A Simple Analytic Expression For The Contrast Sensitivity Of The Human Eye As A Function Of Brightness

1984 ◽  
Author(s):  
Howard Borough
Keyword(s):  
Contrast Sensitivity ◽  
Human Eye ◽  
Simple Analytic Expression ◽  
Analytic Expression

scholarly journals Estimating the Risk of Satellite Collisions in Densely Populated Orbit Shells

2021 ◽  
Author(s):  
William Lee ◽  
Paul Martin ◽  
Ann Smith ◽  
Giancarlo Antonucci ◽  
Georgia Brennan ◽  
...  
Keyword(s):  
Time Dependence ◽  
Low Earth Orbit ◽  
Collision Probability ◽  
Earth Orbit ◽  
Limited Information ◽  
Asymptotic Approach ◽  
Optimal Point ◽  
Single Collision ◽  
Simple Analytic Expression ◽  
Analytic Expression

Low Earth Orbit is becoming crowded with satellites. Updating estimates of collision probabilities is important as new deployments are authorised but is difficult because only limited information is given. This report investigates developing analytic estimates of collision probabilities. A survey of approaches reported in the literature is carried out. A collision involving a satellite from the Iridium cluster is reviewed. A simple analytic expression for the collision probability between two satellites is derived using the smallness of several dimensionless ratios appearing in the problem. Single collision probabilities are then extended to orbital planes populated by n satellites with the aim of finding the optimal point at which to traverse such an orbit. This report demonstrates that analytic estimates relevant to the problem can be made. Further work should focus on: making these estimates rigorous by using a formal asymptotic approach, considering multiple orbital planes and introducing time dependence

scholarly journals A VALUATION FORMULA FOR MULTI-ASSET, MULTI-PERIOD BINARIES IN A BLACK–SCHOLES ECONOMY

2009 ◽  
Vol 50 (4) ◽  
pp. 475-485
Author(s):  
MAX SKIPPER ◽  
PETER BUCHEN
Keyword(s):  
Closed Form ◽  
Present Value ◽  
Simple Analytic Expression ◽  
Black Scholes ◽  
Analytic Expression

AbstractWe present a new valuation formula for a generic, multi-period binary option in a multi-asset Black–Scholes economy. The payoff of this so-called M-binary is the most general possible, subject to the condition that a simple analytic expression exists for the present value. Portfolios of M-binaries can be used to statically replicate many European exotics for which there exist closed-form Black–Scholes prices.

scholarly journals Parking 3-sphere swimmer. I. Energy minimizing strokes

2017 ◽  
Author(s):  
François Alouges ◽  
Giovanni Di Fratta
Keyword(s):  
Dynamical System ◽  
Reynolds Number ◽  
Low Reynolds Number ◽  
Closed Curves ◽  
The Real ◽  
First Order ◽  
Simple Analytic Expression ◽  
3D Space ◽  
Analytic Expression ◽  
Low Reynolds

The paper is about the parking 3-sphere swimmer ($\text{sPr}_3$). This is a low-Reynolds number model swimmer composed of three balls of equal radii. The three balls can move along three horizontal axes (supported in the same plane) that mutually meet at the center of $\text{sPr}_3$ with angles of $120^{\circ}$. The governing dynamical system is introduced and the implications of its geometric symmetries revealed. It is then shown that, in the first order range of small strokes, optimal periodic strokes are ellipses embedded in 3d space, i.e., closed curves of the form $t\in [0,2\pi] \mapsto (\cos t)u + (\sin t)v$ for suitable orthogonal vectors $u$ and $v$ of $\mathbb{R}^3$. A simple analytic expression for the vectors $u$ and $v$ is derived. The results of the paper are used in a second article where the real physical dynamics of $\text{sPr}_3$ is analyzed in the asymptotic range of very long arms.

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