Experimental evaluation of depth-dependent lateral standard deviation for various ions in a-Si from one-dimensional tilted implantation profiles

1999 ◽  
Vol 46 (9) ◽  
pp. 1824-1828 ◽  
Author(s):  
T. Miyashita ◽  
K. Suzuki
Keyword(s):  
Standard Deviation ◽  
Experimental Evaluation ◽  
One Dimensional

Estimation of the integral of the square of derivatives of symmetric probability densities of one-dimensional random variables

Metrologiya ◽  
2020 ◽  
pp. 15-27
Author(s):  
Aleksandr V. Lapko ◽  
Vasiliy A. Lapko
Keyword(s):  
Standard Deviation ◽  
Probability Density ◽  
Random Variables ◽  
Random Variable ◽  
Density Estimates ◽  
One Dimensional ◽  
Probability Densities ◽  
The One ◽  
Derivatives Of ◽  
Selection Of

When substantiating the method of fast selection of the bandwidth of kernel probability density estimates, a constant was found that is a functional of the second density derivative. In this paper, the obtained result is generalized to derivatives of symmetric probability densities of different orders. The functional dependences of the constants under study on the coeffi cient of antikurtosis of a random variable are established. The regularities peculiar to them are investigated. Based on the results obtained, a method for estimating functionals from derived probability densities has been developed, which involves the following actions. In the original sample estimated standard deviation of the one-dimensional random variables and the coeffi cient of antikurtosis. Using the reconstructed functional dependences on the antikurtosis coeffi cient, the constants are estimated, which are functionals of the derivatives of the probability density. With known estimates of the standard deviation of the investigated random variable and the considered constant, the values of the functional from the derivative of the probability density of the selected order are calculated. The obtained results are confi rmed by the analysis of the data of computational experiments. It is established that with increasing order of the derivative, the values of the estimates of the studied functionals increase. This fact is explained by the complication of the integrand function in the considered functionals. The proposed method provides objective results for the fi rst three derivatives of the probability density of a random variable. The obtained conclusions are confi rmed by the results of the confi dence estimation of the investigated functionals.

Combined Use of Two Single-Component Enzymatic Time-Temperature Integrators: Application to Industrial Continuous Rotary Processing of Canned Ravioli

2005 ◽  
Vol 68 (2) ◽  
pp. 375-383 ◽  
Author(s):  
YANN GUIAVARC'H ◽  
FRANÇOIS ZUBER ◽  
ANN VAN LOEY ◽  
MARC HENDRICKX
Keyword(s):  
Heat Transfer ◽  
Standard Deviation ◽  
Single Component ◽  
Transfer Model ◽  
Liquid Food ◽  
One Dimensional ◽  
Temperature Recording ◽  
Combined Use ◽  
Explicit Finite Difference ◽  
Time Temperature Integrator

Two original, highly dehydrated, small single-component enzymatic time-temperature integrator (TTI) systems, TTIL and TTIS, were prepared. Their z-values were 13.9 and 16.4°C, respectively, and they were based on Bacillus licheniformis αamylase and Bacillus subtilis α-amylase, respectively. The isothermal calibration of these two TTIs revealed that (i) they can be used in the temperature range of 100 to 140°C, (ii) results can be read within 5 min, and (iii) they can be used individually for the measurements of process values 13.9°CF121.1°C and 16.4°CF121.1°C up to 98 min and 85 min, respectively. Because these two TTIs have different z-values above 10°C, they could be used in combination with the multicomponent TTI concept to estimate process values 10°CF121.1°C inside particles of a solid or liquid food submitted to rotary processing. Raviolis in tomato sauce sterilized in an industrial-scale reel and spiral continuous retort were examined in this study. Two methods, based on the combination of a one-dimensional explicit finite difference heat-transfer model with the experimental responses of the TTIs, were used to take into account the possible deviations in evaluation of 10°CF121.1°C values. A process value 10°CF121.1°C of 23.6 min with a standard deviation of 1.5 min was determined inside raviolis using the multicomponent TTI approach, and a process value 10°CF121.1°C of 33.6 min with a standard deviation of 1.5 min inside the sauce was calculated from the temperature recording data.

scholarly journals Approximating the Solution Stochastic Process of the Random Cauchy One-Dimensional Heat Model

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
A. Navarro-Quiles ◽  
J.-V. Romero ◽  
M.-D. Roselló ◽  
M. A. Sohaly
Keyword(s):  
Stochastic Process ◽  
Standard Deviation ◽  
Finite Difference ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Sufficient Conditions ◽  
Numerical Approximations ◽  
One Dimensional ◽  
The Mean ◽  
Theoretical Results

This paper deals with the numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme. The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given.

Experimental evaluation of salinity geosynthetics capillary barriers

2021 ◽  
pp. 1-27
Author(s):  
A. Bouazza
Keyword(s):  
Experimental Evaluation ◽  
Preventive Measures ◽  
Saline Water ◽  
Capillary Rise ◽  
Water Entry ◽  
Upward Flow ◽  
Wetting Front ◽  
Capillary Barrier ◽  
One Dimensional ◽  
Capillary Barriers

This paper explores the transient upward flow of saline water in one-dimensional soil and soil-geosynthetics columns to evaluate preventive measures to mitigate salinity rise. Unsaturated soil concepts are utilised to elucidate the salinity movement through geotextile and geocomposite drain interfaces. The presence of a geotextile layer slowed down the capillary rise of the saline water. However, it did not prevent the breakthrough of the saline water due to the hydrophilicity of the geotextile and the suction at the geotextile base being close to the geotextile's water entry suction value.  In contrast, using a geocomposite drain mitigated the upward saline wetting front. It acted as a salinity capillary barrier due to the initial hydrophobicity of its geotextile component and the air gap present in the geonet core.

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