scholarly journals Intersection points of planar curves can be computed

Computability ◽  
2021 ◽  
pp. 1-21
Author(s):  
Klaus Weihrauch
Keyword(s):  
Planar Curves ◽  
Unit Square ◽  
Closed Intervals ◽  
Intersection Points ◽  
Point Of Intersection

Consider two paths ϕ , ψ : [ 0 ; 1 ] → [ 0 ; 1 ] 2 in the unit square such that ϕ ( 0 ) = ( 0 , 0 ), ϕ ( 1 ) = ( 1 , 1 ), ψ ( 0 ) = ( 0 , 1 ) and ψ ( 1 ) = ( 1 , 0 ). By continuity of ϕ and ψ there is a point of intersection. We prove that from ϕ and ψ we can compute closed intervals S ϕ , S ψ ⊆ [ 0 ; 1 ] such that ϕ ( S ϕ ) = ψ ( S ψ ).

Use of a Signal Detection Paradigm to Assess Subjective Intersection Points in a Target Location Task

1984 ◽  
Vol 28 (4) ◽  
pp. 380-382
Author(s):  
William R. Engelman ◽  
Michael J. Patterson ◽  
Gregory M. Corso
Keyword(s):  
Signal Detection ◽  
Target Location ◽  
Decision Criterion ◽  
Intersection Point ◽  
Location Task ◽  
Moving Points ◽  
Within Subjects ◽  
Intersection Points ◽  
Point Of Intersection ◽  
Subject Performance

Numerous tasks require individuals to assess whether two or more moving points are on a collision path. However, evidence available, on decision making in spatial manipulation tasks, is lacking. This study attempted to assess individual's ability to determine the point of intersection between two cursors. The distance between a specified target and the actual intersection point (2 levels), and the extrapolation distance (2 levels) was varied. Using a signal detection paradigm, measures of sensitivity (d') and decision criterion (B) were obtained. Therefore, 2 × 2 within subjects design was employed. Results indicated that distance between the target and actual intersection point had the greatest effects on sensitivity, while extrapolation distance differences were minimal. Conclusions based on the results are limited due to poor subject performance.

Prothrombin Time Standardization: Report of the Expert Panel on Oral Anticoagulant Control

1979 ◽  
Vol 42 (04) ◽  
pp. 1073-1114 ◽  
Keyword(s):  
Prothrombin Time ◽  
Expert Panel ◽  
The Other ◽  
Rabbit Brain ◽  
Calibration Constant ◽  
Freeze Dried ◽  
The Mean ◽  
Point Of Intersection ◽  
And Control ◽  
Standardization Report

SummaryIn collaborative experiments in 199 laboratories, nine commercial thromboplastins, four thromboplastins held by the National Institute for Biological Standards and Control (NIBS & C), London and the British Comparative Thromboplastin were tested on fresh normal and coumarin plasmas, and on three series of freeze-dried plasmas. One of these was made from coumarin plasmas and the other two were prepared from normal plasmas; in each series, one plasma was normal and the other two represented different degrees of coumarin defect.Each thromboplastin was calibrated against NIBS&C rabbit brain 70/178, from the slope of the line joining the origin to the point of intersection of the mean ratios of coumarin/normal prothrombin times when the ratios obtained with the two thromboplastins on the same fresh plasmas were plotted against each other. From previous evidence, the slopes were calculated which would have been obtained against the NIBS&C “research standard” thromboplastin 67/40, and termed the “calibration constant” of each thromboplastin. Values obtained from the freeze-dried coumarin plasmas gave generally similar results to those from fresh plasmas for all thromboplastins, whereas values from the artificial plasmas agreed with those from fresh plasmas only when similar thromboplastins were being compared.Taking into account the slopes of the calibration lines and the variation between laboratories, precision in obtaining a patient’s prothrombin time was similar for all thromboplastins.

