Research
Research
Research
Research
3,962+ open-access research outputs.
We consider the problem of finding the (unique) minimal Walrasian equilibrium price in multi-item, multi-unit auction models: there are multiple indivisible items for sale, with several units of each …
The accurate simulation of interface-dominated solid mechanics problems on complex microstructures remains challenging, particularly when interface-fitted quadrilateral or hexahedral meshes are diffic…
A variant of the flatness problem from integer programming is studied, in which one considers convex bodies in $\mathbb{R}^d$ with at most $k$ interior lattice points. The maximum lattice width of suc…
We prove a necessary and sufficient condition for a $ C^1 $-hypersurface to have all parallel sets nowhere $ C^1 $-regular. As a corollary, we deduce that for a generic $ C^1 $-regular convex body all…
We prove that for $C^{1+\beta}$ flows whose generating vector fields may have singularities, every weakly mixing hyperbolic SRB measure is Bernoullian.…
The fine curve graph of a surface is a graph whose vertices are essential simple closed curves and whose edges connect disjoint curves. Following a rich history of hyperbolicity of various graphs asso…
We show that closed surfaces with minimal total absolute curvature in Cartan-Hadamard 3-manifolds bound flat convex bodies. This generalizes Chern-Lashof's theorem for surfaces in Euclidean space and …
We introduce the concise secant varieties, which are, informally speaking, modular partial desingularisations of secant varieties to Segre embeddings. More precisely, they are projective and birationa…
A computational method is developed for desensitized optimal guidance using adaptive Gaussian quadrature collocation. The method computes a reference trajectory that reduces the sensitivity to uncerta…
In the $n$-body problem, when bodies tend to a total collision, then its normalized shape curve converges to the set of normalized central configurations, which has $SO(3)$ symmetry in the planar case…
We study edge-colorings of the complete $p$-graph on $n$ vertices that contain no three edges $A,B,C$ of distinct colors such that the symmetric difference of $A$ and $B$ is contained in $C$. For $p…
We study mixed finite element/Crank--Nicolson discretizations of a nonlinear Oldroyd problem with general nonsingular and weakly singular memory kernels. Direct evaluation of the history term requires…
We determine the border subrank of higher order structure tensors of several families of algebras, and in particular obtain the following results. (1) We determine tight bounds on the border subrank o…
We propose a computational framework for replacing the repeated numerical solution of differential Riccati equations in finite-horizon Linear Quadratic Regulator (LQR) problems by a learned operator s…
Bangladesh exhibits marked year-to-year variability in dengue, partly driven by meteorological fluctuations that shape \textit{Aedes} breeding-site persistence, mosquito development, and transmission.…
Varkonyi and Domokos (2006) proved mono-monostatic convex homogeneous bodies exist, and Sloan (2023) provided analytical equations. However, no verified open geometry exists and the relationship betwe…
Many engineering failures in orientation-dependent systems are geometric failure modes: changing the geometry can eliminate what changing the material merely delays. The mono-monostatic property (exac…
In this paper, we investigate the relationships between the volumes of four convex bodies: the cut polytope, metric polytope, rooted metric polytope, and elliptope, defined on graphs with $n$ vertices…
Unfitted boundary methods are widely used to numerically solve partial differential equations (PDEs) on irregular domains, avoiding the computational burden of generating boundary-conforming grids. In…
If a finite group $G$ acts on a rational homology manifold, then the orbit space is well-known to be a rational homology manifold again. We consider here actions on spaces that may be much more singul…
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