We may thus trace the notion of individual autonomy from its manifestation in religious practice and theological reflection through practical politics and political theory into literature and the arts.

In the rhyming catechism this doctrine is worded thus: `` In Adam's fall We sin-ned all ''.

We have chosen to give it at the end of the section since it deals with differential equations and thus is not purely linear algebra.

We thus have an optimal policy which maximizes the expected value of the objective function for a given Af.

We will make a few simplifying assumptions: that the uncompressed volume of the cylinder is 1000cc's ( one liter ), that the gas within is nearly pure nitrogen ( thus a diatomic gas with five degrees of freedom and so

We know that is opaque and thus follows that is opaque, so in the above equation, each operator can be written as a convex combination:

Leary received an honorary doctorate and spoke briefly at his alma mater's undergraduate commencement ceremony on May 16, 2005 ; he is thus credited as " Dr. Denis Leary " on the cover of his 2009 book, Why We Suck.

We have explained that ' regularity ' must be understood to exclude all pseudo-initiatic organizations, which, regardless of pretention and outward appearance, in no way possess any spiritual influence and thus are incapable of transmitting anything .”

The EPR paper says: " We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

Here, we are told, ' We need to go beyond the pleasure principle, the reality principle, and repetition compulsion to ... the fantasy principle ' - ' not, as Freud did, reduce fantasies to wishes ... consider all other imaginable emotions '; and thus envisage emotional fantasies as a possible means of moving beyond stereotypes to more nuanced forms of personal and social relating.

We thus obtain a functor from the category of pointed topological spaces to the category of groups.

We have thus over-counted the actual number of states.

We thus say that dog and dogs are different forms of the same lexeme.

In response to the claim in Whewell's treatise that " We may thus, with the greatest propriety, deny to the mechanical philosophers and mathematicians of recent times any authority with regard to their views of the administration of the universe ", Charles Babbage published what he called The Ninth Bridgewater Treatise, A Fragment.

We sent it in, and Schopf reacted strongly against it — thus signaling the tenor of the reaction it has engendered, though for shifting reasons, down to the present day.

We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

We thus obtain the inequality in terms of dimensions of kernel, which can then be converted to the inequality in terms of ranks by the rank-nullity theorem.

We are enabled thus to contrast Tacitus with Josephus, who warped his narrative to do honour to Titus.

We can thus understand the high importance of barriers, whether of land or water, which separate our several zoological and botanical provinces.

We can thus understand the localisation of sub-genera, genera, and families ; and how it is that under different latitudes, for instance in South America, the inhabitants of the plains and mountains, of the forests, marshes, and deserts, are in so mysterious a manner linked together by affinity, and are likewise linked to the extinct beings which formerly inhabited the same continent ... On these same principles, we can understand, as I have endeavoured to show, why oceanic islands should have few inhabitants, but of these a great number should be endemic or peculiar ; ...

We thus say that in order to solve this problem, the computer needs to perform a number of steps that grows linearly in the size of the problem.

i. e., z is a vector orthogonal to the vector v ( Indeed, z is the projection of u onto the plane orthogonal to v .) We can thus apply the Pythagorean theorem to

We obtain the same variation in probability amplitudes by allowing the time at which the photon left the source to be indeterminate, and the time of the path now tells us when the photon would have left the source, and thus what the angle of its " arrow " would be.

We recognize this genre ; thus, expectations are set.

We have also come to understand Harvey's somewhat unorthodox method of dealing with his gout, here cited completely: "... his ( Harvey's ) cure was thus: he would sit with his legs bare ... put them into a pail of water till he was almost dead with cold, then betake himself to his stove, and so ' twas gone ".

We can use this consensus as a pragmatic guide, either on the assumption that it seems to approximate some kind of valid reality, or simply because it is more " practical " than perceived alternatives.

We need to approximate this ratio by common fractions: the numerators and denominators then give the multiples of the two periods-draconic and synodic months-that ( approximately ) span the same amount of time, representing an eclipse cycle.

We can further approximate the integral on the right-hand side by bringing the absolute value into the integrand, and replacing the term in f ' by an upper bound:

We can similarly approximate the gravity field of the Earth by a spherically symmetric field:

We want to approximate the solution of the differential equation

We have now traced on a spherical surface the area in which we say the inhabited world is situated ; and the man who would most closely approximate the truth by constructed figures must necessarily take for the earth a globe like that of Crates, and lay off on it the quadrilateral, and within the quadrilateral put down the map of the inhabited world.

We say that the metric has approximate midpoints if for any and any pair of points and in there exists in such that and are both smaller than

We can approximate the integral by generating sample paths and then taking an average.

We could say that the crime occurred in a city of 1, 000, 000 people, of whom 15 % meet the requirements of being the same sex, age group and approximate description as the perpetrator.

Petrie wrote in the 1892 excavation report that " We see then that there is an exactly analogous theory for the dimensions of Medum to that of the Great Pyramid ; in each the approximate ratio of 7: 44 is adopted, as referred to the radius and circle ..".

We can then approximate the expression with only the first two terms:

We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.

We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.

We have just observed that we can write Af where D is diagonalizable and N is nilpotent, and where D and N not only commute but are polynomials in T.

We first define a function b{t} as follows: given the set of squares such that each has three corners on C and vertex at t, b{t} is the corresponding set of positive parametric differences between T and the backward corner points.

We define these values as Af, and define g{t} in the same way for each T.

We can then define the differential map d: C < sup >∞</ sup >( M ) → T < sub > x </ sub >< sup >*</ sup > M at a point x as the map which sends f to df < sub > x </ sub >.

We can show a waveform is periodic by finding some period T for which the following equation is true:

We could also define a Lie algebra structure on T < sub > e </ sub > using right invariant vector fields instead of left invariant vector fields.

We can indeed enumerate algorithms to construct a function T, about which we initially assume that it is a function from the natural numbers onto the reals.

Murray died in 1915, having been responsible for words starting with A – D, H – K, O – P and T, nearly half the finished dictionary ; Bradley died in 1923, having completed E – G, L – M, S – Sh, St and W – We.

We may calculate the ratio of the populations of the two states at room temperature ( T ≈ 300 K ) for an energy difference ΔE that corresponds to light of a frequency corresponding to visible light ( ν ≈ 5 × 10 < sup > 14 </ sup > Hz ).

Crow has also recorded a studio version of " So Glad We Made It " for the " Team USA Olympic Soundtrack " in conjunction with the 2008 US Olympic team sponsors AT & T.

Brian Wilson and Sergio Romo grew out their facial hair, AT & T Park filled with " Fear the Beard " signs, and the slogan " There's Magic Inside " took the place of the one from the previous season, " Yes We Can ".

We wish to determine the period T of small oscillations in a simple pendulum.

We say that the base generates the topology T. Bases are useful because many properties of topologies can be reduced to statements about a base generating that topology, and because many topologies are most easily defined in terms of a base which generates them.

Senior study author said: " We can't say with certainty that T. gondii caused the women to try to kill themselves, but we did find a predictive association between the infection and suicide attempts later in life that warrants additional studies ".

* T. Cateforis ( 2011 ), Are We Not New Wave?

T, and a free variable of T. We say x is bound in M and free in T. If T contains a subterm λ x.

The book also takes its name from the T. S. Eliot poem The Hollow Men, which includes the lines " In this last of meeting places // We grope together // And avoid speech // Gathered on this beach of the tumid river.

We shall mark the current time ( or iteration ) in the algorithm with T, and shall begin ( at time 0, or T = 0 ) by creating distance matrices for each router to its immediate neighbors.