Numerical Solution of Mean-Value Theorem for Downward Continuation of Potential Fields

2018 ◽  
Author(s):  
C. Zhang ◽  
Q. Lv ◽  
J. Yan
Keyword(s):  
Numerical Solution ◽  
Mean Value ◽  
Downward Continuation ◽  
Potential Fields ◽  
Mean Value Theorem

scholarly journals Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential Fields

2018 ◽  
Vol 45 (8) ◽  
pp. 3461-3470 ◽  
Author(s):  
Chong Zhang ◽  
Qingtian Lü ◽  
Jiayong Yan ◽  
Guang Qi
Keyword(s):  
Numerical Solutions ◽  
Mean Value ◽  
Downward Continuation ◽  
Potential Fields ◽  
Mean Value Theorem ◽  
New Methods ◽  
The Mean

scholarly journals Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem

2011 ◽  
Vol 35 (5) ◽  
pp. 2374-2383 ◽  
Author(s):  
Z. Avazzadeh ◽  
M. Heydari ◽  
G.B. Loghmani
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Fredholm Integral Equations

scholarly journals Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem II. High dimensional problems

2013 ◽  
Vol 37 (1-2) ◽  
pp. 432-442 ◽  
Author(s):  
M. Heydari ◽  
Z. Avazzadeh ◽  
H. Navabpour ◽  
G.B. Loghmani
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Mean Value ◽  
High Dimensional ◽  
Mean Value Theorem ◽  
Fredholm Integral Equations

scholarly journals On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1303
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Faraidun Kadir Hamasalh
Keyword(s):  
Time Scale ◽  
Initial Value Problems ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Discrete Fractional Calculus ◽  
Initial Value ◽  
Forward Difference ◽  
The Mean ◽  
Monotonicity Analysis ◽  
Monotonicity Results

Monotonicity analysis of delta fractional sums and differences of order υ∈(0,1] on the time scale hZ are presented in this study. For this analysis, two models of discrete fractional calculus, Riemann–Liouville and Caputo, are considered. There is a relationship between the delta Riemann–Liouville fractional h-difference and delta Caputo fractional h-differences, which we find in this study. Therefore, after we solve one, we can apply the same method to the other one due to their correlation. We show that y(z) is υ-increasing on Ma+υh,h, where the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and then, we can show that y(z) is υ-increasing on Ma+υh,h, where the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) for each z∈Ma+h,h. Conversely, if y(a+υh) is greater or equal to zero and y(z) is increasing on Ma+υh,h, we show that the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and consequently, we can show that the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) on Ma,h. Furthermore, we consider some related results for strictly increasing, decreasing, and strictly decreasing cases. Finally, the fractional forward difference initial value problems and their solutions are investigated to test the mean value theorem on the time scale hZ utilizing the monotonicity results.

scholarly journals On a hybrid version of the Vinogradov mean value theorem

2021 ◽  
Vol 163 (1) ◽  
pp. 1-17
Author(s):  
C. Chen ◽  
I. E. Shparlinski
Keyword(s):  
Mean Value ◽  
Mean Value Theorem

scholarly journals Arithmetic of higher-dimensional orbifolds and a mixed Waring problem

2021 ◽  
Author(s):  
Tim Browning ◽  
Shuntaro Yamagishi
Keyword(s):  
Circle Method ◽  
Rational Points ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Waring’S Problem ◽  
Waring Problem ◽  
Waring's Problem ◽  
Main Conjecture ◽  
Higher Dimensional ◽  
Thin Set

AbstractWe study the density of rational points on a higher-dimensional orbifold $$(\mathbb {P}^{n-1},\Delta )$$ ( P n - 1 , Δ ) when $$\Delta $$ Δ is a $$\mathbb {Q}$$ Q -divisor involving hyperplanes. This allows us to address a question of Tanimoto about whether the set of rational points on such an orbifold constitutes a thin set. Our approach relies on the Hardy–Littlewood circle method to first study an asymptotic version of Waring’s problem for mixed powers. In doing so we make crucial use of the recent resolution of the main conjecture in Vinogradov’s mean value theorem, due to Bourgain–Demeter–Guth and Wooley.

High-precision Downward Continuation of Potential Fields Algorithm Utilizing Adaptive Damping Coefficient of Generalized Minimal Residuals

2021 ◽  
Author(s):  
Zhi-Hou Zhang ◽  
Xiao-Long Liao ◽  
Ze-Yu Shi ◽  
Anthony R. Lowry ◽  
Yao Yu ◽  
...  
Keyword(s):  
High Precision ◽  
Downward Continuation ◽  
Damping Coefficient ◽  
Potential Fields
Sign in / Sign up

Export Citation Format

Share Document