Thus, churches actually had money-changing tables at which each coin would be examined separately and a token of actual worth given to the layperson so that he or she could be seen by the other parishioners as putting money in the basket during that part of the service.

Thus, in 1992 the Ingush joined the newly-created Russian Federation to try to resolve the conflict with Ossetia peacefully, also in the hope that the Russians would return their land as a token of their loyalty.

Thus, there is substantial debate regarding the identity of the book's author.

Thus, Christianity acquired an identity distinct from Rabbinic Judaism, but this distinction was not recognised all at once by the Roman Empire, see Split of early Christianity and Judaism for details.

Thus, Boyarin has argued that " Jewishness disrupts the very categories of identity, because it is not national, not genealogical, not religious, but all of these, in dialectical tension.

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, for Rand, the fact that consciousness must itself possess identity implies the rejection of both universal skepticism based on the " limits " of consciousness and any claim to revelation, emotion or faith based belief.

Thus, for a language to be used at all it must have some public criterion of identity.

Thus, the aggregate term Third World was challenged as misleading even during the Cold War period because it had no consistent or collective identity among the countries it supposedly encompassed.

Thus, it is not correct to establish a strict common origin, but a common cultural identity.

Thus, by combinatorial specifying the identity of particular body regions, Hox genes determine where limbs and other body segments will grow in a developing embryo or larva.

Thus, although other economists focus on the identity or type of legal system of the colonizers to explain institutions, these authors look at the environmental conditions in the colonies to explain institutions.

Thus, for example, groups have a signature containing two operators: the multiplication operator m, taking two arguments, and the inverse operator i, taking one argument, and the identity element e, a constant, which may be considered an operator that takes zero arguments.

Thus the sine law is equivalent to the angle sum identity when the angles sum is between 0 and 180 degrees and when each individual angle is between 0 and 90 degrees.

Thus, individuals with little or no direct ancestry from the Arabian Peninsula could identify themselves or be considered as Arabs, partially by virtue of their home language ( see Arab identity ).

Thus Alexander is attempting to " naturalize " language and national identity via the metaphor of " blood.

Thus the only two field automorphisms of that leave the real numbers fixed are the identity map and complex conjugation.

Thus, groups with a strong sense of unity and identity can benefit from kin selection behavior such as common property and shared resources.

Thus the Orthodox emphasis would be that Christ died, not to appease an angry and vindictive Father, or to avert the wrath of God, but to change people so that they may become divine, that is to say, become God in his energies or operations but not in his essence or identity as God ( see theosis ).

Thus, critics argue that Eurocommunism does not have a well-defined identity and cannot be regarded as a separate movement in its own right.

The notion is closely related to the idea of a multiplicative character in group theory, which is a homomorphism χ from a group G to the multiplicative group of a field F. Thus χ: G → F < sup >×</ sup > satisfies χ ( e ) = 1 ( where e is the identity element of G ) and

Thus, the Jacobi identity for Lie algebras simply becomes the assertion that the action of any element on the algebra is a derivation.

Thus, if the structure of one member of a family is known, a reliable prediction may be made for a second member of the family, and the higher the identity level, the more reliable the prediction.

Thus, the principle of nationalism serves to preserve the cultural traditions of La Familia de La Raza and promotes our identity as a Chicana / Chicano Gente .’ MEChA members themselves differ in their interpretations of " La Raza ".

If the domain has a multiplicative identity ( which we may call 1 ), this is equivalent to saying that 1 ≠ 0 Thus a domain is a nontrivial ring without left or right zero divisors.

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, a player should use Blackwood only when he can ascertain that the partnership holds at least second-round controls in all suits ( kings or, if a suit fit is found, singletons ).

Thus, as an ethnic religion, Judaism holds that others may have their own, different, paths to God ( or holiness, or " salvation "), as long as they are consistent with the Seven Laws of Noah.

" Thus, any activity of production ( which distributism holds to be the most important part of any economy ) ought to be performed by the smallest possible unit.

Thus the no-cloning theorem holds in full generality.

" Thus, Objectivism holds that the mind does not create reality, but rather, it is a means of discovering reality.

Thus, a notrump opener who holds at least four cards in each major suit should " correct " by bidding the other major suit at the lowest level.

Thus the definition of Christian propitiation asserted by Calvin, Packer and Murray holds that within God there is a dichotomy of love and anger, but through propitiation love trumps anger, abolishing it.

Thus certain plants, including the traveler's tree ( so called because its trunk holds potable water ), are found both in Madagascar and on the South American continent, but not in Africa.

Thus it is the structure of the organization rather than the employees, alone, which holds the key to improving the quality of output.

Thus it holds that technical analysis cannot be effective.

Thus, it holds the distinction of being the only city in Kentucky to have served as the county seat of three separate counties.

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

Thus a cask standing on end represents the mountain on which Christ is tempted by the Devil ; thunder is imitated by the report of a gun ; in order to signify that the Devil had entered into him, Judas holds a bird of black plumage before his mouth and makes it flutter.

Thus the intuitive reading of a Hoare triple is: Whenever P holds of the state before the execution of C, then Q will hold afterwards, or C does not terminate.

Thus given no arbitrage opportunities, the above relationship ( put-call parity ) holds, and for any three prices of the call, put, bond and stock one can compute the implied price of the fourth.

Thus, although elected by the Supreme Council, the president is essentially hereditary-the emir of Abu Dhabi holds the position.

Thus all geodesics leaving a point will eventually reconverge after a finite time, provided the appropriate energy condition holds, a result also known as the focusing theorem.

Thus, the holder is one of the only five people in the UK to hold two or more different dukedoms, the others being the Duke of Cornwall and Rothesay, the Duke of Hamilton and Brandon, the Duke of Argyll ( who holds two dukedoms named Argyll ), and the Duke of Richmond, Lennox and Gordon.

where is the point biserial correlation of item i. Thus, if the assumption holds, where there is a higher discrimination there will generally be a higher point-biserial correlation.

Thus, the Duke holds three ( four, if the French Aubigny claim is accepted ) dukedoms, more than any other person in the realm.

Thus, the Duke holds four dukedoms ( including Aubigny-sur-Nère ), more than any other person in the realm.

Thus, the Duke holds four dukedoms ( including the titular Aubigny-sur-Nère ; see Duke of Aubigny ), more than any other person in the realm.

Thus the school's leader ( who holds the dual titles of chancellor and dean ) must obtain funds directly from the California State Legislature, unlike other UC institutions, which receive money from the Regents.