Thus, if public pressure sets the effective limit to the price that the industry may charge, this pressure is itself a function of the wage rate.

Thus, in general, elementary light optical effects, light scatter, and electron scatter determine the obtainable resolution limit.

Thus for a limit ordinal, there exists a δ-indexed strictly increasing sequence with limit α.

Thus, he challenged the arguments of clerical intellectuals who wanted to limit access to classical sources to prevent any moral harm to Christian readers.

Thus, as long as the limit is not " forever ," any limit set by Congress can be deemed constitutional.

Thus according to the central limit theorem, we can model jitter as a gaussian random variable.

Thus, wavelength ratios observed for different ionic species in the absorption spectra of quasi stellar objects ( QSO or quasars ) place a limit on any variation in the fine-structure constant to less than 1 part in 1 million out to a distance in space ( and time ) of z = 3 ( about 6500 megaparsecs or 11. 5 billion light years ); as the fine-structure constant is determined by the relation between the speed of light ( c ), Planck's constant ( h ) and the electron charge ( e ), these physical constants are constrained as well.

Thus, for example, in many states, the blood alcohol level for the commission of the offence of driving under the influence is set sufficiently low that people might exceed the limit without realising that they had consumed enough alcohol to do so.

Thus, the interests which profited from canals, river, and coastal shipping all used their sway in government to limit the construction of railways.

Thus, assuming the Axiom of Choice, we can infer that κ is a strong limit cardinal, which completes the proof of its inaccessibility.

Thus, an issue limit figure never fully reveals the true number actually created.

Thus u is an upper bound for S. To see that it is a least upper bound, notice that the limit of ( u < sub > n </ sub > − l < sub > n </ sub >) is 0, and so l =

Thus in order to limit the spread of blood-borne diseases such as hepatitis and HIV through shared injection equipment, many countries have needle exchange programs in most larger cities.

Thus, in general, knowing that and is not sufficient to calculate the limit

Thus the regularity or singularity of most aleph numbers can be checked depending on whether the cardinal is a successor cardinal or a limit cardinal.

Thus the reservoir extended only to Parrot's Ferry Bridge, below its maximum upriver limit, until the El Niño event of 1982-1983, which filled it to capacity within weeks and even forced Reclamation to open the emergency spillways, prompting the state and federal governments to repeal the limits they had imposed on the reservoir.

Thus one method for increasing the energy limit is to use superconducting magnets, these not being limited by magnetic saturation.

Thus the mortgage is within the category known as " non-recourse limit ".

Thus, the agreement on " voluntary " export restraints is imposed on the exporter under the threat of sanctions to limit the export of certain goods in the importing country.

Thus, while Hakim did attempt to limit Communist influence among the Shi ' a by banning their participation in the party, for the most part he preferred to remain out of politics, at least tacitly agreeing with Baghdad's rulers to keep the hawza's scholars politically neutral in exchange for relative immunity for those scholars.

Thus, the lower size limit for grains in granular material is about 1 µm.

Thus the representation of the center of the Heisenberg group is determined by a scale value, called the quantization value ( in physics terms, Planck's constant ), and if this goes to zero, one gets a representation of the abelian group ( in physics terms, this is the classical limit ).

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 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 Plato and Gottfried Leibniz affirm an objective and knowable reality transcending our subjective awareness — a rejection of epistemological idealism — but propose that this reality is grounded in ideal entities, a form of metaphysical idealism.

Thus debana-waza is ideal.

Thus is a field when is a maximal ideal, that is, when is prime.

Thus, although Enlightenment philosophers saw the Roman Republic as an ideal system, it included no systematic separation of powers, and depended on slave labor.

Thus such elements as collage were introduced, arising partly from an ideal of startling juxtapositions as revealed in Pierre Reverdy's poetry.

Thus planning in Tapiola was collaborative and proactive as it involved targeting specific family types and classes, deciding on an ideal lifestyle for these residents, which accordingly influenced their behaviours.

Thus, each gas molecule occupies the same mean volume in all ideal gases, regardless of the type of gas ( see kinetic theory ).

Thus, in a sense, the notion of a Noetherian ring unifies the ideal structure of various " natural rings ".

Thus these are precisely the class of domains for which Frac ( R )/ Prin ( R ) forms a group, the ideal class group Cl ( R ) of R. This group is trivial if and only if R is a PID, so can be viewed as quantifying the obstruction to a general Dedekind domain being a PID.

Thus a class has an inverse if and only if there is an ideal J such that IJ is a principal ideal.

Thus, if popular fashion says that a ‘ blouse ’ is ideal for a certain situation or ensemble, this idea is immediately naturalized and accepted as truth, even though the actual sign could just as easily be interchangeable with ‘ skirt ’, ‘ vest ’ or any number of combinations.

Thus, as Dika Newlin has pointed out, " in this symphony Mahler returns to the ideal of ' progressive tonality ' which he had abandoned in the Sixth ".

Thus, the number of molecules or atoms in a specific volume of ideal gas is independent of their size or the molar mass of the gas.

Thus the radical is an ideal .</ ref > This is sometimes taken as a definition of radical.

Thus, in the ideal continuous case, detection of zero-crossings in the second derivative captures local maxima in the gradient.

Thus the overall bandwidth of super-regenerator cannot be less than 4 times that of the quench frequency, assuming the quenching oscillator produces an ideal sinewave.

Thus, it's not ideal or possible to implement on any type of Famicom / NES hardware or FPGA type system without extensive modification.

Thus for isentropic processes with an ideal gas,

Thus, the ring of integers of Q (√ d ) is a principal ideal domain ( and hence a unique factorization domain ) if and only if the class number of Q (√ d ) is equal to 1.

Thus, a 21. 5 kiloton ( 9 x 10 < sup > 13 </ sup > joule ) nuclear bomb produces about one gram of heat and electromagnetic radiation, but the mass of this energy would not be detectable in an exploded bomb in an ideal box sitting on a scale ; instead, the contents of the box would be heated to millions of degrees without changing total mass and weight.