Thus, the molecular formula of ethanol may be written in a paper in conformational, three-dimensional, full two-dimensional ( indicating every bond with no three-dimensional directions ), compressed two-dimensional ( CH < sub > 3 </ sub >– CH < sub > 2 </ sub >– OH ), separating the functional group from another part of the molecule ( C < sub > 2 </ sub > H < sub > 5 </ sub > OH ), or by its atomic constituents ( C < sub > 2 </ sub > H < sub > 6 </ sub > O ), according to what is discussed.

Thus, it is this semi-empirical formula for bond energy that underlies Pauling electronegativity concept.

Thus a conventionally corrected form of Newcomb's formula, to incorporate the corrections on the basis of mean solar time, would be the sum of the two preceding expressions:

Thus, this formula is non-constructive.

Thus, a list of possible rational roots of the equation can be derived using the formula.

Thus the amount of the test substance required to produce the same biological effect as a given quantity the unit of a standard preparation is compared and the potency of the unknown is expressed as a % of that of the standard by employing a simple formula.

Thus, exports minus imports — which is the GDP formula — declined from 1 billion to 600 million, while GDP was $ 58. 9 billion, resulting in a trivial effect on GDP of about two-thirds of one percent.

Thus the tidal force can be linearized, resulting in the same formula for F < sub > T </ sub > as given above.

Thus by definition our formula is not a tautology.

Thus creating a fireball requires the following formula: Create Fire.

Thus in most " natural " settings, if a complex number provides a solution to a problem, so does its conjugate, such as is the case for complex solutions of the quadratic formula with real coefficients.

Thus the volume magnetic susceptibility and the magnetic permeability are related by the following formula:

Thus, in their system, the Gödel number of the formula " 0

Thus the above formula for the roots involves only real terms if and only if the three roots are real.

: Thus the formula of the preceding article leads itself to the remarkable Theorem.

Thus the Alexandrian formula adopted by Cyril and Dioscorus was " one nature of God the Word Incarnate " which translated in Greek to " mia physis tou theou logou sesarkomene ", by which Cyril meant " one nature ", " from two natures ".

Thus, today the " law of mass action " sometimes refers to the ( correct ) equilibrium constant formula,

The function f is computable, so there is a formula δ representing f in T. Thus for each formula θ, T proves

** Thus this formula is best applied to stable software development teams which have completed multiple projects.

Thus the equipartition theorem for systems with quadratic energies follows easily from the general formula.

Thus, these very cheap and simple cars were the ' formula one ' in this competition.

Thus the given recurrence relation T ( n ) was in Θ ( n < sup > 2 </ sup >), that complies with the f ( n ) of the original formula.

Thus this formula is used for either multiplication or division.

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: