Therefore, the goals of an aerodynamicist have shifted from understanding the behavior of fluid flow to understanding how to engineer a vehicle to interact appropriately with the fluid flow.

Therefore, every educational program that desires to improve students ' outcomes in political, health and economic behavior should include a Socratically taught set of classes to teach logic and critical thinking.

Therefore, the underlying reason for gay behavior, he argues, must be to rebel against God, to wish to do something forbidden ( perhaps, implying some innate knowledge of its forbidden nature ).

" Therefore, the only type of organized human behavior consistent with the operation of reason is that of voluntary cooperation.

Therefore, in that model of voting behavior, the two-round system passes all criteria that the contingent vote passes, and fails all criteria the contingent vote fails.

Therefore, if left unrestrained, people would engage in selfish behavior which will undoubtedly lead to social unrest.

Therefore theorists predict that rigid gender role behavior may decrease around the ages of 7 or 8.

Therefore specialized tools have been developed to simulate, analyze, visualize and optimize time dynamic queueing line behavior.

Therefore, central banks tend to keep an eye on the control and behavior of the stock market and, in general, on the smooth operation of financial system functions.

Therefore particles can exhibit behavior usually attributed to waves.

Therefore, while saccades serve in humans and other primates to increase the effective visual resolution of a scene, there must be additional reasons for the behavior.

Therefore, handling a lever is a natural behavior that rats do as preparatory feeding activity, and in turn, lever pressing cannot logically be used as evidence for reward or reinforcement to occur.

Therefore, at some point only level 1 and level 3 behavior will be seen in machines.

Therefore, fasting strengthens control of impulses and helps develop good behavior.

“ Therefore, the committee desires to express to the public as its firm belief that both the public and the employees aforesaid have equitable rights and interests in the said mill which cannot be modified or diverted without due process of law ; that the employees have the right to continuous employment in the said mill during efficiency and good behavior without regard to religious, political or economic opinions or associations ; that it is against public policy and subversive of the fundamental principles of American liberty that a whole community of workers should be denied employment or suffer any other social detriment on account of membership in a church, a political party or a trade union ; that it is our duty as American citizens to resist by every legal and ordinary means the unconstitutional, anarchic and revolutionary policy of the Carnegie Company, which seems to evince a contempt public and private interests and a disdain the public conscience.

Therefore, reliance on functional mechanoreception, not vision, is essential for schooling behavior.

Therefore, a MOP determines what a program means and what its behavior is, and it is extensible in that a programmer ( or metaprogrammer ) can alter program behavior by extending parts of the MOP.

" ( Romans 12: 2 ) Therefore a disciple is not simply an accumulator of information or one who merely changes moral behavior in regard to the teachings of Jesus Christ, but seeks a fundamental shift toward the ethics of Jesus Christ in every way, including complete devotion to God.

Therefore, a non-habitual sinner will have an easier time repenting, because he or she will be less likely to repeat the sinful behavior.

Therefore even if the behavior could be computed ahead of time, no way of doing so will be simpler than just observing the outcome of the brain's own computations.

Therefore many diarylethenes have photochromic behavior both in solution and in solid state.

Therefore, during seasons when fruit is abundant, subgroups are larger while scarcity is met with more solitary behavior.

Therefore to keep stuck and following the traditions / saying of the past generations is a behavior / attitude of the sheep and cattle.

Therefore, each column vector of is a linear combination of the columns of.

Therefore, the only possible way to get a linear combination is with these coefficients.

Therefore, there is no way for this to work, and x < sup > 3 </ sup > − 1 is not a linear combination of p < sub > 1 </ sub >, p < sub > 2 </ sub >, and p < sub > 3 </ sub >.

Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refers to one which has real-valued entries.

Therefore, a special linear matrix can be written as the product of a special unitary matrix ( or special orthogonal matrix in the real case ) and a positive definite hermitian matrix ( or symmetric matrix in the real case ) having determinant 1.

Therefore, the linear ratio is:

Therefore all tangent vectors in a point p span a linear space, called the tangent space at point p. For example, taking a 2-dimensional space, like the ( curved ) surface of the Earth, its tangent space at a specific point would be the flat approximation of the curved space.

Therefore, the most important fluid velocities are those inside this very thin region in which the change in velocity can be considered linear with normal distance from the surface.

Therefore the problem of computing derivatives, antiderivatives, integrals, power series expansions, Fourier series, residues, and linear functional transformations of rational functions can be reduced, via partial fraction decomposition, to making the computation on each single element used in the decomposition.

Furthermore, replacing the unit circle by the unit square, the error term for the general problem can be as large as a linear function of r. Therefore getting an error bound of the form

First, recall that the general linear group GL ( V ) acts transitively on the r-dimensional subspaces of V. Therefore, if H is the set of stabilizers of this action, we have

Therefore lines in the projective plane are closed curve, i. e., they are cyclical rather than linear.

Therefore, if the linear absorbers are close enough, individual reflectors will have the option of directing reflected solar radiation to at least two absorbers.

Therefore, testing whether a schedule admits a solution with the optimal number of breaks can be done by solving a linear number of 2-satisfiability problems, one for each choice of the breakless team.

Therefore an even dimensional manifold always admits a ( 1, 1 ) rank tensor pointwise ( which is just a linear transformation on each tangent space ) such that J < sub > p </ sub >< sup > 2 </ sup > = − 1 at each point p. Only when this local tensor can be patched together to be defined globally does the pointwise linear complex structure yield an almost complex structure, which is then uniquely determined.

Therefore we see that U is defined by taking the union of the sets of linear functionals defining the W < sub > i </ sub >.

Therefore they get displaced during linear acceleration, which in turn deflects the ciliary bundles of the hair cells and thus produces a sensory signal.

Therefore, the theorem connects the linear response relaxation of a system from a prepared non-equilibrium state to its statistical fluctuation properties in equilibrium.

Since f < sup > 0 </ sup >< sub > k </ sub > is a constant it does not contribute to the error on f. Therefore, the propagation of error follows the linear case, above, but replacing the linear coefficients, A < sub > ik </ sub > and A < sub > jk </ sub > by the partial derivatives, and.

On a finite-dimensional linear space, a quadratic form x ↦ f ( x ) is always a ( finite ) linear combination of products x ↦ g ( x ) h ( x ) of two linear functionals g and h. Therefore, assuming that the scalars are complex numbers, every sequence x < sub > n </ sub > satisfying g ( x < sub > n </ sub >) → 0 for all linear functionals g, satisfies also f ( x < sub > n </ sub >) → 0 for all quadratic forms f.