Minimal Submanifolds in a Locally Symmetric and Conformally Flat Space

We study minimal submanifolds in the locally symmetric and conformally flat Riemannian manifold and generalize Yau's result obtained in J. Amer. Math. 97 (1975), 76–100.     

一维ZnO纳米结构的电子场发射研究

在大量制备一维ZnO纳米结构的基础上,研究了这些纳米结构的场发射性能。对于四角状ZnO纳米结构,获得1.0m Ac/m2的电流密度只需要4.5V/μm的电场;对于线状Z nO纳米结构,获得1.0mAc/m 2的电流密度需要6.5V/μm的电场。由于其特殊的结构,四角状ZnO一维纳米结构在真空电子器件方面有很好的应用前景。     

A Penrose-like inequality for maximal asymptotically flat spin initial data sets

We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary, dimensionless geometric constants and some normalized Sobolev ratio.     

Reconfiguration Aspects and a Reconfigurable Outer Block Interleaver for 3G Applications

Reconfiguration concept represents reconfigurable functionalities of the radio interface for mobile radio systems. Particularly for the physical layer, some possible reconfigurable architectures can be identified. We focus on outer interleaving for turbo codes, which can improve their performance in flat Rayleigh fading environment. The larger the number of columns in the outer interleaver, the better is the performance, but with the penalty of more complexity and delay. Furthermore, an incorrect choice of the number of columns can increase the bit and frame error rates. Therefore, it would be advantageous to reconfigure the outer interleaver in different operating environments with the optimum number of columns. Using two different data frame lengths, in this contribution simulation results are presented for the four possible outer block interleaver configurations specified for the 3GPP mobile standard in the case of flat Rayleigh fading channel. It is shown that different operating environments require an optimum number of columns in terms of bit error rate and frame error rate performance. Finally, frame fade duration is considered and the effect of the product of the Doppler frequency with the frame duration on the performance for the four different 3GPP outer block interleaver configurations is discussed. Costas Chaikalis was born in Athens, Greece, on March 7, 1973. He received the B.Sc. degree in electrical engineering in 1995 from Technological Educational Institute of Lamia, Greece. He also received the M.Sc. and Ph.D. degrees from Department of Electronics and Telecommunications, University of Bradford, Bradford, UK in 1999 and 2003, respectively. During his doctoral studies he worked as a Research Assistant for Mobile Virtual Center of Excellence (Mobile VCE), Terminals Group, UK. Since 2003, he is a lecturer in the Department of Electrical Engineering, Technological Educational Institute of Lamia, Greece. His research interests are in all areas of mobile communications but especially in forward error correction coding, reconfigurable (software radio) architectures, cross layer architectures and DSP applications.     

Spectral Properties of Four-Dimensional Compact Flat Manifolds

We study the spectral properties of a large class of compact flat Riemannian manifolds of dimension 4, namely, those whose corresponding Bieberbach groups have the canonical lattice as translation lattice. By using the explicit expression of the heat trace of the Laplacian acting on p-forms, we determine all p-isospectral and L-isospectral pairs and we show that in this class of manifolds, isospectrality on functions and isospectrality on p-forms for all values of p are equivalent to each other. The list shows for any p, 1 ≤ p ≤ 3, many p-isospectral pairs that are not isospectral on functions and have different lengths of closed geodesics. We also determine all length isospectral pairs (i.e. with the same length multiplicities), showing that there are two weak length isospectral pairs that are not length isospectral, and many pairs, p-isospectral for all p and not length isospectral. Mathematics Subject Classifications (2000): 58J53, 58C22, 20H15.     

Some conformally flat spin manifolds, Dirac operators and automorphic forms

In this paper we study Clifford and harmonic analysis on some examples of conformal flat manifolds that have a spinor structure, or more generally, at least a pin structure. The examples treated here are manifolds that can be parametrized by U/Γ where U is a subdomain of either Sn or Rn and Γ is a Kleinian group acting discontinuously on U. The examples studied here include RPn and the Hopf manifolds S¹×Sn−1. Also some hyperbolic manifolds will be treated. Special kinds of Clifford-analytic automorphic forms associated to the different choices of Γ are used to construct explicit Cauchy kernels, Cauchy integral formulas, Green's kernels and formulas together with Hardy spaces and Plemelj projection operators for Lp spaces of hypersurfaces lying in these manifolds.     

GENERALIZED CIRCLES AND THEIR CONFORMAL MAPPING IN A SUBSPACE OF A WEYL SPACE

The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions under which a generalized concircular transformation of one Weyl space onto another induces a generalized transformation oil its subspaces. Finally, it is shown that any totally geodesic or totally umbilical hypersurface of a generalized concircularly flat Weyl space is also generalized concircularly flat.     

A note on 4-dimensional locally conformally flat Walker manifolds

A 4-dimensional Walker metric on a semi Riemanian manifold M, for the canonical metric with c = 0, have been investigated by M. Chaichi, E. García—Río and Y. Matsushita. The paper generalizes these notions to the case of constant c ≠ 0. Specially the form of defining functions of this metric in locally conformally flat 4-dimensional Walker manifolds is found.     

局部对称共形平坦黎曼流形中的极小子流形

对局部对称共形平坦黎曼流形中具有平坦法丛的极小子流形作了一些讨论，得到了极小子流形是全测地的两个充分条件。     

On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds

In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature are unique. Therefore we are able to conclude that the foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass outside a given compact subset is unique.