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Research
Research
Research
36,094+ open-access research outputs.
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
This paper studies data-driven approaches to the continuous-time linear quadratic regulator (LQR) problem based on two existing parameterizations, namely a closed-loop (CL) parameterization from behav…
This paper investigates the heat equation on a bounded domain with a Robin boundary condition, where the reactivity parameter (or killing rate) is modeled as a continuous-time Markov chain. We analyze…
In modern parametric model training, full-batch gradient descent (and its variants) suffers due to progressively stronger biasing towards the exact realization of training data; this drives the system…
The Etzion-Silberstein conjecture asserts that, for any finite field $\mathbb F$, Ferrers diagram $\mathcal D$, and integer $d$, there exists a linear matrix code supported on $\mathcal D$ with minimu…
The main theorem of the paper provides an existence criterion of holomorphic discs for higher $A_\infty$ operations. The key step is to show that if a minimal disc in a K\"ahler manifold with boundary…
This work studies numerical integration by the M\"obius-transformed trapezoidal rule, which combines the classical trapezoidal rule with a change of variables induced by a M\"obius transformation that…
We introduce G\r{a}rding polynomials, a class of real multivariate polynomials defined via positivity regions invariant under translation by positive directions and closed under strictly positive affi…
High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscos…
The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $\alpha$ and a Hurst exponent $H$. We consi…
We investigate several aspects of the Bialynicki-Birula decomposition of a smooth complete $\mathbb{G}_m$-variety with finite fixed locus. Our results include novel characterizations of when the Bialy…
Mirror symmetry predicts an action by the fundamental group of a conjectural stringy K\"ahler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space …
The bull is a graph consisting of a triangle and two pendant edges. The P_5 is the chordless path on five vertices. The house is the complement of a P_5. A graph is k-critical if it is k-chromatic but…
This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The…
A fundamental result in 4-manifold topology asserts that every exotic smooth structure on a simply connected closed 4-manifold is determined by a cork -- a codimension-zero compact, contractible subma…
Let $P\subset\mathbb R^n$ be a convex polytope and let $\ell$ be a linear functional which is nonconstant on every edge of $P$. The induced acyclic orientation determines positive and negative Bia{\l}…
Convex maximization encompasses a broad class of optimization problems and is generally NP-hard, even for low-rank objectives. This paper investigates structural conditions under which convex maximiza…
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in …
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the correspond…
We study some interesting hypersurfaces that naturally arise when studying the period map on the moduli space of hypersurfaces, in the context of Sung Gi Park's recent work on studying the GIT moduli …
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