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Thus if a baserunner running from third base crosses home plate with two out before a batter is put out on a ground out or before a fly ball is caught after two outs, then the run that would otherwise score is null ; likewise, if a conventional double play is made with one out on a ground ball involving forces at other bases, the run that would otherwise score before the third out is registered is void.
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Thus and if
Thus, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.
Thus Af if and only if Af.
Thus F satisfies Af if and only if F has the form Af.
Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.
Thus, if public pressure sets the effective limit to the price that the industry may charge, this pressure is itself a function of the wage rate.
Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.
Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.
Thus, if one accelerometer is properly aligned, the other is also.
Thus, if we are to observe American folklore in the twentieth century, we will do well to establish the relationships between folklore, nationalism and imperialism at the outset.
Thus, red wine must, if possible, never be disturbed or shaken ; ;
Thus, if what is at issue is whether `` All S is P '', it is indifferent whether `` Some S is not P '' or `` No S is P '', since in either case the judgment in question is false.
Thus most Affidavits now require to be Apostilled if used for cross border issues.
For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.
Thus throwing a rock at someone for the purpose of hitting him is a battery if the rock in fact strikes the person and is an assault if the rock misses.
Thus, a court officer taking possession of goods under a court order may use force if reasonably necessary.
Thus, there is no assault if an ox gores a man.
Thus, if P is a program in L < sub > 2 </ sub > which is a minimal description of s, then InterpretLanguage ( P ) returns the string s. The length of this description of s is the sum of
Thus, if every historian were to claim that there was a solar eclipse in the year 1600, then though we might at first naively regard that as in violation of natural laws, we'd come to accept it as a fact.
Thus and running
Thus most database systems nowadays are software systems running on general-purpose hardware, using general-purpose computer data storage.
Thus, because of the O ( n log n ) upper bound on heapsort's running time and constant upper bound on its auxiliary storage, embedded systems with real-time constraints or systems concerned with security often use heapsort.
Thus Potsdamer Platz was off and running.
Thus, it is likely that the worst-case running time for any algorithm for the TSP increases exponentially with the number of cities.
Thus, road running, racewalking and track and field are the sports which feature at the competition.
Thus flanged wheels are wheels with a flange on one side to keep the wheels from running off the rails.
Thus, for those making this commitment, they are distinguished within the monastic community under the title of choir nuns, as opposed to " lay Sisters ", who are entrusted with the upkeep of the monastery, or even running errands outside the cloister.
Thus, they joined two powerful political families with strains of madness running through them, both renowned for cruel behavior.
" Thus the town of Newport " shifted " from its location on the flatboat-friendly French Broad to its current location along the railroad running parallel to the Pigeon.
Thus, the most valuable information is gathered by running the engine at high speed and full load, immediately cutting the ignition off and stopping without idling or low speed operation and removing the plugs for reading.
Thus a running horse has not four legs, but twenty, and their movements are triangular.
Thus is contradicted by the Aboriginal people of central Australia, who knew it well and reported that if disturbed, it was capable of running with considerable speed by breaking into a smooth, galloping sprint.
Thus a trademark of the show was slow motion shots of the lifeguards running, most notably done by Erika Eleniak, Pamela Anderson, Yasmine Bleeth, Alexandra Paul, and David Charvet along with Hasselhoff during the height of the show.
Thus the duration of the clock cycle of a moving clock is found to be increased: it is measured to be " running slow ".
More specifically, the running time for testing whether H is a minor of G in this case is O ( n < sup > 3 </ sup >), where n is the number of vertices in G and the big O notation hides a constant that depends superexponentially on H. Thus, by applying the polynomial time algorithm for testing whether a given graph contains any of the forbidden minors, it is possible to recognize the members of any minor-closed family in polynomial time.
Thus, the Ohio Street entrance to the tower is actually the complex's back door with a concourse-style passageway on the second level running over Scioto Street ( the north-south alley between Pennsylvania and Meridian ) to connect the skyscraper ( and its attached parking garage along Pennsylvania Street ) to the main entrance in the original 1960 American National Bank Building at 111 Monument Circle.
Thus much of the North Shore is hilly with many steep valleys running down into the harbour and the rivers on either side.
Thus, running off the end of a piece of data in a stack frame alters data previously entered into the stack frame ; and running off the end of a stack frame places data into the previous stack frame.
Thus, predictions of things like economic recessions are still highly inaccurate, despite the use of enormous models running on fast computers.
Thus, the speed of running may be controlled and measured.
Thus an algorithm running in time O ( n < sup > 1 / ε </ sup >) or even O ( n < sup > exp ( 1 / ε )</ sup >) counts as a PTAS.
Thus, most IRC bots are run from computers which have long uptimes ( generally running a BSD derivative or Linux ) and a fast, stable Internet connection.
Thus, in most districts, only four candidates were running for three seats, guaranteeing not only that there would be a single loser, but that each party would have significant representation — a minimum of one-third of the seats — in the House.
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