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

Thus in strong alkali at high pH, it forms the dually charged full urate ion, but at biological pH or in the presence of carbonic acid or carbonate ions, it forms the singly charged hydrogen or acid urate ion as its pKa < sub > 1 </ sub > is lower than the pKa < sub > 1 </ sub > of carbonic acid.

Thus, for example, the presence of an extra chromosome 21, which is found in Down syndrome, is called trisomy 21.

Thus, the presence of a central vacuole in its cells enables a prolonged survival in sulfidic sediments.

Thus an important influence upon the Dalcassians was the presence of the Hiberno-Norse city of Limerick on an isthmus around which the Shannon River winds ( known today as King's Island or the Island Field ).

Thus CD can be used to survey a large number of solvent conditions, varying temperature, pH, salinity, and the presence of various cofactors.

Thus a consensus definition of what constitutes the presence of a phenotype is essential for determining the penetrance of an allele.

Thus there is a reciprocal link between the god of beginnings and unending motion, who bestows life to the beings of this world ( Cerus Manus ) as well as presiding over its end, and the goddess of the hearth of man, which symbolises through fire the presence of life.

Thus a very high gas pressure of oxygen can be obtained, which can even account for the presence of gas in the swim bladders of deep sea fish like the eel, requiring a pressure of hundreds of bars.

Thus PIE ( traditional ) * anti " in front of and facing " > Greek antí " against "; Latin ante " in front of, before "; ( Sanskrit ánti " near ; in the presence of ").

Thus the presence of an orthonormal basis reduces the study of a finite-dimensional inner product space to the study of R < sup > n </ sup > under dot product.

Thus the presence or absence of gamma rays in a borehole is an indication of the amount of shale or clay in the surrounding formation.

Thus he secured the continued Roman presence in the areas of Gaul and Germania.

Thus Akhenaten extended even further the heretical belief that Aten was not the disc or orb of the sun ( the Egyptian sun god Ra ) but a universal spiritual presence ( see Akhenaten and Atenism ).

Thus, in a sequence alignment, the presence of these features may be an indication of a loop.

Thus in June 2003, the Indianapolis Star reported that the Army, in a March 31 letter to Buyer signed by Army Secretary Thomas White, had rejected Buyer's offer to serve in the Iraq War because " we are able to meet the need without your participation ," and " we are concerned that your presence would put in jeopardy the safety of those serving around you.

Thus the presence of y does not imply the presence of x.

Thus, iodine tincture solutions are characterized by the presence of alcohol, and about the same amount ( weight % content ) of elemental iodine as iodide.

Thus in the presence of h-principle, a differential topological problem reduces to an algebraic topological problem.

Thus, in the motivational example, above, the fact that the sum of residual values is equal to zero it is not accidental but is a consequence of the presence of the constant term, α, in the model.

Thus, when overall estimates are plotted against the variance ( sample size ), a symmetrical funnel is usually formed in the absence of publication bias, while a skewed asymmetrical funnel is observed in presence of potential publication bias.

Thus any two CPP-compatible presence protocol suites are automatically interoperable.

Thus an elevated IgM titre indicates recent primary infection, while the presence of IgG suggests past infection or immunization.

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 although most species in the order are herbaceous, some no more than 15 cm high, there are a number of climbers ( e. g. some species of Asparagus ), as well as several genera forming trees ( e. g. Agave, Cordyline, Yucca, Dracaena ), some of which can exceed 10 m in height.

Thus far the only people who have been attested with a high level of genetic, historical, linguistic and cultural research to be the descendants of the ancient Mesopotamians are the Assyrian Christians of Iraq and its surrounding areas in north west Iran, north east Syria and south eastern Turkey.

Thus, for example, fumaroles from the Laguna Caliente crater of Poás Volcano create extremely high amounts of acid rain and fog, with acidity as high as a pH of 2, clearing an area of any vegetation and frequently causing irritation to the eyes and lungs of inhabitants in nearby settlements.

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

Thus, it is a voltage-controlled device, and shows a high degree of isolation between input and output.

Thus, a high GWP correlates with a large infrared absorption and a long atmospheric lifetime.

Thus, a too high or too low temperature will result in stellar instability.

Thus, harvesting after nitrate buildup results in a crop that is high in nitrates.

Thus, clockwise air circulation is characteristic of high pressure weather cells in the northern hemisphere.

Thus, for Christians, Christ himself is the only high priest, and Christians have no priesthood independent or distinct from participation in the priesthood of Christ, the head of the Church.

Thus far, most of the compounds that show high activity against the eukaryotic type II enzyme contain aromatic substituents at their C-7 positions.

Thus both the approximate age and a high time resolution can be obtained.

Thus, ' old fashioned ' walls-that is high and, relatively, thin-were excellent targets and, over time, easily demolished.

Thus, a particular transistor may be described as silicon, surface mount, BJT, NPN, low power, high frequency switch.

Thus, to meet its emission reduction commitment, the country with initially high energy efficiency might face high costs.

Thus, the combination of poor harvests, the hardships of the peasants, high taxes, lack of representation of the people, and kingly ineptitude are among the causes of the French Revolution.

Thus, a circuit with a low power factor will use higher currents to transfer a given quantity of real power than a circuit with a high power factor.

Thus, a high Q tuned circuit in a radio receiver would be more difficult to tune, but would have greater selectivity, it would do a better job of filtering out signals from other stations that lie nearby on the spectrum.

Thus two tooth cattle are marked on the wither, four tooth on the middle of the back and six tooth on their high bone ( near tail ).

Thus, Fort Souville, on the morning of 12 July 1916, became the high mark of the unsuccessful German offensive against Verdun.