These results might be weaker than, equivalent to, or stronger than the axiom of choice, depending on the strength of the technical foundations.

These were militarily far weaker, as Strabo assessed their combined military potential at just 40, 000 armed men, and were often involved in internecine warfare.

These weaker springs are compressed solely by the radial vibrations from an idling engine.

These evidently weaker axiom pairs are trivial consequences of A3 and A4.

These sources tend to be much weaker than reactors.

These orbitals are classified as antibonding ( weakening the bond order from three to two ), so the diatomic oxygen bond is weaker than the diatomic nitrogen triple bond in which all bonding molecular orbitals are filled, but some antibonding orbitals are not.

These skills were taught first by a group of self-styled " sophists " who were known to charge fees, to " make the weaker argument the stronger ," and to make their students " better " through instruction in excellence.

These semantics are stronger than safe semantics but weaker than atomic semantics: they guarantee that there is a total order to the write operations which is consistent with real-time and that read operations return either the value of the last completed write or that of one of the writes which are concurrent with the read.

These may include pressor beams ( a stronger pressor beam will counteract a weaker tractor beam ) or plane shears aka shearing planes ( a device to " cut " the tractor beam and render it ineffective ).

These type of storms are stronger than the single-cell storm, yet much weaker than the supercell storm.

These are relatively strict, allowing for the model to generate more useful hypotheses with regard to consumer behaviour than weaker assumptions, which would allow any empirical data to be explained in terms of stupidity, ignorance, or some other factor, and hence would not be able to generate any predictions about future demand at all.

These researchers found that backward association was greatly weaker than forward association.

These are placed in the two new corners of the board, which are out of play, to indicate the new location of one of the weaker player's border rows.

These overlie weaker mudstones of the St Maughans Formation-a situation which has contributed to the instability of the hill's steep flanks.

These often have slightly lower power to match the weaker actions present in some of these rifles.

These ghosts are much weaker than Exalted, and they can only respire Essence in the Underworld and Shadowlands.

A number of breweries, particularly in Sussex, produce a weaker style of old ale with some resemblance to a mild ale Examples include King and Barnes ( later W. J King ) ( 4. 5 % ABV ) and Harveys ' ( 4. 3 % ABV ) These are typically consumed on draught dispense.

These snakes are venomous, but possess a weaker venom than many other rattlesnakes.

These changes were visible in the Umbral landscape, as sites associated with Gaia became fewer and weaker, while the Pattern Web of the Weaver and the corrupt influence of the Wyrm became more prominent.

These later works are generally accepted as the weaker part of his canon, his best cultural criticism having shown itself in the form of his literary critical practices.

These bridges also can protect weaker trees from strong winds.

As for the others, some died heroically in battle, and their bodies were brought home to be mummified and entombed within the king's pyramid. These provide cheaper, but slightly weaker characters to lead or support your army.

These were built by noblemen who wanted to assert their power and independence from the Imperial household, which was growing weaker.

These groups see the language of the Apology Resolution as deceptively conflating the strong, universally accepted definition of sovereignty — which the Hawaiian Kingdom possessed as an internationally recognized nation-state — with an immeasurably weaker notion of the " inherent sovereignty " of an " indigenous " or " Native " people within, and subordinate to, the United States.

These quantum numbers only occur in certain combinations of values, and their physical interpretation changes depending on whether real or complex versions of the atomic orbitals are employed.

These are inherently more aerodynamic than upright versions, as the rider may lean back onto a support and operate pedals that are on about the same level as the seat.

These fruit versions sometimes contain colored pearls ( and / or " jelly cubes " as in the related drink taho ), the color chosen to match whatever fruit juice is used.

These, as well as his slouching posture, are references to his earlier mild-mannered Pre-Crisis versions, but he still maintains a sense of authority and his assertive self.

These versions allowed 25 modules be to inserted into a single 5-1 / 4 inch section of racking, and allowed the high densities needed to build a computer.

) These two are further separated, falling into either constructive or destructive versions of Order and Disorder.

These often process data using fixed-point arithmetic, though some more powerful versions use floating point arithmetic.

These models where produced with a 1, 000 cc two-stroke engine, with a choice between or S versions until 1963.

These versions of the DOM became known as the " Intermediate DOM.

These more recent versions, however, maintain that only the subjective, qualitative aspects of mental states are epiphenomenal.

These canon tables or " Eusebian canons " remained in use throughout the Middle Ages, and illuminated manuscript versions are important for the study of early medieval art.

These additional manuscript sources of the Testimonium have furnished additional ways to evaluate Josephus ' mention of Jesus in the Antiquities, principally through a close textual comparison between the Arabic, Syriac and Greek versions to the Testimonium.

These tracks feature the 2001 release bonus songs and previously unissued recordings, including alternate electric backing versions of three songs.

These anisotropic self-assembled nano-structures can then order themselves in much the same way as thermotropic liquid crystals do, forming large-scale versions of all the thermotropic phases ( such as a nematic phase of rod-shaped micelles ).

These models are basically based on Samara technology with a new body and fuel injection engines as standard features, though carburated versions have also been available up until 2001.

These versions would correspond to the addition of one and then another ' frame ' settings of dialogues.

These languages are either designed specially for the purpose, or versions of general purpose languages such as the C programming language.

These early Mach versions included the majority of 4. 3BSD in the kernel, a system known as POE Server, resulting in a kernel that was actually larger than the UNIX it was based on.

These three versions were made directly from the Greek, and are frequently cited in the apparatuses of modern critical editions.

These two versions also differ from each other in their readings of numerous words.

These op-amps were generally improved versions of existing monolithic op-amps.

These newer versions of PGP software eliminate the use of e-mail plug-ins and insulate the user from changes to other desktop applications.

These minor pyrimidines are usually methylated versions of major ones and are postulated to have regulatory functions.

These versions of predestination hold that individual choice is not excluded from the fashioning work of the Creator.

These are made as extremely thin ( 2 – 3 mm ) versions of the popular French fry, but are fried in the manner of regular salted potato chips.