The industry norm can be argued to be anything between 93 %- 96 % when a UPS is in full operational mode, and to reach these figures companies often put their UPS in an ideal scenario.

of a number field K contains an integral ideal of norm not exceeding a certain bound, depending on K, called Minkowski's bound: the finiteness of the class number of an algebraic number field follows immediately.

The government-sponsored image of the conversion process emphasises psychological persuasion and a variety of " soft-sell " techniques ; this is the " ideal norm " in regime reports, according to Tong.

This result gives a bound, depending on the ring, such that every ideal class contains an ideal norm less than the bound.

If a is an ideal of O < sub > K </ sub >, other than the zero ideal we denote its norm by Na.

Hence this norm of an ideal is always a positive integer.

When I is a principal ideal αO < sub > K </ sub > then N ( I ) is equal to the absolute value of the norm to Q of α, for α an algebraic integer.

In commutative algebra, the norm of an ideal is a generalization of a norm of an element in the field extension.

When the less complicated number ring is taken to be the ring of integers, Z, then the norm of a nonzero ideal I of a number ring R is simply the size of the finite quotient ring R / I.

The norm of a principal ideal generated by α is the ideal generated by the field norm of α.

By convention, the norm of the zero ideal is taken to be zero.

The norm of an ideal can be used to bound the norm of some nonzero element by the inequality

Ushering in the modern recording era, he challenged our perception and processes of how recordings could be made, explored the possibilities of modern recording and exploited the potential for the popularity of classical music-and all this while setting standards of artistic achievement, integrity, risk-taking, and of the aesthetic ideal that became our new norm.

A six-partner group marriage ( three male, three female ) is considered the ideal norm in the alien society described in the novel ; the main characters are in a five-partner group marriage, and much of the dramatic tension hinges on there being more than one candidate for the sixth position.

The previous norm, the mortise lock, is a more complex device, and its higher manufacturing cost as well as its more labor intensive installation make the bored cylindrical lock an ideal substitute, both in price and functionality.

* Ideal norm, the ideal theoretic generalization of the field norm

This norm diverges only minimally from the original ideal of " one letter, one sound "; that is, it accepts only minor allophonic variation.

If L / K is a finite extension with rings of integers O and o respectively then the different ideal δ < sub > L / K </ sub >, which encodes the ramification data, is the annihilator of the O-module Ω < sup > 1 </ sup >< sub > O / o </ sub >:

By definition, the different ideal δ < sub > K </ sub > is the inverse fractional ideal I < sup >− 1 </ sup >: it is an ideal of O < sub > K </ sup >.

The nitrogen atom of an ideal amide is sp < sup > 2 </ sup >- hybridized due to resonance, and sp < sup > 2 </ sup >- hybridized atoms have trigonal planar bond geometry.

Let M be a smooth manifold and let x be a point in M. Let I < sub > x </ sub > be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.

Define, where is the discrete valuation corresponding to the ideal P < sub > i </ sub >.

* ( for ideal mixtures ) is the concentration in dimensions of of substance ) length < sup >− 3 </ sup >, example

Gibbs showed that if we use the equation Z = ξ < sup > N </ sup >, the entropy of a classical ideal gas is

The proton pump is the terminal stage in gastric acid secretion, being directly responsible for secreting H < sup >+</ sup > ions into the gastric lumen, making it an ideal target for inhibiting acid secretion.

* If R denotes the ring CY of polynomials in two variables with complex coefficients, then the ideal generated by the polynomial Y < sup > 2 </ sup > − X < sup > 3 </ sup > − X − 1 is a prime ideal ( see elliptic curve ).

If A < sub > i </ sub > in R < sub > i </ sub > is an ideal for each i in I, then A = Π < sub > i in I </ sub > A < sub > i </ sub > is an ideal of R. If I is finite, then the converse is true, i. e. every ideal of R is of this form.

( 43 )</ sup > gives the following expression, based on the equation of state for an ideal Fermi gas:

In early times, horror films such as My Bloody Valentine ( 1981 ), Halloween ( 1978 ), and Friday the 13th ( 1980 ) pertained mostly to a male audience in order to " feed the fantasies of young men ".< ref name = Nowell > Their main focus was to express the fear of women and show them as monsters ; however, this ideal is no longer prevalent in horror films .< ref name = Williams > Women have become not only the main audience and fans of horror films but also the main protagonists of contemporary horror films.

In standard state or STP, with the pressure at 1 atm and temperature at being 273. 16 K, the volume occupied by a mole of an ideal gas would be equal to 22. 414 L.

: = ideal gas constant ( 8. 314472 J /( mol · K ))

* K: The ideal ( x, y ) is not principal.

The converse does not hold since for any field K, K is a UFD but is not a PID ( to prove this look at the ideal generated by It is not the whole ring since it contains no polynomials of degree 0, but it cannot be generated by any one single element ).

" He was explicit about " the humanistic origins of the ‘ invisible ideal in post-modernist thought '", referencing as well the ironically dystopian Philip K. Dick novel Ubik.

The ideal scenario according to Bowen's reaction series would see a granite melt begin crystallizing a cumulate assemblage of plagioclase and hornblende ( i. e. ; tonalite or diorite ), which is low in K ( and hence Rb ) but high in Sr ( as this substitutes for Ca ), which proportionally enriches the melt in K and Rb.

The noise figure is the difference in decibels ( dB ) between the noise output of the actual receiver to the noise output of an “ ideal ” receiver with the same overall gain and bandwidth when the receivers are connected to matched sources at the standard noise temperature ( usually 290 K ).

It is also more accessible than speaking of the noise's power spectral density ( in watts per hertz ) since it is expressed as an ordinary temperature which can be compared to the noise level of an ideal resistor at room temperature ( 290 K ).

The heat capacity at constant volume of nR = 1 J · K < sup >− 1 </ sup > of any gas, including an ideal gas is:

The heat capacity at constant pressure of 1 J · K < sup >− 1 </ sup > ideal gas is:

Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is known to the same precision as the gas constant: R = 8. 314 4621 ( 75 ) J mol < sup >− 1 </ sup > K < sup >− 1 </ sup >, that is a relative standard uncertainty of 9. 1 × 10 < sup >− 7 </ sup >, according to the 2010 CODATA recommended value.

To Macaulay this is regarded as a piece of selfish treachery against his patron ; an analysis shared by G. K. Chesterton: " Churchill, as if to add something ideal to his imitation of Iscariot, went to James with wanton professions of love and loyalty ... and then calmly handed over the army to the invader.

Here Q is the molar activation energy, R is the ideal gas constant, T is absolute temperature, and K < sub > 0 </ sub > is a material dependent factor.

The ring of algebraic integers in a number field K is Noetherian, integrally closed, and of dimension one ( to see the last property, observe that for any nonzero ideal I of R, R / I is finite and recall that a finite integral domain is a field ), so by ( DD4 ) R is a Dedekind domain.

Let R be an integral domain with fraction field K. A fractional ideal is a nonzero R-submodule I of K for which there exists a nonzero x in K such that

( We remark that this is not exactly the same as the definition given on the page describing fractional ideals: the definition given there is that a fractional ideal is a nonzero finitely generated R-submodule of K. The two definitions are equivalent if and only if R is Noetherian.

A principal fractional ideal is one of the form for some nonzero x in K. Note that each principal fractional ideal is invertible, the inverse of being simply.

Let k be a field ( such as the rational numbers ) and K be an algebraically closed field extension ( such as the complex numbers ), consider the polynomial ring kX < sub > n </ sub > and let I be an ideal in this ring.