

These conquests opened up the valley of the Cinca, which he proceeded to conquer as far as Almenar, taken in 1093.

* In 1976, Frederick Brown Jr. Amphitheater was built as a Bicentennial project and opened to the public with the production " Unto These Hills ," which told the story of Chief William McIntosh.

These casinos were closed or moved as larger resorts opened closer to Memphis.

These supposed connections opened a floodgate of local residents seeking historical landmark status for their homes in the twentieth and twenty-first centuries, many of which were denied by the Pennsylvania Historical Commission due to lack of evidence that the events actually took place.

These POs, MOs and TOs have to be effectively managed to synchronize with the changes that often occur within the “ execution horizon .” The execution horizon is the time from which a PO, MO or TO is opened until the time it is closed in the system of record.

These were converted into a wide range of wetland features and habitats before the centre opened in May 2000.

These are almost exclusively found in operating theatres, where the chest is likely to be open, or can be opened quickly by a surgeon.

These treaties opened 11 more ports to Western trade.