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Ling Xiao

Publications and source records attributed to Ling Xiao.

69 records · Page 4Linked to original sources
arXiv2015

Modified Brownian Motion Approach to Modelling Returns Distribution

An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian Motion Model with optimal weighting factors selected by goodness of fit tests, substantially outperform the basic Geometric Brownian Motion model in terms of fitting the returns distribution of historic data price indices. Furthermore we attempt to provide an interpretation of the additional stochastic term in relation to irrational behaviour in financial markets and outline the importance of this novel model.

q-fin.PR↗
arXiv2015

Entire downward translating solitons to the mean curvature flow in Minkowski space

In this paper, we study entire translating solutions $u(x)$ to a mean curvature flow equation in Minkowski space. We show that if $Σ=\{(x, u(x))| x\in\mathbb{R}^n\}$ is a strictly spacelike hypersurface, then $Σ$ reduces to a strictly convex rank k soliton in $\mathbb{R}^{k, 1}$ (after splitting off trivial factors) whose "blowdown" converges to a multiple $λ\in(0, 1)$ of a positively homogeneous degree one convex function in $\mathbb{R}^k$. We also show that there is nonuniqueness as the rotationally symmetric solution may be perturbed to a solution by an arbitrary smooth order one perturbation.

math.DG↗
arXiv2015

On cyclic codes over $\mathbb{Z}_q+u\mathbb{Z}_q$

Let $R=\mathbb{Z}_q+u\mathbb{Z}_q$, where $q=p^s$ and $u^2=0$. In this paper, some structural properties of cyclic codes over the ring $R$ are considered. A necessary and sufficient condition for cyclic codes over the ring $R$ to be free is obtained and a BCH-type bound on the minimum Hamming distance for them is also given.

cs.IT↗
arXiv2013

Minimal Graphs and Graphical Mean Curvature Flow in $M \times \mathbb R$

In this paper, we investigate the problem of finding minimal graphs in $M^n\times\mathbb R$ with general boundary conditions using a variational approach. We look at so called generalized solutions of the Dirichlet Problem that minimize a functional adapted from the area functional. We construct barriers to show that for certain conditions on our boundary data, $ϕ(x)$, the solutions obtain the boundary data $ϕ(x)$. Following Oliker-Ural'tseva we also consider solutions $u^ε$ of a perturbed mean curvature flow for $ε> 0$. We show that there are subsequences $ε_i$ where $u^{ε_i}$ converges to a function $u$ satisfying the mean curvature flow, and subsequences $u(\cdot, t_i)$ converge to a generalized solution $\bar u$ of the Dirichlet problem. Furthermore, $\bar u$ depends only on the choice of sequence $ε_i$.

math.DG↗
arXiv2012

The Weyl problem with nonnegative Gauss curvature in hyperbolic space

In this paper, we discuss the isometric embedding problem in hyperbolic space with nonnegative extrinsic curvature. We prove a priori bounds for the trace of the second fundamental form H and extend the result to n-dimensions. We also obtain an estimate for the gradient of the smaller principal curvature in 2 dimensions.

math.DG↗
arXiv2012

Interior curvature estimates and the asymptotic plateau problem in hyperbolic space

We show that for a very general class of curvature functions defined in the positive cone, the problem of finding a complete strictly locally convex hypersurface in $H^n+1$ satisfying $f(κ)=σ\in(0, 1)$ with a prescribed asymptotic boundary $Γ$ at infinity has at least one smooth solution with uniformly bounded hyperbolic principal curvatures. Moreover if $Γ$ is (Euclidean) starshaped, the solution is unique and also (Euclidean) starshaped while if $Γ$ is mean convex the solution is unique. We also show via a strong duality theorem that analogous results hold in De Sitter space. A novel feature of our approach is a "global interior curvature estimate".

math.DG↗
arXiv2012

Convex Spacelike Hypersurfaces of Constant Curvature in de Sitter Space

We show that for a very general and natural class of curvature functions (for example the curvature quotients $(σ_n/σ_l)^{\frac{1}{n-l}}$) the problem of finding a complete spacelike strictly convex hypersurface in de Sitter space satisfying $f(κ) = σ\in (1,\infty)$ with a prescribed compact future asymptotic boundary $Γ$ at infinity has at least one smooth solution (if l = 1 or l = 2 there is uniqueness). This is the exact analogue of the asymptotic plateau problem in Hyperbolic space and is in fact a precise dual problem. By using this duality we obtain for free the existence of strictly convex solutions to the asymptotic Plateau problem for $σ_l = σ$; $1\leq l < n$ in both deSitter and Hyperbolic space.

math.DG↗
arXiv2011

Curvature flow of complete hypersurfaces in hyperbolic space

In this paper we continue our study of finding the curvature flow of complete hypersurfaces in hyperbolic space with a prescribed asymptotic boundary at infinity. Our main results are proved by deriving a priori global gradient estimates and C^2 estimates.

math.DG↗
arXiv2010

Modified mean curvature flow of star-shaped hypersurfaces in hyperbolic space

We define a new version of modified mean curvature flow (MMCF) in hyperbolic space $\mathbb{H}^{n+1}$, which interestingly turns out to be the natural negative $L^2$-gradient flow of the energy functional defined by De Silva and Spruck in \cite{DS09}. We show the existence, uniqueness and convergence of the MMCF of complete embedded star-shaped hypersurfaces with fixed prescribed asymptotic boundary at infinity. As an application, we recover the existence and uniqueness of smooth complete hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity, which was first shown by Guan and Spruck.

math.DG↗
arXiv2010

Measurement of Spatial Distribution of Cold Atoms in An Integrating Sphere

In this paper, we present an experiment to measure the spatial distribution of cold atoms in a ceramic integrating sphere. An quadrupole field is applied after the atoms are cooled by diffuse light produced in the ceramic integrating sphere, thus the shift of atomic magnetic sub-levels are position-dependent. We move the anti-Helmholtz coil horizontally while keeping the probe laser beam resonant with the cold atoms at the zero magnetic field. The absorption of the probe beam gives the number of cold atoms at different position. The results show that at the center of the integrating sphere, less atoms exist due to the leakage of diffuse light into the hole connecting to the vacuum pump. The method we developed in this paper is useful to detect cold atoms in a region where imaging is not possible.

physics.atom-ph↗
arXiv2009

Enhanced cooling of rubidium atoms in two-frequency diffuse lights

In this paper we describe an experiment of efficient cooling of $^{87}$Rb atoms in two-frequency diffuse laser lights. Compared with single frequency diffuse light, two-frequency diffuse lights have wider velocity capture range and thus can cool more atoms. In our experiment, the maximum number of cooled atoms can reach up to $3.9\times10^9$. Such a result is quite useful in building a compact cold atom clock.

physics.atom-ph↗
arXiv2005

Effect of nano-C doping on the in-situ processed MgB2 tapes

The effect of nano-C doping on the microstructure and superconducting properties of Fe-sheathed MgB2 tapes prepared through the in-situ powder-in-tube method was studied. Heat treatment was performed at a low temperature of 650C for 1 h. Scanning electron microscopy investigation revealed that the smaller grain size of MgB2 in the samples with the C-doping. Further, the a-axis lattice parameter and transition temperature decreased monotonically with increasing doping level, which is due to the C substitution for B. High critical current density Jc values in magnetic fields were achieved in the doped samples because of the very fine-grained microstructure of the superconducting phase obtained with C doping.

cond-mat.supr-con↗