scholarly journals Almost complete convergence for the sequence of approximate solutions in linear calibration problem with α-mixing random data

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3251-3264
Author(s):  
Samia Khalfoune ◽  
Halima Zerouati
Keyword(s):  
Exact Solution ◽  
Complete Convergence ◽  
Approximate Solutions ◽  
Stochastic Method ◽  
Linear Calibration ◽  
Random Data ◽  
Exponential Inequalities ◽  
Numerical Example ◽  
Calibration Problem ◽  
Confidence Domain

In this work, we propose a stochastic method which gives an estimated solution for a linear calibration problem with ?-mixing random data. We establish exponential inequalities of Fuk Nagaev type, for the probability of the distance between the approximate solutions and the exact one. Furthermore, we build a confidence domain for the so mentioned exact solution. To check the validity of our results, a numerical example is proposed.

[A Bayesian Analysis of the Linear Calibration Problem]: Discussion

Technometrics ◽  
1981 ◽  
Vol 23 (4) ◽  
pp. 329 ◽  
Author(s):  
Joan R. Rosenblatt ◽  
Clifford H. Spiegelman
Keyword(s):  
Bayesian Analysis ◽  
Linear Calibration ◽  
Calibration Problem

scholarly journals A perturbed algorithm for strongly nonlinear variational-like inclusions

2000 ◽  
Vol 62 (3) ◽  
pp. 417-426 ◽  
Author(s):  
C.-H. Lee ◽  
Q. H. Ansari ◽  
J.-C. Yao
Keyword(s):  
Exact Solution ◽  
General Setting ◽  
Approximate Solutions ◽  
Strongly Nonlinear ◽  
Special Cases ◽  
The One

In this paper, we define the concept of η- subdifferential in a more general setting than the one used by Yang and Craven in 1991. By using η-subdifferentiability, we suggest a perturbed algorithm for finding the approximate solutions of strongly nonlinear variational-like inclusions and prove that these approximate solutions converge to the exact solution. Several special cases are also discussed.

scholarly journals Satisfying positivity requirement in the Beyond Complex Langevin approach

2018 ◽  
Vol 175 ◽  
pp. 11026 ◽  
Author(s):  
Adam Wyrzykowski ◽  
Błażej Ruba Ruba
Keyword(s):  
Exact Solution ◽  
Approximate Solutions ◽  
Groebner Basis ◽  
Matching Conditions ◽  
Quadratic Equations ◽  
Positive Distribution ◽  
Langevin Approach ◽  
Basis Method ◽  
Special Case ◽  
Complex Density

The problem of finding a positive distribution, which corresponds to a given complex density, is studied. By the requirement that the moments of the positive distribution and of the complex density are equal, one can reduce the problem to solving the matching conditions. These conditions are a set of quadratic equations, thus Groebner basis method was used to find its solutions when it is restricted to a few lowest-order moments. For a Gaussian complex density, these approximate solutions are compared with the exact solution, that is known in this special case.

Transverse Vibrations of Beams, Exact Versus Approximate Solutions

1981 ◽  
Vol 48 (4) ◽  
pp. 923-928 ◽  
Author(s):  
J. R. Hutchinson
Keyword(s):  
Exact Solution ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Approximate Solutions ◽  
Approximate Methods ◽  
Transverse Vibrations ◽  
Elasticity Equations ◽  
Beam Approximation ◽  
Free Beam

An exact solution for the natural frequencies of vibration of a finite length free-free beam with a circular cross section is found and compared to approximate solutions. This exact solution is a series solution of the general linear elasticity equations which converges to correct natural frequencies. Correctness of the frequencies is established by comparison to previous experiments. Comparison of the exact to approximate solutions is made with the Pochhammer-Chree approximation, the Timoshenko beam approximation and the Pickett approximation. The comparisons clearly show the range of applicability of the approximate methods as well as their accuracy. The correct shear coefficient for use in the Timoshenko beam approximation is investigated and conclusions which differ with, yet at the same time complement, those of previous researchers are reached.

A Theory of Lubrication With Turbulent Flow and Its Application to Slider Bearings

1960 ◽  
Vol 27 (1) ◽  
pp. 1-4 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Closed Form ◽  
Governing Equation ◽  
Reynolds Equation ◽  
Three Dimensions ◽  
Slider Bearing ◽  
Numerical Example ◽  
Special Case

The governing equation of turbulent lubrication in three dimensions, equivalent to the Reynolds equation of laminar lubrication, is derived. The problem of a slider bearing with no side leakage is then analyzed. An exact solution is found in closed form. Bearing characteristics are also established. It is found that the Reynolds number is an important parameter in the problem of turbulent lubrication. Furthermore, it is shown that the laminar lubrication may be considered as the special case of the present study. A numerical example is also included.

The General theory of Cylindrical and Conical Tubes Under Torsion and Bending Loads

1949 ◽  
Vol 53 (461) ◽  
pp. 461-483 ◽  
Author(s):  
J. Hadji-Argyris ◽  
P. C. Dunne
Keyword(s):  
General Theory ◽  
Cross Sections ◽  
Approximate Solutions ◽  
Torsional Stiffness ◽  
Numerical Example ◽  
Bending Loads ◽  
Present Part

SummaryParts 1 to 5 of this paper (February, September and November 1947 issues of the JOURNAL) investigated the stresses and deformations of closed tubes in which the thicknesses were governed by the ts* and t* laws. In the present part, the analysis is extended to multi-cell tubes with openings, open tubes with or without St. Venant torsional stiffness, and to tubes formed by joining elements of different cross-sections. To illustrate the theory a numerical example of the stressing of a four-boom wing consisting of seven joined elements is fully worked out. Finally, an appendix gives practical methods of dealing with tubes which do not conform to the ts* and t* laws, and of finding approximate solutions for four-boom tubes with direct stress carrying covers.

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