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 electromagnetism was known to be a wave generated by a changing electric or magnetic field ( a continuous, wave-like entity itself ) an atomic / particle description of electricity and charge was a non sequitur.

Since rocket delta-v has a non linear relationship to mass fraction due to the rocket equation, any small reduction in delta-v gives a relatively large reduction in the required mass fraction ; and starting a mission at higher altitude also helps.

Since then, it has become the series regular opening round in February and a non championship event in December and has also hosted a round of the domestic series, Formula D. The venue has been expanded to accommodate 15, 000 spectators.

Since its foundation the PLD had maintained an implicit non re-election policy, but President Fernández changed that allowing him to campaign against Medina from the Presidential Palace and opt for a second consecutive term in power ( his third ).

Since the first non arena league ( Professional Indoor Football League ) began in the late 1980s, there has often been a pattern of instability.

Since 1 January 2008, foreign women – including asylum applicants, non permanent residents, and those not registered in Sweden – are allowed abortion in the country.

Since 1993 the official Vatican yearbook, the Annuario Pontificio, has included an asterisk behind the title of those nuncios " che ( per ora ) non sono Decani del Corpo Diplomatico " -- " who ( for now ) are not deans of the diplomatic corps.

Since the government is a non profit organization, it was not proper to use mandatory student fees to fund a public political campaign.

Since leaving Parliament, Alston has served as a non executive director of Australian public listed companies Hansen Technologies and Broadcasting Services Australia ( Chairman ).

Since opening complaints have arisen from the public regarding limited choice of books, frequently failing public service machines and spending on non essential peripherals.

Since is non zero ( because is distinct to 1 ), the x-coordinate of is and the y-coordinate of is, i. e., or in projective coordinates.

Since 1944 he has also conducted regularly at the San Francisco Opera, where he made his debut with a memorable performance of Verdi's Falstaff.

Since 1954 the Negro's desire for social justice has led to an ironically anarchical rebellion.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

Since 1953 California has led the nation in enacting guarantees that public business shall be publicly conducted, but not until this year did the lawmakers in Sacramento plug the remaining loopholes in the Brown Act.

Since little is known about autism, and almost nothing has been written for the layman, we'd like to share one experienced mother's comments.

Since it was issued in the spring of 1611, the King James Version has been most generally considered the most poetic and beautiful of all translations of the Bible.

Since the Connally amendment has the effect of giving the same right to the other party to a dispute with the United States, it also prevents us from using the court effectively.

Since he has just shown who is top dog, he may not be ready to receive this highest honor in the gift of the Soviet people.

Since then nothing has happened to save the life of Pope.

Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.

Since then, there has been a notable increase in the number of stations and also the accumulation of additional data and the development of new techniques for using it, leading to a better understanding of propagation phenomena.

Since the Industrial Revolution, when factories emerged, this classical pattern has been followed.

Since Af are linearly independent functions and the exponential function has no zeros, these R functions Af, form a basis for the space of solutions.

Since C is rational, this correspondence has K coincidences, each of which implies a line of the pencil which meets its image.

Since the course, one member has lost her husband.

Since her bereavement this individual has reported to the writer on numerous occasions about how helpful the class discussions were to her in this adjustment crisis.

Since on the one hand school desegregation has come in Virginia hand-in-glove with pupil assignment, shall we support the plan??

Since this book is concerned only incidentally with railroad rates, it will not attempt to analyze the methods by which the staff of the Interstate Commerce Commission has estimated out-of-pocket costs and apportioned residue costs.

Since that time the telegraph office has shifted in location from the railroad station at the Depot and shops at the Center back to the town clerk's office and drugstore at the Village.

Since 1948 the working headquarters has been the Department of Geology and Mineralogy.

Since the removal force is a function of coating thickness, a differential transformer pickup has been incorporated into the instrument to accurately measure film thickness.

Since the mid 1950s, when urethane foam first made its appearance in the American market, growth has been little short of fantastic.

Since interviewing is the basic therapeutic and diagnostic instrument of modern psychiatry, the recording of interviews for playbacks and study has been a boost of Redstone proportions in new research and training.

Since 1949, the St. Louis club has been below on May 1 just four times.

Since 1927, fewer than a dozen men have made serious runs at Babe Ruth's record and each, in turn, has been thwarted.