Biminimal properly immersed submanifolds in the Euclidean spaces

We consider a complete nonnegative biminimal   submanifold M$M$ (that is, a complete biminimal submanifold with λ≥0$\lambda \ge 0$) in a Euclidean space E^N${\mathbb{E}}^N$. Assume that the immersion is proper  , that is, the preimage of every compact set in E^N${\mathbb{E}}^N$ is also compact in M$M$. Then, we prove that M$M$ is minimal. From this result, we give an affirmative partial answer to Chen’s conjecture. For the case of λ<0$\lambda <0$, we construct examples of biminimal submanifolds and curves.     

Percolation of even sites for random sequential adsorption

Consider random sequential adsorption on a red/blue chequerboard lattice with arrivals at rate 1 on the red squares and rate λ$\lambda$ on the blue squares. We prove that the critical value of λ$\lambda$, above which we get an infinite blue component, is finite and strictly greater than 1.     

Pontryagin duality for topological Abelian groups

A topological Abelian group G is Pontryagin reflexive, or P-reflexive for short, if the natural homomorphism of G to its bidual group is a topological isomorphism. We look at the question, set by Kaplan in 1948, of characterizing the topological Abelian groups that are P-reflexive. Thus, we find some conditions on an arbitrary group G that are equivalent to the P-reflexivity of G and give an example that corrects a wrong statement appearing in previously existent characterizations of P-reflexive groups. Received: 10 February 2000 / Published online: 17 May 2001     

Inhomogeneous discrete calderón reproducing formulas for spaces of homogeneous type

In this article a Littlewood-Paley theorem for a new kind of Littlewood-Paley g-functions over spaces of homogeneous type is presented. Based on it the authors establish inhomogeneous discrete Calder43;n reproducing formulas for spaces of homogeneous type, making use of Calder43;n-Zygmund operators.     

Pompeiu sets in compact Heisenberg manifolds

A necessary and sufficient condition is presented for a set to be a Pompeiu subset of any compact homogeneous space with a finite invariant measure. The condition, which is expressed in terms of the intertwining operators of each primary summand of the quasi-regular representation, is then interpreted in the case of the compact Heisenberg manifolds. Examples are presented demonstrating that the condition to be Pompeiu in these manifolds is quite different from the corresponding condition for a torus of the same dimension. This provides a contrast with the existing comparison between the Heisenberg group itself and Euclidean space in terms of Pompeiu sets. In addition, the closed linear span of all translates of any square integrable function on any compact homogeneous space is determined.     

Cr3+掺杂Ca4HfGe3O12宽带近红外荧光粉的发光特性及应用

近红外荧光粉在生物活体成像领域展现出重要的应用前景。但活体成像用近红外荧光粉存在种类匮乏、耐温性差等瓶颈问题。采用固相法合成了宽带近红外Ca₄HfGe₃O₁₂∶ xCr^3&#43;(0≤x≤0.09)荧光粉。X射线衍射和能谱分析的结果表明Cr^3&#43;离子成功进入Ca₄HfGe₃O₁₂晶格。在469 nm蓝光激发下,Ca₄HfGe₃O₁₂∶xCr^3&#43;荧光粉发射出690~1 200 nm的宽带近红外光,峰值波长为825 nm (⁴T₂-⁴A₂),半高宽达到141 nm,Cr^3&#43;掺杂最佳浓度为0.03。依据激发光谱峰形和寿命衰减行为,证实Cr^3&#43;仅占据基质中一种阳离子格位。Ca₄HfGe₃O₁₂∶0.03Cr^3&#43;荧光粉的荧光量子效率为33.63%,该荧光粉发射光谱在400 K下的积分面积为室温下的60.5%,表明该样品具有优良的热稳定性。采用自制近红外荧光粉转换器件照射人手掌和滤波片遮挡的水果,观察到清晰地静脉血管和遮挡水果的轮廓。     

K+掺杂双钙钛矿Cs2AgInCl6的发光性质

采用固相球磨法制备了K^&#43;掺杂双钙钛矿Cs₂AgInCl₆纳米材料,该方法无需配体辅助,绿色环保。通过X射线衍射和拉曼光谱对晶体结构进行研究,通过激发光谱、发射光谱和时间分辨光谱对其发光性能进行研究。结果表明,Cs₂AgInCl₆为立方晶体,属于Fm3m空间群,由于宇称禁戒跃迁,其荧光量子产率(PLQY)低,小于0.1%。低于60%的K^&#43;掺杂主要取代Ag^&#43;的位置,引起Cs₂AgInCl₆的晶格膨胀,消除了晶格结构的反演对称性,打破了宇称禁戒跃迁,掺杂后Cs₂AgInCl₆的光致发光强度显著增强。K^&#43;的最佳掺杂比例为40%,Cs₂Ag_0.6K_0.4InCl₆材料发射中心波长为640 nm,半高宽为180 nm,平均荧光寿命达到29.2 ns,PLQY达到10.5%。当K^&#43;掺杂比例超过60%,K^&#43;开始取代Cs^&#43;的位置,产物发生相变,出现立方相的Cs_2-xK_1&#43;x-yAg_yInCl₆和单斜相的Cs_2-xK_1&#43;xInCl₆产物,这些产物由于强电子-声子耦合,非辐射复合占据主导地位。