5 papers
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 provides a detailed expository and computational account of the elementary methods developed by P. L. Chebyshev and J. J. Sylvester to establish explicit bounds on the p…
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…