Since the Fourier coefficients of the product of two quantities is the convolution of the Fourier coefficients of each one separately, the correspondence with Fourier series allowed Heisenberg to deduce the rule by which

Since by the principle of optimality the remaining stages use an optimal Af-stage policy with respect to Af, we may enter section Af of the table at this state Af and read off the optimal policy for stage Af and the resulting state Af.

Since esterification is highly reversible, the yield of the ester can be improved using Le Chatelier's principle:

Since its first publication in 1946 the principle has been accepted by Germany's Federal Constitutional Court in a variety of cases.

Since air is an insulator, in principle no other substance is needed to keep power where it should be.

Since the flow speed is zero at these points, by Bernoulli's principle the static pressure at these points is at a maximum.

Since bundle theory states that all concrete particulars are merely constructions or ' bundles ' of attributes, or qualitive properties, the substance theorist's indiscernibility argument claims that the ability to recognize numerically different concrete particulars, such as concrete objects, requires those particulars to have discernible qualitative differences in their attributes and that the metaphysical realist who is also a bundle theorist must therefore concede to the existence of ' discernible ( numerically different ) concrete particulars ', the ' identity of indiscernibles ', and a ' principle of constituent identity '.

Since the early 1990s, the legitimatization of the principle of national self-determination has led to an increase in the number of conflicts within states, as sub-groups seek greater self-determination and even full secession, and as their conflicts for leadership within groups and with other groups and with the dominant state become violent.

Since this principle is a key premise in deriving the Liar paradox, the paradox is dissolved.

Since these are unknown in exact detail, cosmological models have been based on the cosmological principle, which states that the universe is homogeneous and isotropic.

Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it.

Since it is absurd to have no logical method by which to settle on one hypothesis amongst an infinite number of equally data-compliant hypotheses, we should choose the simplest theory: " either science is irrational the way it judges theories and predictions probable or the principle of simplicity is a fundamental synthetic a priori truth " ( Swinburne 1997 ).

Since the Pauli exclusion principle forbids electrons from occupying the same state, any additional electron would be forced to occupy a positive-energy eigenstate, and positive-energy electrons would be forbidden from decaying into negative-energy eigenstates.

Since temperature in principle also depends on altitude, one needs a second equation to determine the pressure as a function of height, as discussed in the next section.

Since then a number of exceptions to this principle have been allowed.

The transfer principle states that true first order statements about R are also valid in * R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals ; since R is a real closed field, so is * R. Since for all integers n, one also has for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś ' theorem of 1955.

Since only the level spacing is determined by the correspondence principle, you could always add a small fixed offset to the quantum number --- L could just as well have been.

Since independence in 1971, the country has stressed its principle of friendship towards all, malice towards none in dictating its diplomacy.

Since the travel of the motion system is limited, a principle called ' acceleration onset cueing ' is used.

Since this new field concerns abstract rules, it can in principle address issues relevant to other fields of science.

) Since 1662 in Virginia, children born to enslaved mothers took their legal status as slaves under the principle of partus sequitur ventrem.

Since each queen can be placed in any of the 64 squares, in principle there are 64 < sup > 8 </ sup > = 281, 474, 976, 710, 656 possibilities to consider.

Since the Middle Ages, the semi-Salic principle was prevalent for the inheritance of feudal land in the Holy Roman Empire: inheritance was allowed through females when the male line expired.

Since the F – D distribution was derived using the Pauli exclusion principle, which allows at most one electron to occupy each possible state, a result is that < math > 0 <

Since the Amiga's hardware was more or less fixed ( unlike today's PC industry, where arbitrary combinations of hardware can be put together ), there was competition to test the limits of that hardware and perform theoretically " impossible " feats by refactoring the problem at hand.

Since many common constructions in mathematics are limits or colimits, this provides a wealth of information.

Terminal objects in a category C may also be defined as limits of the unique empty diagram ∅ → C. Since the empty category is vacuously a discrete category, a terminal object can be thought of as an empty product ( a product is indeed the limit of the discrete diagram

Since Montmartre was outside the city limits, free of Paris taxes and no doubt also due to the fact that the local nuns made wine, the hill quickly became a popular drinking area.

Since pre-abelian categories have all finite products and coproducts ( the biproducts ) and all binary equalisers and coequalisers ( as just described ), then by a general theorem of category theory, they have all finite limits and colimits.

Since Wyatt was an off-duty officer, he could not legally search or arrest Tom for carrying a revolver within the city limits -— a misdemeanor offense.

Since they have been introduced, speed limits have been opposed from various sources ; including motoring advocacy groups, anti-motoring groups and others who either consider them to be irrelevant, set too low or set too high.

Since its initial discovery in 1958, the southern limits of the SAA have remained roughly constant while a long-term expansion has been measured to the northwest, the north, the northeast, and the east.

Since the 1970s, in vitro fertilization has made pregnancy possible at ages well beyond " natural " limits, generating ethical controversy and forcing significant changes in the social meaning of motherhood.

Since being incorporated, Lake Forest has expanded its limits to include the communities of Foothill Ranch and Portola Hills.

Since 1994, five new subdivisions have been added to nearly complete the development of all the land within the city limits.

Since the inception of the Federal Highway system in 1926, both routes have gone through the city limits, first using surface streets and now a four-lane highway directly west of the downtown business district.

Since then, Catlettsburg Elementary is the only school within the city limits, and uses the campus of the former high school / jr. high school at 3380 Court Street.

Since then its limits have been greatly reduced.

Since formation by village trustees in 2006, the Department has been subject to corruption as well as using unlicensed officers on patrol which lead to a pursuit initiated by an unlicensed officer that carried into the city limits of Saint Louis and killed a mother of 4.

Since US 74 does not pass through any business or residential areas, its speed limit is 55 MPH even within the city limits.

Since 2004, however, the City of Ranson has annexed approximately of land into the corporate limits, expanding the total land area of the City to approximately.

Since the closing of Ceredo-Kenova and Buffalo-Wayne High Schools in 1998, Kenova Elementary is the lone public education facility within Kenova city limits.

Since this required three hours to be " off limits " to programs aimed at the general public, the networks naturally chose to air them on Saturday morning, when children were already watching.

Since exoskeletons are rigid, they present some limits to growth.

Since the victory of Law or Chaos would cause the Multiverse either to become permanently static or totally formless, the Cosmic Balance enforces certain limits which the powers of Law and Chaos violate at their peril.

Since the one-sided limits are different, the two-sided limit does not exist in the standard framework of the real numbers.

Since an open differential limits total torque applied to both drive wheels to the amount utilized by the lower traction wheel multiplied by a factor of 2, when one wheel is on a slippery surface, the total torque applied to the driving wheels may be lower than the minimum torque required for vehicle propulsion.

Since the onset of knock is sensitive to the in-cylinder pressure, temperature and autoignition chemistry associated with the local mixture compositions within the combustion chamber, simulations which account for all of these aspects have thus proven most effective in determining knock operating limits and enabling engineers to determine the most appropriate operating strategy.