scholarly journals The Informative Power of all Possible Linear Functionals and the Mean-Square Error in the Diccretization of Solutions of the Diriclet Problem for the Laplace Equation in the Circle

2021 ◽  
Vol 134 (1) ◽  
pp. 42-51
Author(s):  
M.Y. Berikkhanova ◽  
◽  
K.Y. Sherniyazov ◽  
Keyword(s):  
Dirichlet Problem ◽  
Mean Square Error ◽  
Laplace Equation ◽  
Boundary Function ◽  
Optimal Order ◽  
Mean Square ◽  
Linear Functionals ◽  
Boundary Properties ◽  
The Mean ◽  
Probabilistic Measures

The Dirichlet problem for the Laplace equation in the case of a circle belongs to the classical ones and in various aspects has been the subject of study in various fields of mathematics. Among them are such topics as - "Boundary properties of analytic functions", in the study of which powerful methods of function theories were created and honed, - The Banach problem on the existence of a basis for a class of functions consisting of continuous in a closed circle and analytic in, - Numerical methods, since this problem as a mathematical model describes many real processes. In this article, we consider the discretization problem of solutions of the Dirichlet problem for the Laplace equation in a circle from finite numerical information obtained from the boundary function as a result of applying all possible linear functionals. The optimal order of discretization error is found and the corresponding optimal operator of discretization is constructed. The problem of constructing probabilistic measures on functional classes is also considered. Probabilistic measures on the Korobov 𝐸𝑟 (0, 2𝜋) and Nikolsky 𝐻𝑟 2 (0, 2𝜋) classes are introduced. Two-sided estimates of the mean-square error of discretization the solution of the problem by operator (𝑇𝑁 𝑓) (𝛼, 𝜃) are established.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals IndoorPlant: A Model for Intelligent Services in Indoor Agriculture Based on Context Histories

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1631
Author(s):  
Bruno Guilherme Martini ◽  
Gilson Augusto Helfer ◽  
Jorge Luis Victória Barbosa ◽  
Regina Célia Espinosa Modolo ◽  
Marcio Rosa da Silva ◽  
...  
Keyword(s):  
Technology Acceptance ◽  
Mean Square Error ◽  
Ease Of Use ◽  
Coefficient Of Determination ◽  
Square Root ◽  
Mean Square ◽  
Use Context ◽  
The Mean ◽  
Acceptance Model ◽  
The Internet Of Things

The application of ubiquitous computing has increased in recent years, especially due to the development of technologies such as mobile computing, more accurate sensors, and specific protocols for the Internet of Things (IoT). One of the trends in this area of research is the use of context awareness. In agriculture, the context involves the environment, for example, the conditions found inside a greenhouse. Recently, a series of studies have proposed the use of sensors to monitor production and/or the use of cameras to obtain information about cultivation, providing data, reminders, and alerts to farmers. This article proposes a computational model for indoor agriculture called IndoorPlant. The model uses the analysis of context histories to provide intelligent generic services, such as predicting productivity, indicating problems that cultivation may suffer, and giving suggestions for improvements in greenhouse parameters. IndoorPlant was tested in three scenarios of the daily life of farmers with hydroponic production data that were obtained during seven months of cultivation of radicchio, lettuce, and arugula. Finally, the article presents the results obtained through intelligent services that use context histories. The scenarios used services to recommend improvements in cultivation, profiles and, finally, prediction of the cultivation time of radicchio, lettuce, and arugula using the partial least squares (PLS) regression technique. The prediction results were relevant since the following values were obtained: 0.96 (R2, coefficient of determination), 1.06 (RMSEC, square root of the mean square error of calibration), and 1.94 (RMSECV, square root of the mean square error of cross validation) for radicchio; 0.95 (R2), 1.37 (RMSEC), and 3.31 (RMSECV) for lettuce; 0.93 (R2), 1.10 (RMSEC), and 1.89 (RMSECV) for arugula. Eight farmers with different functions on the farm filled out a survey based on the technology acceptance model (TAM). The results showed 92% acceptance regarding utility and 98% acceptance for ease of use.

