Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes

2011 ◽  
Vol 62 (8) ◽  
pp. 1199-1212 ◽  
Author(s):  
S. B. Vakarchuk ◽  
V. G. Doronin
Keyword(s):  
Entire Functions ◽  
Mean Square ◽  
Finite Degree ◽  
Straight Line ◽  
Functional Classes

The Design and Experiment of a Two-Dimensional Position Sensitive Detecting (PSD) Sensor Based on Avalanche Breakdown

2014 ◽  
Vol 609-610 ◽  
pp. 1094-1099
Author(s):  
Yuan Yuan Shan ◽  
Ming Qin ◽  
Sheng Qi Chen
Keyword(s):  
Root Mean Square Error ◽  
Comsol Multiphysics ◽  
Process Conditions ◽  
Avalanche Breakdown ◽  
Mean Square ◽  
Two Dimensional ◽  
Pn Junction ◽  
Straight Line ◽  
Psd Sensor ◽  
Position Sensitive

A two-dimensional position sensitive detecting sensor (PSD) based on avalanche breakdown is introduced in this paper. The structure of the sensor is designed under the assumption that the breakdown of the PN junction in the sensor occurs at the bottom of the PN junction. The breakdown structure and characteristics of the sensor are simulated by Medici software and the doping structure and process conditions are calculated by Tsuprem4 software. By using COMSOL Multiphysics, we obtained current allocation of the straight and right angle type electrodes, which is corresponding to the optimal structure. In simulation, the root mean square error of the rectangular-shaped electrode and the straight line-shaped electrode are 0.198, 0.145 respectively. Experiment results show that in the 50% photosensitive area with the center as the origin, the rectangular-shaped electrode error is much smaller than a straight line-shaped electrode and fits in to linear relationship better. But the error of the angle the boundary of the electrode is significantly worse than the line-shaped electrode.

scholarly journals Approximation characteristics of the isotropic Nikol'skii-Besov functional classes

2021 ◽  
Vol 13 (3) ◽  
pp. 851-861
Author(s):  
S.Ya. Yanchenko ◽  
O.Ya. Radchenko
Keyword(s):  
Exponential Type ◽  
Lebesgue Space ◽  
Entire Functions ◽  
Exact Order ◽  
Periodic Functions ◽  
Approximation Of Functions ◽  
Several Variables ◽  
Functions Of Exponential Type ◽  
Functional Classes ◽  
Mixed Smoothness

In the paper, we investigates the isotropic Nikol'skii-Besov classes $B^r_{p,\theta}(\mathbb{R}^d)$ of non-periodic functions of several variables, which for $d = 1$ are identical to the classes of functions with a dominant mixed smoothness $S^{r}_{p,\theta}B(\mathbb{R})$. We establish the exact-order estimates for the approximation of functions from these classes $B^r_{p,\theta}(\mathbb{R}^d)$ in the metric of the Lebesgue space $L_q(\mathbb{R}^d)$, by entire functions of exponential type with some restrictions for their spectrum in the case $1 \leqslant p \leqslant q \leqslant \infty$, $(p,q)\neq \{(1,1), (\infty, \infty)\}$, $d\geq 1$. In the case $2<p=q<\infty$, $d=1$, the established estimate is also new for the classes $S^{r}_{p,\theta}B(\mathbb{R})$.

Iterates of meromorphic functions: I

1991 ◽  
Vol 11 (2) ◽  
pp. 241-248 ◽  
Author(s):  
I. N. Baker ◽  
J. Kotus ◽  
Lü Yinian
Keyword(s):  
Meromorphic Functions ◽  
Entire Functions ◽  
Julia Set ◽  
Exceptional Case ◽  
Straight Line ◽  
Transcendental Entire Functions ◽  
Periodic Cycles

AbstractFor functions meromorphic in the plane, apart from an exceptional case, the Julia set J is the closure of the set of all preimages of poles. The repelling periodic cycles are dense in J. In contrast with the case of transcendental entire functions, J may be a subset of a straight line and general classes of functions for which this is the case can be determined. J may also lie on a quasicircle through infinity which is not a straight line.

Non-Real Periodic Points of Entire Functions

1997 ◽  
Vol 40 (3) ◽  
pp. 271-275 ◽  
Author(s):  
Walter Bergweiler
Keyword(s):  
Complex Plane ◽  
Entire Functions ◽  
Periodic Points ◽  
Transcendental Function ◽  
Entire Transcendental Function ◽  
Straight Line

AbstractIt is shown that if f is an entire transcendental function, l a straight line in the complex plane, and n ≥ 2, then f has infinitely many repelling periodic points of period n that do not lie on l.

scholarly journals On the best mean-square approximation by entire functions of finite type on the line

2021 ◽  
Vol 17 ◽  
pp. 36
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Finite Type ◽  
Entire Functions ◽  
Jackson Type ◽  
Mean Square ◽  
Differentiable Functions

Jackson-type inequalities have been obtained for the best mean square approximation of differentiable functions by means of the entire functions of finite type on the line.

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