Remark on the energy determination of high-energy nucleons by means of the absorption calorimeter

1968 ◽  
Vol 46 (10) ◽  
pp. S1107-S1111 ◽  
Author(s):  
A. Somogyi ◽  
G. Válas ◽  
A. Varga
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Analytical Method ◽  
Probability Distribution Function ◽  
High Energy ◽  
Primary Energy ◽  
Numerical Calculations ◽  
Energy Determination ◽  
Ionization Calorimeter

The sources of error in energy determinations carried out by means of an ionization calorimeter are well known as are the values of the relevant corrections. Very little if anything is known, however, of the statistical uncertainties of these corrections. An analytical method has been worked out in order to determine the probability that a certain fraction of the primary energy leaves a calorimeter of a given thickness and thus escapes detection. The method makes due allowance for the fluctuation of the inelasticity coefficient. Numerical calculations have been carried out assuming various forms for the probability distribution function of the inelasticity coefficient, and the results of the calculations are given for various calorimeter thicknesses.

Quantitative risk-based inspection approach for high-energy piping using a probability distribution function and modification factor

2021 ◽  
Vol 189 ◽  
pp. 104281
Author(s):  
Jung Soo Song ◽  
Vanno Lok ◽  
Kee Bong Yoon ◽  
Young Wha Ma ◽  
Byeong Ook Kong
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
High Energy ◽  
Modification Factor

An Efficient Numerical Method for Calculating the Statistical Distribution of Combined First-Order and Wave-Drift Response

1992 ◽  
Vol 114 (3) ◽  
pp. 195-204 ◽  
Author(s):  
A. Naess ◽  
J. M. Johnsen
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Numerical Method ◽  
Probability Distribution Function ◽  
Numerical Procedure ◽  
Offshore Structures ◽  
Numerical Calculations ◽  
Hydrodynamic Loads ◽  
First Order ◽  
Wave Drift

The paper describes an efficient and accurate numerical procedure for calculating the probability distribution function of combined first-order and slowly varying, second-order hydrodynamic loads and response of compliant offshore structures. No approximations are made except those inherent in the numerical calculations. The method does not require extensive computer capacity; in fact it can be implemented on any standard PC. Several example calculations serve to illustrate the method, and its accuracy is demonstrated by comparison with cases where exact analytical results are available. The accuracy of previously proposed approximations are also discussed.

Evaluation of Probability Distribution Function for the Life of Pavement Structures

2000 ◽  
Vol 1730 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Stefan A. Romanoschi ◽  
John B. Metcalf
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Failure Time ◽  
Time To Failure ◽  
Closed Form Solutions ◽  
Monte Carlo Algorithms ◽  
Pavement Structures ◽  
Bootstrap Algorithm

Determination of the probability distribution function for the time to failure is essential for the development of pavement life models, because the probability distribution function reflects the variability in pavement degradation. The pavement life and failure time are associated with the number of equivalent standard axle load applications for which the degradations reach a critical level. When the critical degradation level is reached, maintenance and rehabilitation work needs to be done to improve pavement condition. Research was undertaken to identify the appropriate statistical models for determination of the probability distribution function for the time to failure of pavement structures. The study used the rutting data collected on a test lane at the first full-scale accelerated pavement test in Louisiana. The research indicated that closed-form solutions or Monte Carlo algorithms can be used when the degradation models have a known form. The bootstrap algorithm can be used to determine the confidence intervals for probability of failure at a given time. If the form of the degradation model is not known, the survival analysis method based on censored observations must be used. The methods can be used not only for rutting life models but also for other pavement life models: cracking initiation time, cracking life, roughness, and serviceability lives.

scholarly journals Extension of Cherenkov Light LDF Approximation for Yakutsk EAS Array

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
A. A. Al-Rubaiee ◽  
Y. Al-Douri ◽  
U. Hashim
Keyword(s):  
Distribution Function ◽  
Cosmic Ray ◽  
High Energy ◽  
Primary Energy ◽  
Cherenkov Light ◽  
Primary Proton ◽  
Air Showers ◽  
High Energies ◽  
Primary Particles

The simulation of the Cherenkov light lateral distribution function (LDF) in extensive air showers (EAS) was performed using CORSIKA code for configuration of Yakutsk EAS array at high energy range for different primary particles (p, Fe, and O2) and different zenith angles. Depending on Breit-Wigner function a parameterization of Cherenkov light LDF was reconstructed on the basis of this simulation as a function of primary energy. A comparison of the calculated Cherenkov light LDF with that measured on the Yakutsk EAS array gives the possibility of identification of the particle initiating the shower and determination of its energy in the knee region of the cosmic ray spectrum. The extrapolation of approximated Cherenkov light LDF for high energies was obtained for primary proton and iron nuclei.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

scholarly journals Position-dependent matter density probability distribution function

2020 ◽  
Vol 102 (12) ◽  
Author(s):  
Drew Jamieson ◽  
Marilena Loverde
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Matter Density

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.

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