Since the city authorities would not allow the new line to breach the customs wall, still standing at the time, it had to stop just short, at Potsdamer Platz, but it was this that kick-started the real transformation of the area, into the bustling focal point that Potsdamer Platz would eventually become.

Since late 2004, he has suffered from a reemergence of his focal dystonia which has affected his ability to draw for lengthy periods on paper, though it causes no real problem now that he draws the comic on a graphics tablet.

Since the 1980s and especially since the ratification of the North American Free Trade Agreement in 1994, the focal point of economic activity has shifted from agriculture to international trade, health care, retail and tourism.

Since the 1980s and especially since the ratification of the North American Free Trade Agreement in 1994, the focal point of economic activity has shifted from agriculture to international trade, health care, retail and tourism.

Since the original convolution discards data, some algorithms use additional data acquired at nearby focal points to make up some of the lost information.

Since the lens is placed after the focal plane of the objective it also allowed for use of a micrometer at the focal plane ( used for determining the angular size and / or distance between objects observed ).

Since light can pass through a lens in either direction, a lens has two focal points — one on each side.

Since the horses had to be running at top speed for the best visual impact, Marton chose to film the chariot race with a smaller lens with a much shorter minimum focal length.

Since the focal plane is curved, these plates had to be preformed in a special jig before being loaded into the camera.

Since the magnification provided by a telescope and eyepiece is equal to the telescope's focal length divided by the eyepiece's focal length, this has the effect of increasing the magnification of the image.

* Since adaptation level results from the pooled effect of all other relevant stimuli, the nurse examines the contextual and residual stimuli associated with the focal stimulus to ascertain the zone within which positive family coping can take place and to predict when the given stimulus is outside that zone and will require nursing intervention.

Since the mosque's establishment, it has become a focal point for the Birmingham Muslim community, providing education for children and adults, lectures and seminars, counselling and a marriage bureau along with sporting and recreational activities and workshops.

Since the absorption of radio waves in rocklike material varies with wave length, it should be possible to sample the temperature variation at different depths beneath the surface and possibly detect changes in the structure or composition of the lunar surface material.

Since 1996 estimates, there has been a significant reduction in the total length of unpaved highway in Botswana-between 1996 and 1999 total length of unpaved highway fell from 14, 139 km to 4, 597 km.

Since the desired effect is computational difficulty, in theory one would choose an algorithm and desired difficulty level, thus decide the key length accordingly.

The proof of this fact relies on an algorithm which, given the first n digits of Ω, solves Turing's halting problem for programs of length up to n. Since the halting problem is undecidable, Ω can not be computed.

Since the compression ratio is the ratio between dynamic and static volumes of the combustion chamber the Atkinson cycle's method of increasing the length of the powerstroke compared to the intake stroke ultimately altered the compression ratio at different stages of the cycle.

Since work is defined as a force acting through a distance ( a length of space ), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.

Since the stored energy in the barrier is less than the energy stored in a barrier-free region of the same length due to destructive interference, the group delay for the energy to escape the barrier region is shorter than it would be in free space, which according to Winful is the explanation for apparently superluminal tunneling.

Since 1983, it has been defined as " the length of the path travelled by light in vacuum during a time interval of of a second.

Since rifles were used by sharpshooters who didn't routinely fire over other men ’ s shoulders, long length was not required to avoid the forward line.

Since then, changes to the line length have been a relatively common variant, such that Stephen Burt has written: " sestinas, as the form exists today, not require expertise with inherited meter …".

Since the most common trailer used in the U. S. is 53 feet ( 16 m ) in length, the difference in freight capacity between cab-over and conventional cab tractor / trailer combinations is negligible.

Since all matter and energy gravitate, gravity's effects are cumulative ; by contrast, the effects of positive and negative charges tend to cancel one another, making electromagnetism relatively insignificant on cosmological length scales.

Since the end of the series rumors have circulated that a feature length movie was in the works.

