Thus, the energy required to break any single pair is related to the energy required to break all of the pairs ( or more than just two electrons ).

Thus the division form of Euclid's algorithm starts with a pair of positive integers and forms a new pair that consists of the smaller number and the remainder obtained by dividing the larger number by the smaller number.

For example, in peas the allele for green pods, G, is dominant to that for yellow pods, g. Thus pea plants with the pair of alleles either GG ( homozygote ) or Gg ( heterozygote ) will have green pods.

Thus, in DNA, the purines adenine ( A ) and guanine ( G ) pair up with the pyrimidines thymine ( T ) and cytosine ( C ), respectively.

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 a phonemic split has occurred in London English, exemplified by the minimal pair wholly vs. holy.

Thus, if the pair is subsequently reused to support applications that require higher frequencies ( such as analog or digital carrier systems or DSL ), any loading coils that were present on the line must be removed or replaced with one which is transparent to DSL.

f. Thus, every pair of ( mutually ) inverse elements gives rise to two idempotents, and ex

Thus to find the median, order the list according to its elements ' magnitude and then repeatedly remove the pair consisting of the highest and lowest values until either one or two values are left.

Thus, what came out in the media: from newspapers, magazines, TV, and the movies, was a product of the stereotypes of the 30s and 40s — though garbled — of a cross between a 1920s Greenwich Village bohemian artist and a Bop musician, whose visual image was completed by mixing in Daliesque paintings, a beret, a Vandyck beard, a turtleneck sweater, a pair of sandals, and set of bongo drums.

( Thus each unicorn can reach only 30 of the board's cubes ; each player's pair, 60.

Thus, if the triangle is red, then the (" triangle ", " red ") pair will be in the function, but the pair (" yellow triangle ", " red ") is not.

Thus, many speakers do not differentiate between the vowel sounds ( as in " dress ") and ( as in < trap >), except in cases where a minimal pair such as < bed >/< bad > exists in the vocabulary of the speaker.

Thus, even though White possesses the bishop pair, it is usually advisable for Black to open the game quickly to exploit his lead in development.

Thus, one obtains a form which Taoist texts liken to a pair of fishes nestling head to tail against each other.

Thus the pair of pants is a cobordism between M and N.

Thus, a parent and child pair has a value of r = 0. 5, siblings have a value of r = 0. 5, a parent's sibling has r = 0. 25, and first cousins have r = 0. 125.

Thus the changes in both the initial and the tone were each conditioned by the other, represented by different characters in the fanqie pair.

Thus, only one empirical value is available in a pair of electrodes and it is not possible to determine the value for each electrode in the pair using the empirically obtained galvanic cell potential.

Thus, the standing pair would be King Edward ( in black chaperon, standing on right ) mirroring his wife, Queen Eleanor of Aragon ( standing on left ).

" Thus an interval cycle or pair of cycles may be reducible to a representation of the chromatic scale.

Thus, variable only depends directly on variable, rather than depending on the entire set of variables.

Thus, cloud ceiling and flight visibility are the most important variables for safe operations during all phases of flight.

Thus, functions can be assigned as values to variables or passed as arguments to functions.

This question has two fundamental physical units: time t and length, and three dimensional variables: distance D, time taken T, and velocity V. Thus there is 3 − 2 = 1 dimensionless quantity.

There are 3 fundamental physical units in this equation: time t, mass m, and length l, and 4 dimensional variables, T, M, L, and g. Thus we need only 4 − 3 = 1 dimensionless parameter, denoted π, and the model can be re-expressed as

Thus the set of functions, where g is any one-argument function, represents the entire set of functions in variables x, y that could have produced the x-partial derivative 2x + y.

Thus, it can be seen that reflexives and reciprocals are bound variables ( known technically as anaphors ) while true pronouns can be free variables in some grammatical structures or variables that cannot be bound in other grammatical structures.

Carl Friedrich Gauss in his 1827 Disquisitiones generales circa superficies curvas ( General investigations of curved surfaces ) considered a surface parametrically, with the Cartesian coordinates x, y, and z of points on the surface depending on two auxiliary variables u and v. Thus a parametric surface is ( in today's terms ) a vector valued function

Thus, the risk of stack overflow can be reduced by minimizing the parameters and internal variables of the recursive procedure, and / or by using an explicit stack structure.

Thus, it's really only necessary to encode three of the four possibilities as dummy variables.

Thus, the less random error in the variables, the higher the possible correlation between them.

Thus they do not do very well with the isolation of a relationship among variables, as against a representation of a set of exemplars.

Thus once the domain of the first-order variables is established, the meaning of the remaining quantifiers is fixed.

Thus, Murdock's hypotheses regarding the relationships between the sexual division of labor and postmarital residence were basically correct, though, as has been shown by Korotayev, the actual relationships between those two groups of variables are more complicated than he expected ( see, e. g., Korotayev A.

Thus, the density of the sum of m + n terms of a sequence of independent identically distributed variables equals the convolution of the densities of the sums of m terms and of n term.

Thus, for a response Y and two variables x < sub > 1 </ sub > and x < sub > 2 </ sub > an additive model would be:

Thus, the plural logic comprehension schema does not yield Russell's paradox because the quantification of plural variables does not quantify over the domain.

Thus, additional research is required, using a more complex model of crime and control to include variables such as opportunities or incentives relative to a country's standard of living, potential punishment, chance of being caught, law enforcement efforts and expenditures on theft and property crime relative to other crimes, size of the country's criminal population, education levels, and other socio-economic factors.

Thus, there are four basic types of generating functions, depending on the choice of variables.

Thus an expression represents a function whose inputs are the value assigned the free variables and whose output is the resulting value of the expression.

Thus, a definite description ( of the general form ' the F is G ') becomes the following existentially quantified phrase in classic symbolic logic ( where ' x ' and ' y ' are variables and ' F ' and ' G ' are predicates-in the example above, F would be " is an emperor of Germany ", and G would be " is gray "):

Thus, an indefinite description ( of the general form ' an D is A ') becomes the following existentially quantified phrase in classic symbolic logic ( where ' x ' and ' y ' are variables and ' D ' and ' A ' are predicates ):