Although Zermelo's fix allows a class to describe arbitrary ( possibly " large ") entities, these predicates of the meta-language may have no formal existence ( i. e., as a set ) within the theory.

Although there are computational methods that can be used to estimate the behavior of a mixture of arbitrary components, the only way to obtain accurate vapor-liquid equilibrium data is by measurement.

Although the Fortune Deck works as a randomizer, the results obtained by it are entirely arbitrary and subjective, and the GM's absolute power over the game is further emphasized by the three resolution systems: Karma ( the higher character ability wins, modified by situation ), Drama ( the GM decides what happens, by what they think most appropriate ), and Fortune ( more or less the same as the above, with interpretation flavored by a card draw ).

Although three subspecies have been described, these are arbitrary selections from a cline and are not generally accepted as valid.

Although the TPM can only store a single cryptographic key securely, secure storage of arbitrary data is by extension possible by encrypting the data such that it may only be decrypted using the securely stored key.

Although iSCSI can communicate with arbitrary types of SCSI devices, system administrators almost always use it to allow server computers ( such as database servers ) to access disk volumes on storage arrays.

Although it is well known that the usual choice in logic of AND, OR and NOT is somewhat arbitrary, Codd made a similar arbitrary choice for his algebra.

Although analytical solutions to this problem are scarce, there are upper and lower bounds to these functions including the famous Shannon lower bound ( SLB ), which in the case of squared error and memoryless sources, states that for arbitrary sources with finite differential entropy,

Although the difference between more than one sequel and a series is somewhat arbitrary, it is clear that some media franchises have enough sequels to become a series, whether originally planned as such or not.

Although sophisticated analogue waveshaping is possible, the greater simplicity and arbitrary waveforms of digital systems like direct digital synthesis led to most later instruments adopting entirely digital oscillator designs.

Although the labeling may be quite arbitrary, temperature is just such a labeling process which uses the real number system for tagging.

Although it would be scientifically expedient to raise children under arbitrary experimental conditions, such as on a remote island with a fabricated enculturation, it is obviously a violation of ethics and human rights.

Although the programme is in its early days, it also offers the prospect of avoiding some of the problems that have plagued other European procurement collaborations, without arbitrary workshare divisions and with a clear project leadership role to be provided by the UK.

Although an arbitrary polynomial with rational or real coefficients may not have distinct roots, it is natural to ask at this stage whether or not there exists an irreducible polynomial with rational or real coefficients that does not have distinct roots.

" Although this is a time when art is more individual and arbitrary than ever, it would be a mistake to call it anarchic.

Although it was possible to represent equations of an arbitrary degree ( he once treated the 1458th degree ) with negative coefficients, there were no symbols corresponding to parentheses, equality, or division.

Although the theft often seems arbitrary, signs that are unusual or amusing tend to be stolen more frequently.

Although appearing to make rather arbitrary use of language, a distinction is often made between orchestration ( a local view from the perspective of one participant ) and choreography ( coordination from a global multi-participant perspective, albeit without a central controller ).

Although the attacker could make the code return anywhere, is the most likely target, as it is always linked to the program, and it provides useful calls for an attacker ( such as the call to execute an arbitrary program, which needs only one argument ).

Although Polk protested the " arbitrary and unlawful order " to the Secretary of War and demanded a court of inquiry, he was not restored to his position and Davis once again retained Bragg in army command, despite the protestations of a number of his subordinate generals.

Although wrongful dismissal is usually associated with lack of notice sometimes it can also be caused by arbitrary dismissal where no notice was required but certain grounds were specified in the contract as being the only ones available but none existed.

Although at first the choice of the solution to this regularized problem may look artificial, and indeed the matrix seems rather arbitrary, the process can be justified from a Bayesian point of view.

Although TDM can be used to carry arbitrary bit streams at the rates defined in G. 702, there are standardized methods of carrying bit streams in larger units each containing the same number of bits, called frames.

Although the Copenhagen interpretation is often confused with the idea that consciousness causes collapse, it defines an " observer " merely as that which collapses the wave function.

