The equicontinuity of a set of functions is a generalization of the concept of uniform continuity.

The main condition is the equicontinuity of the family of functions.

* For equicontinuity, δ may depend on ε, and x < sub > 0 </ sub >.

* For uniform equicontinuity, δ may solely depend on ε.

A typical Fredholm integral equation gives rise to a compact operator K on function spaces ; the compactness property is shown by equicontinuity.

Compactness may be shown by invoking equicontinuity.

The notion of equicontinuity was introduced at around the same time by and.

The guru therefore appears with the yidam and dakini in the Three Roots refuge formulation of the three factors essential for tantric attainments.

" According to Mindy MacLeod and Bernard Mees, the inscription " seems to begin as a benevolent formulation before abruptly switching to the infliction of distress and misery, presumably upon the recipient of the charm rather than the baleful valkyrie ", and they posit the final line appears " to constitute a rather spiteful kind of charm aimed at securing the love of a woman ".

But no one today appears to have a clear idea of what a finitistic proof would be like that is not capable of formulation within arithmetic.

However, according to the process offered by ISPO, what appears to be new is that citizens who " adopt " the Simultaneous Policy ( Simpol ) take the formulation of global policy into their own hands.

The Kagyu lineage divides the mahāmudrā teachings into three types, " sutra mahāmudrā ," " tantra mahāmudrā ," and " essence mahāmudrā ," in a formulation that appears to originate with Jamgon Kongtrul.

The clearest single statement appearing in the literature, from an orthodox EM perspective, appears in Rawls ' formulation spanning pages 40 – 41 of, Ethnomethodology's Program.

In Guru Arjan by whose time the formulation Vahiguru appears to have become current and acquired distinctiveness as the Name Divine, the phrase ‘ Gur Vahu ’ figures in Asa measure ( GG, 376 ).

Kirby's original formulation involved two kinds of move, the " blow-up " and the " handle slide "; Roger Fenn and Colin Rourke exhibited an equivalent construction in terms of a single move, the Fenn – Rourke move, that appears in many expositions and extensions of the Kirby calculus.

The Ishta-deva appears as one of the Three Roots in the Tibetan Buddhist ' Inner ' refuge formulation.

The dakini is so central to the requirements for a practitioner to attain full enlightenment as a Buddha that she appears in a tantric formulation of the Buddhist Three Jewels refuge formula known as the Three Roots.

The phrase ex nihilo also appears in the classical philosophical formulation ex nihilo nihil fit, which means " Out of nothing comes nothing ".

According to (), the first historical mention of the statement of this theorem appears in ().

The Chinese remainder theorem appears as an exercise in Sun Zi's Suan Ching ( also known as The Mathematical Classic of Sun Zi ( 3rd, 4th or 5th century CE.

The Poynting vector appears in Poynting's theorem ( see this article for the derivation of the theorem and vector ), an energy-conservation law,

Although this at first appears to be a stronger statement, it is a direct consequence of the other form of the theorem, through the use of successive polynomial division by linear factors.

The theorem appears in the Arithmetica of Diophantus, translated into Latin by Bachet in 1621.

Hence it often appears in illustrations of the Pythagorean theorem.

A version of van Kampen's theorem appears there, and is proved along quite different lines than in algebraic topology, namely descent theory.

If H < sub > 1 </ sub > is a separable space ( in particular, if it is a Euclidean space ) the result is true in Zermelo – Fraenkel set theory ; for the fully general case, it appears to need some form of the axiom of choice ; the Boolean prime ideal theorem is known to be sufficient.

The equipartition theorem shows that in thermal equilibrium, any degree of freedom ( such as a component of the position or velocity of a particle ) which appears only quadratically in the energy has an average energy of k < sub > B </ sub > T and therefore contributes k < sub > B </ sub > to the system's heat capacity.

More generally, the equipartition theorem states that any degree of freedom x which appears in the total energy H only as a simple quadratic term Ax < sup > 2 </ sup >, where A is a constant, has an average energy of ½k < sub > B </ sub > T in thermal equilibrium.

From this description, it appears that as one considers larger and larger primes, the frequency of a prime splitting completely approaches 1 / 2, and likewise for the primes that remain primes in Z. Dirichlet's theorem on arithmetic progressions demonstrates that this is indeed the case.

A closely related concept also appears in quantum mechanics ; see the Stone-von Neumann theorem and canonical commutation relations for details.

A final question of on the possibility of an analogue of Fáry's theorem for linkless graphs appears not to have been answered: when does the existence of a linkless or flat embedding with curved or piecewise linear edges imply the existence of a linkless or flat embedding in which the edges are straight line segments?

In mathematical folklore, the " no free lunch " theorem ( sometimes pluralized ) of Wolpert and Macready appears in the 1997 " No Free Lunch Theorems for Optimization.

It is uncertain who actually discovered the theorem ; however, the oldest extant exposition appears in Spherics by Menelaus.

According to an interview with David X. Cohen, he proved a theorem which appears in the Futurama episode " The Prisoner of Benda ".

1 − b + b ln b, hence ab ≤ e < sup > a </ sup > − b + b ln b for all non-negative a and b. This estimate is useful in large deviations theory under exponential moment conditions, because b ln b appears in the definition of relative entropy, which is the rate function in Sanov's theorem.

