Thus, he supported funding to the state to assist the expansion of the East Tennessee and Virginia Railroad.

Thus, on January 16, 1997, the Diamondbacks were officially voted into the National League while their expansion counterparts in Tampa Bay were voted into the American League.

Thus Dürer contributed to the expansion in German prose which Martin Luther had begun with his translation of the Bible.

Thus with the expansion of the universe, radiation becomes less dominant than matter.

Thus, the capital of Kazakhstan lent its name to the Alma-Ata Declaration, in which eleven of the fifteen Soviet republics announced the expansion of the thirteen-day-old CIS.

Thus, the fundamental solution may be found by performing the continued fraction expansion and testing each successive convergent until a solution to Pell's equation is found.

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.

where D denotes the continuum derivative operator, mapping f to its derivative f. The expansion is valid when both sides act on analytic functions, for sufficiently small h. Thus, T < sub > h </ sub >= e < sup > D </ sup >, and formally inverting the exponential yields

Thus a better understanding of the possible links between El Niño, Western Pacific Warm Pool, Indonesian Throughflow, wind pattern off western Australia, and ice volume expansion and contraction can be obtained by studying the behaviour of the LC during Quaternary at close stratigraphic intervals.

Thus a cycle of expansion and compression ( swelling and shrinking ) is maintained.

Thus, in the West, the notion of ethnicity, like race and nation, developed in the context of European colonial expansion, when mercantilism and capitalism were promoting global movements of populations at the same time that state boundaries were being more clearly and rigidly defined.

Thus the sonic boom associated with the passage of a supersonic aircraft is the sound wave resulting from the degradation and merging of the shock wave and the expansion wave produced by the aircraft.

Thus plans were made to build an expansion.

Thus, in the early 1920s the growing University had to look for a more spacious campus as its original site at George Street, Brisbane has limited room for expansion.

Thus the redshift is explained by the fact that the Universe is currently in an expansion phase.

Thus it can be understood that the Zulu Nation's adoption of " Factology vs Beliefs ," was an effort to reorganize the Nation to be more accessible by more people of even more different belief systems, due to the ever expansion of Hip Hop culture worldwide causing a bigger need for a much more universal Hip Hop preservation society.

Thus, the Ayyubids required Nubia to guarantee the protection of Aswan and Upper Egypt, but like their Fatimid predecessors, were discouraged from further expansion by the poverty of the region.

Thus, he wrote: " if 0 is interpreted as falsehood, 1 as truth, and other numbers in the interval 0-1 as the degrees of probability corresponding to various possibilities, a many-valued logic is obtained which is expansion of three-valued logic and differs from the latter in certain details.

Thus, the outcome of a full partial fraction expansion expresses that function as a sum of fractions, where:

Thus the network has registered a sevenfold growth since independence, with the focus of the expansion primarily in rural areas.

Thus, the basic method of navigation using Guide was the expansion button, in which a section was replaced when selected and in which an expansion would provide additional levels of detail.

Thus, for example, if a researcher were interested in US resistance to communist expansion as a theoretical focus, then the Korean War might be taken to be the subject, the lens, the case study through which the theoretical focus, the object, could be viewed and explicated.

Thus began the Commodore's rapid expansion into parts of Indochina, the Middle East and South Africa badged as the Chevrolet Lumina, to Brazil as the Chevrolet Omega 3. 8 V6, and later on with the Monaro to the United States, where it was sold by Pontiac under the GTO nameplate.

Thus, breathing occurs via a change in the volume of the body cavity which is controlled by contraction of intercostal muscles in all reptiles except turtles.

Thus, when a patient reaches for an enlarged object, he or she is overcoming that physiological contraction.

Thus, as it is required by the principle of relativity ( according to which the laws of nature must assume the same form in all inertial reference frames ), length contraction is symmetrical: If the rod is at rest in the train, it has its proper length in S ' and its length is contracted in S. However, if the rod comes to rest relative to the station, it has its proper length in S and its length is contracted in S '.

Thus, breathing occurs via a change in the volume of the body cavity which is controlled by contraction of intercostal muscles in all reptiles except turtles.

Thus a contraction mapping is strictly metric, but not necessarily the other way around.

Thus, the tropomyosin-troponin complex again covers the binding sites on the actin filaments and contraction ceases.

Thus, contraction following extracellular application of high-potassium solution depends on the influx of the extracellular calcium ions through voltage-gated calcium channels.

Thus, to cite but one example, the Pax Britannica of the nineteenth century, whether with the British navy ruling the seas or with the City of London ruling world finance, was strictly national in motivation, however much other nations ( e.g., the United States ) may have incidentally benefited.

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 Faulkner reminds us, and wisely, that the `` new '' South has gradually evolved out of the Old South, and consequently its agrarian roots persist.

Thus, the avant-garde choreographers have extended the scope of materials available for dance composition.

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus, paradoxically, the beat writers resort to `` religious '' metaphors: they are in search of mana, the spiritual, the numinous, but not anything connected with formal religion.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus, on the highroad, a troop of soldiers `` marched in their own dust and sang '', while on the footpath one man walks alone.

Thus the image of man has suffered complete fragmentation in personal and spiritual qualities, and complete objectification in sub-human and quasi-mechanistic powers.

Thus the fictional detective is much more than a simple businessman.

Thus the transformation of Adam Smith's ideal entrepreneur into a mythological detective coincides closely with the decline of the real entrepreneur in economic life.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.

Thus in both types attention is focused on the community itself, and its phenomenological life.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

Thus with regard to the loss of tradition, in the change from order to disorder the metaphysics of change works itself out as a disruption of the individual soul, a change in which man continues as an objective ontological existent, but no longer as a man.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Thus earth has fallen to the center of the universe.

Thus, Margenau remarks: `` A large number of unrelated epicycles was needed to explain the observations, but otherwise the ( Ptolemaic ) system served well and with quantitative precision.

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus he complains, with considerable justice, that the Tory writers have resorted to libel instead of answering his arguments.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus the student of literature may sometimes find it helpful to classify a poem or an essay as being in idea or in ideal content or subject matter typical or atypical of its period.

Thus ideas like `` grace '', `` salvation '', and `` providence '' cluster together in traditional Christianity.