2 citations · 2 across the 11 of their papers we have counts for
15 papers
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…
An expository review of the Chebyshev-Sylvester method in prime number theory
Tsogtgerel Gantumur
This paper gives a self-contained expository and computational account of the elementary methods developed by P.L. Chebyshev and J.J. Sylvester to obtain explicit bounds for the di…
Rotationally invariant dynamical lattice regulators for Euclidean quantum field theories
Tsogtgerel Gantumur
We introduce a dynamical lattice regulator for Euclidean quantum field theories on a fixed hypercubic graph , in which the embedding is pr…
A direct proof of the equivalence between Dirichlet's principle and Perron's method
Tsogtgerel Gantumur
We give a short proof that for a bounded domain and continuous boundary data admitting a continuous finite-energy extension $ϕ\in H^{1}(Ω…
Convergence rates of adaptive methods, Besov spaces, and multilevel approximation
Tsogtgerel Gantumur
This paper concerns characterizations of approximation classes associated to adaptive finite element methods with isotropic h-refinements. It is known from the seminal work of Bine…
On the convergence theory of adaptive mixed finite element methods for the Stokes problem
Tsogtgerel Gantumur
In the first part of this paper, we establish a conditional optimality result for an adaptive mixed finite element method for the stationary Stokes problem discretized by the stand…
Adaptive boundary element methods with convergence rates
Tsogtgerel Gantumur
This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. Th…