scholarly journals Upper bound estimate of incomplete Cochrane sum

2017 ◽  
Vol 15 (1) ◽  
pp. 852-858
Author(s):  
Yuankui Ma ◽  
Wen Peng ◽  
Tianping Zhang
Keyword(s):  
Upper Bound ◽  
Dirichlet Character ◽  
Kloosterman Sum ◽  
Upper Bound Estimate ◽  
Cochrane Sum

Abstract By using the properties of Kloosterman sum and Dirichlet character, an optimal upper bound estimate of incomplete Cochrane sum is given.

scholarly journals Second Hankel determinant for certain class of bi-univalent functions defined by Chebyshev polynomials

2019 ◽  
Vol 12 (02) ◽  
pp. 1950017
Author(s):  
H. Orhan ◽  
N. Magesh ◽  
V. K. Balaji
Keyword(s):  
Unit Disk ◽  
Upper Bound ◽  
Chebyshev Polynomials ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
Upper Bound Estimate

In this work, we obtain an upper bound estimate for the second Hankel determinant of a subclass [Formula: see text] of analytic bi-univalent function class [Formula: see text] which is associated with Chebyshev polynomials in the open unit disk.

On the speed of convergence to limit distributions for Hecke L-functions associated with ideal class characters

Analysis ◽  
2006 ◽  
Vol 26 (3) ◽  
Author(s):  
Kohji Matsumoto
Keyword(s):  
Upper Bound ◽  
Ideal Class ◽  
Speed Of Convergence ◽  
Limit Distributions ◽  
Upper Bound Estimate

We prove an upper bound estimate of the speed of convergence to limit distributions

Fixed time synchronization of a class of chaotic systems based via the saturation control

2021 ◽  
Vol 67 (4 Jul-Aug) ◽  
pp. 041401
Author(s):  
Jiaojiao Fu ◽  
Runzi Luo ◽  
Meichun Huang ◽  
Haipeng Su
Keyword(s):  
Upper Bound ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Fixed Time ◽  
Stability Theorem ◽  
Backstepping Method ◽  
Time Stability ◽  
Saturation Control ◽  
New Chaotic System ◽  
Upper Bound Estimate

In this paper, we discuss the fixed time synchronization of a class of chaotic systems based on the backstepping control with disturbances. A new and important fixed time stability theorem is presented. The upper bound estimate formulas of the settling time are also given which are different from the existing results in the literature. Based on the new fixed time stability theorem, a novel saturation controller for the fixed time synchronization a class of chaotic systems is proposed via the backstepping method. Finally, the new chaotic system is taken as an example to illustrate the applicability of the obtained theory.

Hardy–Orlicz Spaces of Dirichlet Series: An Interpolation Problem on Abscissae of Convergence

2019 ◽  
Author(s):  
Maxime Bailleul ◽  
Pascal Lefèvre ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Dirichlet Series ◽  
Hardy Spaces ◽  
Upper Bound ◽  
Interpolation Problem ◽  
Orlicz Spaces ◽  
Elementary Method ◽  
Abscissa Of Convergence ◽  
Upper Bound Estimate

Abstract The study of Hardy spaces of Dirichlet series denoted by $\mathscr{H}^p$ ($p\geq 1$) was initiated in [7] when $p=2$ and $p=\infty $, and in [2] for the general case. In this paper we introduce the Orlicz version of spaces of Dirichlet series $\mathscr{H}^\psi $. We focus on the case $\psi =\psi _q(t)=\exp (t^q)-1,$ and we compute the abscissa of convergence for these spaces. It turns out that its value is $\min \{1/q\,,1/2\}$ filling the gap between the case $\mathscr{H}^\infty $, where the abscissa is equal to $0$, and the case $\mathscr{H}^p$ for $p$ finite, where the abscissa is equal to $1/2$. The upper-bound estimate relies on an elementary method that applies to many spaces of Dirichlet series. This answers a question raised by Hedenmalm in [6].

scholarly journals An explicit upper bound for |L(1,χ)| when χ(2) = 1 and χ is even

2016 ◽  
Vol 12 (08) ◽  
pp. 2299-2315 ◽  
Author(s):  
Sumaia Saad Eddin
Keyword(s):  
Upper Bound ◽  
Dirichlet Character ◽  
Primitive Dirichlet Character

Let [Formula: see text] be a primitive Dirichlet character of conductor [Formula: see text] and let us denote by [Formula: see text] the associated [Formula: see text]-series. In this paper, we provide an explicit upper bound for [Formula: see text] when [Formula: see text] is a primitive even Dirichlet character with [Formula: see text].

scholarly journals An upper-bound estimate for the accuracy of volume-area scaling

2013 ◽  
Vol 7 (3) ◽  
pp. 2293-2331 ◽  
Author(s):  
D. Farinotti ◽  
M. Huss
Keyword(s):  
Volume Change ◽  
Upper Bound ◽  
Synthetic Data ◽  
Volume Changes ◽  
Real World Data ◽  
Secondary Importance ◽  
Ice Volume ◽  
Volume Measurements ◽  
Upper Bound Estimate ◽  
The Impact

Abstract. Volume-area scaling is the most popular method for estimating the ice volume of large glacier samples. Here, a series of resampling experiments based on different sets of synthetic data are presented in order to derive an upper-bound estimate (i.e. a level achieved only with ideal conditions) for the accuracy of its application. We also quantify the maximum accuracy expected when scaling is used for determining the glacier volume change, and area change of a given glacier population. A comprehensive set of measured glacier areas, volumes, area and volume changes is evaluated to investigate the impact of real-world data quality on the so assessed accuracies. For populations larger than a few thousand glaciers, the total ice volume can be recovered within 30% if all measurements available worldwide are used for estimating the scaling coefficients. Assuming no systematic biases in ice volume measurements, their uncertainty is of secondary importance. Knowing the individual areas of a glacier sample for two points in time allows recovering the corresponding ice volume change within 40% for populations larger than a few hundred glaciers, both for steady-state and transient geometries. If ice volume changes can be estimated without bias, glacier area changes derived from volume-area scaling show similar uncertainties as for the volume changes. This paper does not aim at making a final judgement about the suitability of volume-area scaling, but provides the means for assessing the accuracy expected from its application.

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