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Page "Proper time" ¶ 25
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For and any
For the answer cannot be derived from any socially cohesive element in the disrupting community.
For the truth formerly experienced by the community no longer has existential status in the community, nor does any answer elaborated by philosophers or theoriticians.
William Wimsatt and Cleanth Brooks, it seems to me, have a penetrating insight into the way in which this control is effected: `` For if we say poetry is to talk of beauty and love ( and yet not aim at exciting erotic emotion or even an emotion of Platonic esteem ) and if it is to talk of anger and murder ( and yet not aim at arousing anger and indignation ) -- then it may be that the poetic way of dealing with these emotions will not be any kind of intensification, compounding, or magnification, or any direct assault upon the affections at all.
For if Serenissimus made the sign of the Cross with his right hand, and meant it, with his left he beckoned lewdly to any lady who happened to catch his eye.
For them only a little more needed to be learned, and then all physical knowledge could be neatly sorted, packaged and put in the inventory to be drawn on for the solution of any human problem.
For one thing, there wasn't going to be any ceremony at all this year.
For that reason any democratic reform and effort to bring genuine representative government to the Dominican Republic will need the greatest sympathy and help.
For those communities which have financial difficulties in effecting adjustments, there are a number of alternatives any one of which alone, or in combination with others, would minimize if not even eliminate the problem.
For United States expenditures under subsections ( A ), ( B ), ( D ), ( E ), ( F ), ( H ) through ( R ) of Section 104 of the Act or under any of such subsections, the rupee equivalent of $200 million.
For the making of selections on the basis of excellence requires that any foundation making the selections shall have available the judgments of a corps of advisors whose judgments are known to be good: such judgments can be known to be good only by the records of those selected, by records made subsequent to their selection over considerable periods of time.
For the near term, however, it must be realized that the industrial and commercial market is somewhat more sensitive to general business conditions than is the military market, and for this reason I would expect that any gain in 1961 may be somewhat smaller than those of recent years ; ;
For any house.
For proper accreditation of schools, teachers in any course must have a degree at least one level above that for which the student is a candidate.
For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square.
For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.
For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.
For any choice of admissible policy Af in the first stage, the state of the stream leaving this stage is given by Af.
For in the modern world neither `` spirit '' nor `` matter '' refer to any generally agreed-upon elements of experience.
For in Christ Jesus neither circumcision nor uncircumcision but a new creation is of any account.
For example for any ( even infinite ) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks ( assumed to have no distinguishing features ), such a selection can be obtained only by invoking the axiom of choice.
: For any set X of nonempty sets, there exists a choice function f defined on X.
: For any set A, the power set of A ( with the empty set removed ) has a choice function.
: For any set A there is a function f such that for any non-empty subset B of A, f ( B ) lies in B.

For and spacetime
For nearby astronomical objects ( such as stars in our galaxy ) luminosity distance D < sub > L </ sub > is almost identical to the real distance to the object, because spacetime within our galaxy is almost Euclidean.
For example, the motion of planets around the sun may be described in a particular type of spacetime, or the motion of light around a rotating star may be described in another type of spacetime.
For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional ( 2D ) surface.
For this reason wormholes have been defined geometrically, as opposed to topologically, as regions of spacetime that constrain the incremental deformation of closed surfaces.
For the operator γ < sup > μ </ sup >∂< sub > μ </ sub > to remain invariant, the gammas must transform among themselves as a contravariant vector with respect to their spacetime index.
For the purposes of proving the Penrose – Hawking singularity theorems, a spacetime with a singularity is defined to be one that contains geodesics that cannot be extended in a smooth manner.
For example, in the case of the bosonic open string theory in 26-dimensional flat spacetime, a general element of the Fock-space of the BRST quantized string takes the form ( in radial quantization in the upper half plane ),
For example, astronauts return from missions slightly younger than they would have been if they had remained on Earth, and Global Positioning System | GPS satellites work because they adjust for similar bending of spacetime to coordinate with systems on earth.
For example, there is no known complete solution for a spacetime with two massive bodies in it ( which is a theoretical model of a binary star system, for example ).
For instance, in the BF model, the spacetime is a two-dimensional manifold M, the observables are constructed from a two-form F, an auxiliary scalar B, and their derivatives.
For example, it requires a fixed choice of the topology and dimensionality of the spacetime, while any consistent quantum theory of gravity should include topology change as a dynamical process.
For example, the supersymmetry of F-theory on a flat background corresponds to type IIB ( i. e. ( 2, 0 )) supersymmetry with 32 real supercharges which may be interpreted as the dimensional reduction of the chiral real 12-dimensional supersymmetry if its spacetime signature is ( 10, 2 ).
For two operators and that depend on spacetime locations x and y we define:
For example, if a massive object causes some curvature in spacetime, the trajectory of an object with negligible mass over that curvature would follow the line element according to the geodesic equation.
More precisely, let be the Minkowski fiber bundle over the spacetime manifold M. For each point, the fiber is an affine space.
For each value of τ and σ, these functions specify a unique spacetime vector:
For example, the anomalies in the usual 4 spacetime dimensions arise from triangle Feynman diagrams.
For example, the anomalies in the usual 4 spacetime dimensions arise from triangle Feynman diagrams.
For matter objects whose own gravitational influence cannot be neglected, the laws of motion are somewhat more complicated than for test particles, although it remains true that spacetime tells matter how to move.
For example, crystal defects can look like curvature and torsion in an Einstein-Cartan spacetime.
For this spacetime, the Killing horizon is located at
For example, Killing vector fields may be used to classify spacetimes, as there is a limit to the number of global, smooth Killing vector fields that a spacetime may possess ( the maximum being 10 for 4-dimensional spacetimes ).
For a spherically symmetric spacetime, there are precisely 3 rotational Killing vector fields.

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