The elementary forms of digital culture. Knowledge, connections and sociality

2020 ◽  
pp. 316-328
Author(s):  
Vincenzo Susca
Keyword(s):  
Public Opinion ◽  
Daily Life ◽  
Digital Culture ◽  
Social Boundaries ◽  
Public Spheres ◽  
The Public ◽  
Nation States ◽  
The Senses ◽  
Point Of Intersection ◽  
Dark Web

Contemporary communicative platforms welcome and accelerate a socio-anthropological mutation in which public opinion (Habermas, 1995) based on rational individuals and alphabetic culture gives way to a public emotion whose emotion, empathy and sociality are the bases, where it is no longer the reason that directs the senses but the senses that begin to think. The public spheres that are elaborated in this way can only be disjunctive (Appadurai, 2001), since they are motivated by the desire to transgress the identity, political and social boundaries where they have been elevated and restricted. The more the daily life, in its local intension and its global extension, rests on itself and frees itself from projections or infatuations towards transcendent and distant orders, the more the modern territory is shaken by the forces that cross it and pierce it. non-stop. The widespread disobedience characterizing a significant part of the cultural events that take place in cyberspace - dark web, web porn, copyright infringement, trolls, even irreverent ... - reveals the anomic nature of the societal subjectivity that emerges from the point of intersection between technology and naked life. Behind each of these offenses is the affirmation of the obsolescence of the principles on which much of the modern nation-states and their rights have been based. Each situation in which a tribe, cloud, group or network blends in a state of ecstasy or communion around shared communications, symbols and imaginations, all that surrounds it, in material, social or ideological terms, fades away. in the air, being isolated by the power of a bubble that in itself generates culture, rooting, identification: transpolitic to inhabit

scholarly journals Affine Subspaces of Curvature Functions from Closed Planar Curves

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese
Keyword(s):  
Arc Length ◽  
Planar Curves ◽  
Affine Subspaces ◽  
Planar Curve ◽  
Real Functions ◽  
Discrete Counterpart ◽  
Equivalent Conditions

AbstractGiven a pair of real functions (k, f), we study the conditions they must satisfy for $$k+\lambda f$$ k + λ f to be the curvature in the arc-length of a closed planar curve for all real $$\lambda $$ λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.

scholarly journals Clothoid fitting and geometric Hermite subdivision

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Ulrich Reif ◽  
Andreas Weinmann
Keyword(s):  
Building Block ◽  
Numerical Results ◽  
Normal Vector ◽  
Subdivision Schemes ◽  
Planar Curves ◽  
Nonlinear Subdivision ◽  
New Strategy ◽  
Vector Information ◽  
Hermite Subdivision

AbstractWe consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.

scholarly journals Constitutive Modeling of the Densification Behavior in Open-Porous Cellular Solids

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2731
Author(s):  
Ameya Rege
Keyword(s):  
Constitutive Model ◽  
Cell Walls ◽  
Compressive Strain ◽  
Pore Collapse ◽  
Compressive Response ◽  
Linear Elastic ◽  
Nonlinear Springs ◽  
Different Types ◽  
Point Of Intersection ◽  
Good Agreement

The macroscopic mechanical behavior of open-porous cellular materials is dictated by the geometric and material properties of their microscopic cell walls. The overall compressive response of such materials is divided into three regimes, namely, the linear elastic, plateau and densification. In this paper, a constitutive model is presented, which captures not only the linear elastic regime and the subsequent pore-collapse, but is also shown to be capable of capturing the hardening upon the densification of the network. Here, the network is considered to be made up of idealized square-shaped cells, whose cell walls undergo bending and buckling under compression. Depending on the choice of damage criterion, viz. elastic buckling or irreversible bending, the cell walls collapse. These collapsed cells are then assumed to behave as nonlinear springs, acting as a foundation to the elastic network of active open cells. To this end, the network is decomposed into an active network and a collapsed one. The compressive strain at the onset of densification is then shown to be quantified by the point of intersection of the two network stress-strain curves. A parameter sensitivity analysis is presented to demonstrate the range of different material characteristics that the model is capable of capturing. The proposed constitutive model is further validated against two different types of nanoporous materials and shows good agreement.

scholarly journals A non-Borel special alpha-limit set in the square

2021 ◽  
pp. 1-11
Author(s):  
STEPHEN JACKSON ◽  
BILL MANCE ◽  
SAMUEL ROTH
Keyword(s):  
Dynamical Systems ◽  
Limit Set ◽  
Limit Sets ◽  
Unit Square

Abstract We consider the complexity of special $\alpha $ -limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necessarily Borel, even in the case of a surjective map on the unit square. This answers a question posed by Kolyada, Misiurewicz, and Snoha.

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