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 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.

Thus, in the immemorial way -- in the way of the right hand that knows and the left that does not -- was the stage set for tragedy at Bari.

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:

Thus, Abulafia in the 13th century assumed that the language spoken in Paradise had been different from Hebrew, and rejected the claim then current also among Christian authors, that a child left unexposed to linguistic stimulus would automatically begin to speak in Hebrew.

Thus the Hellenic laws treated all forms of theft, assault, rape, and murder as private wrongs, and left action for enforcement up to the victims or their survivors.

Thus dates can be sorted using simple string comparison algorithms, and indeed by any left to right collation.

Thus the modern population of Hungary do not feel that they belong in the Western Siberia that the Hungarian Magyars left 12 centuries ago ; and the English descendants of the Angles, Saxons and Jutes do not yearn to reoccupy the plains of Northwest Germany.

Thus iron left exposed to air and water will continue to rust until all of the iron is oxided.

Thus traditional exegesis supposes that after his release Paul sailed from Rome into Asia, passing Crete by the way, and that there he left Titus " to set in order the things that were wanting.

Thus, when the Winter War broke out, Finland was left alone to resist the Soviet attack.

This identifies the tangent space T < sub > e </ sub > at the identity with the space of left invariant vector fields, and therefore makes the tangent space at the identity into a Lie algebra, called the Lie algebra of G, usually denoted by a Fraktur Thus the Lie bracket on is given explicitly by = < sub > e </ sub >.

Thus, Nauru was left to handle the immense and expensive task of restoring large chunks of land which were destroyed by the mining.

Thus, the word ' left ' in American political parlance may refer to ' liberalism ' and be identified with the Democratic Party, whereas in a country such as France these positions would be regarded as relatively more right-wing, and ' left ' is more likely to refer to ' socialist ' positions rather than ' liberal ' ones.

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 this type of land appropriation did not violate the Lockean proviso – there was " still enough, and as good left.

Thus, the left side of the body is slightly forward of the right side of the body and the left hand is more forward than the right one.

Thus, expressions are not entered wholesale from right to left but calculated one piece at a time, most efficiently from the center outwards.

Thus it has been supposed that the difference between the numbers is accounted for a garrison of 12 ships left at Aegina.

Thus, it is not surprising that people left Alsace, not only for Paris – where the Alsatian community grew in numbers, with famous members such as Baron Haussmann – but also for more distant places like Russia and the Austrian Empire, to take advantage of the new opportunities offered there: Austria had conquered lands in Eastern Europe from the Ottoman Empire and offered generous terms to colonists as a way of consolidating its hold on the new territories.

Thus, any gait can completely be described in terms of the beginning and end of stance phase of three limbs relative to a cycle of a reference limb, usually the left hindlimb.

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, this album was recorded for Buddah, with the band signed to Kama Sutra, which left them close to penniless after extricating themselves from A & M.

" Thus Ambrose refused to be drawn into a false conflict over which particular local church had the " right " liturgical form where there was no substantial problem.

Thus, from a consequentialist standpoint, a morally right act ( or omission ) is one that will produce a good outcome, or consequence.

Thus an outcome of yì is doing the right thing for the right reason.

Thus, from a consequentialist standpoint, a morally right action is one that produces a good outcome, or consequence.

Thus, an applicant must prove discrimination in the enjoyment of a specific right that is guaranteed elsewhere in the Convention ( e. g. discrimination based on sex-Article 14-in the enjoyment of the right to freedom of expression-Article 10 ).

Thus, for example, if we can obtain a decomposition of into a hierarchical composition of functions such that,,, as shown in the figure at right, this would probably be considered a highly valuable decomposition.

Thus, intellectual property ensures this right when it comes to production.

Thus, while people have the right to private property, they should give it away as enlightened altruists.

Thus literate lay defendants often also claimed the right to benefit of clergy ; furthermore, as the Biblical passage used for the literacy test was always Psalm 51 ( Miserere mei, Deus ...-" O God, have mercy upon me ..."), an illiterate person who had memorized the psalm could also claim benefit of clergy.

Thus the HyperCard stack became a self-contained application in its own right, distributable as a single entity that end-users could run without the need for additional installation-steps.

Thus, this would let light of the right frequency to make this happen sum to a larger probability amplitude, and as such possess a larger probability of reaching the appropriate final point.

Thus, the current state of the law is that, while the federal government may not restrict use of peyote in ceremony, individual states do have a right to restrict its use.

Jeff Snyder is a spokesman for the view that gun possession is a civil right, and that therefore arguments about whether gun restrictions reduce or increase violent crime are beside the point: " I am not here engaged in ... recommending ... policy prescriptions on the basis of the promised or probable results crime ... Thus these essays are not fundamentally about guns at all.

Thus a single-unit streetcar capable of only operating on a shared right of way is not generally considered “ light rail ”.

Thus an ex facie absolute disposition, qualified by a back-bond expressing the limited nature of the right actually held by the person to whom the disposition is made, would constitute what in England is termed a deed of trust.