Pseudo-effective and numerically flat reflexive sheaves

In this note, we discuss the concept of pseudoeffective vector bundle and also introduce pseudoeffective torsion-free sheaves over compact K\"ahler manifolds. We show that a pseudoeffective reflexive sheaf over a compact K\"ahler manifold with vanishing first Chern class is in fact a numerically flat vector bundle. A proof is obtained through a natural construction of positive currents representing the Segre classes of pseudoeffective vector bundles.Comment: 45 pages, rewrite section 3 and section

Canonical duality approach in the approximation of optimal Monge mass transfer mapping

This paper mainly addresses the Monge mass transfer problem in the 1-D case. Through an ingenious approximation mechanism, one transforms the Monge problem into a sequence of minimization problems, which can be converted into a sequence of nonlinear differential equations with constraints by variational method. The existence and uniqueness of the solution for each equation can be demonstrated by applying the canonical duality method. Moreover, the duality method gives a sequence of perfect dual maximization problems. In the final analysis, one constructs the approximation of optimal mapping for the Monge problem according to the theoretical results.Comment: 15 pages, 0 figure. arXiv admin note: substantial text overlap with arXiv:1607.0655

An approximation method for the optimization of pp-th moment of Rn\mathbb{R}^n-valued random variable

This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which can be converted into a sequence of nonlinear differential equations with constraints by variational approach. The existence and uniqueness of the solution for each equation can be demonstrated by applying the canonical duality method. Moreover, the dual transformation gives a sequence of perfect dual maximization problems. In the final analysis, one constructs the approximation of the probability density function accordingly.Comment: 11 pages, 0 figure. arXiv admin note: substantial text overlap with arXiv:1607.0655

Control of Spin in La(Mn,Zn)AsO Alloy by Carrier Doping

The control of spin without magnetic field is one of challenges in developing spintronic devices. In an attempt to solve this problem, we proposed a novel hypothetic LaMn0.5Zn0.5AsO alloy from two experimentally synthesized rare earth element transition metal arsenide oxides, i.e. LaMnAsO and LaZnAsO. On the basis of the first-principles calculations with strong-correlated correction, we found that the LaMn0.5Zn0.5AsO alloy is an antiferromagnetic semiconductor at ground state, while bipolar magnetic semiconductor at ferromagnetic state. Both electron and hole doping in the LaMn0.5Zn0.5AsO alloy induces the transition from antiferromagnetic to ferromagnetic, as well as semiconductor to half metal. In particular, the spin-polarization direction is switchable depending on the doped carrier's type. As carrier doping can be realized easily in experiment by applying a gate voltage, the LaMn0.5Zn0.5AsO alloy stands for a promising spintronic material to generate and control the spin-polarized carriers with electric field.Comment: 16 pages, 4 figure

A new multi-component CKP hierarchy

We construct a new multi-component CKP hierarchy based on the eigenfunction symmetry reduction. It contains two types of CKP equation with self-consistent sources which Lax representations are presented. Also it admits reductions to $k$-constrained CKP hierarchy and to a (1+1)-dimensional soliton hierarchy with self-consistent source, which include two types of Kaup-Kuperschmidt equation with self-consistent sources and of bi-directional Kaup-Kuperschmidt equation with self-consistent sources.Comment: 8 page

Two new multi-component BKP hierarchies

We firstly propose two kinds of new multi-component BKP (mcBKP) hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources which Lax representations are presented. The two mcBKP hierarchies both admit reductions to the $k-$constrained BKP hierarchy and to integrable (1+1)-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of bi-directional SK equations with self-consistent sources.Comment: 12 page

Pose Invariant 3D Face Reconstruction

3D face reconstruction is an important task in the field of computer vision. Although 3D face reconstruction has being developing rapidly in recent years, it is still a challenge for face reconstruction under large pose. That is because much of the information about a face in a large pose will be unknowable. In order to address this issue, this paper proposes a novel 3D face reconstruction algorithm (PIFR) based on 3D Morphable Model (3DMM). After input a single face image, it generates a frontal image by normalizing the image. Then we set weighted sum of the 3D parameters of the two images. Our method solves the problem of face reconstruction of a single image of a traditional method in a large pose, works on arbitrary Pose and Expressions, greatly improves the accuracy of reconstruction. Experiments on the challenging AFW, LFPW and AFLW database show that our algorithm significantly improves the accuracy of 3D face reconstruction even under extreme poses .Comment: 8 page

On the hard Lefschetz theorem for pseudoeffective line bundles

In this note, we obtain a number of results related to the hard Lefschetz theorem for pseudoeffective line bundles, due to Demailly, Peternell and Schneider. Our first result states that the holomorphic sections produced by the theorem are in fact parallel, when viewed as currents with respect to the singular Chern connection associated with the metric. Our proof is based on a control of the covariant derivative in the approximation process used in the construction of the section. Then we show that we have an isomorphsim between such parallel sections and higher degree cohomology. As an application, we show that the closedness of such sections induces a linear subspace structure on the tangent bundle. Finally, we discuss some questions related to the optimality of the hard Lefschetz theorem.Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:1401.5432, arXiv:math/0006205 by other author

On a vanishing theorem due to Bogomolov

In this note, we give a new proof of a vanishing result originally due to Bogomolov, and later generalised by Mourougane and Boucksom. The statement holds for arbitrary pseudoeffective line bundles over compact K\"ahler manifolds, under an assumption on the numerical dimension of the line bundle.Comment: 11 page

On the Nakano vanishing theorem

In this note, we state various generalisations of the Nakano vanishing theorem under weak positivity assumptions, and compare them with the known results.Comment: 5 page