Quasi-Local Mass Integrals and the Total Mass

On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown–York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.     

Volume Estimate Via Total Curvature in Hyperbolic Spaces

Let D Hⁿ(–k²) be a convex compact subset of the hyperbolicspace Hⁿ(–k²) with non-empty interior and smooth boundary.It is shown that the volume of D can be estimated by the totalcurvature of D. More precisely, , where K denotes the Gauss–Kronecker curvature of D andVol(S^n–1) denotes the Euclidean volume of the sphere.2000 Mathematics Subject Classification 53C21.     

Low Complexity Methods For Discretizing Manifolds Via Riesz Energy Minimization

Let \(A\) be a compact \(d\) -rectifiable set embedded in Euclidean space \({\mathbb R}^p, d\le p\) . For a given continuous distribution \(\sigma (x)\) with respect to a \(d\) -dimensional Hausdorff measure on \(A\) , our earlier results provided a method for generating \(N\) -point configurations on \(A\) that have an asymptotic distribution \(\sigma (x)\) as \(N\rightarrow \infty \) ; moreover, such configurations are “quasi-uniform” in the sense that the ratio of the covering radius to the separation distance is bounded independently of \(N\) . The method is based upon minimizing the energy of \(N\) particles constrained to \(A\) interacting via a weighted power-law potential \(w(x,y)|x-y|^{-s}\) , where \(s>d\) is a fixed parameter and \(w(x,y)=\left( \sigma (x)\sigma (y)\right) ^{-({s}/{2d})}\) . Here we show that one can generate points on \(A\) with the aforementioned properties keeping in the energy sums only those pairs of points that are located at a distance of at most \(r_N=C_N N^{-1/d}\) from each other, with \(C_N\) being a positive sequence tending to infinity arbitrarily slowly. To do this, we minimize the energy with respect to a varying truncated weight \(v_N(x,y)=\Phi (|x-y|/r_N)\cdot w(x,y)\) , where \(\Phi :(0,\infty )\rightarrow [0,\infty )\) is a bounded function with \(\Phi (t)=0, t\ge 1\) , and \(\lim _{t\rightarrow 0^+}\Phi (t)=1\) . Under appropriate assumptions, this reduces the complexity of generating \(N\) -point “low energy” discretizations to order \(N C_N^d\) computations.     

加权全能量最小的圆环形变北大核心CSCD

主要考虑如下加权全能量极值问题:h∈■^(inf)(A_(1),A_(2))α∫∫A_(1)(|h_(N)|^(2)+|h_(T)|^(2))1/(|h_(z)|^(2))dz+β∫∫A_(1)|h_(N)|^(2)+|h_(T)|^(2)/J(z,h)1/|z|^(2)dz,其中■(A_(1),A_(2))代表从圆环A_(1)到圆环A_(2)的所有保向同胚映射的集合.研究得到唯一的极值映射为径向拉伸映射.这将[Iwaniec T,Onninen J.Hyperelastic deformations of smallest total energy[J].Arch Rational Mech Anal,2009,194:927-986.]的结果推广至非欧情形.同时,也分别研究了圆环上的加权调和能量的极值问题与加权偏差的极值问题.     

Convexity of Reduced Energy and Mass Angular Momentum Inequalities

In this paper, we extend the work in Chru?ciel and Costa (Class. Quant. Grav. 26:235013, 2009), Chru?ciel et al. (Ann. Phy. 323:2591–2613, 2008), Costa (J. Math. Theor. 43:285202, 2010), Dain (J. Diff. Geom. 79:33–67, 2008). We weaken the asymptotic conditions on the second fundamental form, and we also give an L ⁶?norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr–Newman data by proving convexity of the renormalized Dirichlet energy when the target has non-positive curvature. In particular, we give the first proof of the strict mass/angular momentum/charge inequality for axisymmetric Einstein/Maxwell data which is not identical with the extreme Kerr–Newman solution.     

利用近似能量极小构造平面C1三次Hermite插值曲线

研究了利用近似能量极小构造平面$C^1$三次Hermite插值曲线的方法.该方法的主要的目是求出$C^1$三次Hermite插值曲线的最佳切矢.通过将应变能、曲率变化能和组合能的近似函数极小化,得到了求解最佳切矢的线性方程组.通过求解发现,近似曲率变化能极小不存在唯一解, 而近似应变能极小和近似组合能极小由于方程系统的系数矩阵为严格对角占优故都存在唯一解.最后, 通过实例表明了本文方法构造平面$C^1$三次Hermite插值曲线的有效性.     

