If internal responsibility suggests acceptance of the socialist ideal of equality, then external responsibility implies adherence to principles of ideological supranationalism.

** 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.

If the ideals A and B of R are coprime, then AB = A ∩ B ; furthermore, if C is a third ideal such that A contains BC, then A contains C. The Chinese remainder theorem is an important statement about coprime ideals.

If one takes the median of 17 of these 22 compositions for rockets ( 75 % nitrates, 9. 06 % sulfur, and 15. 94 % carbon ), it is nearly identical to the modern reported ideal gunpowder recipe of 75 % potassium nitrate, 10 % sulfur, and 15 % carbon.

If the air density and temperature are the same above and below a wing, a naive application of the ideal gas law requires that the pressure also be the same.

If that ideal size is large enough to supply the whole market, then that market is a natural monopoly.

If met with ideal conditions on a new planet's surfaces, the bacteria become active and the process of evolution begins.

If the number of participants is large, and some of their physical or network distancee are great, then the probability of complete success ( which is, in ideal circumstances, required for system security ) will be rather low.

* 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 ).

The key result is the structure theorem: If R is a principal ideal domain, and M is a finitely

If M is a free module over a principal ideal domain R, then every submodule of M is again free.

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.

# If n = 2k + 1, then the action of the unit vector u on the left ideal decomposes the space into a pair of isomorphic irreducible eigenspaces ( both denoted by Δ ), corresponding to the respective eigenvalues + 1 and − 1.

If I is a right ideal of R, then I is simple as a right module if and only if I is a minimal non-zero right ideal: If M is a non-zero proper submodule of I, then it is also a right ideal, so I is not minimal.

If we isolate thermally the tank and move the paddle wheel with a pulley and a weight we can relate the increase in temperature with the height descended by the mass.

If this theory is correct, then the transition to a conductive state could be explained by a rearrangement at the pore edge, in which the lipid heads fold over to create a hydrophilic interface.

If both of the A and B inputs are high, then both the NMOS transistors ( bottom half of the diagram ) will conduct, neither of the PMOS transistors ( top half ) will conduct, and a conductive path will be established between the output and V < sub > ss </ sub > ( ground ), bringing the output low.

If either of the A or B inputs is low, one of the NMOS transistors will not conduct, one of the PMOS transistors will, and a conductive path will be established between the output and V < sub > dd </ sub > ( voltage source ), bringing the output high.

If the conductive part of the hearing loss is more than 30 – 35 dB, an air conduction device could have problems overcoming this gap.

If toner spills into the laser printer, a special type of vacuum cleaner with an electrically conductive hose and a high efficiency ( HEPA ) filter may be needed for effective cleaning.

If the electric field is strong enough, a conductive discharge ( called a positive streamer ) can develop from these points.

If radio waves strike an electrically conductive object of any size, they are slowed according to that object's permeability and permittivity.

If it is too cold, electrically conductive deposits may form on the insulator causing a loss of spark energy or the actual shorting-out of the spark current.

If a piece of electrically conductive metal is close to the coil, eddy currents will be induced in the metal, and this produces an alternating electric field of its own.

If all conductive objects are bonded to the same earth grounding system, the risk of electric shock is minimized.

If too much blood is collected from the patient, the patient risks a hospital-induced anemia and the ratio of blood-to-nutrient broth will tilt in the opposite direction, which also is not conductive to optimal growth.

If the geometry and gradient are such that the ionized region continues to grow until it reaches another conductor at a lower potential, a low resistance conductive path between the two will be formed, resulting in an electric arc.

If the stapes footplate is fixed in position, rather than being normally mobile, then a conductive hearing loss results.

If bodies are prepared with separately uniform temperatures, and are then put into purely thermal communication with each other, by conductive or radiative pathways, they will be in thermal equilibrium with each other just when they have the same temperature, and then there will be no net transfer of heat between them ; but if initially they do not have the same temperature, heat will flow from the hotter to the colder, by whatever pathway, conductive or radiative, is available, and this flow will continue until thermal equilibrium is reached and then they will have the same temperature.

If toner spills into the laser printer, a special type of vacuum cleaner with an electrically conductive hose and a high efficiency ( HEPA ) filter may be needed for effective cleaning.

If they cannot, there is conductive hearing loss in that ear.

If there is conductive hearing loss, it is likely to be louder in the affected ear ; if there is sensorineural hearing loss, it will be quieter in the affected ear.

If, while it is close to the positive charge, the above object is momentarily connected through a conductive path to electrical ground, which is a large reservoir of both positive and negative charges, some of the negative charges in the ground will flow into the object, under the attraction of the nearby positive charge.

If the axoplasm contains many molecules that are not electrically conductive, it will slow the travel of the potential because it will cause more ions to flow across the axolemma ( the axon's membrane ) than through the axoplasm.

If the circuit is double cut with positive and negative wires, any wet conductive earth is likely to blow a fuse on the one hand, and short the detecting relay on the other hand, either of which is almost certain to apply the correct warning signal.

If a simple open-ended waveguide is used as an antenna, without the horn, the sudden end of the conductive walls causes an abrupt impedance change at the aperture, from the wave impedance in the waveguide to the impedance of free space, ( about 377 ohms ).

If they are not able to hear the tuning fork at this point it means that their bone conduction is greater than their air conduction, indicating there is something inhibiting the passage of sound waves to the cochlea ( i. e., there is a conductive hearing loss ).

If excessive heat is applied or applied too quickly, or if the force between the base materials is too low, or the coating is too thick or too conductive, then the molten area may extend to the exterior of the work pieces, escaping the containment force of the electrodes ( often up to 30, 000 psi ).

If the blackbody absorbs 1, 080 watts on its sun-facing surface, it must also emit all 1, 080 watts omnidirectionally.

If a radiation-emitting object meets the physical characteristics of a black body in thermodynamic equilibrium, the radiation is called blackbody radiation.

If, when this was all over, she found the words to tell him about it, she wondered if he would ever understand.

If you don't leave this country within 3 days, your life will be taken the same as Powell's was.

If we was both armed, you wouldn't talk so tough ''.

If it were the enemy, tactically his position was correct.

If the turn was too tight, a barrel roll would bring them out.

If it were not that I knew who it was I could have mistaken it for my Aunt so well did her clothes fit him.

If Franklin was an authentic genius, then Alexander Hamilton, with his exceptional precocity, consuming energy, and high ambition, was a political prodigy.

`` If you can conveniently let me have twenty dollars '', he wrote one friend in 1791 when he was Secretary of the Treasury.

If an automobile were approaching him, he would know what was required of him, even though he might not be able to act quickly enough.

If living Jews were unavailable for study, the Bible was at hand.

If there was ever a thought in her mind she might devote her life to religion, it was now dispelled.

If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.

If she were not at home, Mama would see to it that a fresh white rose was there.

If, as Reid says, `` nearly all his poetry was produced when he was not taking opium '', there may be some reason to doubt that he was under its influence in the period from 1896 to 1900 when he was writing the poems to Katie King and making plans for another book of verse.

If Robinson was a liar and a slanderer, he was also a very canny gentleman, for nothing that Pike could do would pry so much as a single word out of him.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If the historian was convinced of his own correctness, then he should not allow his vision to become fogged by disturbing facts.

If their schedules were to synchronize, there was no point in wasting time.

If he had any worries, it was only the small ones, about Mother in New York, and his daughter Edwina and what she might be doing at this hour, with her Aunt Asia, in Philadelphia.