2 citations · 2 across the 11 of their papers we have counts for
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Projection geometry and relaxed quasi-orthogonality for inf-sup stable Galerkin methods
Tsogtgerel Gantumur
We give an elementary, coordinate-free proof that uniformly inf-sup stable nested Petrov-Galerkin methods on Hilbert spaces satisfy relaxed general quasi-orthogonality. More precis…
Exact ReLU realization of binary affine refinement iterates via reflection folding and cone switching
Boldsaikhan Bolorkhuu, Tsogtgerel Gantumur
We study vector-valued binary affine refinement operators with finitely supported matrix masks and compactly supported continuous piecewise linear input and forcing data. We prove…
Exact ReLU realization of affine one-dimensional refinement iterates via residual memory and offset frames
Boldsaikhan Bolorkhuu, Tsogtgerel Gantumur
We study vector-valued affine refinement operators of the form [ (Wγ)(t)=\sum_{j\in\mathbb{Z}} A_jγ(Mt-j)+B(t), ] with finitely supported matrix mask and compactly supported contin…
Neural network realization of binary refinement iterates via a two-chart atlas selector
Tsogtgerel Gantumur
Refinement operators generate many functions used in wavelet constructions, subdivision schemes, and geometric modeling. Their finite iterates can develop rapidly increasing number…
Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes
Tsogtgerel Gantumur
We study continuous data assimilation for the two-dimensional incompressible Navier-Stokes equations on the periodic torus using a single signed scalar velocity projection in a pre…
Conditional Euclidean-Hamiltonian reductions for sign-problem toy models
Tsogtgerel Gantumur
Euclidean Monte Carlo methods are effective when the path-integral weight is real and nonnegative, but finite-density fermion systems often produce sign-changing or complex scalar…
Exact ReLU realization of tensor-product refinement iterates
Tsogtgerel Gantumur
We study scalar dyadic refinement operators on R^2 of the form (Vf)(x,y) = sum_{(j,k) in Z^2} c_{j,k} f(2x-j, 2y-k), where only finitely many mask coefficients c_{j,k} are nonzero.…
Exact Loop Controllers for ReLU Realization of Homogeneous Curve Refinements
Boldsaikhan Bolorkhuu, Tsogtgerel Gantumur
We study homogeneous refinement operators \((Vγ)(t)=\sum_{j\in\mathbb Z}A_jγ(Mt-j)\), acting on compactly supported continuous piecewise linear curves \(γ:\mathbb R\to\mathbb R^p\)…
Possible Reforms of the Tibetan Lunisolar Calendar
Tsogtgerel Gantumur
The family of Tibetan lunisolar calendars operates on a shared arithmetic axiom (67 lunar months = 65 solar months) that provides a rigid structure but causes observable seasonal d…