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We introduce a new paradigm for geometry denoising using prior knowledge about the surface normal vector. This prior knowledge comes in the form of a set of preferred normal vectors, which we refer to as label vectors. A segmentation…
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
We study the shadows of disformal black holes in vector-tensor Galileons modified gravity. Our analysis shows that the apparent image of the black hole in the observer's sky is non-spherical and cuspy, which is in contrast to the Kerr and…
We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato surface by contracting some divisor (in particular, it is…
We give some general properties of good and bad reduction, and some recent examples (worked out with Dipendra Prasad) of varieties having bad reduction not accounted for by their cohomology. We include some consequences of our remarks for…
In our previous paper entitled "Axiomatic differential geometry -towards model categories of differential geometry-, we have given a category-theoretic framework of differential geometry. As the first part of our series of papers concerned…
First we characterize all the polynomial vector fields in $\R^4$ which have the Clifford torus as an invariant surface. After we study the number of invariant meridians and parallels that such polynomial vector fields can have in function…
Some metric and graphical regularity properties of generalized constraint systems are investigated. Then, these properties are applied in order to penalize (in the sense of Clarke) various scalar and vector optimization problems. This…
Expecting scalar contributions to be less important to a given observable signal than vector ones, in usual scenarios, is a natural intuition. Such assertion should hold for a great part of physically relevant parameter space within most…
We present coset conformal field theories whose spectrum is not determined by the identification current method. In these ``maverick'' cosets there is a larger symmetry identifying primary fields than under the identification current. We…
The paper is concerned with the stability of the set of trajectories of a vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in AB to study…
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch…
We argue that spontaneous Lorentz violation may generally lead to metastable domain walls related to the simultaneous violation of some accompanying discrete symmetries. Remarkably, such domain wall solutions exist for space-like Lorentz…
It is well known that positivity properties of the curvature of a vector bundle have implications on the algebro-geometric properties of the bundle, such as numerical positivity, vanishing of higher cohomology leading to existence of global…
We introduce various spaces of vector fields of bounded mean oscillation ($BMO$) defined in a domain so that normal trace on the boundary is bounded when its divergence is well controlled. The behavior of "normal" component and "tangential"…
Signatures provide a succinct description of certain features of paths in a reparametrization invariant way. We propose a method for classifying shapes based on signatures, and compare it to current approaches based on the SRV transform and…
Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions…
We experimentally demonstrate for the first time that a radially polarized field can be focussed to a spot size significantly smaller (0.16(1) lambda^2) than for linear polarization (0.26 lambda^2). The effect of the vector properties of…
A survey is presented of the dynamic features of non-itinerant off-center defects in crystals, such as rotation-like reorientation of isolated species by either impurity or host ions. The occurrence of off-center displacements in…