考虑非合意产出的全要素能源效率研究

本文运用1995-2008年中国省域面板数据,选择基于DEA前沿面方法的Malmquist指数模型,测算了不同非合意产出组合的全要素能源效率(TFEE),并对TFEE构成进行分解,检验TFEE收敛性。研究发现,考虑环境因素的不同产出组合的TFEE具有显著差异性;中国1995 2008年TFEE呈现U型演变特征;TFEE的提高主要来源于技术进步的贡献;区域TFEE差异大,节能潜力大;TFEE具有周期性波动演化的复杂特征。     

Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems

For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.     

粒子超非线性的总能和de Broglie波的理论

用Lourent级数对高速运动粒子的速度(～c)展开并取得总能量表达式.总能包含静能和动能二项.由能量-动量的关系得到了de-Broglie波的理论,其中相速度仍是小于光速c的结论.     

On the Formulation of Mass,Momentum and Energy Conservation in the KdV Equation

The Korteweg-de Vries (KdV) equation is widely recognized as a simple model for unidirectional weakly nonlinear dispersive waves on the surface of a shallow body of fluid. While solutions of the KdV equation describe the shape of the free surface, information about the underlying fluid flow is encoded into the derivation of the equation, and the present article focuses on the formulation of mass, momentum and energy balance laws in the context of the KdV approximation. The densities and the associated fluxes appearing in these balance laws are given in terms of the principal unknown variable η representing the deflection of the free surface from rest position. The formulae are validated by comparison with previous work on the steady KdV equation. In particular, the mass flux, total head and momentum flux in the current context are compared to the quantities Q, R and S used in the work of Benjamin and Lighthill (Proc. R. Soc. Lond. A 224:448–460, 1954) on cnoidal waves and undular bores.     

基于三阶段DEA模型的中国省际全要素能源效率研究

基于三阶段DEA(数据包络分析)模型测算了我国2009年29个省市的全要素能源效率及其分解变量.研究结果表明:环境因素对于各地区全要素能源效率有显著影响.各地区政府财政支出与对外开放程度的提高是全要素能源效率改善的有利因素;各地区第三产业增加值占GDP的比重与各地区工业总产值占中国所有工业总产值的比重的增加是全要素能源效率提高的不利因素.另一方面在剔除环境和随机因素影响后,全国平均规模效率的降低是全要素能源效率的下降主要因素.最后由全要素能源效率的聚类分析结果发现,我国全要素能源效率的区域差异明显,东部表现最优,中部次之,西部最次.     

Decorrelation Estimates for a 1D Tight Binding Model in the Localized Regime

In this article, we prove decorrelation estimates for the eigenvalues of a 1D discrete tight-binding model near two distinct energies in the localized regime. Consequently, for any integer n ≥ 2, the asymptotic independence for local level statistics near n distinct energies is obtained.     

Uniform Mixtures Via Posterior Means

The problem of identification of uniform mixtures via posterior means is studied. For linear posterior means a complete solution is given. It determines a family of prior distributions involving beta of both kinds and gamma. Identifiability via any consistent posterior mean is also investigated.     

Tensioned Quasi-Interpolation Via Geometric Continuity

The paper proposes a method for the construction of C ² quasi-interpolating functions with tension properties. The constructed quasi-interpolant is a parametric cubic curve and its shape can be easily controlled via tension parameters which have an immediate geometric interpretation. Numerical examples are presented.     

Variable Selection Via Subtle Uprooting

This article proposes a variable selection method termed “subtle uprooting” for linear regression. In this proposal, variable selection is formulated into a single optimization problem by approximating cardinality involved in the information criterion with a smooth function. A technical maneuver is then employed to enforce sparsity of parameter estimates while maintaining smoothness of the objective function. To solve the resulting smooth nonconvex optimization problem, a modified Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm with established global and super-linear convergence is adopted. Both simulated experiments and an empirical example are provided for assessment and illustration. Supplementary materials for this article are available online.     

Non-Convex Strong Duality Via Subdifferential

In this article, the strong duality is treated. It is shown that the strong duality is equivalent to the non-emptiness of the subdifferential of a sort map involving the constraint functions. It is also noted that this technique is useful to verify the Assumption S. Indeed, the linearity of a constraint function h is not required as usually seen in the literature. Moreover, it is shown that this condition is easer to verify in the applications. We apply this new principle to the bi-obstacle problem, to the elastic-plastic torsion problem and to the continuum model of transportation.     

Vector Majorization Via Hessenberg Matrices

In this paper it is proved that, for real n-vectors x and y,x is majorized by y if and only if x = PHQy for some permutationmatrices P, Q, and for some doubly stochastic matrix H whichis a direct sum of doubly stochastic Hessenberg matrices. Thisresult reveals that any n-vector which is majorized by a vectory can be expressed as a convex combination of at most (n² –n + 2)/2 permutations of y.