Spin structures on instanton moduli spaces

We determine the necessary and sufficient conditions for the based SU(l)-instanton moduli spaces over CP² and the unbased SU(2)-instanton moduli spaces over S⁴ having spin structures.     

Local Gromov-Witten invariants and tautological sheaves on Hilbert schemes

Abstract We study the local Gromov-Witten invariants of O(k)⊕O(-k-2) → P1 by localization techniques and the Marino-Vafa formula, using suitable circle actions. They are identified with the equivariant Riemann-Roch indices of some power of the determinant of the tautological sheaves on the Hilbert schemes of points on the affine plane. We also compute the corresponding Gopakumar-Vafa invariants and make some conjectures about them.     

Mixed needlets

The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008) [14], and Geller et al. (2008, 2009) [12] and [13]. Here we focus on an alternative proposal for needlets on this spin line bundle, in which needlet coefficients arise from the usual, rather than the spin, spherical harmonics, as in the previous constructions. We label this system mixed needlets and investigate in full their properties, including localization, the exact tight frame characterization, reconstruction formula, decomposition of functional spaces, and asymptotic uncorrelation in the stochastic case. We outline astrophysical applications.     

基于Lagrange乘子法的一种二阶椭圆问题混合元格式

本文利用Lagrange乘子法的思想,修改了传统的混合变分形式,将二阶椭圆问题转化为与其等价的新的变分形工,给出了针对该新形式进行离散求解的一种混合元格式,与现在已知格式相比,用较少的自由度获得了较高的逼近阶。     

A Mixed Mann Iteration Process for Fixed Points of Mixed Increasing Operators in Ordered Banach Spaces

In this paper, we develop a new mixed Mann iteration process to approximate the fixed points of mixed increasing operators in ordered Banach spaces and discuss the convergence analysis of the iterative sequences generated by the iteration process. As an application, we develop a new iterative method for solving a class of nonlinear integral equations.     

Laplace方程混合边值问题的一个注记

本文讨论了一个角形区域上边界条件有间断点的Laplace方程混合边值问题 的适定性,并给出了完整的解答.     

一种求解扩散方程的混合格式

本文提出了一种求解扩散方程的新型混合格式，具有明显的并行性，很高的精度与稳定性．文中给出了一数值例子，其在一具有五个ｔｒａｎｓｐｕｔｅｒ的并行机上的并行加速达３．５．     

混合成本分解式的比较

本文对两个期间混合成本分解式中的固定成本和单位成本变动率进行比较，进而能从数量方面评价两种不同的成本管理措施优劣。     

On Associative Ring Multiplication on Abelian Mixed Groups

An abelian group is called a mixed one if it is neither torsion nor torsion-free. It is to be proved that every mixed group can be provided with a nonzero associative ring structure. Our methods of proofs are straightforward and elementary.     

求解stokes问题的一个新的非协调混合元格式

构造一个新的非协调混合元格式求解stokes问题,证明了该元满足B-B条件,并且有2阶收敛速度.     

The decomposition of global conformal invariants IV: A proposition on local Riemannian invariants

This is the fourth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant, a divergence and of the Chern-Gauss-Bonnet integrand.The present paper lays out the second half of this entire work: The second half proves certain purely algebraic statements regarding local Riemannian invariants; these were used extensively in the first two papers in this series, see Alexakis (2007, 2009) [2] and [3]. These results may be of independent interest, applicable to related problems.     

一类发展方程的混合方法

本文研究了一类发展方程的适定性问题和混合方法,征明了连续问题和离散问题解的存在唯一性,并对离散解作了误差估计.     

Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.     

