G-锥度量空间中压缩映射的不动点定理

给出了G-锥度量空间的概念,利用迭代法探究了G-锥度量空间中压缩映射不动点定理,证明了在G-锥度量空间中锥没有正规性的条件下压缩映射存在唯一不动点.     

Landau定理中上界的一个改进

通过相关文献给出的穿孔平面C\{0,1}的双曲度量的密度函数的新的下界估计,借助广义Schwarz引理我们对Landau定理中关于上界做了进一步改进并得到了一个带参数的上界表达式.并且当参数取到0时,此结论正好为相关文献得到的结果.     

Partial Hölder continuity for Q-valued energy minimizing maps

We consider multivalued maps between Ω ? ?^N open (N ≥ 2) and a smooth, compact Riemannian manifold 𝒩 locally minimizing the Dirichlet energy. An interior partial Hölder regularity results in the spirit of R. Schoen and K. Uhlenbeck is presented. Consequently a minimizer is Hölder continuous outside a set of Hausdorff dimension at most N ? 3. Almgren's original theory includes a global interior Hölder continuity result if the minimizers are valued into some ?^m. It cannot hold in general if the target is changed into a Riemannian manifold, since it already fails for “classical” single valued harmonic maps.     

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum,Fragmentation, and the Variance of Entropy

We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge field, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well as the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation—multiple macroscopic eigenvalues of the reduced one-body density matrix—emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.     

Bouncing scenario of general relativistic hydrodynamics in extended gravity

In this paper,we have framed bouncing cosmological model of the Universe in the presence of general relativistic hydrodynamics in an extended theory of gravity.The metric assumed here is the flat Friedmann–Robertson–Walker space–time and the stress energy tensor is of perfect fluid.Since general relativity(GR)has certain issues with late time cosmic speed up phenomena,here we have introduced an additional matter geometry coupling that described the extended gravity to GR.The dynamical parameters are derived and analyzed.The dynamical behavior of the equation of state parameter has been analyzed.We have observed that the bouncing behavior is mostly controlled by the coupling parameter.     

Characterizations of Sobolev spaces associated to operators satisfying off‐diagonal estimates on balls

Let be a metric measure space of homogeneous type and L be a one‐to‐one operator of type ω on for ω ∈[0, π /2). In this article, under the assumptions that L has a bounded H _∞ ‐functional calculus on and satisfies (p _L , q _L ) off‐diagonal estimates on balls, where p _L ∈[1, 2) and q _L ∈(2, ∞ ], the authors establish a characterization of the Sobolev space , defined via L ^{α /2}, of order α ∈(0, 2] for p ∈(p _L , q _L ) by means of a quadratic function S _{α , L} . As an application, the authors show that for the degenerate elliptic operator L _w : =? w  ^? 1div(A ?) and the Schrödinger type operator with a ∈(0, ∞ ) on the weighted Euclidean space with A being real symmetric, if n ?3, with q ∈[1, 2], , p ∈(1, ∞ ) and with , then, for all , , where the implicit equivalent positive constants are independent of f , denotes the class of Muckenhoupt weights, the reverse Hölder class, and D (L _w ) and the domains of L _w and , respectively. Copyright © 2016 John Wiley & Sons, Ltd.     

Well-posedness for general parametric quasi-variational inclusion problems

In this paper, we aim to suggest the new concept of well-posedness for the general parametric quasi-variational inclusion problems (QVIP). The corresponding concepts of well-posedness in the generalized sense are also introduced and investigated for QVIP. Some metric characterizations of well-posedness for QVIP are given. We prove that under suitable conditions, the well-posedness is equivalent to the existence of uniqueness of solutions. As applications, we obtain immediately some results of well-posedness for the parametric quasi-variational inclusion problems, parametric vector quasi-equilibrium problems and parametric quasi-equilibrium problems.     

球面上具有四个不同主曲率的Moebius等参超曲面

设x:M→S~(n+1)(n≥5)是(n+1)-维单位球面上不含脐点的超曲面,在S~(n+1)的Moebius变换群下浸入x的四个基本不变量是:Moebius度量g;Moebius第二基本形式B;Moebius形式Φ和Blaschke张量A.本文给出S~(n+1)上具有重数1,1,1,m(m≥2)的四个不同Moebius主曲率的Moebius等参超曲面的分类.     

Fermat point for a triangle in three dimensions using the taxicab metric

This article explores the process of finding the Fermat point for a triangle ABC in three dimensions. Three examples are presented in detail using geometrical methods. A delightfully simple general method is then presented that requires only the comparison of coordinates of the vertices A, B and C.