A Criterion for Projective Modules

In case G is a finite group, there is a well-known criterion for projective modules: A ? G-module M is projective if and only if it is ? -free and has finite projective dimension. We first investigate whether only finite groups satisfy the above criterion. In the class of groups L H 𝔉, we conclude that this is true. Secondly, we consider the problem when a stably flat Γ-module is projective, where Γ is an arbitrary group. We show that if Γ is an L H 𝔉-group, then every stably flat cofibrant ? Γ-module is projective.     

生长温度对纳米氧化锌场发射性能的影响

采用锌粉和银粉为蒸发源,用热蒸发法不同温度下制备了四针状纳米氧化锌,并以单独的锌粉做对照。采用扫描电子显微镜(SEM)观察其形貌,X射线衍射(XRD)谱表征其晶体结构。采用丝网印刷方法将其制备为场致电子发射阴极,将阴极与印刷有荧光粉的阳极板组装成二极结构场致发射显示屏,并进行了场致电子发射特性对比实验。结果表明较高温度制备的氧化锌具有较好的场致发射性能;掺杂银粉的蒸发源制备的样品的发射性能明显优于没有掺杂银粉的样品。实验证明ZnO是一种优良的场致发射冷阴极材料,在真空电子方面具有广阔的应用前景。     

On Gorenstein Projective Dimensions of Unbounded Complexes

Let R → S be a ring homomorphism and X be a complex of R-modules. Then the complex of S-modules S?_R~L X in the derived category D(S) is constructed in the natural way. This paper is devoted to dealing with the relationships of the Gorenstein projective dimension of an R-complex X(possibly unbounded) with those of the S-complex S?_R~L X.It is shown that if R is a Noetherian ring of finite Krull dimension and φ : R → S is a faithfully flat ring homomorphism, then for any homologically degree-wise finite complex X, there is an equality Gpd_RX = GpdS(S?_R~L X). Similar result is obtained for Ding projective dimension of the S-complex S?_R~L X.     

Flat Complex Vector Bundles,the Beltrami Differential and W-Algebras

Since the appearance of the paper by Bilal et al. in 1991, it has been widely assumed that W-algebras originating from the Hamiltonian reduction of an SL(n,C)-bundle over a Riemann surface give rise to a flat connection, in which the Beltrami differential may be identified. In this Letter, it is shown that the use of the Beltrami parametrization of complex structures on a compact Riemann surface over which flat complex vector bundles are considered, allows the construction of the above mentioned flat connection. It is stressed that the modulus of the Beltrami differential is of necessity less than one, and that solutions of the so-called Beltrami equation give rise to an orientation-preserving smooth change of local complex coordinates. In particular, the latter yields a smooth equivalence between flat complex vector bundles. The role of smooth diffeomorphisms which induce equivalent complex structures is specially emphasized. Furthermore, it is shown that, while the construction given here applies to the special case of the Virasoro algebra, the extension to flat complex vector bundles of arbitrary rank does not provide generalizations of the Beltrami differential usually considered as central objects for such non-linear symmetries.     

Electrochromic Detection of Latent Fingermarks on Metal Surface Using 1,1′-Dibenzyl-4,4′-bipyridinium Dichloride

The electrochromic detection of latent fingermarks on polished or unpolished, flat or curved metal surfaces is described using electrochromic material, 1,1’-dibenzyl-4,4’-bipyridinium dichloride. The surface area covered by fingermarks acts as an insulating mask, causing 1,1’-dibenzyl-4,4’-bipyridinium dichloride to change color and produce inversed images of the fingermark. By changing the applied potential, the optical properties of 1,1’-dibenzyl-4,4’-bipyridinium dichloride can be continuously and reversibly adjusted to optimize the visual contrast of fingermarks, so as to realize the detection of latent fingermarks on stainless steel surface. It is demonstrated that the fabricated electrochromic devices can detect the fingermarks on these types of surfaces within twenty seconds at −1.0∼−2.0 V. This work can qualify as a tangible improvement in fingermark detection of the natural fingermarks on the never-cleaned (more than 3 years) and curved surfaces of daily-used container, e. g. cup, and the handle of cleaning tool, mop.     

Nayatani's metric and conformal transformations of a Kleinian manifold

According to Schoen and Yau (1988), an extensive class of conformally flat manifolds is realized as Kleinian manifolds. Nayatani (1997) constructed a metric on a Kleinian manifold which is compatible with the canonical flat conformal structure. He showed that this metric has a large symmetry if is a complete metric. Under certain assumptions including the completeness of , the isometry group of coincides with the conformal transformation group of . In this paper, we show that may have a large symmetry even if is not complete. In particular, every conformal transformation is an isometry when corresponds to a geometrically finite Kleinian group.

     

Compact Manifolds Covered by a Torus

Let X be a compact complex manifold which is the image of a complex torus by a holomorphic surjective map A→X. We prove that X is Kähler and that up to a finite étale cover, X is a product of projective spaces by a torus.