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 Heisenberg principle limits the precision of any measurement of the combination of an electron's momentum ( related to energy ) and its position, in a crystal effectively the available energy levels form a continuous band of allowed energy levels.

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 a national interpretation cannot be avoided it is unfortunate that the elections were not held in a way to maximize party responsibility and the educational effect of mass political participation.

The number of neutrons, N, is known as the neutron number of the atom ; thus, A = Z + N. Since protons and neutrons have approximately the same mass ( and the mass of the electrons is negligible for many purposes ), and the mass defect is usually very small compared to the mass, the atomic mass of an atom is roughly equal to A.

Since conference and of the Food and Agriculture Organization's publication World Festival of Trees, and a resolution of the United Nations in 1954: " The Conference, recognising the need of arousing mass consciousness of the aesthetic, physical and economic value of trees, recommends a World Festival of Trees to be celebrated annually in each member country on a date suited to local conditions "; it has been adopted by the Netherlands.

Since then, there have been many refinements to increase the field of view, mass and position resolution, and data acquisition rate of the instrument.

Since the publication of Nineteen Eighty-Four, the term " Big Brother " has entered the lexicon as a synonym for abuse of government power, particularly in respect to civil liberties, often specifically related to mass surveillance.

Since the mass numbers of these are 12, 13 and 14 respectively, the three isotopes of carbon are known as carbon-12, carbon-13, and carbon-14, often abbreviated to < sup > 12 </ sup > C, < sup > 13 </ sup > C, and < sup > 14 </ sup > C.

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since life began on Earth, several major mass extinctions have significantly exceeded the background extinction rate.

The event temporarily warmed air temperature by 1. 5 ° C, compared to the usual increase of 0. 25 ° C associated with El Niño events .< ref name =" Trenberth "> Since then, mass coral bleaching has become common worldwide, with all regions having suffered " severe bleaching ".

Since this gas is in approximate hydrostatic equilibrium with the overall cluster gravitational field, the total mass distribution can be determined.

Since the 1920s this discrepancy has been explained by the presence of isotopes ; the atomic mass of any isotope is very close to satisfying the whole number rule, with the mass defect caused by differing binding energies being significantly smaller.

Since then, Labour Day has been not only a public holiday but also a day of mass community involvement around the country.

Since 1889, the kilogram has been defined as the mass of the international prototype kilogram, and as such is independent of the meter, or the properties of water.

* The atomic mass unit ( u ) is defined so that a single carbon-12 atom has a mass of 12 u ; 1 u is approximately .< ref group =" note "> Since the Avogadro constant N < sub > A </ sub > is defined as the number of atoms in 12 g of carbon-12, it follows that 1 u is exactly 1 /( 10 < sup > 3 </ sup > N < sub > A </ sub >) kg .</ ref > The atomic mass unit is convenient for expressing the masses of atoms and molecules.

Since energy is dependent on reference frame ( upon the observer ) it is convenient to formulate the equations of physics in a way such that mass values are invariant ( do not change ) between observers, and so the equations are independent of the observer.

Since gravitational effects are all around us, it is impossible to pin down the exact date when humans first discovered gravitational mass.

Since the particle speed < math > v < c </ math > for any particle that has mass ( according to special relativity ), the phase velocity of matter waves always exceeds c, i. e.

Since a walrus's hide usually accounts for about 20 % of its body weight, the total body mass of these two giants is estimated to have been at least.