An explicit compact universal space for real flows

The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.     

Partial widths and branching ratios for the emitted electron resulting from interatomic Coulombic decay in quantum wells heterostructure

Interatomic coulomb decay (ICD) is a decay process relying on the Coulombic interaction between neighbouring atoms, molecules or nanostructures. Due to this process, an electron is emitted into the continuum. We study the ICD process in a system of the double quantum well heterostructure and investigate how we can manipulate the structure's parameters such that a better detection of the ICD's emitted electron is achieved. For this purpose, we calculated the partial widths (PWs) and branching ratios (BRs) of the ICD's emitted electron to the left and right asymptotes of the heterostructure; these will give an estimation of the detection current. We manipulated the structure's parameters and took into account the repulsion from the electron in the ground state located in the left well. By introducing two small barriers in the vicinity of the right QW, we observed a BR three times larger than in the structure without the barriers. We also investigate the effect of repulsion due to the second electron. This work gives a better understanding of the dynamics of the scattered ICD's electron, and realisation of better design rules for future experimental observation of ICD in nanostructures.     

Distribution function estimates by Wasserstein metric and Bernstein approximation for C-1 functions

The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learningBased on the classical Bernstein approximation, a scheme is presented.To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1functions, which was rarely discussed in the classical approximation theoryFinally, we get a probability estimate by the statistical distance.     

一类Bernstein型算子线性组合加Jacobi权的逼近

给出了一类用广义杨辉三角阵定义的Bernstein型算子线性组合加Ja-cob i权的逼近在一致逼近意义下的特征刻划.     

Binding energy effects in the decay properties of charmonia

The di-gamma and di-gluon decay widths of P-wave cc mesons are computed in nonrelativistic phenomenological quark-antiquark potential of the type V (r) =-4 3 α s r+ Ar ν with different choices of ν using spectroscopic parameters.The numerically obtained radial solutions are employed to obtain the di-gamma and di-gluon decay widths.The computed decay widths are consistent with other model predictions as well as with the known experimental values in the range of potential index 0.7 ≤ν≤ 1.1.     

Line shape analysis of two-colour photoassociation spectra on the example of the Cs ground state

Two-photon photoassociation spectra in a Λ-type excitation scheme are analysed under the systematically varied experimental conditions of frequency detunings and laser intensities. Line shape fits are presented as well as the investigation of intensity and detuning dependent line shifts. From both we determine the attained spectroscopic precision, that is corrected for a systematic line shift due to the thermal distribution of atoms in the trap. An energy correction for this effect is given. Information about the feasibility of generating translationally cold molecules in a well defined rotational and vibrational level by the photoassociation process is derived from the analysis. Received 21 May 2002 Published online 15 October 2002 RID="a" ID="a"Current address e-mail: christian.lisdat@ptb.de RID="b" ID="b"e-mail: pierre.pillet@lac.u-psud.fr     

Stable constant mean curvature hypersurfaces in ℝ n+1 and ℍ n+1(−1)

In this paper, we show that all complete stable hypersurfaces in ⁿ⁺¹(or ⁿ⁺¹ (-1)) (n = 3, 4, 5) with constant mean curvature H > 0 (or H > 1, respectively) and finite L ² norm of traceless second fundamental form are compact geodesic spheres. Keywords: stable hypersurface, constant mean curvature, isometric immersion, Bernstein theorem.*Supported by PolyU grant G-T575.**Partially supported by CNPq of Brazil.     

激光金等离子体中Au~(49+)能级寿命的相对论多组态计算

根据扩展的相对论多组态Dirac Fock理论,采用"多功能相对论原子结构程序",计算了类锌Au49+的能级寿命、能级宽度和光谱跃迁波长。计算所得的波长值与实验结果符合较好;能级寿命与能级宽度的大小关系符合海森堡的能量与时间测不准原理。