[permalink] [id link]
While Maxwell's equations are consistent within special and general relativity, there are some quantum mechanical situations in which Maxwell's equations are significantly inaccurate: including extremely strong fields ( see Euler – Heisenberg Lagrangian ) and extremely short distances ( see vacuum polarization ).
from
Wikipedia
Some Related Sentences
While and Maxwell's
While his crystals were growing, Rabi read James Clerk Maxwell's 1873 A Treatise on Electricity and Magnetism, which inspired an easier method.
While special relativity showed that Maxwell's equations do not require the aether, there were some early modern aether theories.
While and equations
While individual equations present a kind of puzzle and have been considered throughout history, the formulation of general theories of Diophantine equations ( beyond the theory of quadratic forms ) was an achievement of the twentieth century.
While they arise quite naturally when modeling many phenomena, they are particularly useful since many non-linear equations may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some " background " state.
While studying these languages, Abel published his first notable work in 1824, Mémoire sur les équations algébriques où on démontre l ' impossibilité de la résolution de l ' équation générale du cinquième degré ( Memoir on algebraic equations, in which the impossibility of solving the general equation of the fifth degree is proven ).
While linear, this equation has a more complex form than the equations given above, as it must account for both longitudinal and transverse motion:
While he was directed by George Birkhoff to work on differential equations, his interests continued to shift to logic.
While these result in some contradictions and lack completeness in a mathematical sense ( being based on axioms that are " merely " self-evident, but not robust under the stresses of radical scepticism ), the paradoxes can nonetheless be analysed rationally using the subatomic applications of quantum cosmology-particularly through the employment of the Schrödinger wave equations.
While de Broglie – Bohm theory has Lagrangians and Hamilton-Jacobi equations as a primary focus and backdrop, with the icon of the quantum potential, Bohmian mechanics considers the continuity equation as primary and has the guiding equation as its icon.
While time value of money can be understood without using the framework of differential equations, the added sophistication sheds additional light on time value, and provides a simple introduction before considering more complicated and less familiar situations.
While still a student, Ambartsumian thoroughly studied the theory of atomic structure, the formation of energy levels, and the Schrödinger equation and its properties, and when he mastered the theory of eigenvalues of differential equations, he pointed out the apparent analogy between discrete energy levels and the eigenvalues of differential equations.
While not seriously advocated after Einstein's development of relativity, Newtonian gravity can be used to model the universe and non-rigorously derive the Friedmann equations that are used in the big bang universe.
While explicit solutions can be found for equations that are quadratic, cubic, and quartic in y, the same is not in general true for quintic and higher degree equations, such as
While still a student Hambardzumyan was very much interested in quantum physics, and thoroughly studied the theory of atomic structure, the formation of energy levels, and Schroedinger's equation and its properties, and when he mastered the theory of eigenvalues of differential equations, he pointed out the apparent analogy between discrete energy levels and the eigenvalues of differential equations.
While usually not included in the above definition of a constraint satisfaction problem, arithmetic equations and inequalities bound the values of the variables they contain and can therefore be considered a form of constraints.
While homogeneous equations are relatively easy to solve, this method allows the calculation of the coefficients of the general solution of the inhomogeneous equation, and thus the complete general solution of the inhomogeneous equation can be determined.
While there they discovered techniques to study the clearance of particulate matter from the blood by the RES ( reticuloendothelial system ), and devised equations that govern this process in mammals.
While a set of equations, known as the Liouville equations, exists to determine the initial uncertainty in the model initialization, the equations are too complex to run in real-time, even with the use of supercomputers.
While and are
While white is the coolest summer shade, there are lots of pastel hues along with tintable fabrics that will blend with any wardrobe color.
While it is easy enough to ridicule Hawkins' pronouncement in Pleas Of The Crown from a metaphysical point of view, the concept of the `` oneness '' of a married couple may reflect an abiding belief that the communion between husband and wife is such that their actions are not always to be regarded by the criminal law as if there were no marriage.
While there are now allegations of the withholding of `` favorable evidence developed at the hearing '' and a denial of a `` full and fair hearing '', no such claim was made by petitioner at any stage of the administrative process.
While 2-year-olds are still gaining most of the attention at the track, green horses are starting to go a bit, and Jimmy Cruise has several that can really make it.
While individual sportsmen are aware of this situation, too many of our political, social, educational and even religious leaders too often forget it.
While some suppression and some denial are not only necessary but healthy, the worker's clinical knowledge must determine how these defenses are being used, what healthy shifts in defensive adaptation are indicated, and when efforts at bringing about change can be most effectively timed.
While there are many different possibilities for the timing of casework intervention, the experiments recently reported from a variety of traditional settings all point up the importance of an immediate response to the client's initial need for help.
While the interpretations that have been given are inferences only, they gain support from such comments as the following, which was made by one of the Kohnstamm-negative subjects who did not, on the first trial, perceive the tilt illusion.
While this influence is a complex matter, depending upon personality factors in the individual as well as upon his social-class experience, there probably are some general statements about social-class background and educational policy that can be made with a fair degree of truth.
While costs on this order are sometimes separately charged for in residential and commercial rates, in the form of a mere `` service charge '', they are more frequently wholly or partly covered by a minimum charge which entitles the consumer to a very small amount of gas or electricity with no further payment.
