Research
Research
Research
Research
23,682+ open-access research outputs.
We propose new formulations of geometric curvature flows -- referred to as \emph{dual formulations} -- that are equivalent to the original formulations but provide a novel framework for constructing l…
The multi-scale and non-linear nature of phase-field models of solidification requires fine spatial and temporal discretization, leading to long computation times. This could be overcome with artifici…
We prove existence of weak solutions and weak-strong uniqueness for a mathematical model which couples the evolution of a phase-parameter $\varphi$ satisfying a Cahn-Hilliard type relation with the on…
Mathematical programs with complementarity constraints (MPCCs) are a challenging class of nonlinear optimization problems, because their nonlinear programming reformulations violate standard constrain…
Line planning in public transport is the strategic problem of selecting lines and their operating frequencies. This problem is important as it defines the passenger service, based on available connect…
Future inverter-dominated power systems feature higher variability and more stressed operating conditions, which motivates the consideration of stability in operational settings. Existing approaches t…
Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. Let $\mathbb{A}_K$ denote the imperfect coefficient ring of $(\varphi,\Gamma)$-…
We present new representations of Gauss--Legendre polynomials and their derivatives in the shifted power basis and in bases related to symmetric orthogonal Jacobi polynomials. Using these representati…
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…
This paper develops a semidefinite-programming-based method for online feedback control of nonlinear systems using a state-dependent representation. We formulate sequences of time-varying SDPs whose o…
In this paper, we study generating functions of Erd\'{e}lyi's multivariate Laguerre polynomials $L_{n_1,\cdots,n_k}^{(\alpha)}(x_1,\cdots,x_k)$ with a varying complex parameter. Our main result is a m…
We study conditions for the well-posedness of nonautonomous perturbation of evolution equations of the form \[ u'(t)=(A+B(t))u(t), \quad t \in [a,b], \] where $A$ generates a $\mathrm{C}_0$-semigroup …
Understanding the evolution of connectivity in spatiotemporal systems requires mathematical frameworks capable of encoding not only instantaneous interactions but also their cumulative causal structur…
This paper studies an online trading variant of the classical secretary problem, called secretary problem variant trading (SPVT), from the perspective of an intermediary who facilitates trade between …
The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional flow of interacting particles on a 1D-lattice that is much used in systems biology and statistical …
Let $\mathbb{F}_{q}$ be a finite field, and $A:=\mathbb{F}_{q}[T]$. In this article, we give explicit criteria, involving concrete valuations, on the coefficients of the Drinfeld $A$-modules of rank $…
In this workshop, we discuss several algorithms for mathematical programs with equilibrium constraints (MPECs). The unifying theme is that MPECs are optimization problems whose feasible set contains a…
One of the essential questions of the theory of multidimensional integrals concerns the evaluation of integrals taken in given domains. In the simplest case, when integrating over parallelepipeds, eva…
Brion's Formula realizes the Laurent polynomial of lattice points in a lattice polytope P as the sum of rational functions associated to the vertices of P. In this paper, we consider the special case …
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