Burst Erasures and the Mean-Square Error for Cyclic Parseval Frames

2011 ◽  
Vol 57 (7) ◽  
pp. 4622-4635 ◽  
Author(s):  
Bernhard G. Bodmann ◽  
Pankaj K. Singh
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Parseval Frames ◽  
The Mean

A MODIFIED RATIO TYPE ESTIMATOR OF FINITE POPULATION MEAN UNDER STRATIFIED RANDOM SAMPLING SCHEME

2021 ◽  
pp. 58-60
Author(s):  
Naziru Fadisanku Haruna ◽  
Ran Vijay Kumar Singh ◽  
Samsudeen Dahiru
Keyword(s):  
Mean Square Error ◽  
Random Sampling ◽  
Minimum Mean Square Error ◽  
Real Life ◽  
Population Data ◽  
Auxiliary Variable ◽  
Mean Square ◽  
Data Set ◽  
Population Mean ◽  
The Mean

In This paper a modied ratio-type estimator for nite population mean under stratied random sampling using single auxiliary variable has been proposed. The expression for mean square error and bias of the proposed estimator are derived up to the rst order of approximation. The expression for minimum mean square error of proposed estimator is also obtained. The mean square error the proposed estimator is compared with other existing estimators theoretically and condition are obtained under which proposed estimator performed better. A real life population data set has been considered to compare the efciency of the proposed estimator numerically.

scholarly journals Comparing plastic syringes and disposable columns to extract n-alkanes in forage and concentrate feeds

2010 ◽  
Vol 40 (8) ◽  
pp. 1844-1847 ◽  
Author(s):  
Dimas Estrasulas de Oliveira ◽  
Luis Orlindo Tedeschi
Keyword(s):  
Gas Chromatography ◽  
Linear Regression ◽  
Mean Square Error ◽  
Carbon Chain ◽  
Carbon Chain Length ◽  
Square Root ◽  
Mean Square ◽  
Alternative Material ◽  
The Mean ◽  
Disposable Plastic

Saturated aliphatic hydrocarbons (n-alkanes) were extracted from feed, orts, and bovine fecal samples using disposable, plastic 5mL-syringes as an alternative material to disposable columns, which are normally used in the liquid-solid extraction phase of n-alkanes. For both methods, the n-alkane extracts (carbon chain length between 31 and 36 atoms) were identified using gas chromatography. The linear regression between methods were: 1) feces: column Alkane=2.63+0.92×syringeAlkane [r²=0.94, square root of the mean square error (RMSE)=13.7mg kg-1, n=30] from which the intercept and the slope did not simultaneously differ from zero and unity (P>0.05), respectively; 2) feeds: column Alkane=0.36+1.12×syringeAlkane (r²=0.85, RMSE=1.9mg kg-1, n=21) from which the intercept and the slope did not simultaneously differ from zero and unity (P>0.05), respectively; 3) orts: column Alkane=0.49+0.92×syringeAlkane (r²=0.98, RMSE=1.2mg kg-1, n=15) from which the intercept and the slope did not simultaneously differ from zero and unity (P>0.05), respectively. Materials with low concentration of n-alkanes may affect the values obtained in both methods. These results suggested that disposable plastic syringes might be a viable alternative to columns thus, reducing analytical costs.

scholarly journals On MSE-Optimal Circular Crossover Designs

2021 ◽  
Vol 15 (4) ◽  
Author(s):  
C. Neumann ◽  
J. Kunert
Keyword(s):  
Optimal Design ◽  
Mean Square Error ◽  
Current Treatment ◽  
Mean Square ◽  
Crossover Designs ◽  
Carryover Effects ◽  
Circular Structure ◽  
Balanced Designs ◽  
Preceding Period ◽  
The Mean

AbstractIn crossover designs, each subject receives a series of treatments, one after the other in p consecutive periods. There is concern that the measurement of a subject at a given period might be influenced not only by the direct effect of the current treatment but also by a carryover effect of the treatment applied in the preceding period. Sometimes, the periods of a crossover design are arranged in a circular structure. Before the first period of the experiment itself, there is a run-in period, in which each subject receives the treatment it will receive again in the last period. No measurements are taken during the run-in period. We consider the estimate for direct effects of treatments which is not corrected for carryover effects. If there are carryover effects, this uncorrected estimate will be biased. In that situation, the quality of the estimate can be measured by the mean square error, the sum of the squared bias and the variance. We determine MSE-optimal designs, that is, designs for which the mean square error is as small as possible. Since the optimal design will in general depend on the size of the carryover effects, we also determine the efficiency of some designs compared to the locally optimal design. It turns out that circular neighbour-balanced designs are highly efficient.

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