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

Thus, presence of high levels of peptidoglycan is the primary determinant of the characterisation of bacteria as gram-positive.

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.

Sahra-ye Mahshar ( Armageddon ) ( 1947 ), Talkh-o Shirin ( Bitter and Sweet ) ( 1955 ), Kohne va Now ( Old and New ) ( 1959 ), Qair az Khoda Hichkas Nabud ( None Existed Except God ) ( 1961 ), Asman-o Risman ( The Blue Yonder and Rope ) ( 1965 ), Qesse-ha-ye Kutah Bara-ye Bachcheha-ye Rish-dar ( Short Stories for Bearded Children for Adults ) ( 1974 ), and Qesse-ye Ma be Akhar Rasid ( Thus Ends Our Story ) ( 1979 ) were written during this phase of his literary activity.

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

Thus, when you have prepared your foundation and laid the floor, these can be trucked to the site and erected with a small crew of friends in a weekend.

Thus the film can be applied to back-lighted translucent plastics faces ; ;

Thus, direct comparisons can be drawn with free burning arcs which have been studied in detail during the past years and decades by numerous investigators ( Ref. 3 ).

Thus, for aqueous media, we can think of the idealized organic active as an oleophilic or hydrophobic surface-active agent, and of an idealized builder as a oleophobic or hydrophilic surface-active agent.

Thus, the larvae of the intruder can develop at the expense of the rightful inhabitants and the store of beebread.

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

Thus the unstressed it of it rarely snows here gets its significance from its use with snows: nothing can snow snow but `` it ''.

Thus in it's incredible what that boy can eat dominant stress is likely to be on incredible, and eat will have strong stress also.

Thus, besides the training provided to youth in school, the existence of the school program can have supplementary benefits to industry which make it an asset to industrial development efforts.

Thus, for non-negative changes in the basic wage rate, the industry becomes the active wage-setter, since any increase in the basic wage rate can occur only by reason of industry acquiescence.

Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.

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, man can readily deduce that the primary objective end of the conjugal act is procreation, the propagation of the race.

Thus, while it remains possible that the Babylonians and/or the Pythagoreans may perhaps have had the magic square of three before the Chinese did, more definite evidence will have to turn up from the Middle East or the Classical World before China can lose her claim to the earliest known magic square by more than a thousand years.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

Thus an algorithm can be an algebraic equation such as y

Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system.

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.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus areas can be measured in square metres ( m < sup > 2 </ sup >), square centimetres ( cm < sup > 2 </ sup >), square millimetres ( mm < sup > 2 </ sup >), square kilometres ( km < sup > 2 </ sup >), square feet ( ft < sup > 2 </ sup >), square yards ( yd < sup > 2 </ sup >), square miles ( mi < sup > 2 </ sup >), and so forth.

The evaluation order does not affect the value of such expressions, and it can be shown that the same holds for expressions containing any number of operations .< ref > Thus, when is associative, the evaluation order can be left unspecified without causing ambiguity, by omitting the parentheses and writing simply: