Uniqueness method: Multiloop calculations in QCD

1987 ◽  
Vol 73 (3) ◽  
pp. 1264-1274 ◽  
Author(s):  
D. I. Kazakov ◽  
A. V. Kotikov
Keyword(s):  
Uniqueness Method ◽  
Multiloop Calculations

scholarly journals A note on the exact boundary controllability for an imperfect transmission problem

2021 ◽  
Author(s):  
S. Monsurrò ◽  
A. K. Nandakumaran ◽  
C. Perugia
Keyword(s):  
Exact Controllability ◽  
Dirichlet Condition ◽  
Adjoint Problem ◽  
Imperfect Interface ◽  
External Boundary ◽  
Exact Boundary Controllability ◽  
Multipliers Method ◽  
Exact Boundary ◽  
Hilbert Uniqueness Method ◽  
Uniqueness Method

AbstractIn this note, we consider a hyperbolic system of equations in a domain made up of two components. We prescribe a homogeneous Dirichlet condition on the exterior boundary and a jump of the displacement proportional to the conormal derivatives on the interface. This last condition is the mathematical interpretation of an imperfect interface. We apply a control on the external boundary and, by means of the Hilbert Uniqueness Method, introduced by J. L. Lions, we study the related boundary exact controllability problem. The key point is to derive an observability inequality by using the so called Lagrange multipliers method, and then to construct the exact control through the solution of an adjoint problem. Eventually, we prove a lower bound for the control time which depends on the geometry of the domain, on the coefficients matrix and on the proportionality between the jump of the solution and the conormal derivatives on the interface.

scholarly journals Multiloop calculations in QED by superparticle path integrals

1995 ◽  
Vol 39 (2-3) ◽  
pp. 306-308 ◽  
Author(s):  
M.G. Schmidt ◽  
C. Schubert
Keyword(s):  
Path Integrals ◽  
Multiloop Calculations

scholarly journals Multiloop calculations in the string-inspired formalism: The single spinor loop in QED

1996 ◽  
Vol 53 (4) ◽  
pp. 2150-2159 ◽  
Author(s):  
Michael G. Schmidt ◽  
Christian Schubert
Keyword(s):  
Multiloop Calculations

The method of uniqueness, a new powerful technique for multiloop calculations

1983 ◽  
Vol 133 (6) ◽  
pp. 406-410 ◽  
Author(s):  
D.I. Kazakov
Keyword(s):  
Powerful Technique ◽  
Multiloop Calculations

Many-loop calculations: The uniqueness method and functional equations

1985 ◽  
Vol 62 (1) ◽  
pp. 84-89 ◽  
Author(s):  
D. I. Kazakov
Keyword(s):  
Functional Equations ◽  
Uniqueness Method

Multiloop calculations in theσmodel

1976 ◽  
Vol 13 (6) ◽  
pp. 1621-1641 ◽  
Author(s):  
M. Margulies
Keyword(s):  
Multiloop Calculations

scholarly journals Observability and uniqueness theorem for a coupled hyperbolic system

2000 ◽  
Vol 24 (6) ◽  
pp. 423-432 ◽  
Author(s):  
Boris V. Kapitonov ◽  
Joel S. Souza
Keyword(s):  
Uniqueness Theorem ◽  
Lagrange Multiplier ◽  
Hyperbolic System ◽  
Exact Controllability ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Inverse Inequality ◽  
Hilbert Uniqueness Method ◽  
Uniqueness Method

We deal with the inverse inequality for a coupled hyperbolic system with dissipation. The inverse inequality is an indispensable inequality that appears in the Hilbert Uniqueness Method (HUM), to establish equivalence of norms which guarantees uniqueness and boundary exact controllability results. The term observability is due to the mathematician Ho (1986) who used it in his works relating it to the inverse inequality. We obtain the inverse inequality by the Lagrange multiplier method under certain conditions.

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