However implausible this is, it is certainly the case that Aristotle's rigid separation of action from production, and his justification of the subservience of slaves and others to the virtue – or arete – of a few justified the ideal of aristocracy.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case.

Contrary to brownian motion, which is the diffusion of a single particle, interactions between particles may have to be considered, unless the particles form an ideal mix with their solvent ( ideal mix conditions correspond to the case where the interactions between the solvent and particles are identical to the interactions between particles and the interactions between solvent molecules ; in this case, the particles do not interact when inside the solvent ).

In case of an ideal mix, the particle diffusion equation holds true and the diffusion coefficient D the speed of diffusion in the particle diffusion equation is independent of particle concentration.

In this case, the director's cut and the director's ideal preferred cut are distinctly separate versions.

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.

AA # 9, however, will fill the case much better, and the slow burn rate of AA # 9 is ideal for magnum handgun rounds, producing 20 % higher velocities ( at maximum levels ) while still producing less pressure than the fast burning AA # 2.

Much advancement has undoubtedly been made toward cooperation between architect and librarian, and many good designers have made library buildings their specialty, nevertheless it seems that the ideal type of library is not yet realized — the type so adapted to its purpose that it would be immediately recognized as such, as is the case with school buildings at the present time.

Murray Bookchin has put it this way " what of the syndicalist ideal of " collectivized " self-managed enterprises that are coordinated by like occupations on a national level and coordinated geographically by " collectives " on a local level ?... Here, the traditional socialist criticism of this syndicalist form of economic management is not without its point: the corporate or private capitalist, " worker-controlled " or not "” ironically, a technique in the repertoire of industrial management that is coming very much into vogue today as " workplace democracy " and " employee ownership " and constitutes no threat whatever to private property and capitalism ... In any case, " economic democracy " has not simply meant " workplace democracy " and " employee ownership.

In either case, the ideal value for the feedback resistors ( to give minimum offset voltage ) will be such that the two resistances in parallel roughly equal the resistance to ground at the non-inverting input pin.

This quantity exactly equals the kinetic power of the jet, so in this ideal case, the efficiency is 100 %, since all the energy in the jet is converted to shaft output.

" Parks was the ideal plaintiff for a test case against city and state segregation laws, as she was a responsible, mature woman with an excellent reputation.

Due to Columbia's heavier weight, it was less ideal for NASA to use it for missions to the International Space Station, though modifications were made to the Shuttle during its last refit in case the spacecraft was needed for such tasks.

In that ideal case, the atoms are positioned on a perfect lattice, the electron density is perfectly periodic, and the Fourier transform F ( q ) is zero except when q belongs to the reciprocal lattice ( the so-called Bragg peaks ).

Just as, in the case of the original Adam, woman was constructed from man, and their carnal cleaving together was portrayed as becoming one flesh, so the ideal for kabbalists is the reconstitution of what Wolfson calls the male androgyne.

The ideal shrapnel design would have had a timer fuze in the shell base to avoid the need for a central tube, but this was not technically feasible due to the need to manually adjust the fuze before firing, and was in any case rejected from an early date by the British due to risk of premature ignition and irregular action.

This includes, but is not limited to, the ideal case of a lossless line.

Note that this is only the case if the source is close to an ideal point source.

In our case we want to take the two-sided ideal I < sub > Q </ sub > in T ( V ) generated by all elements of the form

Theoretical considerations aside, in real world use the mechanical advantage of the trucker's hitch is significantly less than the ideal case due to the effects of friction.

In ideal case, the reaction produces a well-separated melt of metal and slag.

* Norton's theorem: Any network of voltage or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.

In modern mathematical language, the ideal generated by a and b is the ideal generated by g alone ( an ideal generated by a single element is called a principal ideal, and all ideals of the integers are principal ideals ).

In particular, in ideal play from a single heap of n objects, the second player can win iff

In abstract algebra, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i. e., can be generated by a single element.

* Z: the ring of all polynomials with integer coefficients --- it is not principal because the ideal generated by 2 and X is an example of an ideal that cannot be generated by a single polynomial.

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 ).

Among the integers, the ideals correspond one-for-one with the non-negative integers: in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number.

The revised definition seems to imply that the ideal atomic clock contains a single caesium atom at rest emitting a single frequency.

For gases, the volume ratio is ideally the same by the ideal gas law, but the mass ratio of a single reaction has to be calculated from the molecular masses of the reactants and products.

" Tramp " was originally thought to be the ideal follow-up single to " Golden Brown "; however " La Folie " was chosen after Burnel convinced his bandmates of its potential.

For example, the sampling process in any standard image sensor ( CCD or CMOS camera ) is relatively far from the ideal sampling which would measure the image intensity at a single point.

Supposed to transmit a single, ideal Dirac pulse of electromagnetic power at time 0, i. e.

The sinewave output of an ideal oscillator is a single line in the frequency spectrum.

In less than ideal vintages, some producers will produce a wine from only that single vintage and still label it as non-vintage rather than as " vintage " since the wine will be of lesser quality and the producers have little desire to reserve the wine for future blending.

In fact, it is possible to give a proof that is a Noetherian ring without appealing to its order structure and this proof applies more generally to principal ideal rings ( i. e., rings in which every ideal is generated by a single element ).

Even if the image is sharp, it may be distorted compared to ideal pinhole projection.

Because of their highly ordered and repetitive structure, crystals give diffraction patterns of sharp Bragg reflection spots, and are ideal for analyzing the structure of solids.

Captain Richard Hayden, a prominent shipbuilder, had advertised his Black Prince in a New York City newspaper as " a 315 ton sharp schooner that would make an ideal privateer.

Cheap, plentifully available as galena and easily workable, lead has many of the ideal characteristics, but on its own it lacks the necessary hardness and does not make castings with sharp details because molten lead shrinks and sags when it cools to a solid.

" They praised Vonnegut for " blending skilfully a psychological study of the persistent human problems in a mechanistically ' ideal ' society, a vigorous melodramatic story-line, and a sharp Voltairean satire.

The high or broad forehead represents good luck or the sharp, contemplative mind of the ideal Mende woman.

He was the first scientist to explain mathematically the origin of aerodynamic lift, through his circulation hypothesis, the first to dimension the lift force generated by a body moving through an ideal fluid as proportional to the velocity and the circulation around the body, and through a mathematical conformal transformation the first to define the shape of the aerodynamic profile having as essential elements a rounded nose ( leading edge ), double surface ( finite thickness ), cambered or symmetrical, and a sharp tail ( trailing edge ).

Advance Nanotech developed a doped diamond dust, whose sharp corners appeared to be an ideal emitter.

For log drives, the ideal river would have been straight and uniform, with sharp banks and a predictable flow of water.

He appeared in the eyes of his sisters as the ideal of the Christian prince, in sharp contrast with their father who was a notorious womanizer.

The field of battle was not ideal as the land falls away into sharp gullies on one side, but it was not bad enough to prohibit a battle.

Her lively, sharp thought, dressed in emotional complexity, sort of rushes out of her poems, looking for spiritual wholesomeness and ideal harmony ", one critic wrote.

Marx noted that the forms prices take are highly variegated, and he drew a sharp distinction between real prices and ideal prices.