The image on the left shows a p-V diagram for the ideal Diesel cycle ; where is pressure and is specific volume.

And the ideal Otto cycle formula stated above does not include throttling losses, which do not apply to Diesel engines.

These advantages also make the Diesel engine ideal for use in the heavy-haul railroad environment.

Dense vegetation ( such as that of tropical rainforests ) and urban habitats are not ideal for the establishment of the human transmission cycle.

Comparing the two formulae it can be seen that for a given compression ratio (), the ideal Otto cycle will be more efficient.

Since very few actual implementations of heat engines exactly match their underlying thermodynamic cycles, one could say that a thermodynamic cycle is an ideal case of a mechanical engine.

The ideal thermodynamic cycle used to analyze this process is called the Rankine cycle.

The CIRUS was an ideal facility to develop the plutonium bomb, therefore Nehru had refused to accept the nuclear fuel from Canada, and started the programme to develop the ingenious nuclear fuel cycle.

In an ideal pulse train ( one having rectangular pulses ), the duty cycle is the pulse duration divided by the pulse period.

The above discussion is based on the ideal vapor-compression refrigeration cycle, and does not take into account real-world effects like frictional pressure drop in the system, slight thermodynamic irreversibility during the compression of the refrigerant vapor, or non-ideal gas behavior ( if any ).

The novels of the Culture cycle, therefore, mostly deal with people at the fringes of the Culture: diplomats, spies, or mercenaries ; those who interact with other civilizations, and who do the Culture's dirty work in moving those societies closer to the Culture ideal, sometimes by force.

Their total life cycle can be as short as one year, but may be several years in ideal conditions.

In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility.

Since the Otto cycle is an isentropic process the isentropic equations of ideal gases and the constant pressure / volume relations can be used to yield Equations 3 & 4.

( The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting ).

The use of this technology to replace larger vapor-compression refrigeration units, which typically achieve performance coefficients of 60 % of that of a theoretical ideal Carnot cycle is unlikely in the near term.

Professor Israel Urieli writes: "... the various ' ideal ' cycles ( such as the Schmidt cycle ) are neither physically realizable nor representative of the Stirling cycle "

This is known as an " ideal Stirling cycle ", because it is an " idealized " model, and not necessarily an optimized cycle.

Theoretically, the " ideal cycle " does have high net work output, but it is rarely used in practical applications, in part because other cycles are simpler or reduce peak stresses on bearings and other components.

Since a maximal ideal in A is closed, is a Banach algebra that is a field, and it follows from the Gelfand-Mazur theorem that there is a bijection between the set of all maximal ideals of A and the set Δ ( A ) of all nonzero homomorphisms from A to C. The set Δ ( A ) is called the " structure space " or " character space " of A, and its members " characters.

The diameter of an ideal nanotube can be calculated from its ( n, m ) indices as follows

This follows the Incident Command System ( ICS ) principle of Span of control until the ideal distribution is achieved: one or more teams are formed at each neighborhood within a community.

The ideal gas law may also be expressed as follows

The property ( EF1 ) can be restated as follows: for any principal ideal I of R with nonzero generator b, all nonzero classes of the quotient ring R / I have a representative r with.

Peirce defines truth as follows: " Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth.

In an ideal transformer, the induced voltage in the secondary winding ( V < sub > s </ sub >) is in proportion to the primary voltage ( V < sub > p </ sub >) and is given by the ratio of the number of turns in the secondary ( N < sub > s </ sub >) to the number of turns in the primary ( N < sub > p </ sub >) as follows:

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.

This follows immediately from the Galois connection between ideals of and closed subsets of and the observation that, by the definition of, each prime ideal of corresponds to a generic point of the closed subset associated to via the Galois connection.

Liberals ' ideal conceptualization follows the model of the " nurturant parent " family, while Conservatives ' follow the model of the " strict father " family.

However, if R is the ring of algebraic integers in an algebraic number field, or more generally a Dedekind domain, the multiplication defined above turns the set of fractional ideal classes into an abelian group, the ideal class group of R. The group property of existence of inverse elements follows easily from the fact that, in a Dedekind domain, every non-zero ideal ( except R ) is a product of prime ideals.

Given a ring R and a two-sided ideal I in R, we may define an equivalence relation ~ on R as follows:

It follows from condition ( 3 ) that every left or right ideal is a subalgebra.

Indeed, as a student, Anker summed up his approach to art as follows: " One has to shape an ideal in one's imagination, and then one has to make that ideal accessible to the people.

