Thus, the combined efficiency of the elements replaced by the two fiber plates ( with a combined efficiency of 0.25 ) is 0.043 or about six times less than that of the two fiber plates.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

) Thus a set is completely determined by its elements ; the description is immaterial.

Thus, covalent bonding does not necessarily require the two atoms be of the same elements, only that they be of comparable electronegativity.

Thus the cofinality of a finite partially ordered set is equal to the number of its maximal elements.

Thus designers of calculators strive to minimize the number of logic elements on the chip, not the number of clock cycles needed to do a computation.

Thus for instance the determinant of a matrix with integer coefficients will be an integer, and the matrix has an inverse with integer coefficients if and only if this determinant is 1 or − 1 ( these being the only invertible elements of the integers ).

Thus the only concentration of troops in Conakry appeared to be the armoured battalion, with a modest number of Soviet medium tanks manufactured in the late 1940s, as well as Soviet APCs, and elements of the engineer battalion.

Thus for a ring in which 2 is invertible, the idempotent elements correspond to involutions in a one-to-one manner.

Thus, the Middle-earth legendarium, despite its lack of overt religious elements, can be interpreted as a profoundly religious work.

Thus, contrary to the first impression its name might convey, and as realized in specific approaches and disciplines ( e. g. Fuzzy Sets and Systems ), intuitionist mathematics is more rigorous than conventionally founded mathematics, where, ironically, the foundational elements which Intuitionism attempts to construct / refute / refound are taken as intuitively given.

Thus a point y in V is a cluster point of the net if and only if every neighborhood Y of y contains infinitely many elements of the sequence.

" Thus, it is She who becomes the time and space, the cosmos, it is She who becomes the five elements, and thus all animate life and inanimate forms.

Thus the power relationship is between the conversion of the mechanical energy of the pump mechanism and the fluid elements within the pump.

Thus, certain color contrasts may look fuzzier than others, depending on the allocation of the primary colors ( green has twice as many elements as red or blue in the Bayer arrangement ).

Thus, the " add " instruction replaces the two topmost elements of the stack with their sum.

Thus, non-narrative elements of religion, such as ritual, are not myths.

Thus such elements as collage were introduced, arising partly from an ideal of startling juxtapositions as revealed in Pierre Reverdy's poetry.

Thus younger stars will tend to have a higher portion of heavy elements in their atmospheres than do the older stars.

Thus, in terms of abundances, only about 0. 54 % of Vega consists of elements heavier than helium.

Thus, the 1979 Puebla Conference was an opportunity for orthodox bishops to reassert control of the radical elements ; but they failed.

Thus, these elements have half lives too long to be measured by any means, direct or indirect.

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

Thus, skete life has elements of both solitude and community, and for this reason is called the " middle way ".

Thus, the new definition of trademark in India broadly encompasses almost all the elements of trade dress under the US law.

" Thus the work on the house of God in Jerusalem came to a standstill until the second year of the reign of Darius king of Persia.

Thus, the Dhrystone score counts only the number of program iteration completions per second, allowing individual machines to perform this calculation in a machine-specific way.

Thus, interlaced video captures samples the scene motion twice as often as progressive video does, for the same number of frames per second.

Thus the second experiment gives us 8 times as much precision for the estimate of a single item, and estimates all items simultaneously, with the same precision.

Thus, the total of entropy of the room plus the entropy of the environment increases, in agreement with the second law of thermodynamics.

Thus was conceived their second child – not a son, but another daughter, Alix of France.

Thus if a represents Socrates then Phil ( a ) asserts the first proposition, p ; if a instead represents Plato then Phil ( a ) asserts the second proposition, q.

Thus an hour was 144 conventional minutes ( more than twice as long as a conventional hour ), a minute was 86. 4 conventional seconds ( 44 % longer than a conventional minute ), and a second was 0. 864 conventional seconds ( 13. 6 % shorter than a conventional second ).

However, a second definition and usage has historically been in practice in many fields of computer science and information technology, which defines the prefix kilo when used with byte or bit units of data as 1024 ( 2 < sup > 10 </ sup >); this is due to the mathematical coincidence that Thus, in these fields 1 kilobyte is equal to 1 kibibyte, a new unit standardized as part of the binary prefixes to resolve the ambiguity.

Thus C1 restores its charge and prepares for the next State 1 when it will act again as a time-setting capacitor ... and so on ... ( the next explanations are a mirror copy of the second part of Step 1 ).

Thus the total light received from the second shell is the same as the total light received from the first shell.

Thus, one would expect to find a factor that roughly corresponds to " left " and " right ", as this is the dominant framing for politics in our society, but the basis of Eysenck's " tough / tender-minded " thesis ( the second, " T "- factor ) may well represent nothing beyond an abstract mathematical construct.

Thus will find the matching string " ex " in two possible locations, ( 1 ) at the beginning of words, and ( 2 ) between two characters in a string, where the first is not a word character and the second is a word character.

Thus the second could now be reliably measured.

Thus, the 1960 SI definition abandoned any explicit relationship between the scientific second and the length of a day, as most people understand the term.

Thus, the physical portion of the boat that is below water can be regarded as functioning as a " second sail.

Thus, Septimius Severus spent the remainder of his second term as quaestor on the island.

Thus, if a burglar is verbally challenged by the property owner and sustains injury when jumping from a second story window to escape apprehension, there is no cause of action against the property owner even though that injury would not have been sustained but for the property owner's intervention.

Thus, when embarking upon a second system, an engineer should be mindful that he is susceptible to over-engineering it.

Thus technological innovation and scientific crop management with synthetic nitrogen fertilizer, irrigation and wheat breeding were the main drivers of wheat output growth in the second half of the century.

Thus, it was Gibbs who first combined the first and second laws of thermodynamics by expressing the infinitesimal change in the energy a system in the form:

Thus, an object starting from rest will attain a velocity of 9. 81 m / s ( 32. 2 ft / s ) after one second, 19. 62 m / s ( 64. 4 ft / s ) after two seconds, and so on, adding 9. 81 m / s ( 32. 2 ft / s ) to each resulting velocity.

Thus we cannot get a simple generalization of the Schrödinger equation under the naive assumption that the wave function is a relativistic scalar, and the equation it satisfies, second order in time.

Thus, the molecules are " held in " the liquid more strongly when a second molecule is present.