On the best approximation in the mean of continuous functions by polynomials, which are majorized by a given function

1972 ◽  
Vol 11 (4) ◽  
pp. 226-231
Author(s):  
V. A. Kaminskii
Keyword(s):  
Best Approximation ◽  
Continuous Functions ◽  
The Best Approximation ◽  
The Mean

Mean alveolar gases and alveolar-arterial gradients in pulmonary patients

1979 ◽  
Vol 46 (3) ◽  
pp. 534-540 ◽  
Author(s):  
U. C. Luft ◽  
J. A. Loeppky ◽  
E. M. Mostyn
Keyword(s):  
Steady State ◽  
Mass Spectrometer ◽  
Dead Space ◽  
Best Approximation ◽  
The Other ◽  
Mean Values ◽  
The Best Approximation ◽  
The Mean ◽  
End Tidal ◽  
Better Than

In view of uncertainties about the best way to estimate mean alveolar gases in patients with ventilation-perfusion inequalities, three different methods were evaluated on 54 patients. 1) O2 and CO2 were recorded by mass spectrometer on an O2 (x)-CO2 (y) diagram. The coordinates at the intersect of the expiratory record with the mixed expired R line (RE) ives the mean alveolar values (PAo2 and PAco2. 2)pa'co2 was calculated with the Bohr equation using a predicted anatomic dead space and PA'o2 was derived with the alveolar equation. 3) End-tidal (ET) P02 were averaged over 1 min at rest in steady state. Mean RET calculated from 3 was identical with RE. Mean values for PAco2, PA'CO2. and PETco2 differed by less that 1 Torr, but the variance was least with the end-tidal method. There was a highly significant correlation between delta aAPco2 using PETco2 and VD/VT, better than with either of the other methods. The end-tidal measurement appears to give the best approximation of mean alveolar gas in pulmonary patients.

scholarly journals Upper Estimates of the angle best approximations of generalized Liouville-Weyl derivatives

2021 ◽  
Vol 103 (3) ◽  
pp. 54-67
Author(s):  
A.E. Jetpisbayeva ◽  
◽  
A.A. Jumabayeva ◽  
Keyword(s):  
Best Approximation ◽  
Three Dimensional ◽  
Continuous Functions ◽  
Trigonometric Polynomials ◽  
Dimensional Case ◽  
Best Approximations ◽  
Approximation Of Functions ◽  
The Best Approximation

In this article we consider continuous functions f with period 2π and their approximation by trigonometric polynomials. This article is devoted to the study of estimates of the best angular approximations of generalized Liouville-Weyl derivatives by angular approximation of functions in the three-dimensional case. We consider generalized Liouville-Weyl derivatives instead of the classical mixed Weyl derivative. In choosing the issues to be considered, we followed the general approach that emerged after the work of the second author of this article. Our main goal is to prove analogs of the results of in the three-dimensional case. The concept of general monotonic sequences plays a key role in our study. Several well-known inequalities are indicated for the norms, best approximations of the r-th derivative with respect to the best approximations of the function f. The issues considered in this paper are related to the range of issues studied in the works of Bernstein. Later Stechkin and Konyushkov obtained an inequality for the best approximation f^(r). Also, in the works of Potapov, using the angle approximation, some classes of functions are considered. In subsection 1 we give the necessary notation and useful lemmas. Estimates for the norms and best approximations of the generalized Liouville-Weyl derivative in the three-dimensional case are obtained.

scholarly journals On approximation of continuous functions by piecewise-constant ones in integral metrics

1998 ◽  
Vol 6 ◽  
pp. 128
Author(s):  
O.V. Chernytska
Keyword(s):  
Upper Bound ◽  
Best Approximation ◽  
Continuous Functions ◽  
Moduli Of Continuity ◽  
Piecewise Constant ◽  
Integral Metrics ◽  
The Best Approximation ◽  
Piecewise Constant Functions ◽  
Approximation Of Continuous Functions ◽  
Decreasing Functions

We obtain upper bound of the best approximation of the classes $H^{\omega} [a, b]$ by piecewise-constant functions over uniform split in metrics of $L_{\varphi}[a, b]$ spaces, which are generated by continuous non-decreasing functions $\varphi$ that are equal to zero in zero. We study the classes of functions $\varphi$, for which the obtained bound is exact for all convex moduli of continuity.

Sign in / Sign up

Export Citation Format

Share Document