复射影曲线上特殊线丛的射影正规性

本文给出复射影曲线上特殊线丛正规生成的一系列充分条件.     

求解二维三温能量方程的基于AMG预条件子的Krylov子空间迭代法

本文对一类二维三温能量方程的实际应用问题，建立了一种半粗化的代数多重网格法（SAMG），进而得到了以该SAMG方法为预条件子的Krylov子空间迭代法。数值实验结果表明，该方法对求解二维三温能量方程的实际问题是十分有效和健壮的。     

关于二维合作自治系统的闭轨线

本文主要研究二维合作自治系统的闭轨线，推广了［１］的结果，得到了定理１于定理５。为简便计，本文采用［１］的术语，而未说明的概念或符号引自［２］。     

一类二维微分差分方程具有多个周期的周期解的一个条件

本文给出二维微分差分方程{dx/dt=f(x(t-1),y(t-1),dy/dt=g(x,y,x(t-1),y(t-1))具有周期为4/2n 1,4/2n-1,4/2n-3,…,4/7,4/5,4/3,4的周期解的一个条件，并在定理的证明过程中给出了如何求出其相应周期解的方法。     

二维带形无界区域中Navier－Stokes方程整体吸引子及其维数估计

该文讨论二维无界带形区域中Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程其中Ω＝（０，ｄ）×Ｒ，ｄ＞０为一常数，ｕ与ｐ为未知量，其中ｕ＝（ｕ１，ｕ２）为速度场，ｐ表示压力．我们证明了当ｕ０∈Ｈ，ｆ∈Ｖ且ｆ［ｌｏｇ（ｅ＋｜ｘ｜２）］１／２∈Ｌ２（Ω）时，问题（Ｉ）在Ｈ中存在整体吸引子Ａ，它是的一个子集．对Ａ的Ｈａｕｓｄｏｒｆｆ维数与Ｆｒａｃｔａｌ维数我们也给出了估计．     

一类二维非线性Schroedinger方程的吸引子及其维数

本研究了一类二维非线性Schrodinger方程解的有限维行为，我们得到了此方程存在吸引子，并得到了此吸引子维数的上界估计     

Chaplygin气体带有三片常状态初值的二维Riemann问题

本文研究了具有三片常状态初值的Chaplygin气体的Euler方程组的二维Riemann问题.三片常状态初值由y轴的正半轴和x轴来划分.假设原点外的初始数据的每一次间断都恰好只产生一个平面激波、中心稀疏波或滑移面,我们利用广义特征分析的方法详细给出了解的结构.事实上,我们将其分为十种情形进行讨论,并说明其中只有四个子情形是合理的.     

一类无限维完备李代数的2-局部齐次导子北大核心CSCD

通过对复数域上单李代数的Loop代数进行一维导子扩张,得到一类无限维完备李代数;利用其根空间分解及无外导子的性质,证明了这类无限维完备李代数的2-局部齐次导子都是导子.     

M.P. Appell's Function and Vector Bundles of Rank 2 on Elliptic Curves

This paper is devoted to the function introduced by M.P. Appell in connection with decomposition of elliptic functions of the third kind into simple elements. We show that this function is related to global sections of rank-2 vector bundles on elliptic curves. We derive analogues of theta-identities for this function and prove the divisibility property for the action of the modular group, that should be considered as a replacement of the functional equation.     

Remarks on Normal Generation of Special Line Bundles on Algebraic Curves

Let L be a very ample line bundle with h ¹(L) ≥2 on a curve of genus g. We prove that L is normally generated if deg(L) ≥2g ? 1 ? 4h ¹(L) for large enough genus g.     

Restriction of Stable Rank Two Vector Bundles in Arbitrary Characteristic

Let X be a smooth variety defined over an algebraically closed field of arbitrary characteristic and 𝒪 _X (H) be a very ample line bundle on X. We show that for a semistable X-bundle E of rank two, there exists an integer m depending only on Δ(E) · H ^dim(X)?2 and H ^dim(X) such that the restriction of E to a general divisor in |mH| is again semistable. As corollaries, we obtain boundedness results, and weak versions of Bogomolov's Theorem and Kodaira's vanishing theorem for surfaces in arbitrary characteristic.     

Rank 2 Ample Vector Bundles on Some Smooth Rational Surfaces

Several classification results for ample vector bundles of rank 2 on Hirzebruch surfaces, and on Del Pezzo surfaces, are obtained. In particular, we classify rank 2 ample vector bundles with _c2 less than seven on Hirzebruch surfaces, and with _c2 less than four on Del Pezzo surfaces.     

Interpolation Problems for Vector Bundles on Algebraic Curves

In this paper we study meromorphic maps between vector bundles on a Riemann surface. We are mainly interested in stable vector bundles. For a huge number of numerical data we prove the existence of a meromorphic map between two vector bundles with a prescribed number of zeroes and a prescribed number of poles.     

Projectivized Rank Two Toric Vector Bundles are Mori Dream Spaces

We prove that the Cox ring of the projectivization P(?) of a rank two toric vector bundle ?, over a toric variety X, is a finitely generated k-algebra. As a consequence, P(?) is a Mori dream space if the toric variety X is projective and simplicial.     

Vector Variational Inequalities Involving Vector Maximal Points

This paper considers the existence of solutions and the equivalence of four kinds of vector variational inequalities (VVI). More precisely, a sufficient condition is provided under which the solution sets of these VVIs are nonempty and equal. An example is given, showing that such a sufficient condition is essential to ensure the results. Actually, the main theorems in this paper can be regarded as a suitable correction and a refinement of recent results due to Chang et al. (Ref. 1).     

一类Hopf曲面上的全纯线丛的上同调

Let X be a non-primary Hopf Surface with Abelian fundamental groupπ_1 (X)(?) Z(?)Z_m, L a line bundle on X, we give a formula for computing the dimension of cohomology H~q(X,Ω~P(L)) and the explicit results for non-primary exceptional Hopf surface.     

Some Remarks on Syzygies of Adjoint Line Bundles

In this article, we construct examples of n-folds X carrying an ample line bundle A ∈ Pic X such that property N _p fails for K _X  + (n + 1 + p)A. This shows that the condition of Mukai's conjecture is optimal for every n ≥ 1 and p ≥ 0.     

Horizontal Laplace Operator in Real Finsler Vector Bundles

A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E.