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 collective societal welfare is improved, but the providers have no way of monetizing the benefit, less of the good will be produced than would be optimal for society as a whole.

Since the search space is large, this process will produce a “ sufficient ” rather than “ globally optimal ” solution.

Since the ultimate fate of the propellant is not a concern, the fastest possible burn is usually the optimal procedure.

Since the head can move in a vastly varied number of ways, it is not possible to search for all possible candidates ; nor is there right now an algorithm that provides a globally optimal solution independent of the first transformations we try in a chain.

Since the optimal survival conditions for this life-form ( low-temperature vacuum ) are drastically different from those needed by humans ( room temperature aerial atmosphere and adequate water supply ), Lilly predicted ( or " prophesised ", based on his ketamine-induced visions ) a dramatic conflict between the two forms of intelligence.

For example, if city A and city B are next to each other, while city C is farther away, the total distance traveled will be shorter if cities A and B are visited one after the other before visiting city C. Since finding an optimal solution to the TSP is an NP-hard task, heuristic-based approximation methods ( such as local searches ) are useful for devising close-to-optimal solutions.

Since the normative, optimal decision often creates hypotheses for testing against actual behaviour, the two fields are closely linked.

Since hydrogen density is a desirable characteristic for hypothetical lunar bases, this information may be useful in choosing optimal sites for possible long-term Moon missions.

Since most of the variables will be non-basic and assume a value of zero in the optimal solution, only a subset of variables need to be considered in theory when solving the problem.

Since this decision has no obvious correct answer, the optimal answer depends on the needs of the customer.

Since a query may return all intervals, for example if the query is a large interval intersecting all intervals in the collection, this is asymptotically optimal ; however, we can do better by considering output-sensitive algorithms, where the runtime is expressed in terms of m, the number of intervals produced by the query.

Since the campus is located at an optimal height above the Yilan plain, the view at night is even more stunning, making it the best holiday leisure spot of choice for Yilan area residents.

Since tires are rated for specific loads at certain pressure, it is important to keep the pressure of the tire at the optimal amount.

Since the brain doesn't necessarily perceive distinctions in each channel to the same degree as in other channels, it is possible that differing the number of bits allocated to each channel will result in more optimal storage ; in particular, for RGB images, compressing the blue channel the most and the red channel the least may be better than giving equal space to each.

Since the optimal mix of input levels depends on the wage and rental rates, these rates are also arguments of the conditional demand functions for the inputs.

Since the optimal update attenuation in both space and time is about two, the result is a periodic proactive update, with fractal power-of-two node hop distances for the data ( e. g. hop distances of 1, 2, 1, 4, 1, 2, 1, 8 ...).

Since later television designs include composite, S-Video, and component video jacks, which skip the modulation and demodulation steps, modulators are no longer included as standard equipment, and RF modulators are now largely a third-party product, purchased primarily to run newer equipment such as DVD players with an old television set.

Since I have already discussed his moral position, that discussion is incorporated by reference into the following pages, which will focus on the empirical and analytic side of Fromm's treatment.

" Since there was already a " Jim " on the show, the manager began calling him " Bob.

Since we already deduced that NP is a subset of co-NP it follows that they are the same.

Since copper metallurgy was already known to have existed in Europe since 7000 BC, with heavy axes of natural bronze produced in bulk since 5500 BC, and since true bronze, made by deliberately alloying copper with tin had already been used in parts of east-central Europe since 3700 BC, Ötzi's axe came as no surprise to archaeologists.

Since there are many stars older than the Sun, or since intelligent life might have evolved earlier elsewhere, the question then becomes why the galaxy has not been colonized already.

Since there was already an existing road between Mabura and Kurupukari, and between Annai and Lethem, it was now possible for vehicles to travel between Georgetown and Lethem.

Since the document was signed by Plotina, it has been suggested that Trajan may have already been dead.

Since their games were text-based, patrons of bookstores were drawn to the Infocom games as they were already interested in reading.

Since the content has already been produced, the station merely adds the low-cost on-air programming between records.

Since DuMont already owned three stations, the FCC did not allow DuMont to buy any more stations as long as Paramount owned a portion of DuMont.

Since his predecessor Meinfried had already accepted Christianity, it followed that Pribislav had already been baptized in childhood, in contrast to the ideas of medieval chroniclers that the prince had first been baptized as an adult.

" Since any sequel to the original Quake had already been refused, it became a viable way of continuing the series without actually continuing the storyline or setting of the first game.

Since we have already proved what the volume is, we can substitute V:

Since he was eleven years her elder, already married, and a Buddhist, May-ling's mother vehemently opposed the marriage between the two, but finally agreed after Chiang showed proof of his divorce and promised to convert to Christianity.

Since Hume had already made many of the same " moral attacks upon Christianity " that Paine popularized in The Age of Reason, scholars have concluded that Paine probably read Hume's works on religion or had at least heard about them through the Joseph Johnson circle.

Since none have been proven to exist already then the drive is impossible to construct, even if the metric is physically meaningful.

Since Pope Clement VII had already rejected Henry's petition for annulment in 1530, Catherine continues to believe herself Henry's wife until her death.

Since the essential requirements for cave life were probably already present prior to the settlement of these habitats, this may be described as exaptation.

The naval staff hoped to gain a success to influence postwar budget debates ... Since Raeder had already discussed with Hitler on 20 May the possibility of invading Britain, such a waste of German naval strength off the North Cape counts as one of the most egregious naval misjudgements of the war.

Since the name Marakanda was already in existence 2300 years ago and long before anyone had heard of Turks in that region of Transoxiana, this version is likely a folk etymology.

Since antitoxin does not neutralize toxin that is already bound to tissues, delaying its administration is associated with an increase in mortality risk.

At another point, Lazarus offers to recount the fate of the Jockaira, from Methuselah's Children, but another character cuts him off, saying, " Since that lie is already in his memoirs in four conflicting versions, why should we be burdened with a fifth?

Since Prittwitz had already ordered the German troops to pull back via train, Ludendorff directed I Corps to alight near Deutsch-Eylau to cover the left flank of XX Corps, who had been in front of the Second Army since before the battle at Gumbinnen.