Thus, in place of one unchallenged military commander, the province now had five officers, each with command of only a small fraction of the garrison.

Thus, adding two integers never yields some other type of number, such as a fraction.

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, intuitively we could interpret the fraction of as representing the ratio of the labor one has to perform when going from a randomly chosen configuration to another randomly chosen configuration, relative to the difficulty of having to cross the " most difficult " path of length which involves moving all the disks from one peg to another.

Thus, written records tend to reflect the biases, assumptions, cultural values and possibly deceptions of a limited range of individuals, usually only a fraction of the larger population.

Thus, the image on the retina gets stable for a fraction of a second.

Thus the sea urchins only need to eat the roots of the kelp, a tiny fraction of the plant's biomass, to remove it from the ecosystem.

Thus the partial fraction decomposition may be seen as the inverse procedure of the more elementary operation of addition of algebraic fractions, that produces a single rational function with a numerator and denominator usually of high degree.

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

Thus, many players believed they had no option but to cheat in order to see more than a fraction of it, by asking the first Pygmy to his right about " ten pints ".

Thus, if 105 g can ( only just ) be distinguished from 100 g, the jnd ( or differential threshold ) is 5 g. If the mass is doubled, the differential threshold also doubles to 10 g, so that 210 g can be distinguished from 200 g. In this example, a weight ( any weight ) seems to have to increase by 5 % for someone to be able to reliably detect the increase, and this minimum required fractional increase ( of 5 / 100 of the original weight ) is referred to as the " Weber fraction " for detecting changes in weight.

Thus, the gas in the rebreather's circuit remains breathable and supports life and the diver needs only carry a fraction of the gas that would be needed for an open-circuit system.

Thus, although the above figures for outstanding notionals are very large, in the absence of default the net cash flows are only a small fraction of this total: for a 100 bp

Thus, the clay fraction produced by the ground scouring of the important glaciation was ready to be blown-out.

Thus, these materials do not have free conduction electrons, and the bonding electrons reflect only a small fraction of the incident wave.

Thus in comparison with other ‘ desalination ’ processes that may be used for make-up water the energy consumption is a fraction of these with the added advantage of the low fouling propensity of a forward osmosis process.

Thus, Brazil would be only a fraction of its present-day size.

Thus the fraction 3 / 4 is also used to represent the ratio 3: 4 ( the ratio of the part to the whole ) and the division 3 ÷ 4 ( three divided by four ).

Thus, the net effect of BNP and ANP is a decrease in blood volume which lowers systemic blood pressure and afterload, yielding an increase in cardiac output, partly due to a higher ejection fraction.

Thus, the primary classification is a fraction between

Thus, even by 1939, only a fraction of the Hill-country Tamils had been granted the franchise.

The degree distribution P ( k ) of a network is then defined to be the fraction of nodes in the network with degree k. Thus if there are n nodes in total in a network and n < sub > k </ sub > of them have degree k, we have P ( k )

Thus, the more trade becomes " globalised ", the greater the intermediation between producers and consumers ; consequently, the intermediaries appropriate a growing fraction of the final value of the products, while the direct producers obtain only a small fraction of that final value.

Thus, natural beryllium bombarded either by alphas or gammas from a suitable radioisotope is a key component of most radioisotope-powered nuclear reaction neutron sources for the laboratory production of free neutrons.

Thus, calreticulin can act as an important modulator of the regulation of gene transcription by nuclear hormone receptors.

Thus, no two nuclear powers have yet fought a conventional war directly, with the exception of brief skirmishes between for example, China and Russia in the 1969 Sino-Soviet conflict and between India and Pakistan in the 1999 Kargil War.

Thus was born the practical nuclear chain reaction by the mechanism of neutron-induced nuclear fission.

Thus, a nearly complete separation of zirconium and hafnium is necessary for their use in nuclear power.

Thus, because of Klaus Fuchs, leaders of the Soviet Union knew the United States was not prepared for a nuclear war at the end of the 1940s, or even in the early 1950s.

Thus, even in this age of nuclear reactors, naturally-occurring radon is responsible for the majority of the public exposure to ionizing radiation.

Thus, some have argued, as time passes, these deep storage areas have the potential to become " plutonium mines ", from which material for nuclear weapons can be acquired with relatively little difficulty.

Thus, given the same mass as the original S-IVB, one can expect a moderate increase in overall performance using a nuclear engine.

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 it was possible to conduct analyses of elastic materials, which were possible prior to this only with nuclear reactors via neutron scattering.

Thus, they tended to disperse large amounts of unused fissile material, and the fission products, which are on average much more dangerous, in the form of nuclear fallout.

Thus it no longer produces its energy through nuclear fusion and, in evolutionary terms, it is now becoming a compact white dwarf star.

Thus they show strong optical continuum emission, broad and narrow emission lines, and strong X-ray emission, together with nuclear and often extended radio emission.

Thus the current view of the nuclear atom-a structure with a positively charged center ( nucleus ) of high density and negatively charged electron particles moving around the nucleus at relatively large distances compared to the nuclear radius-was created.

Thus, Mao announced his decision to develop China's own strategic weapons, including nuclear bombs and associated missiles for the warheads, during a Communist Party of China ( CPC ) Central Committee meeting held on January 15, 1955.

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.

Thus, no mass ( or, in the case of a nuclear bomb, no matter ) would be " converted " to energy in such a process.

Thus, the Soviet Union acquired the capability to neutralise NATO's tactical nuclear forces with surgical nuclear strikes.

Thus, when reactions ( whether chemical or nuclear ) release energy in the form of heat and light, if the heat and light is not allowed to escape ( the system is closed and isolated ), the energy will continue to contribute to the system rest mass, and the system mass will not change.

Thus, the USA was completely safe from nuclear threat, ending the era of Mutual Assured Destruction.