Thus, Walsh modified the vertical passing scheme he had learned during his time with the Raiders, designing a horizontal passing system that relied on quick, short throws-often spreading the ball across the entire width of the field.

Thus, the broadcast domain is the entire inter-connected layer two network, and the segments connected to each switch / bridge port are each a collision domain.

Thus, what started as an effort to translate between languages evolved into an entire discipline devoted to understanding how to represent and process natural languages using computers.

Thus, body forces are specified by vector fields which are assumed to be continuous over the entire volume of the body, i. e. acting on every point in it.

Thus, the only logical possibilities are to accept non-Euclidean geometry as physically real, or to reject the entire notion of physical tests of the axioms of geometry, which can then be imagined as a formal system without any intrinsic real-world meaning.

Thus any non-constant entire function must have a singularity at the complex point at infinity, either a pole for a polynomial or an essential singularity for a transcendental entire function.

Thus, the Sheikh of al-Azhar in Cairo, Muhammad Sayid Tantawy, who is the leading religious authority in the Sunni Muslim establishment in Egypt, alongside the Grand Mufti of Egypt, said the following about fatwās issued by himself or the entire Dar al-Ifta:

Thus the entire society from top to bottom is bound by feudalism.

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

Thus the tonewheel assembly generates 91 frequencies, which are all that are required for the entire organ.

Thus as a result of the three Carnatic Wars, the British East India Company gained exclusive control over the entire Carnatic region of India.

Thus, the cost is minimized over a sample of the data rather than the entire data set.

implies that the entire NC hierarchy " collapses " down to some level i. Thus, there are 2 possibilities:

Thus the entire field of quantum physics emerged, leading to its wider acceptance at the Fifth Solvay Conference in 1927.

Thus, amber mutants are an entire class of virus mutants that can grow in bacteria that contain amber suppressor mutations.

Thus single decade scales C and D range from 1 to 10 across the entire width of the slide rule while double decade scales A and B range from 1 to 100 over the width of the slide rule.

Thus a single-stage rocket is at a disadvantage because it must carry its entire vehicle mass to orbit, which in turn reduces payload capacity.

Thus, it was possible that an east-west line extending east from Lake Michigan's southern tip may have intersected Lake Erie somewhere east of Maumee Bay, or worse, may not have intersected the lake at all ; the farther south that Lake Michigan actually extended, the more land Ohio would lose, perhaps even the entire Lake Erie shoreline west of Pennsylvania.

Thus, by changing the value of one of these parameters at one location in the Metafont file, one can produce a consistent change throughout the entire font.

Thus, in the scaleogram of a continuous wavelet transform of this signal, such an event marks an entire region in the time-scale plane, instead of just one point.

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 in a fraction of the nuclear events ( the recoil-free fraction, given by the Lamb – Mössbauer factor ), the entire crystal acts as the recoiling body, and these events are essentially recoil-free.

Thus the magnitude of the shift is related not to the Compton wavelength of the electron, but to the Compton wavelength of the entire atom, which can be upwards of 10 000 times smaller.

Thus, in Keith Petersen ’ s words, “ teachers assumed responsibility for shaping a district's entire educational policy .”

Thus, giving grades and promotions based only on an individual's performance relative to a small local group, as is common, may reduce cooperative behaviors in the group.

Thus, while altruistic persons may under some circumstances be outcompeted by less altruistic persons at the individual level, according to group selection theory the opposite may occur at the group level where groups consisting of the more altruistic persons may outcompete groups consisting of the less altruistic persons.

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, 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 this class of molecules belong to the D < sub > 2d </ sub > point group.

Thus the discovery report by the Berkeley group reads: " It is suggested that element 97 be given the name berkelium ( symbol Bk ) after the city of Berkeley in a manner similar to that used in naming its chemical homologue terbium ( atomic number 65 ) whose name was derived from the town of Ytterby, Sweden, where the rare earth minerals were first found.

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 the probability of two failures in a same RAID group in time proximity is much smaller ( approximately the probability squared, i. e., multiplied by itself ).

Thus the probability of two failures in a same RAID group in time proximity is much smaller ( approximately the probability squared, i. e., multiplied by itself ).

Thus, it has been argued that a voucher system would lead students who do not belong to a preferred religious or ethnic group, or those with disabilities, to become concentrated within the public school system.

Thus one has the fundamental groupoid instead of the fundamental group, and this construction is functorial.

Thus the DTFT of the s sequence is also the Fourier transform of the modulated Dirac comb function .< ref group =" note "> We may also note that:

Thus the group of left and right handed 4x4 quaternion matrcies is Sp ( 8 ) xSU ( 2 ) which does include the standard model bosons:

Thus a resin can be tailored to a particular toxic group.

Hence, those with less pigmented skin survived and had children at higher rates because their skin allowed more UV light for the production of vitamin D. Thus, the skin of those in the group that left the African continent and went far north gradually developed adaptations for relatively greater translucence compared to equatorial hues.

Thus, for example, two objects may be group isomorphic without being ring isomorphic, since the latter isomorphism selects the additional structure of the multiplicative operator.

Thus, although the composition of the group is slightly different in each instance, the large majority of men present are always close neighbors.

But this group found it increasingly difficult to prove that they were not labourers because the 1882 act defined excludables as ‘ skilled and unskilled labourers and Chinese employed in mining .’ Thus very few Chinese could enter the country under the 1882 law.

Thus Euclidean geometry corresponds to the choice of the group E ( 3 ) of distance-preserving transformations of the Euclidean space R < sup > 3 </ sup >, conformal geometry corresponds to enlarging the group to the conformal group, whereas in projective geometry one is interested in the properties invariant under the projective group.