Some inequalities on the distribution of ladder epochs

1981 ◽  
Vol 18 (3) ◽  
pp. 770-775 ◽  
Author(s):  
D.Y. Downham ◽  
S.B. Fotopoulos
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Ladder Epoch

An algorithm for calculating the probability distribution of ladder epochs is derived. Two theorems are given for bounds on the distribution function of ladder epoch probabilities.

Some inequalities on the distribution of ladder epochs

1981 ◽  
Vol 18 (03) ◽  
pp. 770-775
Author(s):  
D.Y. Downham ◽  
S.B. Fotopoulos
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Ladder Epoch

An algorithm for calculating the probability distribution of ladder epochs is derived. Two theorems are given for bounds on the distribution function of ladder epoch probabilities.

scholarly journals An Online Application for ΔR Calculation

Radiocarbon ◽  
2016 ◽  
Vol 59 (5) ◽  
pp. 1623-1627 ◽  
Author(s):  
Ron W Reimer ◽  
Paula J Reimer
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Calibration Curve ◽  
Probability Distribution Function ◽  
Museum Collections ◽  
Online Program ◽  
Online Application ◽  
Radiocarbon Calibration

AbstractA regional offset (ΔR) from the marine radiocarbon calibration curve is widely used in calibration software (e.g. CALIB, OxCal) but often is not calculated correctly. While relatively straightforward for known-age samples, such as mollusks from museum collections or annually banded corals, it is more difficult to calculate ΔR and the uncertainty in ΔR for 14C dates on paired marine and terrestrial samples. Previous researchers have often utilized classical intercept methods that do not account for the full calibrated probability distribution function (pdf). Recently, Soulet (2015) provided R code for calculating reservoir ages using the pdfs, but did not address ΔR and the uncertainty in ΔR. We have developed an online application for performing these calculations for known-age, paired marine and terrestrial 14C dates and U-Th dated corals. This article briefly discusses methods that have been used for calculating ΔR and the uncertainty and describes the online program deltar, which is available free of charge.

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

The Strength Evaluation and Reliability Analysis of Periodic Symmetric Struts Support

2011 ◽  
Vol 462-463 ◽  
pp. 1164-1169
Author(s):  
Jing Xiang Yang ◽  
Ya Xin Zhang ◽  
Mamtimin Gheni ◽  
Ping Ping Chang ◽  
Kai Yin Chen ◽  
...  
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Stress Distribution ◽  
Least Squares ◽  
Reliability Analysis ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Distribution Model ◽  
Different Types ◽  
Nonlinear Least Squares Method

In this paper, strength evaluations and reliability analysis are conducted for different types of PSSS(Periodically Symmetric Struts Supports) based on the FEA(Finite Element Analysis). The numerical models are established at first, and the PMA(Prestressed Modal Analysis) is conducted. The nodal stress value of all of the gauss points in elements are extracted out and the stress distributions are evaluated for each type of PSSS. Then using nonlinear least squares method, curve fitting is carried out, and the stress probability distribution function is obtained. The results show that although using different number of struts, the stress distribution function obeys the exponential distribution. By using nonlinear least squares method again for the distribution parameters a and b of different exponential functions, the relationship between number of struts and distribution function is obtained, and the mathematical models of the stress probability distribution functions for different supports are established. Finally, the new stress distribution model is introduced by considering the DSSI(Damaged Stress-Strength Interference), and the reliability evaluation for different types of periodically symmetric struts supports is carried out.

Audio feature extraction using probability distribution function

2015 ◽  
Author(s):  
Suhaib A. ◽  
Khairunizam Wan ◽  
Azri A. Aziz ◽  
D. Hazry ◽  
Zuradzman M. Razlan ◽  
...  
Keyword(s):  
Feature Extraction ◽  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Audio Feature ◽  
Audio Feature Extraction
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