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.

Thus, it was Gibbs who first combined the first and second laws of thermodynamics by expressing the infinitesimal change in the energy a system in the form:

Thus an ex facie absolute disposition, qualified by a back-bond expressing the limited nature of the right actually held by the person to whom the disposition is made, would constitute what in England is termed a deed of trust.

… Thus, when we so use it in the sentence, < nowiki >'</ nowiki > This is good ,' we merely refer to this, and the addition of " is good " makes no difference whatever to our reference … it serves only as an emotive sign expressing our attitude to this, and perhaps evoking similar attitudes in other persons, or inciting them to actions of one kind or another.

Thus, Creating a sharp boundary between the cells expressing the transcription factor Nkx2. 2 ventral to the cells expressing Olig2.

Thus, a given language may exhibit more than one strategy for expressing futurity.

Thus in the West the acronym became even the more undesired and using it was often considered either unreflecting or even expressing naïve Communist sympathies.

Thus, a share is an indivisible unit of capital, expressing the proprietary relationship between the company and the shareholder.

Thus, Conservative ideology, under its philosophy of pluralism, supports a range of views on this subject, from views similar to the Orthodox view to views expressing a need for a contemporary reorientation.

Thus a phrase or passage, or a whole sutta, might be classed as neyyattha or samuti or vohāra, but it is not regarded at this stage as expressing or conveying a different level of truth.

Thus Cooke received a letter from the company dated 12 October 1837, expressing no further interest to pursue any use of the electric telegraph as viable.

Thus cells expressing beta-galactosidase grown in the presence of X-gal and IPTG ( to induce the expression ) will turn blue.

" Thus, it is debatable whether intoxication refers to literal drunkenness as an escape or if symbolizes the pleasure found in writing and expressing oneself.

Thus, axons from the anterior retina, expressing the lowest level of Ephs, can project to the posterior tectum, even though this is where Ephrins are highly expressed.

Thus if I say ' He is always right ', I mean that the propositions he asserts are always true, and there does not seem to be any way of expressing this without using the word ' true '.

Thus for sentimental reasons and for expressing his reverence, he adopted her name, Manalo.

In particular, she took advantage of his handling of opposites and their transitions and his tone, which she recognized as expressing “ total surrender of the self to the tone .” Thus, Offertorium is an example of a piece crafted both for and from the person to whom it was composed and dedicated.

Thus in the presence of large quantum computers an n-bit key can provide at least n / 2 bits of security.

Thus it can be interpreted without any reference to the zero-point energy ( vacuum energy ) or virtual particles of quantum fields.

Thus, if the rate of any pathway changes, both the excited state lifetime and the fluorescence quantum yield will be affected.

" Thus irreal works such as Italo Calvino's Cosmicomics and Jorge Luis Borges ' Ficciones can be seen as an attempt to find a new allegorical language to explain our changed perceptions of the world that have been brought about by our scientific and technical culture, especially concepts such as quantum physics or the theory of relativity.

Thus if we wish to claim that no-cloning is a uniquely quantum result, some care is necessary in stating the theorem.

Thus the entire field of quantum physics emerged, leading to its wider acceptance at the Fifth Solvay Conference in 1927.

Thus, measuring a quantum state described by complex coefficients ( a, b ,..., h ) gives the classical probability distribution and we say that the quantum state " collapses " to a classical state as a result of making the measurement.

Thus, at least in the low-energy regime, the model is indeed a predictive quantum field theory.

Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.

Thus the conquest of actual infinity may be considered an expansion of our scientific horizon no less revolutionary than the Copernican system or than the theory of relativity, or even of quantum and nuclear physics.

Thus, quantum physics casts reasonable doubt on the traditional determinism of classical, Newtonian physics in so far as reality does not seem to be absolutely determined.

Thus, the ontology of pilot wave theory contains as the trajectory we know from classical mechanics, as the wave function of quantum theory.

Thus a quantum mechanical ensemble is specified by a mixed state in general.

Thus, the quantum number has the value

Thus decoherence is the process by which information of a quantum system is altered by the system's interaction with its environment ( which form a closed system ), hence creating an entanglement between the system and heat bath ( environment ).

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

Thus, if the oscillator is in the quantum state it is also with nonzero probability in the other quantum state

Thus, the instanton field solution of the ( 1 + 1 )- dimensional field theory ( first quantized quantum mechanical system ) allows to be interpreted as a tunneling effect between the two vacua of the physical Minkowskian system.

Thus, the many-worlds quantum model is proved to be both real, and accessible, a fantastic achievement.

Thus, according to the theory, even the vacuum has a vastly complex structure and all calculations of quantum field theory must be made in relation to this model of the vacuum.

Thus, negative temperature is a strictly quantum phenomenon.