To see the connection with the classical picture, note that for any set S of polynomials ( over an algebraically closed field ), it follows from Hilbert's Nullstellensatz that the points of V ( S ) ( in the old sense ) are exactly the tuples ( a < sub > 1 </ sub >, ..., a < sub > n </ sub >) such that ( x < sub > 1 </ sub >-a < sub > 1 </ sub >, ..., x < sub > n </ sub >-a < sub > n </ sub >) contains S ; moreover, these are maximal ideals and by the " weak " Nullstellensatz, an ideal of any affine coordinate ring is maximal if and only if it is of this form.

Peirce emphasized fallibilism, considered the assertion of absolute certainty a barrier to inquiry, and in 1901 defined truth as follows: " Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth .".

The easiest way to prove that the radical of I of a ring A is an ideal is to note that it is the pre-image of the ideal of nilpotent elements in .< ref > A direct proof can be give as follows:

For commutative rings, this is just the nilradical and closely follows the definition of the radical of an ideal.

Prelude was written before the Apollo missions landed men on the moon and follows the ideal that space travel is realistic and within the grasp of the population.

An internal characterization of left primitive rings is as follows: a ring is left primitive if and only if there is a maximal left ideal containing no nonzero two-sided ideals.

Celibacy was advocated as an ideal rule of life for all monks and nuns by Gautama Buddha, except for Japan where it is not strictly followed due to historical political developments following the Meiji Restoration.

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

An ideal P of a commutative ring R is prime if it has the following two properties:

Formally we mean that is an ideal if it satisfies the following conditions:

For example, if 50 % of a system's user base will be accessing the system via a 56K modem connection and the other half over a T1, then the load injectors ( computers that simulate real users ) should either inject load over the same mix of connections ( ideal ) or simulate the network latency of such connections, following the same user profile.

Averroes, following Plato's paternalistic model, advances an authoritarian ideal.

Given a ring R and a proper ideal I of R ( that is I ≠ R ), I is a maximal ideal of R if any of the following equivalent conditions hold:

For a right ideal A of a ring R, the following conditions are equivalent to A being a maximal right ideal of R:

If S is a commutative associative algebra over R, if I is an ideal of S such that the I-adic topology on S is complete, and if x is an element of I, then there is a unique Φ: R < nowiki ></ nowiki > X < nowiki ></ nowiki > → S with the following properties:

The maximal ideals of R < nowiki ></ nowiki > X < nowiki ></ nowiki > all arise from those in R in the following manner: an ideal M of R < nowiki ></ nowiki > X < nowiki ></ nowiki > is maximal if and only if M ∩ R is a maximal ideal of R and M is generated as an ideal by X and M ∩ R.

If S is a commutative associative algebra over R, if I is an ideal of S such that the I-adic topology on S is complete, and if x < sub > 1 </ sub >, ..., x < sub > r </ sub > are elements of I, then there is a unique Φ: R < nowiki ></ nowiki > X < sub > 1 </ sub >, ..., X < sub > n </ sub >< nowiki ></ nowiki > → S with the following properties:

In algebra, the following construction is common: one starts with a commutative ring R containing an ideal I, and then considers the I-adic topology on R: a subset U of R is open if and only if for every x in U there exists a natural number n such that x + I < sup > n </ sup > ⊆ U. This turns R into a topological ring.

The theory for ideal gases makes the following assumptions:

The World War II SOE training manual identified the following properties of an " ideal " invisible ink:

The ideal gas model depends on the following assumptions:

The ideal inline skate bearing has the following features: 1 ) a proven brand ( such as SKF, NTN, etc ) 2 ) dirt-proof or water-proof seals ( preferred ) 3 ) abec-1 rating for more dirt tolerance if any type of contamination should enter the bearing race and 4 ) be lubricated with a very light grease or gel that will not leak out of the bearing and will protect the race if any water should get in.

In this poem, written more than twenty years after Tennyson's Sir Galahad, Galahad is " fighting an internal battle between the ideal and the human ", believing that he is like God and that he is able to be a " savior capable of imparting grace ", following a dream in which he saves a dying knight with a kiss.

The chemical potential of the ( three dimensional ) ideal Fermi gas is given by the following expansion ( assuming ):

In symbols, we say that a subset L of a K-algebra A is a left ideal if for every x and y in L, z in A and c in K, we have the following three statements.

In the context of network theory a scale-free ideal network is a random network with a degree distribution following the scale-free ideal gas density distribution.