When one wants to work over a base ring R ( commutative ), there is the group scheme concept: that is, a group object in the category of schemes over R. Affine group scheme is the concept dual to a type of Hopf algebra.

:* Affine scheme –

Affine and projective planes of order n exist whenever n is a prime power ( a prime number raised to a positive integer exponent ), by using affine and projective planes over the finite field with n = p < sup > k </ sup > elements.

** Frequency-hopping spread spectrum ( FHSS ) applies a special scheme for channel release

The empty scheme ( equal to the prime spectrum of the trivial ring ) is an initial object.

The actual colors shown differ, but many of the designs are based on the traditional scheme of red, orange, yellow, green, blue, indigo and violet, or some more modern division of the rainbow spectrum ( often excluding indigo, and sometimes including cyan instead ).

The code division multiple access ( CDMA ) scheme is based on spread spectrum, meaning that a wider radio spectrum in Hertz is used than the data rate of each of the transferred bit streams, and several message signals are transferred simultaneously over the same carrier frequency, utilizing different spreading codes.

Within this scheme, the full spectrum of autoimmunity can be included.

A scheme is a locally ringed space such that every point has a neighbourhood, which, as a locally ringed space, is isomorphic to a spectrum of a ring.

In parallel to the whole spectrum of road pricing measures, the government has invested heavily in public transport and implemented a park-and-ride scheme, with thirteen fringe car parks, hence providing car users a real alternative to switch travel modes.

An equivalent but streamlined construction is given by the Proj construction, which is an analog of the spectrum of a ring, denoted " Spec ", which defines an affine scheme.

According to Pierre Cartier, the word scheme was first used in the 1956 Chevalley Seminar, in which Chevalley was pursuing Zariski's ideas ; and it was André Martineau who suggested to Serre the move to the current spectrum of a ring in general.

An affine scheme is a locally ringed space isomorphic to the spectrum of a commutative ring.

The functor associates to every commutative ring its spectrum, the scheme defined by the prime ideals of the ring.

Any affine group scheme is the spectrum of a commutative Hopf algebra ( over a base S, this is given by the relative spectrum of an O < sub > S </ sub >- algebra ).

For an arbitrary group scheme G, the ring of global sections also has a commutative Hopf algebra structure, and by taking its spectrum, one obtains the maximal affine quotient group.

ColorCode 3D, a stereoscopic color scheme, uses the RG color space to simulate a broad spectrum of color in one eye ; the blue portion of the spectrum transmits a black-and-white ( black-and-blue ) image to the other eye to give depth perception.

For example, there is a duality between commutative rings and affine schemes: to every commutative ring A there is an affine spectrum, Spec A, conversely, given an affine scheme S, one gets back a ring by taking global sections of the structure sheaf O < sub > S </ sub >.

To improve spectrum utilization, Phase 2 has been developed using a 2-slot TDMA scheme.

As an example, consider Code Division Multiplexed Access ( CDMA ) spread spectrum, which is not a particularly spectral efficient encoding scheme when considering a single channel or single user.

During his time as prime minister, average living standards steadily rose while numerous social reforms were carried out such as the 1956 Clean Air Act, the 1957 Housing Act, the 1960 Offices Act, the 1960 Noise Abatement Act, the Factories Act 1961, the introduction of a graduated pension scheme to provide an additional income to retirees, and a reduction in the standard workweek from 48 to 42 hours.

After unsuccessful attempts to interest the authorities in Ireland and revolutionary France, he started trying to persuade the prime minister, William Pitt, to revive an earlier abandoned scheme for a National Penitentiary in England, this time to be built as a Panopticon.

Basically, a variety is a scheme whose structure sheaf is a sheaf of k-algebras with the property that the rings R that occur above are all integral domains and are all finitely generated k-algebras, i. e., quotients of polynomial algebras by prime ideals.

If S is the complement of a prime ideal I the localization is denoted by R < sub > I </ sub >, and R < sub > f </ sub > is used to denote the localization by the powers of an element f. The two latter cases are fundamental in algebraic theory and scheme theory.

Technically, a scheme is a topological space together with commutative rings for all of its open sets, which arises from gluing together spectra ( spaces of prime ideals ) of commutative rings along their open subsets.

In 2011, he and former Liberal prime minister Malcolm Fraser were among 140 Australian community leaders who pledged support for an emissions trading scheme.

However, Spanish procrastination led to a scheme in which France's prime minister, Cardinal Mazarin, pretended to seek a marriage for his master with Margaret Yolande of Savoy.

He refused to accept Yahya's scheme to appoint Bengali politician Nurul Amin as Prime minister, with Bhutto as deputy prime minister.

Additionally to the scheme above, it uses another generator h of the prime group and a random number r. The commitment is set.

419 prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, highly cototient number, Mertens function returns 0, also refers to the Nigerian advance fee fraud scheme ( after the section of the Nigerian Criminal Code it violates )

* All users of the signature scheme agree on a group with generator of prime order in which the discrete log problem is hard.

* If p = 0 in S for some prime number p, then the taking of pth powers induces an endomorphism of G < sub > a </ sub >, and the kernel is the group scheme α < sub > p </ sub >.

She joined the Republican and Democratic Movement ( MDR ), an opposition party, in 1992, and four months later was appointed Minister of Education by Dismas Nsengiyaremye, the first opposition prime minister under a power-sharing scheme negotiated between President Juvénal Habyarimana and five major opposition parties.

In 1997, while still serving as prime minister, he was implicated in a scheme to sell Vanuatuan passports to foreigners, and the Office of the Vanuatu Ombudsman recommended that he resign from his post.

Following the closure of the RAF station the site was handed over to Defence Estates, who in turn passed it to the prime plus contractor for Project MoDEL, VSM Estates, a company formed by developers Vinci and St Modwen who are responsible for developing proposals and the subsequent disposal of the site to developers who will realise the scheme.

The success was so spectacular that in 1995, the then Indian prime minister P. V. Narsimha Rao hailed the success of the project and suggested that the scheme be implemented all over the country, and thus began the " National Programme for Nutrition Support to Primary Education ".

Its early prime focus was upon the first offenders where a program of employment, educational opportunities, physical education in addition to the scheme of restricted association was credited for a relatively low level of re-offending.

Balfour succeeded Salisbury as prime minister in 1902, and the government would eventually falter after Chamberlain proposed his scheme for tariff reform, whose partial embrace by Balfour led to the resignation of the more orthodox free traders in the Cabinet.

He was one of the prime movers in the scheme to supplant General Washington as commander-in-chief by General Horatio Gates.

In his last chance to prove his innocence, he talks non-stop for about 24 hours, reaffirming the American ideals of freedom and disclosing the true motives of the dam scheme.

With the addition of brass buttons, the unit wore a black-red-gold colour scheme, a combination that became associated with republican ideals.

As many Lützow Free Corps veterans took part in the first Wartburg festival of 1817, demanding German unity and democratic reforms, their black-red-gold uniform colour scheme became associated with republican ideals.

Aside from this, Ian is a typical sitcom child ; most plots involve him either failing at an elaborate scheme or trying desperately to survive in a world that doesn't seem to fit his ideals.

In support of the scheme, NMP Paulin Tay Straughan said in Parliament on 26 April 2010 that it neither compromises the democratic process nor perpetuates the dominance of the ruling party, because during elections Singaporeans vote for the political parties that best represent their interests and ideals, and the presence of NMPs in the House does not factor into this choice.

Non-constituency Member of Parliament Sylvia Lim has stated that it is the Workers ' Party's position that the NMP scheme cannot be improved as it goes against the most fundamental democratic ideals of fair representation and elections.