Therefore, because the breasts are especially sensitive to developmental interference ( genetic and environmental ), breast symmetry indicates a woman of good health and thus of good breeding stock, who shall successfully bear more ( surviving ) children than will a woman with asymmetrical breasts.

Therefore, the often-perceived symmetry between Mahāyāna and Hīnayāna can be deceptive, as the terms were not actually coined in relation to one another in the same era.

Therefore, it will have to be constant in the external reference frame, but the moment of inertia tensor ( I ) is non-constant in this frame because of the lack of symmetry.

Therefore, aperiodic or quasiperiodic structures can be divided into two main classes: those with crystallographic point-group symmetry, to which the incommensurately modulated structures and composite structures belong, and those with non-crystallographic point-group symmetry, to which quasicrystal structures belong.

Therefore, to obtain a full set of Fourier transform data, it is necessary to rotate the crystal through slightly more than 180 °, or sometimes less if sufficient symmetry is present.

Therefore the Lorentz group is said to express the fundamental symmetry of many of the known fundamental Laws of Nature.

Therefore, in a way, this frieze group contains the " largest " symmetry groups, which consist of all such transformations.

Therefore mirror symmetry allows one to find the full nonperturbative solutions to the theory.

Therefore a symmetry group of rotational symmetry is a subgroup of E < sup >+</ sup >( m ) ( see Euclidean group ).

Therefore, Cs < sub > 2 </ sub > C < sub > 2 </ sub > O < sub > 4 </ sub > is more closely approximated by a D < sub > 2d </ sub > symmetry structure because the two CO < sub > 2 </ sub > planes are staggered.

Therefore, the SO ( 3 ), SO ( 4 ) and SO ( 3, 1 ) groups cited above are not the full symmetry groups of their orbits ; the full groups are O ( 3 ), O ( 4 ) and O ( 3, 1 ), respectively.

Equivalently, is conjugate to in if and only if and satisfy the Cauchy – Riemann equations in As an immediate consequence of the latter equivalent definition, if is any harmonic function on the function is conjugate to, for then the Cauchy – Riemann equations are just and the symmetry of the mixed second order derivatives, Therefore an harmonic function admits a conjugated harmonic function if and only if the holomorphic function has a primitive in in which case a conjugate of is, of course, So any harmonic function always admits a conjugate function whenever its domain is simply connected, and in any case it admits a conjugate locally at any point of its domain.

Therefore the symmetry condition can be written in matrix form as

Therefore the global Poincaré symmetry, consisting of translational symmetry, rotational symmetry and the inertial reference frame invariance central to the theory of special relativity must apply.

Therefore the symmetry group is Z.

Therefore, this group is generally now either included in the Brassicaceae or as its own family, Cleomaceae.

Therefore Latinos are Americans who are descendants of the Latin group ( namely Spain, France, Italy and Portugal ) and Hispanic refers to the descendants from the Iberian Peninsula ( also known as Ibero-American ).

Therefore, negative values of the group velocity will occur in these areas.

Therefore, one may alternatively define a group action of G on X as a group homomorphism from G into the symmetric group Sym ( X ) of all bijections from X to X.

Therefore, in addition to its strictly communicative uses, language also has many social and cultural uses, such as signifying group identity, social stratification, as well as for social grooming and entertainment.

Therefore the topology on a topologically finitely-generated profinite group is uniquely determined by its algebraic structure.

Therefore, f induces a group homomorphism from the ( multiplicative ) group of units of R to the ( multiplicative ) group of units of S.

Therefore in 1863, the tribes from the area surrounding the middle Sacramento and Feather rivers, the Konkow group, were removed and marched forcibly to the Round Valley Indian Reservation near the Eel River.

Therefore its fundamental group H is free.

Therefore, in general Euclidean spaces every similarity is an affine transformation, because the Euclidean group E ( n ) is a subgroup of the affine group.

Therefore these arguments held that a group of people can join a government because it has the capacity to exercise a single will and make decisions with a single voice in the absence of sovereign authority — a notion rejected by Hobbes and later contract theorists.

Therefore group theoretic arguments underlie large parts of the theory of those entities.

) Therefore a subgroup of a group G is a subset S of G such that:

Therefore, according to its meaning in common usage in English, any given people, ethnic group or community may be described as being indigenous in reference to some particular region or location.