Although several versions of many-worlds have been proposed since Hugh Everett's original work, they all contain one key idea: the equations of physics that model the time evolution of systems without embedded observers are sufficient for modelling systems which do contain observers ; in particular there is no observation-triggered wave function collapse which the Copenhagen interpretation proposes.

Although the campaign was largely unsuccessful, it created a wave of new followers, and some of Baba ’ s views found their way into academic debate on the merits and dangers of hallucinogens.

Although the saucer section was safely separated before the breach, the shock wave from the exploding engineering hull threw it out of control, and caused it to crash land on Veridian III.

Although much of the earlier Undertones material drew influence from punk rock and new wave, the Undertones also incorporated elements of rock, glam rock and post-punk into material released after 1979, before citing soul and Motown as the influence for the material released upon their final album.

Although the meanings of " tidal " include " resembling " or " having the form or character of " the tides, and the term tsunami is no more accurate because tsunami are not limited to harbours, use of the term tidal wave is discouraged by geologists and oceanographers.

Although the principle is more visually intuitive in the wave mechanics formalism, it was first derived and is more easily generalized in the matrix mechanics formalism.

Although this picture is somewhat simplified ( to the non-relativistic case ), it is adequate to capture the essence of current thinking on the phenomena historically called " wave – particle duality ".

Although there is still debate as to whether one should accept the field as " real ", the debate over using the term wave or particle is rendered meaningless.

Although it is difficult to draw a line separating wave – particle duality from the rest of quantum mechanics, it is nevertheless possible to list some applications of this basic idea.

Although the above statements are meaningless in the case of waves that do not require a medium, they reveal a characteristic that is relevant to all waves regardless of origin: within a wave, the phase of a vibration ( that is, its position within the vibration cycle ) is different for adjacent points in space because the vibration reaches these points at different times.

Although physical modelling was not a new concept in acoustics and synthesis, having been implemented using finite difference approximations of the wave equation by Hiller and Ruiz in 1971, it was not until the development of the Karplus-Strong algorithm, the subsequent refinement and generalization of the algorithm into the extremely efficient digital waveguide synthesis by Julius O. Smith III and others, and the increase in DSP power in the late 1980s that commercial implementations became feasible.

Although for Z > 137, the wave function of the Dirac ground state is oscillatory, rather than bound, and there is no gap between the positive and negative energy spectra, as in the Klein paradox, more accurate calculations taking into account the effects of the finite size of the nucleus indicate that the binding energy first exceeds 2mc < sup > 2 </ sup > for Z > Z < sub > cr </ sub > ≈ 173.

Although, the people who created the first wave in Seattle acknowledge Crazy George's wave at a baseball stadium, they claim to have popularized the phenomenon, since Crazy George's wave was a one time event.

Although Foo Fighters continued to be one of the most successful rock acts, with albums like In Your Honor ( 2005 ) reaching number two in the US and UK, many of the first wave of post-grunge bands began to fade in popularity.

Although trenches would seem to be positionally stable over time, it is hypothesized that some trenches, particularly those associated with subduction zones where two oceanic plates converge, retrograde, that is, they move backward into the plate which is subducting, akin to a backward-moving wave.

Although the Berbers are the most probable ancestors of the Guanches, it is deduced that important human movements ( e. g., the Islamic-Arabic conquest of the Berbers ) have reshaped Northwest Africa after the migratory wave to the Canary Islands " and the " results support, from a maternal perspective, the supposition that since the end of the 16th century, at least, two-thirds of the Canarian population had an indigenous substrate, as was previously inferred from historical and anthropological data.

Although they tried frantically to swim against the tidal wave they were powerless to do so and were drowned.

Although closely associated with classic rock in its later years, the King Biscuit Flower Hour dedicated much air time to new and emerging artists, including new wave and modern rock artists in the late 1970s and early 1980s.

Although more complex arrangements are used, the most common clock signal is in the form of a square wave with a 50 % duty cycle, usually with a fixed, constant frequency.

Although the first wave arrived in May from California, news of the rush eventually attracted many Chinese from China itself.