The Dirichlet kernel is not a positive kernel, and in fact, its norm diverges, namely

By the Rule of St Benedict, which, until the Cluniac reforms, was the norm in the West, the abbot has jurisdiction over only one community.

Due to financial difficulties fighter pilots have 60 hours of flying time per year, only a third of the national norm of 180 hours.

So, for example, while R < sup > n </ sup > is a Banach space with respect to any norm defined on it, it is only a Hilbert space with respect to the Euclidean norm.

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

*: The condition number computed with this norm is generally larger than the condition number computed with square-summable sequences, but it can be evaluated more easily ( and this is often the only measurable condition number, when the problem to solve involves a non-linear algebra, for example when approximating irrational and transcendental functions or numbers with numerical methods.

The sharper the strife became, the more Wycliffe had recourse to his translation of Scripture as the basis of all Christian doctrinal opinion, and expressly tried to prove this to be the only norm for Christian faith.

Rainfall is not always adequate for rice cultivation, however, and the relatively high average precipitation conceals years where rainfall may be only half or less of the norm, causing significant declines in rice yields.

Hare, and Simon Blackburn have argued in favor of the fact / norm distinction, meanwhile, with Gibbard going so far as to argue that, even if conventional English has only mixed normative terms ( that is, terms that are neither purely descriptive nor purely normative ), we could develop a nominally English metalanguage that still allowed us to maintain the division between factual descriptions and normative evaluations.

In fact, Mexico was considered a bastion of continued constitutional government in times where coup d ' états and military dictatorships were the norm in Latin America, in that the institutions were renovated electorally, even if only in appearance and with little participation of the opposition parties at the local level.

The baptised name was possibly chosen on purpose, as it means not only " crown " as mentioned, but also " norm, standard " in Hebrew.

So customary units are still widely used on consumer products and in industrial manufacturing ; only in military, medical, and scientific contexts are SI units generally the norm.

While the supercomputers of the 1970s used only a few processors, in the 1990s, machines with thousands of processors began to appear and by the end of the 20th century, massively parallel supercomputers with tens of thousands of " off-the-shelf " processors were the norm.

While the supercomputers of the 1970s used only a few processors, in the 1990s, machines with thousands of processors began to appear and by the end of the 20th century, massively parallel supercomputers with tens of thousands of " off-the-shelf " processors were the norm.

( The only break from this norm is in the second episode produced and broadcast, " Daisy's Song ", where Bo wears a red shirt for much of the story, and a sequence in the fifth episode, " High Octane ", where he wears a light blue shirt.

This gives only two options: either the norm of is a prime number, or the square of a prime number.

This paper not only introduced the Gaussian integers and proved they are a unique factorization domain, it also introduced the terms norm, unit, primary, and associate, which are now standard in algebraic number theory.

Not only did this tend to proliferate unwieldy titles ( e. g. Princess Katherine of Anhalt-Zerbst and Karl, Count Palatine of Zweibrücken-Neukastell-Kleeburg and Prince Christian Charles of Schleswig-Holstein-Sonderburg-Plön-Norburg ), but as agnatic primogeniture gradually became the norm in the Holy Roman Empire by the end of the 18th century, another means of distinguishing the monarch from other members of his dynasty became necessary.

Weber emphasized that it was very unusual to find only one of these orientations: combinations were the norm.

In order for the album to contain fourteen songs ( the norm for British 12 " vinyl pop albums at that time was to have seven songs on each side, while American albums usually had only five or six songs per side ) ten more tracks were needed to add to the four sides of their first two singles recorded and released previously.

During the 20th century, ghetto came to be used to describe the areas inhabited by a variety of groups that mainstream society deemed outside the norm, including not only Jews but poor people, gay men and lesbians, racial minorities, hobos, prostitutes and bohemians.

( Religious tensions occurred in the 1930s, but were the norm only in Northern Ireland ).

Normative Judaism only recognizes matrilineal descent ; however, patrilineal descent was the norm among the Israelites who lived prior to its adoption.

:... high Mass is the norm ; it is only in the complete rite with deacon and subdeacon that the ceremonies can be understood.

Some investigators have found a parallelism between remissions and return of the sympathetic reactivity of the hypothalamus to the normal level as indicated by the Mecholyl test and, conversely, between clinical impairment and increasing deviation of this test from the norm.

* Old Bulgarian ( 9th to 11th century, also referred to as Old Church Slavonic ) – a literary norm of the early southern dialect of the Common Slavic language from which Bulgarian evolved.

* Middle Bulgarian ( 12th to 15th century ) – a literary norm that evolved from the earlier Old Bulgarian, after major innovations were accepted.

Consider a complete orthonormal system ( basis ),, for a Hilbert space H, with respect to the norm from an inner product.

During the winter, storms blowing from the Sahara sometimes form dense dust clouds that obscure the sun ; however, sunny days are the norm year round.

From 1400 to 1700, group litigation gradually switched from being the norm in England to the exception.

To summarize, the probability distribution of the outcome is the normalized square of the norm of the superposition, over all paths from the point of origin to the final point, of waves propagating proportionally to the action along each path.

The " Progressive Education Movement ," starting in the 1880s and lasting for sixty years, helped boost American public schools from a budding idea to the regular norm.

An important example is a Hilbert space, where the norm arises from an inner product.

Naked sun bathing and swimming are the norm on beaches away from inhabited areas.

He also sought to break from the class-conscious conventions of the 1930s and early 40s, when top hat and tails or tuxedos were the norm, by dancing in casual or everyday work clothes, so as to make his dancing more relevant to the cinema-going public.

Later models of removable pack drives, from IBM and others, became the norm in most computer installations and

In other cases, defection from the norm can pose a real risk, particularly if the international environment is changing.

This has led to the conclusion that invertebrates are a group that deviates from the norm, vertebrates.

Central to the Pure Theory of Law is the notion of a ' basic norm ( Grundnorm )'— a hypothetical norm, presupposed by the jurist, from which in a hierarchy all ' lower ' norms in a legal system, beginning with constitutional law, are understood to derive their authority or ' bindingness '.

Most keyboards are rigid, but this keyboard demonstrates one of many variations from the norm.

Midwives are specialists in low-risk pregnancy, childbirth, and postpartum, although they are trained to recognize and deal with deviations from the norm as well as certain high risk situations.

We often omit p or ‖·‖ and just write V for a space if it is clear from the context what ( semi ) norm we are using.

This follows from the triangle inequality and homogeneity of the norm.

This is also the norm in England, except for a few cases where severe injustice results from a harsh application.

Regulation of parties may run from a crackdown on or repression of all opposition parties, a norm for authoritarian governments, to the repression of certain parties which hold or promote ideals which run counter to the general ideology of the state's incumbents ( or possess membership by-laws which are legally unenforceable ).

Scores derived by classical test theory do not have this characteristic, and assessment of actual ability ( rather than ability relative to other test-takers ) must be assessed by comparing scores to those of a " norm group " randomly selected from the population.

Until recently, no norm was defined for a standard QWERTY keyboard layout allowing the typing of accented characters, apart from the US-International layout.

Although Orbison is counted as a rock and roll pioneer, and has been cited by numerous critics as one of the genre's most influential musicians, his style was noted for how it departed from the norm.