A Polynomial-Time Algorithm to Approximate the Mixed Volume within a Simply Exponential Factor

Let K=(K ₁,…,K _n ) be an n-tuple of convex compact subsets in the Euclidean space R ⁿ , and let V(⋅) be the Euclidean volume in R ⁿ . The Minkowski polynomial V _K is defined as V _K (λ ₁,…,λ _n )=V(λ ₁ K ₁+⋅⋅⋅+λ _n K _n ) and the mixed volume V(K ₁,…,K _n ) as

A Survey on Some Anisotropic Hardy-Type Function Spaces

Let $A$ be a general expansive matrix on $\mathbb{R}^n$. The aims of this article are twofold. The first one is to give a survey on the recent developments of anisotropic Hardy-type function spaces on $\mathbb{R}^n$, including anisotropic Hardy–Lorentz spaces, anisotropic variable Hardy spaces and anisotropic variable Hardy–Lorentz spaces as well as anisotropic Musielak–Orlicz Hardy spaces. The second one is to correct some errors and seal some gaps existing in the known articles. Some unsolved problems are also presented.     

A Survey of the Homotopy Properties of Inclusion of Certain Types of Configuration Spaces into the Cartesian Product

Let X be a topological space.In this survey the authors consider several types of configuration spaces,namely,the classical(usual)configuration spaces F_n(X)and D_n(X),the orbit configuration spaces F_n~G(X)and F_n~G(X)/S_nwith respect to a free action of a group G on X,and the graph configuration spaces F_n~Γ(X)and F_n~Γ(X)/H,whereΓis a graph and H is a suitable subgroup of the symmetric group S_n.The ordered configuration spaces F_n(X),F_n~G(X),F_n~Γ(X)are all subsets of the n-fold Cartesian product ∏_1~nX of X with itself,and satisfy F_n~G(X)?F_n(X)?F_n~Γ(X)?∏_1~nX.If A denotes one of these configuration spaces,the authors analyse the difference between A and ∏_1~nXfrom a topological and homotopical point of view.The principal results known in the literature concern the usual configuration spaces.The authors are particularly interested in the homomorphism on the level of the homotopy groups of the spaces induced by the inclusionι:A-→∏_1~nX,the homotopy type of the homotopy fibre I_ιof the mapιvia certain constructions on various spaces that depend on X,and the long exact sequence in homotopy of the fibration involving I_ιand arising from the inclusionι.In this respect,if X is either a surface without boundary,in particular if X is the 2-sphere or the real projective plane,or a space whose universal covering is contractible,or an orbit space S~k/Gof the k-dimensional sphere by a free action of a Lie group G,the authors present recent results obtained by themselves for the first case,and in collaboration with Golasi′nski for the second and third cases.The authors also briefly indicate some older results relative to the homotopy of these spaces that are related to the problems of interest.In order to motivate various questions,for the remaining types of configuration spaces,a few of their basic properties are described and proved.A list of open questions and problems is given at the end of the paper.     

Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems

We construct and analyze a mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order PDEs in the state variable (e.g., pressure) and its flux (e.g., Darcy velocity). An important point is that no staggered grids or covolumes are used to stabilize the system. Only a single primary grid system is adopted, and the degrees of freedom are imposed on the interfaces. The approximate flux is sought in the lowest-order Raviart-Thomas space and the pressure field in the rotated- nonconforming space. Furthermore, we demonstrate that the present finite volume method can be interpreted as a rotated- nonconforming finite element method for the pressure with a simple local recovery of flux. Numerical results are presented for a variety of problems which confirm the usefulness and effectiveness of the method.

     

二维Minkowski空间R~(2.1)中混合型时空曲面的等温参数

对于三维Minkowski空间中的混合型时空曲面，证明了其在类空部分和类时部分上分别存在光滑的，并且连续到交界线上的等温参数．进一步，给出了混合型时空曲面存在在其类空部分和类时部分上是光滑的，而在交界线上是连续的等温多数的一个必要条件．     

A Characteristic Mixed Finite Element Two-Grid Method for Compressible Miscible Displacement Problem

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The concentration equation is treated by a mixed finite element method with characteristics (CMFEM) and the pressure equation is treated by a parabolic mixed finite element method (PMFEM). Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations. Moreover, the $L^q$ error estimates are conducted for the pressure, Darcy velocity and concentration variables in the two-grid solutions. Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.