Examples of infinity

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By their very definition these morphisms 'live at infinity'.
The only minimal immersions, which are regular at infinity and have two ends, are the catenoid and a pair of planes.
Therefore, the weight parameter controls the behaviour of the function w near the points +x and the weight parameter controls its behaviour at infinity.
His view is that there are three independent sources of discrete infinity : phonology, syntax, and semantics.
However, the bristle and the pipe wall cannot sustain thrust forces of infinity.
Closed curve here means that the number of real circuits is limited to one and that the circuit does not extend to infinity.
When is changed from zero to infinity, the passive axis condition of the bearing is changed from rigid to passive.
However, if is chosen close to infinity, the numerical calculation becomes unstable.
On the other hand, while the piston is approaching the upper and lower dead positions, ke tends to approach infinity.
At this point the simulation stops with the electron density diverging to infinity.
The force-free factor of this field approaches infinity at the singular current-density surface.
As shown in this figure, the paramagnetic effect increases with increasing relativistic factor and approaches a limit as the relativistic factor approaches infinity.
In the differential equation, v can vary from zero to infinity, but for the numerical solution we must assume v ?
The later form, called multiplet, is the only form of infinity that we will consider here.
All three points move to infinity as t tends to either 0 or infinity.
We consider confluence where the regular singular point at a merges with that at infinity to create an irregular singular point there.
Individuals who are not related have infinity as distance.
The flow near the cusps either flows inward toward the cusps or diverges to infinity.
The ineffable is thus characterised by a sublime yet accessible infinity, while the unsayable posits an infinity beyond reach.
Since the behaviour of the solution at infinity is now known, we can again apply 'scattering' techniques to find (parts) of the spectrum.
The last two equations must be solved self-consistently, with the condition that 0 (r) tends to zero at infinity.
The answer can be anything between four and infinity.
There may be an infinity of different opposites.
We believe, however, that, if locations have no natural structure, then double infinity pairs should be judged incomparable.
With the above choice of and the exponential decay of 1, this term tends to zero when n tends to infinity.
The equivalence classes defined by this relationship are called irreducible classes at infinity.
A point in the inverse limit is then a consistent prescription for constructing a tiling out to infinity.
On the other hand, we do not know how rapidly the partial quotients of our irrationals tend to infinity.
The key here is to choose p decaying sufficiently slowly at infinity.
The calculated viscosities of the magmas approach infinity as crystal content approaches the value assumed for maximum packing of the crystals (0.59).
Furthermore, as the top boundary is moved to infinity, its contribution becomes negligibly small.
The mean energy flux at infinity can be calculated either directly or by means of the group velocity for each wave component.
In addition, there is a boundary condition at infinity, namely (5), and the requirement that the solution be finite everywhere.
The line at infinity is completely invariant under f and the restriction of f to is, under our hypotheses, a hyperbolic rational map.
Recall that the restriction of f to the line at infinity is a hyperbolic rational map.
However, when the fluid at infinity is rotating in the opposite sense to that of the disk, the process diverges.
Summation of (12) and (16) gives a solution to (10) which satisfies the boundary conditions at infinity.
The white regions form the basin of infinity.
The corresponding change in the driving frequency of the pressure oscillation at infinity can be evaluated using (36) and (74).
The only non-zero contribution is therefore from the region of trajectories entering from infinity and intersecting the contact surface.
The fjord length diverges to infinity when the starting points get closer to the tip.
A hollow spherical cavity of radius ro, centred at the origin, is surrounded by a uniform viscous liquid extending to infinity.
One does find a long wake in practice as every sailor knows when he is 'covered', but it does not extend to infinity.
A major problem in dynamical systems is how to describe the typical asymptotic behaviour of trajectories as time (continuous or discrete) goes to infinity.
The same argument applies when infinity is a repelling fixed point of f (the case a < 1).
Thus, we have a saddle connection between the finite saddle at the origin and the two saddles at infinity.
The next result follows from the fact that the densities are bounded away from zero and infinity.
In this paper we consider variants of geometrical optics, which are asymptotic approximations obtained when the frequency tends to infinity.
The case of parallel lines can be considered a limit case where the intersection is at a "point at infinity" (projective geometry).
Why couldn't the same double infinity allow for a random price level?
Pascal proves that none of these endeavors carry their purpose in themselves, but point beyond themselves into infinity; all are therefore contradictory.
They are designed to go to infinity at the equilibrium point and decay to zero at the obstacles.
In theory, r must tend towards infinity in order for the constraints to be exactly satisfied.
The line equation (7) presents the line from minus infinity to plus infinity and is collinear with the manipulator link.
The eye was corrected to infinity with gas-permeable contact lenses.
In the 20th century, curiosity and the outward urge took astrobiology and popular culture to infinity, and beyond.
The condition number, on the contrary, becomes infinity at singularities and hence, produces numerical overflows.
One is v (x, s), which does not satisfy the boundary condition at 0 and which is bounded at infinity.
On the other hand the same is true of an infinity of other solutions.
Therefore, in looking for a sufficient condition for stability, we take the even solution of equation (1.18) which satisfies the boundary condition at infinity.
At infinity, the basic flow is from left to right.
The flow produced by an infinite rotating disk when the fluid at infinity is in a state of solid rotation is investigated numerically.
I will furthermore assume some regularity at infinity, namely, the associated canonical 1-form will be supposed to be continuously differentiable.
We are going to check that each term in the right-hand side converges to 0 as goes to infinity.
Naturally, one is led to consider a finer tool to measure the size of the real slice as seen from infinity.
However, there is one special case, namely the case in which the source is placed at infinity, when an elementary experiment can be performed.
I n effect, specifying 0" determines the pressure at infinity.
The function q50 can satisfy the boundary condition at infinity if it tends to any constant, including zero.
Because they are coming from infinity, these trajectories satisfy (2.21).
They form a sixth-order set of equations, with three boundary conditions a t r = 1 and three a t infinity.
One may be struck with the stark contrast between the finite individual and the spatial and temporal infinities of universe.
However, the foregoing arithmetic is illegitimate: (_k_jx) does not necessarily sum to x, because the positive and subtracted infinities may be of different magnitudes.
However, it seems that in the work of this paper the infinities are restricted to those that can be accessed effectively through free algebra constructions.
The views are taken from infinity and translated onto each intervening face of the cube.
Ironically, it is through this dying that the depth of non-ego and its infinity and eternity can be glimpsed.
An alternative trajectory that is bounded with respect to time and thus does not tend towards positive or negative infinity is the exponential function.
We consider a competition-diffusion system and study its singular limit as the interspecific competition rate tend to infinity.
The relation shows that there are no waves at infinity upstream.
Both of these examples were chosen because the diffusivities decrease at a rate faster than u-2 as ux tends to infinity.
We are tacitly assuming that the function is so concentrated that integral limits can be taken at infinity.
A different scaling for may be appropriate if different behaviour at infinity is specified.
Such waves radiate out from a moving dislocation, thereby dissipating energy to infinity.
From the first-passage times we try to extrapolate towards infinity to get estimates.
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