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 theorems opened the way for much more refined studies: of embedding, immersion and also of smoothing: that is, the possibility of having various smooth structures on a given topological manifold.

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 illiterate boors conscripted from villages all across the Czarina's empire had, Suvorov may have told Lewis, just two things a commander could count on: physical fitness and personal courage.

These deductions may not be claimed if you elect to use the Standard Deduction or Tax Table.

These publications may be secured as follows: The Annual Catalog from the Director of Admissions and other issues from the Publications Office.

These minimum costs may come to $1 per month, more or less, for residential and small commercial customers, although they are substantially higher for large industrial users, who require more costly connections and metering devices.

These may be consulted in the office of the Architect of the Capitol, or the Library of Congress.

These tubes may differ both in the choice of the electron optical system and in the design of the coupling members.

These cases, for all their rarity, are so dramatic that friends and relations repeat the story until the general population may get an entirely false notion of how often the hymen is a serious problem to newly-weds.

These regional differences of sensitivity to pain may be of crucial significance during the earliest intercourse.

These tractors are not entirely satisfactory for plowing, particularly on heavier soils, so you may still want to hire someone to do the plowing.

These things may be happening many miles away from us but really they are right next door.

These penetrate the jelly envelope after the eggs are laid and may increase the supply of oxygen to the embryo through photosynthesis.

These regions are presented to the attacking animal and their secretions may be foul-tasting or cause various physical or neurological symptoms.

These provinces may take the form of national churches ( such as in Canada, Uganda, or Japan ) or a collection of nations ( such as the West Indies, Central Africa, or Southeast Asia ).

These single-cell fibers of the sciatic nerve may extend a meter or even longer.

These antibiotics may also be prescribed to patients with a documented allergy to penicillin.

These and most other cities and large towns are now connected with asphalt-paved roads, while smaller towns are often connected by dirt roads, which may require a four-wheel-drive vehicle.

These findings may corroborate the evidence for social behaviour in Albertosaurus, although some or all of the above localities may represent temporary or unnatural aggregations.

These principles may flourish and triumph in the schools ; where it is, indeed, difficult, if not impossible, to refute them.

These may have been multiples of the customary acre, rather than the statute acre.

These unconscious reactions may even be partly constitutive of what makes our judgment a judgment that the landscape is sublime.

These weapons may be mounted on a pintle, affixed directly to the vehicle or placed in a turret or cupola.

Bibas argues, " These procedures may be constitutional and efficient, but they undermine key values served by admissions of guilt in open court.

These narratives may be true and may be false ; the veracity of the stories is not a determining factor.