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Gang Liu

Publications and source records attributed to Gang Liu.

At least 217 records · Page 12Linked to original sources
arXiv2016

Temperature effect on lattice and electronic structures of WTe$_2$ from first-principles study

Tungsten ditelluride (WTe$_2$) exhibits extremely large and unsaturated magnetoresistance (MR). Due to the large spatially extensions of Te-5p and W-5d orbitals, the electronic properties of WTe$_2$ are sensitive to the lattice structures, which can probably affect the strongly temperature dependent MR found in experiment. Based on first-principle calculations, we investigate the temperature effect on the lattice and electronic structures of WTe$_2$. Our numerical results show that the thermal expansion coefficients of WTe$_2$ are highly anisotropic and considerably large. However, the temperature (less than 300 K) has ignorable effect on the Fermi surface of WTe$_2$. Our theoretical results clarify that the thermal expansion is not the main reason of the temperature-induced rapid decrease of magnetoresistance.

cond-mat.mtrl-sci↗
arXiv2016

Domains of holomorphy for irreducible admissible uniformly bounded representations of simple Lie groups

In this note, we address a question raised by Krötz on the classification of domains of holomorphy of irreducible admissible Banach representations for connected non-compact simple real Lie groups G. When G is not of Hermitian type, we give a complete description of the domains of holomorphy for irreducible admissible uniformly bounded representations on uniformly convex uniformly smooth Banach spaces and, in particular, for all irreducible uniformly bounded Hilbert representations. When the group G is Hermitian, we determine the domains of holomorphy only when the representations considered are highest or lowest weight representations.

math.RT↗
arXiv2016

Simultaneous band gap narrowing and carrier lifetime prolongation of organic-inorganic trihalide perovskites

The organic-inorganic hybrid lead trihalide perovskites have been emerging as the most attractive photovoltaic material. As regulated by Shockley-Queisser theory, a formidable materials science challenge for the next level improvement requires further band gap narrowing for broader absorption in solar spectrum, while retaining or even synergistically prolonging the carrier lifetime, a critical factor responsible for attaining the near-band gap photovoltage. Herein, by applying controllable hydrostatic pressure we have achieved unprecedented simultaneous enhancement in both band gap narrowing and carrier lifetime prolongation (up to 70~100% increase) under mild pressures at ~0.3 GPa. The pressure-induced modulation on pure hybrid perovskites without introducing any adverse chemical or thermal effect clearly demonstrates the importance of band edges on the photon-electron interaction and maps a pioneering route towards a further boost in their photovoltaic performance.

cond-mat.mtrl-sci↗
arXiv2016

On the tangent cone of Kähler manifolds with Ricci curvature lower bound

Let $X$ be the Gromov-Hausdorff limit of a sequence of pointed complete Kähler manifolds $(M^n_i, p_i)$ satisfying $Ric(M_i)\geq -(n-1)$ and the volume is noncollapsed. We prove that, there exists a Lie group isomorphic to $\mathbb{R}$, acting isometrically, on the tangent cone at each point of $X$. Moreover, the action is locally free on the cross section. This generalizes the metric cone theorem of Cheeger-Colding to the Kähler case. We also discuss some applications to complete Kähler manifolds with nonnegative bisectional curvature.

math.DG↗
arXiv2016

Texture Synthesis Through Convolutional Neural Networks and Spectrum Constraints

This paper presents a significant improvement for the synthesis of texture images using convolutional neural networks (CNNs), making use of constraints on the Fourier spectrum of the results. More precisely, the texture synthesis is regarded as a constrained optimization problem, with constraints conditioning both the Fourier spectrum and statistical features learned by CNNs. In contrast with existing methods, the presented method inherits from previous CNN approaches the ability to depict local structures and fine scale details, and at the same time yields coherent large scale structures, even in the case of quasi-periodic images. This is done at no extra computational cost. Synthesis experiments on various images show a clear improvement compared to a recent state-of-the art method relying on CNN constraints only.

cs.CV↗
arXiv2016

Hausdorffness for Lie algebra homology of Schwartz spaces and applications to the comparison conjecture

