Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c < sub > 1 </ sub >-− 3 c < sub > 1 </ sub > will cause them to be renumbered from 0 through 9 and 4 through 23, respectively.

Thus a regular space encountered in practice can usually be assumed to be T < sub > 3 </ sub >, by replacing the space with its Kolmogorov quotient.

Thus, the rupee of 100 cents became Ceylon's money of account and sole legal tender effective 1 January 1872, replacing British currency at a rate of 1 rupee =

Thus if a sky hook has been created, it can effectively convert waste asteroid or lunar material thrown to it, into high grade rocket fuel ( that is by replacing the fuel spent to maintain its own orbit ), by virtue of their kinetic energy.

Thus, Ver increasingly became the second most powerful government official in the country, replacing Enrile who held the status since the imposition of Martial Law on 1972 when Marcos named him as martial law administrator.

Thus for his time Marten was unusual in his political stance, being unashamedly in favour not of reforming the monarchy but of replacing it with a republic.

Thus ARA was considerably more complex than similar solutions for IP, replacing many parts of the AppleTalk stack and seriously modifying others.

Thus instead of replacing the Volga, GAZ was tasked with creating a new vehicle that would be suitable for the mid-class of the Soviet nomenklatura.

Thus replacing hard drives probably requires economically collecting around 100 Millipede devices into a single enclosure.

Thus abroutes, may be read as abrouwes (), with tau () replacing a digamma.

Thus, in 1849, the college was organized, replacing and expanding the academy ’ s program.

Thus, replacing an incoming boson with an outgoing antiboson with opposite momentum yields the same S-matrix element.

Thus, Class II RPDs clasp onto teeth that are more towards the front of the mouth, as well as on teeth that are more towards the back of the mouth of the side on which teeth are not missing, while replacing the missing more-back-of-the-mouth teeth on one side with false denture teeth.

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, it might be used to challenge the sharp distinction made in U. S. v. E. C. Knight ( 1895 ) between commerce, which was subject to federal regulation, and manufacturing, which was not.

Thus Euclidean geometry corresponds to the choice of the group E ( 3 ) of distance-preserving transformations of the Euclidean space R < sup > 3 </ sup >, conformal geometry corresponds to enlarging the group to the conformal group, whereas in projective geometry one is interested in the properties invariant under the projective group.

Thus, the most common letter in English, the letter " E ," has the shortest code, a single dot.

Thus optical amplification, and laser operation, can take place at a frequency of ν < sub > 32 </ sub > ( E < sub > 3 </ sub >- E < sub > 2 </ sub > = hν < sub > 32 </ sub >).

Thus Dumézil conceives of Víðarr as a spatial god ( per the hypothesized Víð -/ wide root-O. E.

While this equation suggests that the activation energy is dependent on temperature, in regimes in which the Arrhenius equation is valid this is cancelled by the temperature dependence of k. Thus, E < sub > a </ sub > can be evaluated from the reaction rate coefficient at any temperature ( within the validity of the Arrhenius equation ).

Thus the total time is O ( E log E ) = O ( E log V ).

Thus, according to Paul L. Maier, the majority of Herod biographers and theologians hold that the Massacre of the Innocents is " legend and not historical ": Geza Vermes and E. P. Sanders, for example, regard the story as part of a creative hagiography.

Thus, by charging a higher per unit price and a lower lump-sum fee, the firm has generated area E more profit than if it had charged a lower per-unit price and a higher lump-sum fee.

Thus, E ( k ) dk represents the contribution to the kinetic energy from all the Fourier modes with k < | k | < k + dk, and therefore,

Thus, what we call the year 3053 A. D. ( the year the novel begins ) is in the novel the year 1108 A. E.

Thus the three notes ( E, C and A ) are played in quick succession at relative ease to the player.

Light's wavenumber is proportional to frequency, and therefore also proportional to light's quantum energy E. Thus,.

Thus, if a road is built across the fault as in the figure panel Time 1, it is perpendicular to the fault trace at the point E, where the fault is locked.

Given two tensor bundles E → M and F → M, a map A: Γ ( E ) → Γ ( F ) from the space of sections of E to sections of F can be considered itself as a tensor section of if and only if it satisfies A ( fs ,...) = fA ( s ,...) in each argument, where f is a smooth function on M. Thus a tensor is not only a linear map on the vector space of sections, but a C < sup >∞</ sup >( M )- linear map on the module of sections.

