The lower estimate for the linear combinations of Bernstein–Kantorovich operators

AbstractIn this paper we obtain a new strong type of Steckin inequality for the linear combinations of Bernstein–Kantorovich operators, which gives the optimal approximation rate. On the basis of this inequality, we further obtain the lower estimate for these operators

Point cloud representation

Reconstructing a surface out of a three-dimensional set of points, which is obtained by sampling an object\u27s boundary, is done by generating an arbitrary triangular mesh. Our approach is to obviate the computation of such a mesh connectivity and to represent the object\u27s surface only by the point cloud. We discuss how such a point cloud representation can be visualized and present processing steps like coarsifying and smoothing, which are important for dealing with the objects. Further we apply a multiresolution method to point cloud representations and use this technique as well as others for modelling purposes

Geometry-Aware Face Completion and Editing

Face completion is a challenging generation task because it requires generating visually pleasing new pixels that are semantically consistent with the unmasked face region. This paper proposes a geometry-aware Face Completion and Editing NETwork (FCENet) by systematically studying facial geometry from the unmasked region. Firstly, a facial geometry estimator is learned to estimate facial landmark heatmaps and parsing maps from the unmasked face image. Then, an encoder-decoder structure generator serves to complete a face image and disentangle its mask areas conditioned on both the masked face image and the estimated facial geometry images. Besides, since low-rank property exists in manually labeled masks, a low-rank regularization term is imposed on the disentangled masks, enforcing our completion network to manage occlusion area with various shape and size. Furthermore, our network can generate diverse results from the same masked input by modifying estimated facial geometry, which provides a flexible mean to edit the completed face appearance. Extensive experimental results qualitatively and quantitatively demonstrate that our network is able to generate visually pleasing face completion results and edit face attributes as well

Fan Clouds - An Alternative To Meshes

A fan cloud is a set of triangles that can be used to visualize and work with point clouds. It is fast to compute and can replace a triangular mesh representation: We discuss visualization,multiresolution reduction, refinement, and selective refinement. Algorithms for triangular meshes can also be applied to fan clouds. They become even simpler, because fans are not interrelated. This localness of fan clouds is one of their main advantages. No remeshing is necessary for local or adaptive refinement and reduction

Pattern preservation during the decay and growth of localized wave packet in two-dimensional channel flow

In this paper, the decay and growth of localized wave packet (LWP) in two-dimensional plane-Poiseuille flow are studied numerically and theoretically. When the Reynolds number ($Re$) is less than a critical value $Re_c$, the disturbance kinetic energy $E_k$ of LWP decreases monotonically with time and experiences three decay periods, i.e. the initial and the final steep descent periods, and the middle plateau period. Higher initial $E_k$ of a decaying LWP corresponds to longer lifetime. According to the simulations, the lifetime scales as $(Re_c-Re)^{-1/2}$, indicating a divergence of lifetime as $Re$ approaches $Re_c$, a phenomenon known as "critical slowing-down". By proposing a pattern preservation approximation, i.e. the integral kinematic properties (e.g. the disturbance enstrophy) of an evolving LWP are independent of $Re$ and single valued functions of $E_k$, the disturbance kinetic energy equation can be transformed into the classical differential equation for saddle-node bifurcation, by which the lifetimes of decaying LWPs can be derived, supporting the $-1/2$ scaling law. Furthermore, by applying the pattern preservation approximation and the integral kinematic properties obtained as $Re<Re_c$, the Reynolds number and the corresponding $E_k$ of the whole lower branch, the turning point, and the upper-branch LWPs with $E_k<0.15$ are predicted successfully with the disturbance kinetic energy equation, indicating that the pattern preservation is an intrinsic feature of this localized transitional structure

Origins of Large Voltage Hysteresis in High Energy-Density Metal Fluoride Lithium-Ion Battery Conversion Electrodes

Metal fluoride and oxides can store multiple lithium-ions through conversion chemistry to enable high energy-density lithium-ion batteries. However, their practical applications have been hindered by an unusually large voltage hysteresis between charge and discharge voltage-profiles and the consequent low energy efficiency (< 80%). The physical origins of such hysteresis are rarely studied and poorly understood. Here we employ in situ X-ray absorption spectroscopy (XAS), transmission electron microscopy (TEM), density-functional-theory (DFT) calculations, and galvanostatic intermittent titration technique (GITT) to first correlate the voltage profile of iron fluoride ($FeF_3$), a representative conversion electrode material, with evolution and spatial distribution of intermediate phases in the electrode. The results reveal that, contrary to conventional belief, the phase evolution in the electrode is symmetrical during discharge and charge. However, the spatial evolution of the electrochemically active phases, which is controlled by reaction kinetics, is different. We further propose that the voltage hysteresis in the $FeF_3$ electrode is kinetic in nature. It is the result of Ohmic voltage drop, reaction overpotential, and different spatial distributions of electrochemically-active phases (i.e. compositional inhomogeneity). Therefore, the large hysteresis can be expected to be mitigated by rational design and optimization of material microstructure and electrode architecture to improve the energy efficiency of lithium-ion batteries based on conversion chemistry