For exponentially closed ordinals $\alpha$, we consider recognizability of constructible subsets of $\alpha$ for $\alpha$-(w)ITRMs and their distribution in the constructible hierarchy.
We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools.
Numerical Analysis Numerical Analysis Computational Physics
We introduce a novel symplectic (in the Hamiltonian picture) resonance-based method on the example of the KdV equation that allows for low-regularity approximations to the solution while preserving the underlying geometric structure of the continuous problem on the discrete level.
Numerical Analysis Numerical Analysis 65M12, 65M70, 35Q53
We classify the finite groups of orthogonal transformations in 4-space, and we study these groups from the viewpoint of their geometric action, using polar orbit polytopes.
Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory.
We introduce a two parameter family of Dirac operators on quantum SU(2) and analyse their properties from the point of view of non-commutative metric geometry.
Operator Algebras Functional Analysis Metric Geometry 58B32, 58B34, 46L89, 46L30, 81R60
Moreover, an explicit relation between the switching time distribution and the autocovariance function of the switch process stationary counterpart is obtained, which allows parallel results for the stationary switch process and its covariance function.
Probability 60K05 (Primary) 60G55, 60E07, 60G10 (Secondary)
Since the 1980s, it has been known that essential surfaces in alternating link complements can be isotoped into a form that satisfies certain combinatorial restrictions, interacting with the link diagram.
Geometric Topology 57K12, 57K10, 57K30