Therefore every finite simple group has even order unless it is cyclic of prime order.

Therefore, this group of compounds causes electrons to accumulate on chlorophyll molecules.

Therefore, in the context of Meyerhoff ’ s research, " eh " can be equated as a device to establish and maintain a group identity.

Therefore the existence and number of inner automorphisms that are not the identity mapping is a kind of measure of the failure of the commutative law in the group.

Therefore, it has the formula RCO -, where R represents an alkyl group that is attached to the CO group with a single bond.

Therefore, in Euclidean geometry, any two lines that are both perpendicular to a third line are parallel to each other, because of the parallel postulate.

" Therefore any result in Euclidean geometry that follows from these three postulates will hold in elliptic geometry, such as proposition 1 from book I of the Elements, which states that given any line segment, an equilateral triangle can be constructed with the segment as its base.

Therefore the vectors of the root system are in eight-dimensional Euclidean space: they are described explicitly later in this article.

Therefore, finding the Euclidean minimum spanning tree as a spanning tree of the complete graph or as a spanning tree of the Delaunay triangulation both take O ( dn < sup > 2 </ sup >) time.

Therefore, the Euclidean shortest path problem may be decomposed into two simpler subproblems: constructing the visibility graph, and applying a shortest path algorithm such as Dijkstra's algorithm to the graph.

Therefore, when continuum mechanics refers to a point or particle in a continuous body it does not describe a point in the interatomic space or an atomic particle, rather an idealized part of the body occupying that point.

Therefore, the careful searching of radio emissions from space for non-natural signals may lead to the detection of alien civilizations.

Therefore, under certain conditions, when the orbitals of the unpaired outer valence electrons from adjacent atoms overlap, the distributions of their electric charge in space are further apart when the electrons have parallel spins than when they have opposite spins.

Therefore, these equations allow self-sustaining " electromagnetic waves " to travel through empty space ( see electromagnetic wave equation ).

Therefore, uranium was positioned below tungsten, and thorium below zirconium, leaving the space below tantalum empty, and until the 1950s periodic tables were published with this structure.

Therefore, the absence of life in Venus, with a somewhat similar composition to Earth's primitive conditions or the absence of life on Mars, given the proposed " resilience " of life in space, damages the panspermia theory, at least based on observations of our own Solar System-the theory suggests that life would be more abundant in the Solar system.

Therefore LQG predicts that not just matter, but also space itself, has an atomic structure.

Therefore, its quantum state can be represented as a wave of arbitrary shape and extending over space as a wave function.

Therefore, the dimension of the column space of is.

Therefore, the dimension of the row space of is and suppose that is a basis of the row space of.

Therefore, the column space of is a subspace of the column space of.

Therefore, the space Δ is also a Lie algebra representation of called a spin representation.

Therefore, they may be represented as two radial vectors in a sphere in reciprocal space, which shows the values of q that are sampled in a given diffraction image.

Therefore, the convex hull of a set X of three or more points in the plane is the union of all the triangles determined by triples of points from X, and more generally in N-dimensional space the convex hull is the union of the simplices determined by at most N + 1 vertices from X.

Therefore, those without access to a private space are often criminalized.

Therefore, the receiver would choose to partition the space into " spheres " with 2 < sup > n </ sup > / 2 < sup > nR </ sup > = 2 < sup > n ( 1 − R )</ sup > potential outputs each.

Therefore, this space is ever filled up completely by the woman ( or the feminine principle ) surely.

Therefore the space is recommended in the SI / ISO 31-0 standard, and the International Bureau of Weights and Measures states that " for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading.

Therefore, the column space of A consists of all possible products Ax, for x ∈ R < sup > n </ sup >.

) Therefore, the first, second, and fourth columns of the original matrix are a basis for the column space:

Therefore, since ( according to the Heisenberg uncertainty principle ) < span style =" white-space: nowrap "> ΔpΔx ≥ ħ / 2 </ span > where Δp is the uncertainty in the particle's momentum and Δx is the uncertainty in position, then we must say that their momentum is extremely uncertain since the particles are located in a very confined space.

Therefore LQG predicts that not just matter, but also space itself, has an atomic structure.