Mathematical model of the influence of the time of start reaction in 100 m sprint run

The purpose of this study is to explain the influence of the time of start reaction tR to the results of sprinters in a 100 m run, using a new simple mathematical model based on the measured values for distance s, corresponding time t, and tR. The research is based on IAAF data obtained by measuring the segment length, the time of start reaction, transient times in 100 m run, and final times for the top sprinters C. Lewis (1988); M. Green (2011), and U. Bolt (2009) (men) and F. Griffith-Joyner (1988); E. Ashford (1988), and H. Drechsler (1988) (women). The values of the start reaction tR for both male and female top sprinters indicate that there appear no substantial differences in the values of tR based on gender which would directly favor male or female sprinters in achieving the top results in the 100m run. The influence of the time of start reaction tR decreases exponentially with the time t during the run (t>tR) and ends up at about 30 m, influencing the initial velocity vR although it is not directly related to the result of the run. Due to its applicative simplicity, the presented mathematical model and related conclusions can represent a solid basis for future studies concerning sprint running.

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Uncertainty in Collision Avoidance Manoeuvring

Journal of Navigation ◽

10.1017/s0373463300009577 ◽

1990 ◽

Vol 43 (2) ◽

pp. 238-245 ◽

Cited By ~ 7

Author(s):

Donald H. Taylor

Keyword(s):

Mathematical Model ◽

Probability Theory ◽

Collision Avoidance ◽

Simple Mathematical Model ◽

Model Based

Meeting encounters, in which it is uncertain at what range the give-way ship will manoeuvre, are analysed using a model based on probability theory. Course alteration ranges of both giveway and (if necessary) stand-on ships are closely fitted by a simple mathematical model, which is also used to interpret the efficiency of the Collision Regulations.

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A Simple Mathematical Model Based on the Cancer Stem Cell Hypothesis Suggests Kinetic Commonalities in Solid Tumor Growth

PLoS ONE ◽

10.1371/journal.pone.0026233 ◽

2012 ◽

Vol 7 (2) ◽

pp. e26233 ◽

Cited By ~ 36

Author(s):

Rodolfo Molina-Peña ◽

Mario Moisés Álvarez

Keyword(s):

Mathematical Model ◽

Stem Cell ◽

Cancer Stem Cell ◽

Tumor Growth ◽

Solid Tumor ◽

Simple Mathematical Model ◽

Solid Tumor Growth ◽

Cancer Stem Cell Hypothesis ◽

Model Based

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Fabrication and property of auxetic warp-knitted spacer structures with mesh

Textile Research Journal ◽

10.1177/0040517517716910 ◽

2017 ◽

Vol 88 (19) ◽

pp. 2206-2213 ◽

Cited By ~ 4

Author(s):

Yuping Chang ◽

Pibo Ma

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Inclination Angle ◽

Three Dimensional ◽

Simple Mathematical Model ◽

Model Based ◽

Fabric Density ◽

Auxetic Structure ◽

Experimental Sampling

For the purpose of reconstructing a three-dimensional auxetic structure adopting spacer warp-knitting techniques, a simple mathematical model based on the structure of auxetic warp-knitted spacer hexagonal meshes was established and several samples were produced using an E22 RD7/2-12EN warp-knitting machine. It is predicted from synthesizing the results of both mathematical modeling and experimental sampling that auxetic performance of this structure mainly depends on the contraction distortion before stretching in three directions, especially in the y-axis. When it comes to knitting parameters, yarn fineness, machine gauge, fabric density, movement of guide bars, and inclination angle of wales all matter for the auxetic performance, which is also affected by the stiffness of materials and the lodging of spacer yarns. It is also concluded that successive inlaying in the same direction of the spacer guide bar favors contraction distortion in the y-axis, which means auxetic performances can be more easily achieved in this way.

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`Markedness' is an epiphenomenon of random phonetically grounded sound change

Proceedings of the Annual Meetings on Phonology ◽

10.3765/amp.v7i0.4484 ◽

2019 ◽

Vol 7 ◽

Author(s):

Andrea Ceolin ◽

Ollie Sayeed

Keyword(s):

Mathematical Model ◽

Sound Change ◽

Simple Mathematical Model ◽

Model Based ◽

Recent Movement ◽

Evolutionary Phonology

The concept of `markedness' has been influential in phonology for almost a century, but a recent movement in the field has argued that phonological theories do not need to make reference to the concept; instead, if it is meaningful at all, markedness should be thought of as emergent. In this paper, we propose a simple mathematical model based on the principles of Evolutionary Phonology (EP; Blevins 2004) to explore how a theory without markedness can replicate some of the insights of the markedness-based worldview. We see that markedness can be treated as an epiphenomenon of random, phonetically grounded sound change.

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