ON HADAMARD COMPOSITION WITH ALGEBRAIC-LOGARITHMIC SINGULARITIES

1958 ◽  
Vol 9 (1) ◽  
pp. 68-72
Author(s):  
R. WILSON
Keyword(s):  
Logarithmic Singularities ◽  
Hadamard Composition

MONODROMY APPROACH TO QUANTUM COMPUTING

2002 ◽  
Vol 16 (30) ◽  
pp. 4593-4605 ◽  
Author(s):  
G. GIORGADZE
Keyword(s):  
Quantum Computing ◽  
Hilbert Problem ◽  
Holomorphic Vector Bundle ◽  
Classical System ◽  
Unitary Operators ◽  
Unitary Matrices ◽  
Classical Procedure ◽  
Logarithmic Singularities ◽  
The Given ◽  
Riemann Hilbert Problem

In this work, a gauge approach to quantum computing is considered. It is assumed that there exists a classical procedure for placing certain classical system in a state described by a holomorphic vector bundle with connection with logarithmic singularities. This bundle and its connection are constructed with the aid of unitary operators realizing the given algorithm using methods of the monodromic Riemann–Hilbert problem. Universality is understood in the sense that for any collection of unitary matrices there exists a connection with logarithmic singularities whose monodromy representation involves these matrices.

scholarly journals Approximation to Logarithmic-Cauchy Type Singular Integrals with Highly Oscillatory Kernels

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 728 ◽  
Author(s):  
SAIRA ◽  
Shuhuang Xiang
Keyword(s):  
Singular Integrals ◽  
Oscillatory Integral ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Cauchy Kernel ◽  
Cauchy Type ◽  
Highly Oscillatory ◽  
Logarithmic Singularities ◽  
Highly Oscillatory Integrals ◽  
Modified Moments

In this paper, a fast and accurate numerical Clenshaw-Curtis quadrature is proposed for the approximation of highly oscillatory integrals with Cauchy and logarithmic singularities, ⨍ − 1 1 f ( x ) log ( x − α ) e i k x x − t d x , t ∉ ( − 1 , 1 ) , α ∈ [ − 1 , 1 ] for a smooth function f ( x ) . This method consists of evaluation of the modified moments by stable recurrence relation and Cauchy kernel is solved by steepest descent method that transforms the oscillatory integral into the sum of line integrals. Later theoretical analysis and high accuracy of the method is illustrated by some examples.

scholarly journals The realization of the degree zero part of the motivic polylogarithm on abelian schemes in Deligne–Beilinson cohomology

2017 ◽  
Vol 13 (09) ◽  
pp. 2471-2485 ◽  
Author(s):  
Danny Scarponi
Keyword(s):  
Chow Groups ◽  
Degree Zero ◽  
Deligne Cohomology ◽  
Abelian Scheme ◽  
Logarithmic Singularities ◽  
Abelian Schemes

In 2014, Kings and Rössler showed that the realization of the degree zero part of the abelian polylogarithm in analytic Deligne cohomology can be described in terms of a class of currents which was previously defined by Maillot and Rössler and strongly related to the Bismut–Köhler higher torsion form of the Poincaré bundle. In this paper we show that, if the base of the abelian scheme is proper, Kings and Rössler’s result can be refined to hold already in Deligne–Beilinson cohomology. More precisely, by means of Burgos’ theory of arithmetic Chow groups, we prove that the class of currents defined by Maillot and Rössler has a representative with logarithmic singularities at the boundary and therefore defines an element in Deligne–Beilinson cohomology. This element coincides with the realization of the degree zero part of the motivic polylogarithm on abelian schemes in Deligne–Beilinson cohomology.

AVOIDING MOVING LOGARITHMIC SINGULARITIES IN 3N FADDEEV EQUATIONS

2009 ◽  
Vol 24 (11n13) ◽  
pp. 779-784
Author(s):  
H. WITAŁA ◽  
W. GLÖCKLE
Keyword(s):  
Elastic Scattering ◽  
Faddeev Equation ◽  
Breakup Reaction ◽  
Standard Approach ◽  
Faddeev Equations ◽  
Logarithmic Singularities ◽  
Good Agreement

We present an approach to solve the three-nucleon Faddeev equation which avoids the complicated singularity pattern going with the moving logarithmic singularities of the standard approach. Very good agreement of the new and old approaches in the application to nucleon-deuteron elastic scattering and the breakup reaction is found.

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