相关论文: Stable simplex spline bases for $C^3$ quintics on …
A triangulated piecewise-linear minimal surface in Euclidean 3-space defined using a variational characterization is critical for area amongst all continuous piecewise-linear variations with compact support that preserve the simplicial…
Generalizing tensor-product splines to smooth functions whose control nets outline topological polyhedra, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each…
A solenoidal basis is constructed to compute velocities using a certain finite element method for the Stokes problem. The method is conforming, with piecewise linear velocity and piecewise constant pressure on the Powell-Sabin split of a…
We estimate the number of lines on a non-K3 quartic surface. Such a surface with only isolated double point(s) contains at most twenty lines; this bound is attained by a unique configuration of lines and by a surface with a certain limited…
Stable surfaces and their log analogues are the type of varieties naturally occuring as boundary points in moduli spaces. We extend classical results of Kodaira and Bombieri to this more general setting: if $(X,\Delta)$ is a stable log…
We study the GIT compactification $\mathbb{P}(\mathrm{Sym}^3\mathbb{C}^7)//\mathrm{SL}(7)$ of the moduli space of cubic fivefolds $X\subset\mathbb{P}^6$ and give an explicit description of its strictly semistable boundary. We construct…
This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework. We define dimensional stability as an invariant within the…
Univariate polynomials are called stable with respect to a domain $D$ if all of their roots lie in $D$. We study linear slices of the space of stable univariate polynomials with respect to a half-plane. We show that a linear slice always…
We prove a multi-valued $C^{1,\alpha}$ regularity theorem for the varifolds in the class $\mathcal{S}_2$ (i.e., stable codimension one stationary integral $n$-varifolds admitting no triple junction classical singularities) which are…
We prove that half spaces are the only stable nonlocal $s$-minimal cones in $\mathbb{R}^3$, for $s\in(0,1)$ sufficiently close to $1$. This is the first classification result of stable $s$-minimal cones in dimension higher than two. Its…
We study stable surfaces, i.e., second order minima of the area for variations of fixed volume, in sub-Riemannian space forms of dimension $3$. We prove a stability inequality and provide sufficient conditions ensuring instability of…
Globally symmetric spinor condensates in free space are argued not to support stable topological defects in either two or three dimensions. In the latter case, however, we show that a topological Skyrmion can be stabilized by forcing it to…
A piecewise Chebyshevian spline space is a space of spline functions having pieces in different Extended Chebyshev spaces and where the continuity conditions between adjacent spline segments are expressed by means of connection matrices.…
In this paper we consider spaces of bivariate splines of bi-degree (m, n) with maximal order of smoothness over domains associated to a two-dimensional grid. We define admissible classes of domains for which suitable combinatorial technique…
In this note we investigate three new pencils of symmetric surfaces in complex projective three-space. These have degree 6, 8 resp. 12 and are invariant under the action of subgroups of SO(4) containing the Heisenberg group. The pencils of…
Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…
In the context of cubic splines, the authors have contributed to a recent paper dealing with the computation of nonlinear derivatives at the interior nodes so that monotonicity is enforced while keeping the order of approximation of the…
Problems involving approximation from scattered data where data is arranged quasi-uniformly have been treated by RBF methods for decades. Treating data with spatially varying density has not been investigated with the same intensity, and is…
A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. The peaks may include a…
A general net of quadric surfaces, together with a choice of a base point, defines a net of plane cubics via the Gale transformation of the remaining seven base points. To both nets, one can also naturally associate the same smooth plane…