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Flow Matching with Semidiscrete Couplings
Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points $(\mathbf{x}_0,\mathbf{x}_1)$ and ensuring that the velocity field is aligned, on average, with $\mathbf{x}_1-\mathbf{x}_0$ when ...
Mousavi-Hosseini, Alireza +3 more
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Runge-Kutta time semidiscretizations of semilinear PDEs with non-smooth data. [PDF]
Numer Math (Heidelb), 2016 Wulff C, Evans C.
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Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions [PDF]
, 2002 Acosta, Gabriel +3 more
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Error analysis for discretizations of parabolic problems using continuous finite elements in time and mixed finite elements in space. [PDF]
Numer Math (Heidelb), 2017 Bause M, Radu FA, Köcher U.
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Nonlinear Stability of Semidiscrete Shock Waves
SIAM Journal on Mathematical Analysis, 2003This work is devoted to the asymptotic stability of the semidiscrete waves generated by discrete in space and continuous in time systems of conservation laws (lattice dynamical systems). The authors describe the semidiscrete conservative systems, study spectral stability of semidiscrete shocks, pointwise Green's function bounds for the linear lattice ...
Benzoni-Gavage, S. +2 more
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A semidiscrete Gardner equation
Frontiers of Mathematics in China, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, Haiqiong, Zhu, Zuonong
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Stability of Semidiscretizations of Hyperbolic Problems
SIAM Journal on Numerical Analysis, 1983zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jeltsch, Rolf, Nevanlinna, Olavi
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Tree Algebras, Semidiscreteness, and Dilation Theory
Proceedings of the London Mathematical Society, 1994We introduce a class of finite dimensional algebras built from a partial order generated as a transitive relation from a finite tree. These algebras, known as tree algebras, have the property that every locally contractive representation has a *-dilation. Furthermore, they satisfy an appropriate analogue of the Sz. Nagy-Foiaş commutant lifting theorem.
Davidson, K. R. +2 more
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Acta Mathematica Hungarica, 1989
Extract from the paper: ``In 1938 Sz. Nagy characterized \(L^ 2\)-spaces of commutative \(W^*\)-algebras in the following way: A Hilbert space H, which is ordered by a selfdual cone \(H^+\) having the Riesz interpolation property, is isomorphic to \(L^ 2(X,\mu)\) for some measure space (X,\(\mu)\).
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Extract from the paper: ``In 1938 Sz. Nagy characterized \(L^ 2\)-spaces of commutative \(W^*\)-algebras in the following way: A Hilbert space H, which is ordered by a selfdual cone \(H^+\) having the Riesz interpolation property, is isomorphic to \(L^ 2(X,\mu)\) for some measure space (X,\(\mu)\).
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Conservation laws of semidiscrete Hamiltonian equations
Journal of Mathematical Physics, 2001Many evolution partial differential equations (PDEs) can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs [P. J. Olver, Applications of Lie Groups to Differential Equations (Springer, New York, 1986)].
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