Thus, the dotted line shown in figure 4 was taken as typical for the temperature distribution for all blowing rates.

Thus differential geometry may study differentiable manifolds equipped with a connection, a metric ( which may be Riemannian, pseudo-Riemannian, or Finsler ), a special sort of distribution ( such as a CR structure ), and so on.

Thus the distribution of Symbiodinium on coral reefs and its role in coral bleaching presents one of the most complex and interesting current problems in reef ecology.

Thus, a non-intuitive ( e. g., a higher-energy for at least one species ) distribution of electrons in the combination of iron and oxygen must exist, in order to explain the observed diamagnetism and no unpaired electrons.

Thus, there is the idea that in the capitalist mode of production the behaviour of actors in the market economy ( means of production, distribution and exchange, the relations of production ) plays the major role in configuring society.

Thus, liquid crystal sheets are often used in industry to look for hot spots, map heat flow, measure stress distribution patterns, and so on.

Thus the MPPC lost the ability to control the American film industry through patent licensing, and had to rely instead on its subsidiary, the General Film Company, formed in 1910, which monopolized film distribution in America.

Thus, measuring a quantum state described by complex coefficients ( a, b ,..., h ) gives the classical probability distribution and we say that the quantum state " collapses " to a classical state as a result of making the measurement.

Expected to make use of devices with which listeners could press a button to indicate whether they liked or disliked a particular piece of music, Adorno bristled with distaste and astonishment: “ I reflected that culture was simply the condition that precluded a mentality that tried to measure it .” Thus Adorno suggested using individual interviews to determine listener reactions and, only three months after meeting Lasarzfeld, completed a 160-page memorandum on the Project ’ s topic, “ Music in Radio .” Adorno was primarily interested in how the musical material was affected by its distribution through the medium of radio and thought it imperative to understand how music was affected by its becoming part of daily life.

Thus, if each person votes to get as much cake as possible, choice 4 would be third from the top in everyone's list, and would in any direct choice lose 2 to 1 against an unequal distribution.

Thus, the system can be analyzed with Schrödinger's equation and the guiding equation, with an initial distribution for the particles in the system ( see the section on the conditional wave function of a subsystem for details ).

Thus, the conditional probability distribution is:

Thus compatibility with data in the old format may need to be kept when switching to a different format, even when decoding from ( as with many MPEG formats ), or distribution in ( as has at least been planned with H. 264 ) the old format requires paying royalties.

A loss which exceeds the VaR threshold is termed a “ VaR break .” Thus, VaR is a piece of jargon favored in the financial world for a percentile of the predictive probability distribution for the size of a future financial loss.

Thus were born dedicated hydrographic organizations for the collection, organization, publication and distribution of hydrography incorporated into charts and sailing directions.

Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.

Thus, education is the method by which to reform society, and there are few limits to the drastic social improvements that could be brought about by the appropriate distribution of education.

Thus, CO enables the efficient distribution of all other mechanisms, and also the distribution of a mix of different ( any ) local mechanisms, for achieving distributed and global serializability.

Thus the warden's duty in this respect was similar to that of the sheriff who received the writs for distribution to the barons in the shires.

Thus distribution of questions, the variety of topics, or the answers, risks losing the opportunity to compare, with precision, the candidates one-to-another.

Thus when " well-to-wheels " is cited, one should keep in mind that the discussion is no longer about the vehicle, but rather about the entire energy supply infrastructure-in the case of fossil fuels this should also include energy spent on exploration, mining, refining, and distribution.

Thus mutual information can also be understood as the expectation of the Kullback-Leibler divergence of the univariate distribution p ( x ) of X from the conditional distribution p ( x | y ) of X given Y: the more different the distributions p ( x | y ) and p ( x ), the greater the information gain.

Thus the A < sub > n </ sub >( 0 )'s satisfy the axioms for a probability distribution.

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: