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Let $\Gamma$ denote a distance-regular graph with diameter $D \ge 3$. Assume $\Gamma$ has classical parameters $(D,b,\alpha,\beta)$ with $b < -1$. Let $X$ denote the vertex set of $\Gamma$ and let $A \in MX$ denote the adjacency matrix of…

We determine the global behavior of every C^2-solution to the two-dimensional degenerate Monge-Ampere equation, u_{xx}u_{yy}-u_{xy}^2=0, over the finitely punctured plane. With this, we classify every solution in the once or twice punctured…

This paper presents an anlysis of the NP-hard minimization problem $\min \{\|b - Ax\|_2: \ x \in [0,1]^n, | \text{supp}(x) | \leq \sigma\}$, where $\text{supp}(x) = \{i \in [n]: x_i \neq 0\}$ and $\sigma$ is a positive integer. The object…

The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

We consider min-max optimization problems for polynomial functions, where a multivariate polynomial is maximized with respect to a subset of variables, and the resulting maximal value is minimized with respect to the remaining variables.…

Let $D$ be the set of $n\times n$ positive semidefinite matrices of trace equal to one, also known as the set of density matrices. We prove two results on the hardness of approximating $D$ with polytopes. First, we show that if $0 <…

A novel approach is introduced to a very widely occurring problem, providing a complete, explicit resolution of it: minimisation of a convex quadratic under a general quadratic, equality or inequality, constraint. Completeness comes via…

We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter $s$ when $s\rightarrow 1^-$. As a consequence, we obtain that all the nonlocal minimal cones are flat and that all the…

We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter $\varepsilon$. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous.…

We investigate the homogenization through Gamma-convergence for the L^2(\Omega)-weak topology of the conductivity functional with a zero-order term where the matrix-valued conductivity is assumed to be non strongly elliptic. Under proper…

We are presenting a simple and numerical stable algorithm for the solution of the cone projection problem which is suitable for relative small data sets and for simulation purposes needed for convexity tests. Not even one pseudo-inverse…

Let $\Gamma$ be a smooth, closed, oriented, $(n-1)$-dimensional submanifold of $\mathbb{R}^{n+1}$. We show that there exist arbitrarily small perturbations $\Gamma'$ of $\Gamma$ with the property that minimizing integral $n$-currents with…

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse…

The behaviour of the moment-sums-of-squares (moment-SOS) hierarchy for polynomial optimal control problems on compact sets has been explored to a large extent. Our contribution focuses on the case of non-compact control sets. We describe a…

We consider rotating black hole solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and a generic value of the Chern-Simons coupling constant $\lambda$. Using both analytical and…

We discover some very general configuration results for constructing area-minimizing cones. In particular, given any closed minimal submanifold in some Euclidean sphere, every cone over the minimal product of sufficiently many copies of the…

We consider faithful actions of simple algebraic groups on self-dual irreducible modules, and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the…

We consider positive solutions of a semilinear Dirichlet problem \[ \Delta u+\lambda f(u)=0, \;\; \mbox{for $|x|<1$}, \;\; u=0 , \;\; \mbox{when $|x|=1$} \] on a unit ball in $R^n$. For four classes of self-similar equations it is possible…

For $\Omega_\e=(0,\e)\times (0,1)$ a thin rectangle, we consider minimization of the two-dimensional nonlocal isoperimetric problem given by \[ \inf_u E^{\gamma}_{\Omega_\e}(u)\] where \[ E^{\gamma}_{\Omega_\e}(u):=…