Thus, a peak in E ’’ is observed at the frequency.

Thus, on July 19, 1990, the Konkan Railway Corporation Limited ( KRCL ) was incorporated as a public limited company under the Companies Act, 1956, with its headquarters at CBD Belapur in Navi Mumbai and E. Sreedharan, a senior railway official, as its first Chairman and Managing Director.

Thus we are compelled to face the urbanization of the South -- an urbanization which, despite its dramatic and overwhelming effects upon the Southern culture, has been utterly ignored by the bulk of Southern writers.

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, 1745 corresponded to the invention of the `` Leiden '' jar by Kleist, 1764 that of the electrophorus by Wilcke, 1782 produced the condenser of Volta, and 1801 the voltaic pile.

Thus, direct comparisons can be drawn with free burning arcs which have been studied in detail during the past years and decades by numerous investigators ( Ref. 3 ).

Thus, his estimate lies between Oliver's suggestion of at least 37 feet and the 50-foot `` monstrous freaks '' intimated by Heuvelmans.

Thus cortico-fugal discharges induced by topical application of strychnine to a minute area in the neocortex summate with spikes present in the hypothalamus and cause increased convulsive discharges.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus we obtain g{t} by introducing an oblique g{t}-axis in the Aj.

Thus, although the agenda of external assistance in the economic sphere are cumulative, and many of the policies suggested for nations in the earlier stages remain relevant, the basic purpose of American economic policy during the later stages of development should be to assure that movement into a stage of self-sustaining growth is not prevented by lack of foreign exchange.

Thus he may be referring to some concrete thing, or incident, in his immediate environment by some symbolic-sounding, hyperbolic reference to transcendental events on the global scene.

Thus, the public-limit price is raised further by a given wage increase the longer it has been since the previous price increase.

Thus, for non-negative changes in the basic wage rate, the industry becomes the active wage-setter, since any increase in the basic wage rate can occur only by reason of industry acquiescence.

Thus, the efficiency **yt couplers is given by -- Af or approximately 50 percent each.

Thus, the combined efficiency of the elements replaced by the two fiber plates ( with a combined efficiency of 0.25 ) is 0.043 or about six times less than that of the two fiber plates.

Thus Af where the maximization is over all admissible policies Af, and Af is related to Af by ( 5 ).

Thus, when Dartmouth's Winter Carnival -- widely recognized as the greatest, wildest, roaringest college weekend anywhere, any time -- was broadcast over a national television hookup, Prexy John Sloan Dickey appeared on the screen in rugged winter garb, topped off by a tam-o'-shanter which he confessed had been acquired from a Smith girl.

Thus, while it remains possible that the Babylonians and/or the Pythagoreans may perhaps have had the magic square of three before the Chinese did, more definite evidence will have to turn up from the Middle East or the Classical World before China can lose her claim to the earliest known magic square by more than a thousand years.

Thus `` America '', the most widely sung of the patriotic songs, was written by a New England Baptist clergyman, Samuel Francis Smith ( 1808-1895 ), while a student in Andover Theological Seminary.

Thus, while altruistic persons may under some circumstances be outcompeted by less altruistic persons at the individual level, according to group selection theory the opposite may occur at the group level where groups consisting of the more altruistic persons may outcompete groups consisting of the less altruistic persons.

Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system.

Thus the only member churches of the present Anglican Communion existing by the mid-18th century were the Church of England, its closely linked sister church, the Church of Ireland ( which also separated from Roman Catholicism under Henry VIII ) and the Scottish Episcopal Church which for parts of the 17th and 18th centuries was partially underground ( it was suspected of Jacobite sympathies ).

Thus a colonial bishop and colonial diocese was by nature quite a different thing from their counterparts back home.

Thus, by the end of 1992, Azerbaijan received arms and military hardware sufficient for approximately four motor rifle divisions with prescribed army units.

Thus, at pH between 2. 2 and 9. 4, the predominant form adopted by α-amino acids contains a negative carboxylate and a positive α-ammonium group, as shown in structure ( 2 ) on the right, so has net zero charge.