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Page "Heath Hen" ¶ 13
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Thus and given
Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.
Thus the multiplicity of Af for a given T must be an even number.
Thus, the public-limit price is raised further by a given wage increase the longer it has been since the previous price increase.
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, when specifically permitted, the operand of a given line on the Autocoder coding sheet may be continued in the operand of from one to four additional lines which immediately follow.
Thus, the efficiency **yt couplers is given by -- Af or approximately 50 percent each.
Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.
Thus for an ion which traverses a 1 m flight path, across a time of 2000 ns, given an initial accelerating voltage of 5000 V and noting that one amu is 1 × 10 < sup >− 27 </ sup > kg, the mass-to-charge ratio ( more correctly the mass-to-ionisation value ratio ) becomes Z amu / charge.
Thus, many users of a given BBS usually lived in the same area, and activities such as BBS Meets or Get Togethers were common, where users of the board would gather at a local restaurant, the SysOp ’ s home or similar venue and meet face to face.
Thus the discovery report by the Berkeley group reads: " It is suggested that element 97 be given the name berkelium ( symbol Bk ) after the city of Berkeley in a manner similar to that used in naming its chemical homologue terbium ( atomic number 65 ) whose name was derived from the town of Ytterby, Sweden, where the rare earth minerals were first found.
Thus, the vector space B ( X, Y ) can be given the operator norm
Thus, in time, the bishop changed from being the leader of a single church confined to an urban area to being the leader of the churches of a given geographical area.
By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.
Thus, at a given angular rate of rotation, a concave surface represents the stable situation, and the more rapid the rotation, the more concave this surface.
Thus, by monitoring eye movements, we can study what information is being processed at a given time.
Thus, the total applied torque about the origin is given by
Thus, the sum of all applied forces and torques ( with respect to the origin of the coordinate system ) in the body can be given by
Thus a person who owns a quarter of the shares of a joint-stock company owns a quarter of the company, is entitled to a quarter of the profit ( or at least a quarter of the profit given to shareholders as dividends ) and has a quarter of the votes capable of being cast at general meetings.
Thus, the law of " interpenetrating opposites " records the inextricable interdependence of components: the " transformation of quantity to quality " defends a systems-based view of change that translates incremental inputs into alterations of state ; and the " negation of negation " describes the direction given to history because complex systems cannot revert exactly to previous states.
Thus, churches actually had money-changing tables at which each coin would be examined separately and a token of actual worth given to the layperson so that he or she could be seen by the other parishioners as putting money in the basket during that part of the service.
Thus a lion, when presented in a given context in medieval literature, could only be interpreted in a single, approved way.
This identifies the tangent space T < sub > e </ sub > at the identity with the space of left invariant vector fields, and therefore makes the tangent space at the identity into a Lie algebra, called the Lie algebra of G, usually denoted by a Fraktur Thus the Lie bracket on is given explicitly by = < sub > e </ sub >.
Thus, contrary to the first impression its name might convey, and as realized in specific approaches and disciplines ( e. g. Fuzzy Sets and Systems ), intuitionist mathematics is more rigorous than conventionally founded mathematics, where, ironically, the foundational elements which Intuitionism attempts to construct / refute / refound are taken as intuitively given.
Thus, " the Law " is understood to be the religious teachings and rules given by God.
Thus, we should amend the expression given above into: Metallic bonding is an extremely delocalized communal form of electron deficient covalent bonding.

Thus and fact
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, 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.
This latter construal is sometimes expressed by saying " there is no fact of the matter as to whether or not P ." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities ( such as natural numbers ), moral categories, the material world, or even thought.
Thus, Annie's strong drive to take revenge on women scholars in general and on Miss de Vine in particular is perfectly comprehensible, and in fact does not in itself prove her to be mentally deranged.
Thus accounts such as that of the miraculous " Image Not Made by Hands ", and the weeping and moving " Mother of God of the Sign " of Novgorod are accepted as fact: " Church Tradition tells us, for example, of the existence of an Icon of the Savior during His lifetime ( the " Icon-Made-Without-Hands ") and of Icons of the Most-Holy Theotokos immediately after Him.
Thus the decision to involve the Inquisition, which therefore did not instigate the trial and in fact showed a reluctance throughout its duration.
Thus, the mergers were not done to see large efficiency gains, they were in fact done because that was the trend at the time.
Thus, for Rand, the fact that consciousness must itself possess identity implies the rejection of both universal skepticism based on the " limits " of consciousness and any claim to revelation, emotion or faith based belief.
Thus, Pakistan is in fact a multi-regional state and not a South Asian state actor only ; its history if analyzed in depth would prove the point.
Thus, while Bolivar knew that the nation of Panama was linked historically and culturally to South America, he was also conscious of the fact that the region was part of the Central American geography.
Thus, the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a twenty-one-year-old would have had only five birthdays, if he was born on a leap day.
Thus, ' truth ' involves both the quality of " faithfulness, fidelity, loyalty, sincerity, veracity ", and that of " agreement with fact or reality ", in Anglo-Saxon expressed by sōþ ( Modern English sooth ).
Thus, while Gandalf exerts a parental influence over Bilbo early on, it is Bilbo who gradually takes over leadership of the party, a fact the dwarves could not bear to acknowledge.
Thus, many of today's users are unaware of the fact that there are two types of DV AVI files.
Thus despite the fact no cigars have been brought into the hotel, each guest can smoke a cigar inside the property.
Thus a social fact is dependent on other social facts, but because each is only dependent on and reducible to other social facts, it is independent of and irreducible to psychological or biological factors.
Thus, the prefix ferro, meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron.
Thus, Henri Rochefort wrote a piece in " L ' Intransigeant ", claiming Zola had committed suicide, having discovered Dreyfus to be in fact guilty.
Thus it would seem that Lewis Carroll did not intend care and hope from the repeating stanza to stand for two women, but was quite pleased with the interpretation after the fact.
Thus, despite appearing brilliant white to observers on Earth, Halley's Comet is in fact pitch black.
Thus, in order to show that any axiomatic system of mathematics is in fact consistent, one needs to first assume the consistency of a system of mathematics that is in a sense stronger than the system to be proven consistent.
Thus the Earth's " conservative potency " ( virtus conservativa ) provided the explanation for the fact that the Earth retains its atmosphere though travelling through space.
Despite his rejection of the Macchiaioli approach, Modigliani nonetheless found favour with his teacher, who referred to him as " Superman ", a pet name reflecting the fact that Modigliani was not only quite adept at his art, but also that he regularly quoted from Nietzsche's Thus Spoke Zarathustra.
Thus, under Kaldor Hicks efficiency, a more efficient outcome can in fact leave some people worse off.
Thus, Internet access across the European Union is relatively open because of the laws forbidding discrimination based on nationality, but the fact of publication in, say, France, limits the target market to those who read French.

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