Related papers: Additive colourful Carath\'eodory type results wit…
We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a Time-Dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled…
We propose a new approach to the study of rotational surfaces in Lorentz-Minkowski space based on the notion of the geometric linear momentum of the generatrix curves with respect to the axes of revolution. This technique allows us to…
We combine functional analytic and geometric viewpoints on approximate Birkhoff and isosceles orthogonality in generalized Minkowski spaces which are finite-dimensional vector spaces equipped with a gauge. This is the first approach to…
We consider the chromatic numbers of unit-distance graphs of various annuli. In particular, we consider radial colorings, which are "nice" colorings, and completely determine the radial chromatic numbers of various annuli.
In this note we apply the general Reilly formula established in \cite{QX} to the solution of a Neumann boundary value problem to prove an optimal Minkowski type inequality in space forms.
The exterior algebra of Minkowski space naturally has the structure of a sixteen-dimensional Clifford algebra representation, and so can be used as the space of spinors. We examine plane, circular, and spherical solutions to the free Dirac…
Conventional Ramsey-theoretic investigations for edge-colourings of complete graphs are framed around avoidance of certain configurations. Motivated by considerations arising in the field of Qualitative Reasoning, we explore edge colourings…
In this paper we characterize the unit disc, the bidisc and the symmetrized bidisc \[ G =\{(z+w,zw):|z|<1,\ |w|<1\} \] in terms of the possession of small classes of analytic maps into the unit disc that suffice to solve all Carath\'eodory…
We propose a general construction of quantum states for linear canonical quantum fields on a manifold, which encompasses and generalizes the "standard" procedures existing in textbooks. Our method provides pure and mixed states on the same…
In this paper, we review modified Cahn-Hilliard equation for image inpainting and explore the effect when the initial condition is uncertain. We study the statistical properties of the solution when the noise is present. The generalized…
In this paper we prove the existence of a radial ground state solution for a quasilinear problem involving the mean curvature operator in Minkowski space.
We survey some principal results and open problems related to colorings of algebraic and geometric objects endowed with symmetries.
We prove a common strengthening of B\'ar\'any's colorful Carath\'eodory theorem and the KKMS theorem. In fact, our main result is a colorful polytopal KKMS theorem, which extends a colorful KKMS theorem due to Shih and Lee [Math. Ann. 296…
We consider a non-trapping $n$-dimensional Lorentzian manifold endowed with an end structure modeled on the radial compactification of Minkowski space. We find a full asymptotic expansion for tempered forward solutions of the wave equation…
Various results ensure the existence of large complete bipartite graphs in properly colored graphs when some condition related to a topological lower bound on the chromatic number is satisfied. We generalize three theorems of this kind,…
Given $d+1$ sets of points, or colours, $S_1,\ldots,S_{d+1}$ in $\mathbb R^d$, a colourful simplex is a set $T\subseteq\bigcup_{i=1}^{d+1}S_i$ such that $|T\cap S_i|\leq 1$, for all $i\in\{1,\ldots,d+1\}$. The colourful Carath\'eodory…
We consider a fourth-order extension of the Allen-Cahn model with mixed-diffusion and Navier boundary conditions. Using variational and bifurcation methods, we prove results on existence, uniqueness, positivity, stability, a priori…
We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.
This thesis is basically devoted to matroids -- fundamental structure of combinatorial optimization -- though some of our results concern simplicial complexes, or Euclidean spaces. We study old and new problems for these structures, with…