scholarly journals A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone

Mathematics ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 35
Author(s):  
Stéphane Chrétien ◽  
Juan-Pablo Ortega
Keyword(s):  
Simple Formula ◽  
Hilbert Metric

Dynamics of Electrodiffusion Friction Probes. I. Shape-Dependent Potentiostatic Transient

1997 ◽  
Vol 62 (3) ◽  
pp. 397-419 ◽  
Author(s):  
Ondřej Wein ◽  
Václav Sobolík
Keyword(s):  
Simple Formula ◽  
Flow Direction ◽  
Voltage Step ◽  
Convex Shape ◽  
Exact Theory ◽  
Working Electrode ◽  
Arbitrary Convex

An exact theory is given of the voltage-step transient under limiting diffusion conditions for an electrodiffusion friction probe of arbitrary convex shape. The actual transient courses are given for the strip, circular, elliptic, triangular, and rectangular probes of any orientation with respect to the flow direction. A simple formula for any probe with a single working electrode of convex shape is suggested to facilitate the calibration of electrodiffusion probes based on the voltage-step transient.

scholarly journals Computation of several Hessenberg determinants

2020 ◽  
Vol 70 (6) ◽  
pp. 1521-1537
Author(s):  
Feng Qi ◽  
Omran Kouba ◽  
Issam Kaddoura
Keyword(s):  
Linear Algebra ◽  
Simple Formula ◽  
Binomial Coefficients ◽  
Explicit Formulas ◽  
Methods And Techniques

AbstractIn the paper, employing methods and techniques in analysis and linear algebra, the authors find a simple formula for computing an interesting Hessenberg determinant whose elements are products of binomial coefficients and falling factorials, derive explicit formulas for computing some special Hessenberg and tridiagonal determinants, and alternatively and simply recover some known results.

Simple formula for the ground band spectrum of even-mass rotational nuclei

1982 ◽  
Vol 25 (5) ◽  
pp. 2837-2840 ◽  
Author(s):  
A. Partensky ◽  
C. Quesne
Keyword(s):  
Simple Formula ◽  
Band Spectrum ◽  
Ground Band

SIMPLE FORMULA FOR CALCULATION OF THE PÆDIATRIC DOSE

The Lancet ◽  
1962 ◽  
Vol 280 (7263) ◽  
pp. 990
Author(s):  
J.E. Cullis
Keyword(s):  
Simple Formula ◽  
Paediatric Dose

A new risk-adjusted Bernoulli cumulative sum chart for monitoring binary health data

2016 ◽  
Vol 25 (6) ◽  
pp. 2704-2713 ◽  
Author(s):  
Giuseppe Rossi ◽  
Simone Del Sarto ◽  
Marco Marchi
Keyword(s):  
Simple Formula ◽  
Efficient Solution ◽  
Real Data ◽  
Health Data ◽  
Data Sets ◽  
Cumulative Sum ◽  
Baseline Incidence ◽  
Health Event ◽  
Control Limits ◽  
Underlying Risk

To monitor a health event in patients with a specific risk of developing the event, a risk-adjusted cumulative sum chart is needed. The risk-adjusted cumulative sum chart proposed in the literature has some limitations. Setting appropriate control limits is not straightforward, there is no simple formula for constructing them, and they remain sensitive to changes in the underlying risk distribution and the baseline incidence rate. To overcome these limits, we propose a new risk-adjusted Bernoulli cumulative sum chart as a simple and efficient solution. Analyses of simulated and real data sets illustrate the performance and usefulness of the proposed procedure.

Load Distribution of Parallel Springs With Random Length and Stiffness

1987 ◽  
Vol 109 (4) ◽  
pp. 402-406 ◽  
Author(s):  
Go¨ran Gerbert ◽  
Jacques de Mare´
Keyword(s):  
Uniform Distribution ◽  
Load Distribution ◽  
Simple Formula ◽  
Mechanical Design ◽  
Numerical Results ◽  
Maximal Length ◽  
Major Influence ◽  
Length Variation ◽  
Spring Stiffness ◽  
Failure Risk

There are many applications in mechanical design where load distribution is modelled with parallel springs. Here random variation in spring length and spring stiffness is considered. Length variation is assumed to be the major influence and the case with uniform distribution is analyzed in detail. Small variations in spring stiffness are included. Numerical results are given. A simple formula is presented which gives the maximal length deviation as a function of the number of springs. The formula is based on a 10 percent failure risk which is a common number in practical mechanical design.

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