Thus, at pH between 2. 2 and 9. 4, the predominant form adopted by α-amino acids contains a negative carboxylate and a positive α-ammonium group, as shown in structure ( 2 ) on the right, so has net zero charge.

Thus, almost all positive integers are composite ( not prime ), however there are still an infinite number of primes.

Thus, it has a year 0, the years before that are designated with negative numbers and the years after that are designated with positive numbers.

Thus the integration of the princely states can be viewed as one of the positive aspects of his legacy.

Thus, any other number c that divides both a and b must also divide g. The greatest common divisor g of a and b is the unique ( positive ) common divisor of a and b that is divisible by any other common divisor c.

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.

Thus, when the plate is introduced to a compatible printing ink and water mixture, the ink will adhere to the positive image and the water will clean the negative image.

Thus, the logarithm function is an isomorphism from the group of positive real numbers under multiplication to the group of real numbers under addition, represented as a function:

Thus the bound vector represented by ( 1, 0, 0 ) is a vector of unit length pointing from the origin along the positive x-axis.

: and this exceeds unity by only about r /( 2N-2b ) if N-b is large compared to r. Thus the weight of evidence provided by the sight of a white shoe is positive, but is small if the number of ravens is known to be small compared to the number of non-black objects.

Thus, a large positive return loss indicates the reflected power is small relative to the incident power, which indicates good impedance match from source to load.

Thus, OECD countries witness a stronger positive link in the short term while non-OECD countries experience a stronger positive link in the long term.

if there exists an integer such that .< ref > Thus, divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors.

Thus, this campaign yielded mixed results, but was mostly positive for Edward.

Thus, the emf has the same value but opposite sign as the integral of the electric field aligned with an internal path between two terminals A and B of a source of emf in open-circuit condition ( the path is taken from the negative terminal to the positive terminal to yield a positive emf, indicating work done on the electrons moving in the circuit ).

Thus, rather than being a pest, mistletoe can have a positive effect on biodiversity, providing high quality food and habitat for a broad range of animals in forests and woodlands worldwide.

Thus, the balancing approach to procedural fairness might in some circumstances be prepared to tolerate or accept false positive verdicts in order to avoid unwanted costs ( political ) associated with the administration of criminal process.

Thus the topology of the group SL ( n, C ) is the product of the topology of SU ( n ) and the topology of the group of hermitian matrices of unit determinant with positive eigenvalues.

Thus zero appears in the middle, with the positive numbers to the right and the negative numbers to the left.

Thus every real number other than zero is either positive or negative, while zero itself is not considered to have a sign.

Thus, Modern Orthodoxy holds that Jewish law is normative and binding, while simultaneously attaching a positive value to interaction with the modern world.

Thus the displacement of the Cadell Fault 25, 000 BP lead directly to the formation of the famous Barmah River Red Gum Forests

Thus, power output of a Wankel engine is generally higher than that of a four-stroke piston engine of similar engine displacement in a similar state of tune ; and higher than that of a four-stroke piston engine of similar physical dimensions and weight.

Moreover, a recent study has recommended that the IDP concept should be defined even more narrowly, to be limited to persons displaced by violence .” Thus, despite the non-exhaustive reasons of internal displacement, many consider IDPs as those who would be defined as refugees if they were to cross an international border hence the term refugees in all but name is often applied to IDPs.

Thus, a displacement of the fleet from one locality to another will generally have little effect if the same quota is taken.

Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P. A ' displacement vector ' represents the length and direction of that imaginary straight path.

Thus, a spatial displacement defines a transformation for Plücker coordinates of lines given by

Thus the displacement of the Cadell Fault 25, 000 years BP led directly to the formation of the Barmah River Red Gum Forests.

Thus a displacement sensing keyboard may have greater versatility when it is desired to have both organ and piano behaviour in an input device.

Thus, the present distribution is apparently a relict, and extinction of populations / displacement by the more resilient Penelope guans seems to have played as much or possibly more of a role in shaping the diversity of piping guans of our time than emergence of new lineages ( Grau et al.

Thus, many modern pumps have a molecular drag stage such as a Holweck or Gaede mechanism near the exhaust to reduce the size of backing pump required.

Thus, as with all heat pumps, the Coefficient of Performance ( amount of thermal energy moved per unit of input work required ) decreases with increasing temperature difference.

Thus there exists a maximum engine size of approximately 300 kN of thrust beyond which there is no longer enough nozzle area to heat enough fuel to drive the turbines and hence the fuel pumps.

Thus we are compelled to face the urbanization of the South -- an urbanization which, despite its dramatic and overwhelming effects upon the Southern culture, has been utterly ignored by the bulk of Southern writers.

Thus, paradoxically, the beat writers resort to `` religious '' metaphors: they are in search of mana, the spiritual, the numinous, but not anything connected with formal religion.

Thus, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus there are polynomials Af such that Af.

Thus the Af are projections which correspond to some direct-sum decomposition of the space V.

Thus pencils of tangents to Q are transformed into pencils of tangents.

Thus it follows that the secants of **zg are all invariant.

Thus, although the agenda of external assistance in the economic sphere are cumulative, and many of the policies suggested for nations in the earlier stages remain relevant, the basic purpose of American economic policy during the later stages of development should be to assure that movement into a stage of self-sustaining growth is not prevented by lack of foreign exchange.

Thus the first lines of one of Charles Wesley's hymns are as follows.

Thus in his friends are stranger than his sisters' strong stresses are normal for his and sisters', but in his friends are stranger than his sisters strong stresses are normal for friends and sisters.

Thus his persistence values for some stem frequencies per meaning are: stem identical in 8 languages, 100% ; ;

Thus, the white middle and lower classes are arrayed against the Negro middle and lower classes.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus, in the example cited above Fromm rests his whole case on the premise that the workers are being deprived unconsciously, unknowingly, of fulfillment, and then supports this with survey data reporting conscious, experienced frustrations.

Thus, the three main categories of antisubmarine warfare operations are defense of shipping, defense of naval forces, and area defense.

Thus, the most productive areas are not necessarily the most stressed.

Thus a number of operations of the order of Af are required.

Thus, if we are to observe American folklore in the twentieth century, we will do well to establish the relationships between folklore, nationalism and imperialism at the outset.

Thus, in `` The Story Of Ruth '' we have Ruth, Naomi, and Boaz and sets that are meticulously authentic.

" 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 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.