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Stokes Matrix for the Quantum Cohomology of Cubic Surfaces
"... We prove the conjectural relation between the Stokes matrix for the quantum cohomology of X and an exceptional collection generating D b coh(X) when X is a smooth cubic surface. The proof is based on a toric degeneration of a cubic surface, the Givental’s mirror theorem for toric manifolds, and the ..."
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We prove the conjectural relation between the Stokes matrix for the quantum cohomology of X and an exceptional collection generating D b coh(X) when X is a smooth cubic surface. The proof is based on a toric degeneration of a cubic surface, the Givental’s mirror theorem for toric manifolds
MICROCOPY RESOLUTION lIST CHARI RLEVEL S RELATIONSHIPSBETWEEN ELEMENTS OF THE STOKES MATRIX
, 1981
"... inm! liii 11.01112.0 ..."
Stokes Antenna Temperatures
"... Abstract—The growing importance of polarimetric radiometers has led to the need for a detailed theory for Stokes antenna temperatures. In this paper, we provide a full Stokes vector formulation of an antenna temperature that accounts for the entire antenna pattern, which includes polarization mixing ..."
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the way. We also introduce generalizations of beam efficiency and cross polarization for use with polarimetric radiometers. These provide important metrics in the design of future systems. Index Terms—Jones matrix, Mueller matrix, polarimetry, polarization, radiometry, Stokes parameters.
Condition number of the BEM matrix arising from the Stokes equations in 2D
"... We study the condition number of the system matrices that appear in the Boundary Element Method when solving the Stokes equations at a twodimensional domain. At the boundary of the domain we impose Dirichlet conditions or mixed conditions. We show that for certain critical boundary contours the und ..."
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the underlying boundary integral equation is not solvable. As a consequence, the condition number of the system matrix of the discrete equations is infinitely large. Hence, for these critical contours the Stokes equations cannot be solved with the Boundary Element Method. To overcome this problem the domain can
A Dimensional Split Preconditioner for Stokes and Linearized Navier–Stokes Equations
, 2010
"... In this paper we introduce a new preconditioner for linear systems of saddle point type arising from the numerical solution of the Navier– Stokes equations. Our approach is based on a dimensional splitting of the problem along the components of the velocity field, resulting in a convergent fixedpoi ..."
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Cited by 9 (2 self)
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the convergence behavior for different finite element discretizations of Stokes and Oseen problems are included. Key words. saddle point problems, matrix splittings, iterative methods, preconditioning, Stokes problem, Oseen problem, stretched grids
Preconditioners for Incompressible NavierStokes Solvers
, 2010
"... In this paper we give an overview of the present state of fast solvers for the solution of the incompressible NavierStokes equations discretized by the finite element method and linearized by Newton or Picard’s method. It is shown that block preconditioners form an excellent approach for the solut ..."
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Cited by 4 (0 self)
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for the solution, however if the grids are not to fine preconditioning with a Saddle point ILU matrix (SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated. In case of the standalone Stokes equations special preconditioners increase the efficiency
SyFi An Element Matrix Factory, with Emphasis on the Incompressible NavierStokes Equations
"... Abstract. SyFi is an open source C++ library for defining and using variational forms and finite elements based on symbolic representations of polygonal domains, degrees of freedom and polynomial spaces. Once the finite elements and variational forms are defined, they are used to generate efficient ..."
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Abstract. SyFi is an open source C++ library for defining and using variational forms and finite elements based on symbolic representations of polygonal domains, degrees of freedom and polynomial spaces. Once the finite elements and variational forms are defined, they are used to generate efficient C/C++ code. 1
On Stokes Matrices in terms of Connection Coefficients
"... Abstract: The classical problem of computing a complete system of Stokes multipliers of a linear system of ODEs of rank one in terms of some connection coefficients of an associated hypergeometric system of ODEs, is solved with no genericness assumptions on the residue matrix at zero, by an extensio ..."
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Abstract: The classical problem of computing a complete system of Stokes multipliers of a linear system of ODEs of rank one in terms of some connection coefficients of an associated hypergeometric system of ODEs, is solved with no genericness assumptions on the residue matrix at zero
matrices and monodromy of the quantum cohomology of projective spaces
 Comm. in Math. Physics 207
, 1999
"... In this paper we compute Stokes matrices and monodromy for the quantum cohomology of projective spaces. This problem can be formulated in a “classical ” framework, as the problem of computation of Stokes matrices and monodromy of (systems of) differential equations with regular and irregular singula ..."
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Cited by 25 (3 self)
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singularities. We prove that the Stokes ’ matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves. We also study the monodromy group of the quantum cohomology and we show that it is related to hyperbolic triangular groups. 1
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