Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus for example Heraclitus ' The Allegorist ' quoted fr. 326 and part of fr. 6, about ships in a storm, in his study on Homer's use of allegory.

Thus, study of this Barnum / Forer effect has been mostly focused on the level of acceptance of fake horoscopes and fake astrological personality profiles.

Thus, by monitoring eye movements, we can study what information is being processed at a given time.

Thus this study suggests that full sleep may not be important for optimal performance of memory.

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, it is on the one side, the study of wealth and on the other and more important side, a part of the study of man.

Thus, the search for extrasolar planets also includes the study of planetary habitability, which considers a wide range of factors in determining an extrasolar planet's suitability for hosting life.

Thus, the overall findings of the study are clear and require that even we skeptics, who have long doubted parental claims of the effects of various foods on the behavior of their children, admit we might have been wrong.

Thus followed the line of Lomonosov and the contributions of the Russian school became more frequent through his disciples, and in the nineteenth century we have great geographers as Vasily Dokuchaev who performed works of great importance as a " principle of comprehensive analysis of the territory " and " Russian Chernozem " latter being the most important where introduces the geographical concept of soil, as distinct from a simple geological strata, and thus founding a new geographic area of study: the Pedology.

Thus other than the prophets mentioned in the Quran, Ahmadis, with support from theological study also recognize Buddha, Krishna, founders of Chinese religions to be divinely appointed individuals.

Thus both fields of study are useful.

Thus much of WMCF is, in effect, a study of the epistemological foundations of the calculus.

Thus, genomics is the study of all the genes of a cell, or tissue, at the DNA ( genotype ), mRNA ( transcriptome ), or protein ( proteome ) levels.

Thus biography can form one part of the larger study of the cultural significance, underlying program, or agenda of a work ; a study which gained increasing importance in the 1980s and early 1990s.

Thus, E-Language is not itself a coherent concept, and Chomsky argues that such notions of language are not useful in the study of innate linguistic knowledge, i. e., competence, even though they may seem sensible and intuitive, and useful in other areas of study.

Thus, it cannot be concluded to what extent this study had an effect on " Little Albert's " life.

Thus, he notes that hiring decisions at Hitachi, during the time of his study, were " regulated by very strict qualification standards ", and not very significantly influenced by ascribed characteristics.

" ( 7 ), Thus, Frye launched the pursuit which was to occupy the rest of his career — that of establishing criticism as a " coherent field of study which trains the imagination quite as systematically and efficiently as the sciences train the reason " ( Hamilton 34 ).

Thus many opponents of what they saw as racism in New Zealand in the early 1980s saw it as useful to use the protests against South Africa as a vehicle for wider social action.

Thus, under his definition, Christian violence includes " forms of systemic violence such as poverty, racism, and sexism ".

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: