Related papers: $K^\alpha$-translators of offset surfaces
This paper describes the Volctrans' submission to the WMT21 news translation shared task for German->English translation. We build a parallel (i.e., non-autoregressive) translation system using the Glancing Transformer, which enables fast…
A model based on a convolutional neural network (CNN) is designed to reconstruct the three-dimensional turbulent flows beneath a free surface using surface measurements, including the surface elevation and surface velocity. Trained on…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
We study rotationally symmetric translators for fully nonlinear extrinsic geometric flows driven by a curvature function, and we establish the fine asymptotics of bowl-type evolutions and, when admissible, the construction and…
In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R^3. By means of a…
While it is well known from examples that no interesting `halfspace theorem' holds for properly immersed complete $n$-dimensional self-translating mean curvature flow solitons in Euclidean space $\mathbb{R}^{n+1}$, we show that they must…
Dilation surfaces are generalizations of translation surfaces where the transition maps of the atlas are translations and homotheties with a positive ratio. In contrast with translation surfaces, the directional flow on dilation surfaces…
We provide some general theoretical results to guide the optimization of transverse hydrodynamic phenomena in superhydrophobic channels. Our focus is on the canonical micro- and nanofluidic geometry of a parallel-plate channel with an…
In this paper, we study a class of non-homogeneous anisotropic fully nonlinear curvature flows in $\mathbb{R}^{n+1}$. More precisely, we consider a hypersurface $M$ in $\mathbb{R}^{n+1}$ deformed by a flow along its unit normal with its…
The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: When the curvature of…
In this paper, we investigate the surfaces generated by binormal motion of Bertrand curves, which is called Razzaboni surface, in Minkowski 3-space. We discussed the geometric properties of these surfaces in M^3 according to the character…
If $\xi$ is a Killing vector field of the hyperbolic space $\h^3$ whose flow are parabolic isometries, a surface $\Sigma\subset\h^3$ is a $\xi$-translator if its mean curvature $H$ satisfies $H=\langle N,\xi\rangle$, where $N$ is the unit…
Invertible convolutions have been an essential element for building expressive normalizing flow-based generative models since their introduction in Glow. Several attempts have been made to design invertible $k \times k$ convolutions that…
A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent…
Using Gauss-Manin derivatives of normal functions, we arrive at some remarkable results on the non-triviality of the transcendental regulator for $K_m$ of a very general projective algebraic manifold. Our strongest results are for the…
We consider the algebra of Hecke correspondences (elementary transformations at a single point) acting on the algebraic K-theory groups of the moduli spaces of stable sheaves on a smooth projective surface S. We derive quadratic relations…
This paper proves the following statement: {\it If a convex body can form a twofold translative tiling in $\mathbb{E}^3$, it must be a parallelohedron.} In other words, it must be a parallelotope, a hexagonal prism, a rhombic dodecahedron,…
In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the…
In the present paper, the geometric properties of a soliton surface $\Psi=\Psi(s,t)$ associated with the Betchov-Da Rios (B-DR) equation using the parallel transport frame field in four-dimensional Euclidean space are examined. We obtain…
We prove the existence and uniqueness of a $C^{1,1}$ solution of the $Q_k$ flow in the viscosity sense for compact convex hypersurfaces $\Sigma_t$ embedded in $R^{n+1}$ ($n \geq 2$) . In particular, for compact convex hypersurfaces with…