Let $H$ be a real algebraic group acting equivariantly with finitely many orbits on a real algebraic manifold $X$ and a real algebraic bundle $\mathcal{E}$ on $X$. Let $\mathfrak{h}$ be the Lie algebra of $H$. Let $\mathcal{S}(X,\mathcal{E})$ be the space of Schwartz sections of $\mathcal{E}$. We prove that $\mathfrak{h}\mathcal{S}(X,\mathcal{E})$ is a closed subspace of $\mathcal{S}(X,\mathcal{E})$ of finite codimension. We give an application of this result in the case when $H$ is a real spherical subgroup of a real reductive group $G$. We deduce an equivalence of two old conjectures due to Casselman: the automatic continuity and the comparison conjecture for zero homology. Namely, let $π$ be a Casselman-Wallach representation of $G$ and $V$ be the corresponding Harish-Chandra module. Then the natural morphism of coinvariants $V_{\mathfrak{h}}\to π_{\mathfrak{h}}$ is an isomorphism if and only if any linear $\mathfrak{h}$-invariant functional on $V$ is continuous in the topology induced from $π$. The latter statement is known to hold in two important special cases: if $H$ includes a symmetric subgroup, and if $H$ includes the nilradical of a minimal parabolic subgroup of $G$.

math.RT↗
arXiv2015

Distributed Virtual Resource Allocation in Small Cell Networks with Full Duplex Self-backhauls and Virtualization

Wireless network virtualization has attracted great attentions from both academia and industry. Another emerging technology for next generation wireless networks is in-band full duplex (FD) communications. Due to its promising performance, FD communication has been considered as an effective way to achieve self-backhauls for small cells. In this paper, we introduce wireless virtualization into small cell networks, and propose a virtualized small cell network architecture with FD self-backhauls. We formulate the virtual resource allocation problem in virtualized small cell networks with FD self-backhauls as an optimization problem. Since the formulated problem is a mixed combinatorial and non-convex optimization problem, its computational complexity is high. Moreover, the centralized scheme may suffer from signaling overhead, outdated dynamics information, and scalability issues. To solve it efficiently, we divide the original problem into two subproblems. For the first subproblem, we transfer it to a convex optimization problem, and then solve it by an efficient alternating direction method of multipliers (ADMM)-based distributed algorithm. The second subproblem is a convex problem, which can be solved by each infrastructure provider. Extensive simulations are conducted with different system configurations to show the effectiveness of the proposed scheme.

cs.NI↗
arXiv2015

First-Principles Study of Lattice Thermal Conductivity of Td-WTe2

The structural and thermal properties of bulk Td-WTe2 have been studied by using first-principles calculations. We find that the lattice thermal conductivity of WTe2 is anisotropic, with the highest value along a-axis and lowest one along the c-axis at 300 K. Our calculated size dependent thermal conductivity shows that nanostructuring of WTe2 can possibly further decrease the lattice thermal conductivity. Such extremely low thermal conductivity, even much lower than WSe2, makes WTe2 attractive for use as thermal-insulation material for thermoelectric devices.

cond-mat.mes-hall↗
arXiv2015

Weakly Smooth Structures in Gromov-Witten Theory

In order to establish Fredholm theory on stratified topological Banach manifolds in Gromov-Witten theory, we have introduced flat structures on such manifolds in [L4]. Such a structure is obtained from local flat coordinate charts. The transformations between these charts are only continuous in general. The purpose of this paper is two-fold : firstly to show that on the topological Banach manifolds and bundles appeared in Gromov-Witten and Floer type theories, there are enough smooth functions and sections viewed in any admissible charts and trivializations; secondly to demonstrate some finer aspects about the weakly smooth sections.

math.SG↗
arXiv2015

Gromov-Hausdorff limit of Kähler manifolds and the finite generation conjecture

We study the uniformization conjecture of Yau by using the Gromov-Haudorff convergence. As a consequence, we confirm Yau's finite generation conjecture. More precisely, on a complete noncompact Kähler manifold with nonnegative bisectional curvature, the ring of polynomial growth holomorphic functions is finitely generated. During the course of the proof, we prove if $M^n$ is a complete noncompact Kähler manifold with nonnegative bisectional curvature and maximal volume growth, then $M$ is biholomorphic to an affine algebraic variety. We also confirm a conjecture of Ni on the existence of polynomial growth holomorphic functions on Kähler manifolds with nonnegative bisectional curvature.

