What's the difference between asymptote and pseudosphere?
Asymptote
Definition:
(n.) A line which approaches nearer to some curve than assignable distance, but, though infinitely extended, would never meet it. Asymptotes may be straight lines or curves. A rectilinear asymptote may be conceived as a tangent to the curve at an infinite distance.
Example Sentences:
(1) Temporary threshold shifts increased for the first eight hours of exposure and then were asymptotic.
(2) To evaluate threshold estimates under these conditions, computer simulations of experiments with small numbers of trials were performed by using psychometric functions based on a model of two types of noise: stimulus-related noise (affecting slope) and extraneous noise (affecting upper asymptote).
(3) The proposed fit asymptotically agrees with Mie's set of equations for the low and the high collection efficiency regions.
(4) Experiment 2 showed that although equivalent performance was obtained from extensive conditioning with a weak shock or limited conditioning with strong shock, only extensive conditioning with weak shock resulted in retarded acquisition of an association between that same CS and a footshock level perceived as midway between the two initial training shock intensities as implied by asymptotic performance in Experiment 1.
(5) This finding is contradictory to the generally held view that antagonist-induced opioid receptor up-regulation in brain increases asymptotically, leveling off after a relatively brief treatment period.
(6) One parameter of this equation represents the estimated response rate asymptote.
(7) Accurate to first-order in the reciprocal of the radial distance from the axis of symmetry, the asymptotic solution obtained here can be employed for future comparison with measured experimental distributions.
(8) The asymptotic kinetics of lipoamide oxidoreductions switch between the ping pong and ordered mechanisms by varying pH of the reactions.
(9) The fitting of a curve indicated an asymptote of 0.721.
(10) Thresholds fell asymptotically to a Weber fraction around 0.06 over a period of approx.
(11) This program utilizes both exact and asymptotic methods to provide point estimates, P values, and confidence intervals.
(12) The statistical properties of the estimated asymptotic multiplication rate, stage, or age stable structures and mean generation time are inspected by both a theoretical approach and a simulation procedure.
(13) For biological populations the precise asymptotic behavior of the corresponding dynamic system is probably less important than the question of extinction and survival of species.
(14) In this paper, asymptotic and iterative methods are developed for the solution of such equations.
(15) The ratio of the extravascular lung water measured in this way to that measured gravimetrically also increased, to reach an asymptotic proportion of close to 100%.
(16) After continuous sinusoidal training for 4 h, VOR gain reached an asymptotic level 5% away from perfect suppression in the low-gain training, but 19% away from the actual performance in the high-gain paradigm.
(17) When a function is expressed as an infinite series of spherical harmonics the convergence can be accelerated by subtracting its asymptotic expansion and adding it in analytically closed form.
(18) Confidence limits for low-dose extrapolation are based on the asymptotic distribution of the likelihood ratio.
(19) For stimulation-bound feeding, increases in intensity raise asymptotic ingestion rate, but do not always appreciably change the location of the curve along the frequency axis.
(20) We conclude that the asymptotic behavior of whole body VO2 at maximal WRs is a direct reflection of the VO2 profile at the exercising legs.
Pseudosphere
Definition:
(n.) The surface of constant negative curvature generated by the revolution of a tractrix. This surface corresponds in non-Euclidian space to the sphere in ordinary space. An important property of the surface is that any figure drawn upon it can be displaced in any way without tearing it or altering in size any of its elements.
Example Sentences:
(1) The induced structural change is perceived differently by each subunit as assessed by opposite local motions of Tyr49 in each liganded protomer and leads to the formation of a dimeric complex with a global pseudospherical symmetry although containing domains of local asymmetry.