Thus, ocular albinism occurs more frequently in males as they have a single X and Y chromosome, unlike females, whose genetics are characterized by two X chromosomes.

Thus, molecules exist as electrically neutral units, unlike ions.

Thus, unlike metals, semiconductors become better conductors the higher the temperature.

Thus, unlike some human beings, He has no cause for injustice:

Thus, unlike, for example, Dungeons and Dragons, Rolemaster describes wounds not only in the number of points of damage dealt ( which are then subtracted from an abstract pool of ' Hit Points '), but with specific details of the injury inflicted.

Thus the Penates, unlike the localized Lares, are portable deities.

Thus, many a well-to-do family sent their sons to Hertford College in order to instil in them some disciplined education, unlike the privileged wining and dining had by gentlemen-commoners in other colleges.

Thus, while numerous traditional Catholics opposed voting rights for women, the Pope was in favour, arguing that, unlike the feminist protagonists, most women would vote conservative and thus support traditional Catholic positions.

Thus, unlike the granting of Royal Assent by the Sovereign in person or by Royal Commissioners, the method created by the Royal Assent Act 1967 does not require both Houses to meet jointly for the purpose of receiving the notice of Royal Assent.

Thus, Elendil arrived in an area populated by people who, unlike his contemporaries in Númenor itself, were mainly still friends with the Elves, and who, unlike those in Gondor to the south, retained knowledge of the Elder Days.

Thus, in Sweden, unlike most constitutional monarchies, the Monarch is no longer even the nominal chief executive.

Thus a noninteracting Fermi gas, unlike a Bose gas, is prohibited from condensing into a Bose-Einstein condensate, although interacting Fermi gases might.

Thus, unlike standard versions of functionalism ( often called Functional State Identity Theories ), FSTs do not allow for the multiple realizability of mental states, because the fact that mental states are realized by brain states is essential.

Thus, unlike many other states that have elections for some cabinet-level positions, under the New Jersey State Constitution the governor appoints the entire cabinet, subject to confirmation by the New Jersey Senate.

Thus, unlike the procedure under section 3 of the 25th Amendment, a declaration by the incapacitated President to the effect that he is able to resume the powers and duties of his office does not have immediate effect if the incapacity was declared under section four of the 25th amendment.

Thus, unlike copy editing, proofreading's defining procedure is to work directly with two sets of information at the same time.

Thus, unlike black holes, white holes cannot be continuously observed rather their effect can only be detected around the event itself.

Thus, like the Wooton desk, the fall front desk and others with a hinged desktop, and unlike closable desks with an unmovable desktop like the rolltop desk or the cylinder desk all documents and various items must be removed from the work surface before closing up.

Thus, unlike croquet, one side cannot defensively " stake-out " an opponent's rover in roque.

Thus, the Company continues many of its original trade duties, unlike some of the other Livery Companies which have become entirely charitable or ceremonial institutions.

Thus, unlike many Livery Companies, the Gunmakers have retained a link to their trade.

Thus, unlike a chain which has significant tensile strength, liquids usually have little tensile strength under typical siphon conditions, and therefore the liquid on the rising side cannot be pulled up, in the way the chain is pulled up on the rising side.

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.

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

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.

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, the absence of the ignorable coordinate q < sub > k </ sub > from the Lagrangian implies that the Lagrangian is unaffected by changes or transformations of q < sub > k </ sub >; the Lagrangian is invariant, and is said to exhibit a symmetry under such transformations.

This happens because a magnetic field is produced by an electric current, J, which reverses sign under T. Thus, the motion of classical charged particles in electromagnetic fields is also time reversal invariant.

Thus, under time reversal, an invariant state must have vanishing EDM.

Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon.

Thus, by his Dancing Qualia Argument, Chalmers defends his view that phenomenological properties are organizationally invariant.

Thus the Gaussian curvature is an intrinsic invariant of a surface.

Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian.

Thus, by calculating the invariant mass of pairs of photons in a particle detector, pairs can be identified that were probably produced by pion disintegration.

" Thus, invariant mass is a natural unit of mass used for systems which are being viewed from their center of momentum frame ( COM frame ), as when any closed system ( for example a bottle of hot gas ) is weighed, which requires that the measurement be taken in the center of momentum frame where the system has no net momentum.

Thus, a system's invariant mass may change only because invariant mass is allowed to escape, perhaps as light or heat.

Thus the detailed balance equations are satisfied, implying the chain is reversible and it has invariant distribution.

Thus an Alexander polynomial always exists, and is clearly a knot invariant, denoted.

Thus hyperbolic volume is an invariant of many alternating links.

Thus, in either coordinate system, the volume element takes the same expression: the expression of the volume element is invariant under a change of coordinates.

Thus, the invariant mass of systems of particles is a calculated constant for all observers, as is the rest mass of single particles.