math.DG↗
arXiv2015

On the volume growth of Kähler manifolds with nonnegative bisectional curvature

Let $M$ be a complete Kähler manifold with nonnegative bisectional curvature. Suppose the universal cover does not split and $M$ admits a nonconstant holomorphic function with polynomial growth, we prove $M$ must be of maximal volume growth. This confirms a conjecture of Ni. There are two essential ingredients in the proof: The Cheeger-Colding theory on Gromov-Hausdorff convergence of manifolds; the three circle theorem for holomorphic functions.

math.DG↗
arXiv2015

Meaningful Objects Segmentation from SAR Images via A Multi-Scale Non-Local Active Contour Model

The segmentation of synthetic aperture radar (SAR) images is a longstanding yet challenging task, not only because of the presence of speckle, but also due to the variations of surface backscattering properties in the images. Tremendous investigations have been made to eliminate the speckle effects for the segmentation of SAR images, while few work devotes to dealing with the variations of backscattering coefficients in the images. In order to overcome both the two difficulties, this paper presents a novel SAR image segmentation method by exploiting a multi-scale active contour model based on the non-local processing principle. More precisely, we first formulize the SAR segmentation problem with an active contour model by integrating the non-local interactions between pairs of patches inside and outside the segmented regions. Secondly, a multi-scale strategy is proposed to speed up the non-local active contour segmentation procedure and to avoid falling into local minimum for achieving more accurate segmentation results. Experimental results on simulated and real SAR images demonstrate the efficiency and feasibility of the proposed method: it can not only achieve precise segmentations for images with heavy speckles and non-local intensity variations, but also can be used for SAR images from different types of sensors.

cs.CV↗
arXiv2014

Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton's second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.

cond-mat.mtrl-sci↗
arXiv2014

Three Circle Theorems on Kähler manifolds and applications

The classical Hadamard three circle theorem is generalized to complete Kähler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle theorem. As corollaries, two sharp monotonicity formulae for holomorphic functions are derived. Among applications, we derive sharp dimension estimates (with rigidity) of holomorphic functions with polynomial growth when the holomorphic sectional curvature is nonnegative. When the bisectional curvature is nonnegative, this was due to Ni. Also we study holomorphic functions with polynomial growth near infinity. On a complete noncompact Kähler manifold with nonnegative bisectional curvature, we prove any holomorphic function with polynomial growth is homogenous at infinity. This result is closely related with Yau's conjecture on the finite generation of holomorphic functions (see page $3-4$ for detailed explanation). We also generalize the three circle theorem to Kähler manifolds with holomorphic sectional curvature lower bound. These inequalities are sharp in general. As applications, we establish sharp dimension estimates for holomorphic functions with certain growth conditions when the holomorphic sectional curvature is asymptotically nonnegative. Finally observe that Hitchin constructed some complex manifolds which admit Kähler metric with positive holomorphic sectional curvature, yet do not even admit Kähler metrics with nonnegative Ricci curvature. Thus the set of complete Kähler manifolds with nonnegative holomorphic sectional curvature is strictly wider than those with nonnegative bisectional curvature.

math.DG↗
arXiv2014

New explicit thresholding/shrinkage formulas for one class of regularization problems with overlapping group sparsity and their applications

The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e., regularizer) should be introduced, under the assumption that the solutions have some specific properties, such as sparsity and group sparsity. Widely used regularizers include the $\ell_1$ norm, total variation (TV) semi-norm, and so on. Recently, a new regularization term with overlapping group sparsity has been considered. Majorization minimization iteration method or variable duplication methods are often applied to solve them. However, there have been no direct methods for solve the relevant problems because of the difficulty of overlapping. In this paper, we proposed new explicit shrinkage formulas for one class of these relevant problems, whose regularization terms have translation invariant overlapping groups. Moreover, we apply our results in TV deblurring and denoising with overlapping group sparsity. We use alternating direction method of multipliers to iterate solve it. Numerical results also verify the validity and effectiveness of our new explicit shrinkage formulas.

math.NA↗
arXiv2014

Compact Kähler manifolds with nonpositive bisectional curvature

Let $(M^n, g)$ be a compact Kähler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact Kähler manifold $N^k$ with $c_1 < 0$. This confirms a conjecture of Yau. As a corollary, for any compact Kähler manifold with nonpositive bisectional curvature, the Kodaira dimension is equal to the maximal rank of the Ricci tensor. We also prove a global splitting result under the assumption of certain immersed complex submanifolds.

math.DG↗