Since the path length varies, generally, so will the phases of the waves at that point from each of the slits, and thus will add or subtract from one another to create peaks and valleys, through the phenomenon of additive and destructive interference.

Since the E field is uniform in the direction of wire length, for a conductor having uniformly consistent resistivity ρ, the current density J will also be uniform in any cross-sectional area and oriented in the direction of wire length, so we may write:

Since the real numbers can be used to represent points along an infinitely long line, this implies that a line segment of length 1, which is a part of that line, has the same number of points as the whole line.

Since longitudinal waves have a much greater phase velocity than transverse waves, V < sub > long </ sub > is much greater than V < sub > trans </ sub >, and the relaxation length or mean free path of longitudinal phonons will be much greater.

Since fluidity of the surfactant mixture is also dependent on fatty acid tail length where length leads to increased surfactant fluidity, the change in tail length may indicate a surfactant system adaptation in response to the selection for an effective antiadhesive surfactant in collapsed lungs of diving pinnipeds.

Since the sound waves propagate, not from a single point source, but along the length of the lightning's path, the sound origin's varying distances from the observer can generate a rolling or rumbling effect.

A set S is called countable if there exists an injective function f from S to the natural numbers Since there is an obvious bijection between and it makes no difference whether one considers 0 to be a natural number of not.

Since the possible values of f are well-ordered, this property can be established by proving for any r ( not in I ) with minimal value of f ( r ) in its class.

Since the stopping force F times that distance must be equal to the head's kinetic energy, it follows that F will be much greater than the original driving force f — roughly, by a factor D / d.

Since < ƒ, ƒ > ≥ 0, φ ( f * f ) ≥ 0 for all ƒ in L < sup > 2 </ sup >( m ), where ƒ * is pointwise conjugate of ƒ.

Since f is locally area-preserving, this non-overlapping property would make it area-preserving for all of S, so the area of f ( S ) would be the same as that of S, which is greater than 4.

Since the topology on R < nowiki ></ nowiki > X < nowiki ></ nowiki > is the ( X )- adic topology and R < nowiki ></ nowiki > X < nowiki ></ nowiki > is complete, we can in particular apply power series to other power series, provided that the arguments don't have constant coefficients ( so that they belong to the ideal ( X )): f ( 0 ), f ( X < sup > 2 </ sup >− X ) and f ( ( 1 − X )< sup >− 1 </ sup > − 1 ) are all well defined for any formal power series f ∈ R < nowiki ></ nowiki > X < nowiki ></ nowiki >.

Since equalizers may be constructed from pullbacks and binary products ( consider the pullback of ( f, g ) along the diagonal Δ ), a category is complete if and only if it has pullbacks and products.

* Since m is injective, f ( a ) =

* Since the composition of g and f is trivial, c =

Since the gradient of a function is perpendicular to the contour lines, this is the same as saying that the gradients of f and g are parallel.

Since x is now fixed, f ( x ) is a fixed countable set and has Lebesgue measure zero.

* Since we can predict with virtual certainty that " y is not in f ( x )" after the first dart is thrown, and since this prediction is valid no matter what the first dart does, we should be able to make this prediction before the first dart is thrown.

* Since " y is not in f ( x )" is predictably true, by the symmetry of the order in which the darts were thrown ( hence the name " axiom of symmetry ") we should also be able to predict with virtual certainty that " x is not in f ( y )".

Since f ( X ) is irreducible, ( f ( X )) is a maximal ideal and hence is, in fact, a field.

Since complete lattices cannot be empty, the theorem in particular guarantees the existence of at least one fixed point of f, and even the existence of a least ( or greatest ) fixed point.

The set of ( p < sub > i </ sub >, n < sub > i </ sub >) is thus a sampling of a continuous vector field V. The implicit function f is found by integrating the vector field V. Since not every vector field is the gradient of a function, the problem may or may not have a solution: the necessary and sufficient condition for a smooth vector field V to be the gradient of a function f is that the curl of V must be identically zero.