Thus, Margenau remarks: `` A large number of unrelated epicycles was needed to explain the observations, but otherwise the ( Ptolemaic ) system served well and with quantitative precision.

Thus, an enemy would probably use this weapon for attack on static population centers such as large cities.

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

Thus, a poison that covers surface randomly will tend to reduce the number of uncontaminated large planes but leave proportionally more smaller sites free, thus changing the hydrogenation vs. hydrogenolysis selectivity.

Thus the interior of a metal is filled up with a large number of unattached electrons that travel aimlessly around like a crowd of displaced persons.

In particular, one should think of the condition number as being ( very roughly ) the rate at which the solution, x, will change with respect to a change in b. Thus, if the condition number is large, even a small error in b may cause a large error in x.

Thus, a large amount of aggression occurs 5 – 15 minutes after a reunion.

Thus, explosives are substances that contain a large amount of energy stored in chemical bonds.

Thus, from an evolutionary perspective men may have had more to gain from a large increase in resources than women have had, which may be one explanation for why men, and especially poor men, tend to gamble more than women.

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

Thus, actual address space utilization rates will be small in IPv6, but network management and routing efficiency is improved by the large subnet space and hierarchical route aggregation.

Thus, although the composition of the group is slightly different in each instance, the large majority of men present are always close neighbors.

Thus, according to Keynesian theory, some individually-rational microeconomic-level actions such as not investing savings in the goods and services produced by the economy, if taken collectively by a large proportion of individuals and firms, can lead to outcomes, wherein the economy operates below its potential output and growth rate.

Thus, Islamic architecture started witnessing the introduction of such structures as domes and large, arched entrances, referred to as iwans.

Thus the Mary Rose was subject to salvage from the sixteenth century and later, but a very large amount of material, buried in the sediments, remained to be found by maritime archaeologists of the twentieth century.

Thus, the mergers were not done to see large efficiency gains, they were in fact done because that was the trend at the time.

Thus, Nauru was left to handle the immense and expensive task of restoring large chunks of land which were destroyed by the mining.

Thus, at a general level, there is a large degree of uniformity amongst all Orthodox Jews.

Thus, there is a correlation between the results of measurements performed on entangled pairs, and this correlation is observed even though the entangled pair may have been separated by arbitrarily large distances.

Thus for a large or very distributed company that requires multiple PBXs, users can receive the same services across the network and be unaware of the switch that their telephone is connected to.

Thus, first slavery and then serfdom gradually decreased in Europe as the population grew, but were reintroduced in the Americas and in Russia as large areas of new land with few people became available.

Thus, in the very large cases, the HTSC cost can not be offset by simply reducing the coil size at a higher magnetic field.

Thus, the party's platforms and rhetoric critique any corporate influence and control over government, media, and American society at large.

Thus, a few volts ' difference at the grid would make a large change in the plate current and could lead to a much larger voltage change at the plate ; the result was voltage and power amplification.

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: