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

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

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

Thus in Prokofieff the Union of Soviet Socialist Republics produced one of the great composers of the Twentieth Century.

Thus it was that Barco, apprehended for mere larceny, now began to suspect that one or another of his murders had been uncovered.

Thus, a low intensity of hypothalamic-cortical discharges prevails in sleep and a high one during wakefulness, resulting in synchronous EEG potentials in the former and asynchrony in the latter condition.

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, the writer decided to hold one experimental section of the functional preparation for marriage course in the spring semester of 1960 exclusively for persons already married -- that is, prerequisite: `` marriage ''.

Thus, when more than one distinct form leads to a particular cell in the X-region, a chain of information cells must be created to accommodate the forms, one cell in the chain for each form.

Thus, one can think of a dictionary entry as a word rather than a form.

Thus the first lines of one of Charles Wesley's hymns are as follows.

Thus, in the aggregate, the odd-lot trader is one who buys at the tops and sells at the bottoms, notwithstanding occasional individual exceptions.

Thus one line in five from The Iliad and The Odyssey is to be found somewhere else in the two poems.

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, if one accelerometer is properly aligned, the other is also.

Thus a man who is butting a stone wall at the office may become unusually aggressive in bed -- the one place he can still be champion.

Thus there was really an excess of eighteenth-century charm as one of these light-weight pieces followed another on Saturday night.

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, according to the character Pausanias in Plato's Symposium, Aphrodite is two goddesses, one older while the other younger.

Thus arose the first monastic community, consisting of anchorites living each in his own little dwelling, united together under one superior.

Thus aesthetic judgments might be seen to be based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior, conscious decision, training, instinct, sociological institutions, or some complex combination of these, depending on exactly which theory one employs.

Thus, an analog signal is one represented by a continuous stream of data, in this case along an electrical circuit in the form of voltage, current or charge changes ( compare with digital signals below ).

Thus, while the book exhibits considerable unity and probably reflects much of the historic Ezekiel, it is the product of a long and complex history and does not necessarily preserve the very words of the prophet.

Thus the Sidewinder team replaced a potentially complex control system with a simple mechanical solution.

Thus any popular general-purpose data model usually well balances between being intuitive and relatively simple, and very complex with high expressive power.

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 the distribution of Symbiodinium on coral reefs and its role in coral bleaching presents one of the most complex and interesting current problems in reef ecology.

Thus, while a permit to fill non-federal wetlands might require a permit from a single state agency, larger and more complex endeavors — for example, the construction of a coal-fired power plant — might require approvals from numerous federal and state agencies.

Thus any non-constant entire function must have a singularity at the complex point at infinity, either a pole for a polynomial or an essential singularity for a transcendental entire function.

Thus Hammurabi ascended to the throne as the king of a minor kingdom in the midst of a complex geopolitical situation.

Thus, similar immune systems may be more vulnerable to infectious diseases ( see Major histocompatibility complex and sexual selection ).

Thus, seemingly irreducibly complex structures are merely " very complex ", or they are simply misunderstood or misrepresented.

Thus, textbooks on aerodynamics use more complex models to provide a full description of lift.

Thus, IUPAC recommendations are more closely followed for simple compounds, but not complex molecules.

Thus, his importance as a ' translator ' of their ideas to the common vocabularies of a variety of disciplines in the Anglo-American academic complex is equally as important as his own critical engagement with them.

Thus, in the opinion of Richard Klein, the ability to produce complex speech only developed some 50, 000 years ago ( with the appearance of modern man or Cro-Magnon man ).

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 by the late 1970s, in Jones's words, " Scott's complex personality had been revealed and his methods questioned ".

Thus the Riemann zeta function is a meromorphic function on the whole complex s-plane, which is holomorphic everywhere except for a simple pole at s = 1 with residue 1.

Thus the ( real < ref > The complex spinors are obtained as the representations of the tensor product H ⊗< sub > R </ sub > C = Mat < sub > 2 </ sub >( C ).

Thus it uses a much more complex ruleset for coding than its predecessor ; for example, it tests for approximately 100 different contexts of the use of the letter C alone.

Thus each image is more complex, containing more information than it would in a style in which a smaller area is framed ...

Thus, although a complex system of interaction between thyroid hormone and neurotransmitters has been recognized and examined, no clear-cut explanation for the effect of thyroid hormone on depression has emerged.

Thus, this function is not meromorphic in the whole complex plane.

By using analytic continuation to eliminate removable singularities, meromorphic functions can be added, subtracted, multiplied, and the quotient can be formed unless on a connected component of D. Thus, if D is connected, the meromorphic functions form a field, in fact a field extension of the complex numbers.