arXiv subjects

Kai Tang

Publications and source records attributed to Kai Tang.

83 records · Page 5Linked to original sources

arXiv2021

On almost nonpositive $k$-Ricci curvature

Motivated by the recent work of Chu-Lee-Tam on the nefness of canonical line bundle for compact Kähler manifolds with nonpositive $k$-Ricci curvature, we consider a natural notion of {\em almost nonpositive $k$-Ricci curvature}, which is weaker than the existence of a Kähler metric with nonpositive $k$-Ricci curvature. When $k=1$, this is just the {\em almost nonpositive holomorphic sectional curvature} introduced by Zhang. We firstly give a lower bound for the existence time of the twisted Kähler-Ricci flow when there exists a Kähler metric with $k$-Ricci curvature bounded from above by a positive constant. As an application, we prove that a compact Kähler manifold of almost nonpositive $k$-Ricci curvature must have nef canonical line bundle.

math.DG↗

arXiv2021

High-Resolution Segmentation of Tooth Root Fuzzy Edge Based on Polynomial Curve Fitting with Landmark Detection

As the most economical and routine auxiliary examination in the diagnosis of root canal treatment, oral X-ray has been widely used by stomatologists. It is still challenging to segment the tooth root with a blurry boundary for the traditional image segmentation method. To this end, we propose a model for high-resolution segmentation based on polynomial curve fitting with landmark detection (HS-PCL). It is based on detecting multiple landmarks evenly distributed on the edge of the tooth root to fit a smooth polynomial curve as the segmentation of the tooth root, thereby solving the problem of fuzzy edge. In our model, a maximum number of the shortest distances algorithm (MNSDA) is proposed to automatically reduce the negative influence of the wrong landmarks which are detected incorrectly and deviate from the tooth root on the fitting result. Our numerical experiments demonstrate that the proposed approach not only reduces Hausdorff95 (HD95) by 33.9% and Average Surface Distance (ASD) by 42.1% compared with the state-of-the-art method, but it also achieves excellent results on the minute quantity of datasets, which greatly improves the feasibility of automatic root canal therapy evaluation by medical image computing.

cs.CV↗

arXiv2020

Multi-Axis Support-Free Printing of Freeform Parts with Lattice Infill Structures

In additive manufacturing, infill structures are commonly used to reduce the weight and cost of a solid part. Currently, most infill structure generation methods are based on the conventional 2.5-axis printing configuration, which, although able to satisfy the self-supporting condition on the infills, suffer from the well-known stair-case effect on the finished surface and the need of extensive support for overhang features. In this paper, based on the emerging continuous multi-axis printing configuration, we present a new lattice infill structure generation algorithm, which is able to achieve both the self-supporting condition for the infills and the support-free requirement at the boundary surface of the part. The algorithm critically relies on the use of three mutually orthogonal geodesic distance fields that are embedded in the tetrahedral mesh of the solid model. The intersection between the iso-geodesic distance surfaces of these three geodesic distance fields naturally forms the desired lattice of infill structure, while the density of the infills can be conveniently controlled by adjusting the iso-values. The lattice infill pattern in each curved slicing layer is trimmed to conform to an Eulerian graph so to generate a continuous printing path, which can effectively reduce the nozzle retractions during the printing process. In addition, to cater to the collision-free requirement and to improve the printing efficiency, we also propose a printing sequence optimization algorithm for determining a collision-free order of printing of the connected lattice infills, which seeks to reduce the air-move length of the nozzle. Ample experiments in both computer simulation and physical printing are performed, and the results give a preliminary confirmation of the advantages of our methodology.

cs.GR↗

arXiv2020

Geodesic Distance Field-based Curved Layer Volume Decomposition for Multi-Axis Support-free Printing

This paper presents a new curved layer volume decomposition method for multi-axis support-free printing of freeform solid parts. Given a solid model to be printed that is represented as a tetrahedral mesh, we first establish a geodesic distance field embedded on the mesh, whose value at any vertex is the geodesic distance to the base of the model. Next, the model is naturally decomposed into curved layers by interpolating a number of iso-geodesic distance surfaces (IGDSs). These IGDSs morph from bottom-up in an intrinsic and smooth way owing to the nature of geodesics, which will be used as the curved printing layers that are friendly to multi-axis printing. In addition, to cater to the collision-free requirement and to improve the printing efficiency, we also propose a printing sequence optimization algorithm for determining the printing order of the IGDSs, which helps reduce the air-move path length. Ample experiments in both computer simulation and physical printing are performed, and the experimental results confirm the advantages of our method.

cs.GR↗

arXiv2019

The $\partial\overline{\partial}$-Bochner formulas for holomorphic mappings between Hermitian manifolds and their applications