While ATP appears to be necessary for the occurrence of contraction, its presence and enzymatic hydrolysis of it by the muscle protein myosin are not the only criteria for contraction.
While there are still many bugs to be ironed out, the technique is fast developing.
While nowadays we recognize the fact that there are many causes for bleeding at the nose, not long ago a nosebleed was simply that, and treatment had little variation.
Many years later ( on August 3, 1915 ), Lucy Upton wrote Winslow's daughter soon to be graduated from Smith College: `` While I love botany which, after dabbling in for years, I studied according to the methods of that day exactly forty years ago in a summer school, it must be fascinating to take up zoology in the way you are doing.
While patent suits are still among the most complex and expensive forms of litigation, these rules have saved litigants uncounted sums of money.
While details are still to be worked out, Ratcliff said he expects to tell home folks in Dallas why he thinks Berry's proposed constitutional amendment should be rejected.
While availability of mortgage money has been a factor in encouraging apartment construction, the generally high level of prosperity in the past few years plus rising consumer income are among the factors that have encouraged builders to concentrate in the apartment-building field.
While it must be said that these same Protestants have built some new churches during this period, and that religious population shifts have emptied churches, a principal reason for this phenomenon of redundancy is that fewer Protestants are going to church.
While we are filling outer space with scientific successes, for many the `` inner '' space of their soul is an aching void.
While there is general agreement on these six families, there are some points of disagreement among linguists who study Afroasiatic.
While most alphabets have letters composed of lines ( linear writing ), there are also exceptions such as the alphabets used in Braille, fingerspelling, and Morse code.
While and consistent
While ratings for Coronation Street remained consistent throughout the decade, EastEnders regularly obtained higher viewing figures.
While the transcription of the Chinese words used by Ricci was not very consistent, he systematically used Latin p and t for unaspirated Chinese sounds that Pinyin renders as b and d. Accordingly, Ricci called the adherents of Laozi, Tausu (, Pinyin: Daoshi ), which was rendered as Tausa in an early English translation published by Samuel Purchas ( 1625 ).
While the stories depict a lack of intelligence in many of the individuals, they do not arise from any consistent genetic differences between them and the rest of humankind.
While there are alleged non-physical differences between men and women, major reviews of the academic literature on gender difference find only a tiny minority of characteristics where there are consistent psychological differences between men and women, and these relate directly to experiences grounded in biological difference.
While accounts of the return journey are not entirely consistent, Allen apparently suffered an apoplectic fit en route, and was unconscious by the time they returned home.
While the following conditions ( representing the expected situation ) are consistent with the three formulae above, they are not the only ones.
While many find it unlikely that both epics were composed by the same person, others argue that the stylistic similarities are too consistent to support the theory of multiple authorship.
While other ancient powers such as the Carthaginians maintained a patchwork of force types, and the legions retained such phalanx-style holdovers like the triarri, Marius implemented one consistent standardised approach for all the infantry.
While details of macroevolution are continuously studied by the scientific community, the overall theory behind macroevolution ( i. e. common descent ) has been overwhelmingly consistent with empirical data.
While Jacqueline Kennedy had also faced some press criticism for her spending habits, Reagan's treatment was much more consistent and negative.
While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we can observe only the universe ( i. e., the consistent state contribution to the aforementioned superposition ) that we, as observers, inhabit.
While confirming that quantum mechanics and gravity are indeed consistent at reasonable energies, it is clear that near or above the fundamental cutoff of our effective quantum theory of gravity ( the cutoff is generally assumed to be of the order of the Planck scale ), a new model of nature will be needed.
While sociobiology is predicated on the observation that genes do affect behavior, it is perfectly consistent to be a sociobiologist while arguing that measured IQ variations between individuals reflect mainly cultural or economic rather than genetic factors.
While dryland ( non-irrigated ) cotton is successfully grown in this region, consistent yields are only produced with heavy reliance on irrigation water drawn from the Ogallala Aquifer.
While some historic home museums are fortunate to possess a collection containing many of the original furnishings once present in the home, many face the challenge of displaying a collection consistent with the historical structure.
While most astronomical transient sources have simple and consistent time structures ( typically a rapid brightening followed by gradual fading, as in a nova or supernova ), the light curves of gamma-ray bursts are extremely diverse and complex.
While average highs are somewhat consistent throughout the year, average lows dip to in July.
While beginners sometimes assume that the dealer ( sometimes called the " Chairman ", the " Mao " or the " Grand Master ") and other experienced players are simply making up possibly inconsistent rules ( as in the game Mornington Crescent ), the rules of Mao are consistent within each game and can be followed correctly.
While most historians consider the low English casualty figures to be improbably low, Rogers has argued that they are consistent with reports of casualties on the winning side in other medieval battles.
While features of some stromatolites are suggestive of biological activity, others possess features that are more consistent with abiotic ( non-organic ) precipitation.
While depictions of the dragon in art and literature are largely consistent throughout the cultures in which it is found, there are some regional differences.
While Robby's appearance was generally consistent, there were notable exceptions, such as Twilight Zone episode " Uncle Simon " ( 1962 ), where he was given a slightly more human " face ".
While reorganization discussions had occurred earlier, software limitations prevented the adoption of a consistent organizational scheme.
While some researchers believe that Alpers ' disease is caused by an underlying mitochondrial metabolic defect of POLG, no consistent defect has been identified.
0.366 seconds.