The special case of the noncommutative version of the lemma for right ideals appears in Nathan Jacobson ( 1945 ), and so the noncommutative Nakayama lemma is sometimes known as the Jacobson – Azumaya theorem.

) This theorem appears again, with expanded explanation, as Proposition 1, Theorem 1, of the ' Principia '.

Mathematical remark: the rigorous demonstration of the expression of the density of probability is not as direct as it appears above: from the application of the usual ( 1D ) central limit theorem one can deduce that, and are distributed according to a centered normal distribution of variance.

This notation, besides being used in some automated theorem provers, sometimes appears in catalogs of proofs

It appears to be one of intense dislike, which he makes little effort to conceal even in the presence of Southern friends.

The major effect of these advances appears to lie in the part they have played in the industrial revolution and in the tools which scientific understanding has given us to build and manipulate a more protective environment.

Life is further characterized, in antithesis to Piepsam, as animal: the image of a dog, which appears at several places, is first given as the criterion of amiable, irrelevant interest aroused by life considered simply as a spectacle: a dog in a wagon is `` admirable '', `` a pleasure to contemplate '' ; ;

That this and the closing of the East Berlin-West Berlin border have not been accepted by the Western governments appears in notes which Britain, France, and the United States sent to Moscow after the latter's gratuitous protest over a visit of Chancellor Adenauer and other West German officials to West Berlin.

It is also symptomatic of a change in attitude which appears to be spreading all across the South.

Traffic in the next lane appears to be moving more smoothly so he pokes a tentative fender into Lane B, which is heavily populated by cars also moving at 70 m.p.h..

In fact, one of the major reasons for the failure of the ill-starred expedition appears to have been a lack of full information on the extent to which Cuba has been getting this Russian military equipment.

It was indeed a remarkable feat that a man who had had no experience of bridge building should have applied the principle of the arch, which appears in his famous bridges at Portsmouth, Haverhill, and Philadelphia.

There followed a long and sometimes bitter discussion of the feasibility of elections for the fall of 1957, in which it appears that the Minister of the Interior took the most pessimistic view and that the Istiqlal was something less than enthusiastic.

In general, it appears that trustees and board members attempt to represent the public interest in their administration of educational policy, and this is made easier by the fact that the dominant values of the society are middle-class values, which are generally thought to be valid for the entire society.

If the symbolic name or actual address of an index word or electronic switch appears or is included in the operand of an XRELEASE or SRELEASE statement ( see page 101 ), the specified index word or electronic switch will again be made available, regardless of the method by which it was reserved.

Readers interested in additional information on foams are referred to the Foamed Plastics Chart appearing in the Technical Data section and to the list of references which appears below.

`` It is a much easier course to agree to let one another alone so far as ordinary patents are concerned '', said a trade authority, `` than to continue the costly effort of straightening the tangle in the courts or seeking to reform the patent system, which appears to be getting into deeper confusion every day ''.

Each toe bears a large, robust nail which is somewhat flattened and shovel-like, and appears to be intermediate between a claw and a hoof.

Anatolia is known as the birthplace of minted coinage ( as opposed to unminted coinage, which first appears in Mesopotamia at a much earlier date ) as a medium of exchange, some time in the 7th century BC in Lydia.

However, anxiety should not be confused with fear, it is more of a dreaded feeling about something which appears intimidating and can overcome an individual.

The same word in adjectival form ( purgatorius-a-um, cleansing ), which appears also in non-religious writing, was already used by Christians such as Augustine of Hippo and Pope Gregory I to refer to an after-death cleansing.

Zoroastrianism states that for the righteous souls, a beautiful maiden, which is the personification of the soul's good thoughts, words and deeds, appears.

A letter appears in the line below to which the player must add the existing letters to find a solution.

Alligators differ from crocodiles principally in having wider and shorter heads, with more obtuse snouts ; in having the fourth, enlarged tooth of the under jaw received, not into an external notch, but into a pit formed for it within the upper one ; in lacking a jagged fringe which appears on the hind legs and feet of the crocodile ; in having the toes of the hind feet webbed not more than half way to the tips ; and an intolerance to salinity, alligators strongly preferring fresh water, while crocodiles can tolerate salt water due to specialized glands for filtering out salt.

According to E. A. Wallis Budge, " as a Pantheus, i. e. All-God, he appears on the amulets with the head of a cock ( Phœbus ) or of a lion ( Ra or Mithras ), the body of a man, and his legs are serpents which terminate in scorpions, types of the Agathodaimon.

The most recent cinematic portrayal of Aeneas was in the film Troy, in which he appears as a youth charged by Paris to protect the Trojan refugees, and to continue the ideals of the city and its people.

" The most detailed surviving description of Agathon is in the Thesmophoriazousae, in which Agathon appears as a pale, clean-shaven young man dressed in women's clothes.

The Trojan War is supposed by many to have occurred at the height of the Mycenaean civilization ( see discussion of Troy VII ), roughly the point at which this palace appears to have been abandoned.

Although a bishop was promptly appointed to Hereford, none was named to Worcester, and it appears that Ealdred intended to retain Worcester along with York, which several of his predecessors had done.