In this paper, we derive some $\partial\overline{\partial}$-Bochner formulas for holomorphic maps between Hermitian manifolds. As applications, we prove some Schwarz lemma type estimates, rigidity and degeneracy theorems. For instance, we show that there is no non-constant holomorphic map from a comapct Hermitian manifold with positive (resp. non-negative) $\ell$-second Ricci curvature to a Hermitian manifold with non-positive (resp. negative) real bisectional curvature. These theorems generalize the results \cite{Ni1,Ni2} proved recently by L. Ni on Kähler manifolds to Hermitian manifolds. We also derive an integral inequality for holomorphic map between Hermitian manifolds.

math.DG↗

arXiv2019

Positive curvature operator, projective manifold and rational connectedness

In his recent work \cite{Y1}, X. Yang proved a conjecture raised by Yau in 1982 (\cite{Yau82}), which states that any compact Kähler manifold with positive holomorphic sectional curvature must be projective. In this note, we prove that any compact Hermitian manifold $X$ with positive real bisectional curvature, its hodge number $h^{1,0}=h^{2,0}=h^{n-1,0}=h^{n,0}=0$. In particular, if in addition $X$ is Kähler, then $X$ is projective. Also, it is rationally connected manifold when $n=3$. This partially confirms the conjecture 1.11 \cite{Y1} which is proposed by X. Yang.

math.DG↗

arXiv2018

Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem

Two Morley-Wang-Xu element methods with penalty for the fourth order elliptic singular perturbation problem are proposed in this paper, including the interior penalty Morley-Wang-Xu element method and the super penalty Morley-Wang-Xu element method. The key idea in designing these two methods is combining the Morley-Wang-Xu element and penalty formulation for the Laplace operator. Robust a priori error estimates are derived under minimal regularity assumptions on the exact solution by means of some established a posteriori error estimates. Finally, we present some numerical results to demonstrate the theoretical estimates.

math.NA↗

arXiv2016

Transverse beam size measurement system using visible synchrotron radiation at HLS II

An interferometer system and an imaging system using visible synchrotron radiation (SR) have been installed in HLS II storage ring. Simulations of these two systems are given using Synchrotron Radiation Workshop(SRW) code. With these two systems, the beam energy spread and the beam emittance can be measured. A detailed description of these two systems and the measurement method is given in this paper. The measurement results of beam size, emittance and energy spread are given at the end.

physics.acc-ph↗

arXiv2016

Superconducting nanowire single photon detector at 532 nm and demonstration in satellite laser ranging

Superconducting nanowire single-photon detectors (SNSPDs) at a wavelength of 532 nm were designed and fabricated aiming to satellite laser ranging (SLR) applications. The NbN SNSPDs were fabricated on one-dimensional photonic crystals with a sensitive-area diameter of 42 um. The devices were coupled with multimode fiber (phi=50um) and exhibited a maximum system detection efficiency of 75% at an extremely low dark count rate of <0.1 Hz. An SLR experiment using an SNSPD at a wavelength of 532 nm was successfully demonstrated. The results showed a depth ranging with a precision of ~8.0 mm for the target satellite LARES, which is ~3,000 km away from the ground ranging station at the Sheshan Observatory.

cond-mat.supr-con↗

arXiv2015

Central frequency measurement of the HLS-II storage ring

Central frequency is a key parameter of storage rings. This paper presents the measurement of central frequency of the HLS-II storage ring using the sextupole modulation method. Firstly, the basis of central frequency measurement of the electron storage ring is briefly introduced. Then, the error sources and the optimized measurement method for the HLS-II storage ring are discussed. The workflow of the self-compiled Matlab script used in central frequency measurement is also described. In the end, the results achieved by using two methods to cross-check each other are shown. The measured value of the central frequency demonstrates that the real circumference of the HLS-II storage ring agrees well with the designed value.

physics.acc-ph↗

arXiv2015

Beam size and position measurement based on logarithm processing algorithm in HLS II

A logarithm processing algorithm to measure beam transverse size and position is proposed and preliminary experimental results in Hefei Light Source II (HLS II) are given. The algorithm is based on only 4 successive channels of 16 anode channels of multianode photomultiplier tube (MAPMT) R5900U-00-L16 which has typical rise time of 0.6 ns and effective area of 0.8x16 mm for a single anode channel. In the paper, we firstly elaborate the simulation results of the algorithm with and without channel inconsistency. Then we calibrate the channel inconsistency and verify the algorithm using general current signal processor Libera Photon in low-speed scheme. Finally we get turn-by-turn beam size and position and calculate the vertical tune in high-speed scheme. The experimental results show that measured values fit well with simulation results after channel differences are calibrated and the fractional part of the tune in vertical direction is 0.3628 which is very close to the nominal value 0.3621.

physics.acc-ph↗