Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas

2020 ◽  
pp. 183-228
Author(s):  
Gradimir V. Milovanović ◽  
Yilmaz Simsek
Keyword(s):  
Quadrature Formulas ◽  
Trigonometric Sums ◽  
Hardy Type

On Quadrature Formulas

2018 ◽  
Vol 481 (2) ◽  
pp. 136-137
Author(s):  
V. Chubarikov ◽  
Keyword(s):  
Quadrature Formulas

scholarly journals Positive quadrature formulas III: asymptotics of weights

2008 ◽  
Vol 77 (264) ◽  
pp. 2241-2259 ◽  
Author(s):  
Franz Peherstorfer
Keyword(s):  
Quadrature Formulas ◽  
Positive Quadrature Formulas

scholarly journals Hardy-type estimates for Dirac operators

2007 ◽  
Vol 40 (6) ◽  
pp. 885-900 ◽  
Author(s):  
J DOLBEAULT ◽  
M ESTEBAN ◽  
J DUOANDIKOETXEA ◽  
L VEGA
Keyword(s):  
Dirac Operators ◽  
Hardy Type

scholarly journals Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1799
Author(s):  
Irene Gómez-Bueno ◽  
Manuel Jesús Castro Díaz ◽  
Carlos Parés ◽  
Giovanni Russo
Keyword(s):  
High Order ◽  
Collocation Methods ◽  
Quadrature Formulas ◽  
Balance Laws ◽  
Source Terms ◽  
Time Step ◽  
Systems Of Balance Laws ◽  
Reconstruction Operator ◽  
Non Linear ◽  
Linear Problems

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

scholarly journals Experimental test of the Greenberger–Horne–Zeilinger-type paradoxes in and beyond graph states

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zheng-Hao Liu ◽  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Mu Yang ◽  
Qiang Li ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Success Probability ◽  
Quantum Foundations ◽  
Mixed States ◽  
Graph States ◽  
Hardy Type ◽  
Realistic Description ◽  
Entanglement Detection ◽  
Quantum Paradoxes

AbstractThe Greenberger–Horne–Zeilinger (GHZ) paradox is an exquisite no-go theorem that shows the sharp contradiction between classical theory and quantum mechanics by ruling out any local realistic description of quantum theory. The investigation of GHZ-type paradoxes has been carried out in a variety of systems and led to fruitful discoveries. However, its range of applicability still remains unknown and a unified construction is yet to be discovered. In this work, we present a unified construction of GHZ-type paradoxes for graph states, and show that the existence of GHZ-type paradox is not limited to graph states. The results have important applications in quantum state verification for graph states, entanglement detection, and construction of GHZ-type steering paradox for mixed states. We perform a photonic experiment to test the GHZ-type paradoxes via measuring the success probability of their corresponding perfect Hardy-type paradoxes, and demonstrate the proposed applications. Our work deepens the comprehension of quantum paradoxes in quantum foundations, and may have applications in a broad spectrum of quantum information tasks.

scholarly journals On a weighted inequality of Hardy type in spaces Lp(⋅)

2009 ◽  
Vol 353 (2) ◽  
pp. 521-530 ◽  
Author(s):  
Farman I. Mamedov ◽  
Aziz Harman
Keyword(s):  
Weighted Inequality ◽  
Hardy Type

scholarly journals Some new Hardy-type inequalities on time scales

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ahmed A. El-Deeb ◽  
Hamza A. Elsennary ◽  
Dumitru Baleanu
Keyword(s):  
Time Scales ◽  
Hardy Type Inequalities ◽  
Hardy Type

Trigonometric sums through Ramanujan’s theory of theta functions

2021 ◽  
Author(s):  
K. N. Harshitha ◽  
K. R. Vasuki ◽  
M. V. Yathirajsharma
Keyword(s):  
Theta Functions ◽  
Trigonometric Sums
Sign in / Sign up

Export Citation Format

Share Document