Smith equivalence of representations for finite perfect groups

Using smooth one-fixed-point actions on spheres and a result due to Bob Oliver on the tangent representations at fixed points for smooth group actions on disks, we obtain a similar result for perfect group actions on spheres. For a finite group , we compute a certain subgroup of the representation ring . This allows us to prove that a finite perfect group has a smooth -proper action on a sphere with isolated fixed points at which the tangent representations of are mutually nonisomorphic if and only if contains two or more real conjugacy classes of elements not of prime power order. Moreover, by reducing group theoretical computations to number theory, for an integer and primes , we prove similar results for the group , , or . In particular, has Smith equivalent representations that are not isomorphic if and only if , , .

     

Boundary Amenability of Groups and Positive Scalar Curvature

We show that if a finitely presented discrete group acts amenably on the boundary of a metric compactification of itself, then the Gromov–Lawson–Rosenberg conjecture holds for . Thus, if M is a compact aspherical Spin manifold with fundamental group , then M does not admit a Riemannian metric with positive scalar curvature. The class of groups having such a property includes hyperbolic groups and amenable groups and is closed under semidirect product.     

On the Structure of Cimpact Simply Connected Manifolds of Positive Sectional Curvature

We present a first structure theorem for compact simply connected positively curved manifolds with arbitrarily small pinching constants: For each nN and 0<1, there exists a positive number V = V(n,) such that if (M,g) is a compact simply connected n-dimensional Riemannian manifold with sectional curvature 0相似文献   

Group actions on arrangements of linear subspaces and applications to configuration spaces

For an arrangement of linear subspaces in that is invariant under a finite subgroup of the general linear group we develop a formula for the -module structure of the cohomology of the complement . Our formula specializes to the well known Goresky-MacPherson theorem in case , but for the formula shows that the -module structure of the complement is not a combinatorial invariant. As an application we are able to describe the free part of the cohomology of the quotient space . Our motivating examples are arrangements in that are invariant under the action of by permuting coordinates. A particular case is the ``-equal' arrangement, first studied by Björner, Lovász, and Yao motivated by questions in complexity theory. In these cases and are spaces of ordered and unordered point configurations in many of whose properties are reduced by our formulas to combinatorial questions in partition lattices. More generally, we treat point configurations in and provide explicit results for the ``-equal' and the ``-divisible' cases.

     

Rational Structure of X(N) over Qand Explicit Galois Action on CM Points

This paper reviews a less known rational structure on the Siegel modular variety X(N) = Γ(N)\H_g over Q for integers g, N ≥ 1. The author then describes explicitly how Galois groups act on CM points on this variety. Finally, another proof of the Shimura reciprocity law by using the result and the q-expansion principle is given.     

Photomechanical transduction in Amoeba proteus: An action spectrum

An action spectrum for the light-induced stop reaction of amoeboid movement in Amoeba proteus has been determined. The amoebae show a sensitivity in the blue with a peak between 440 and 470 nm. This agrees with the older qualitative observations (M. R. Harrington and E. Leaming, Am. J. Physiol., 3 (1900) 9 - 16; S. O. Mast, J. Exp. Zool., 9 (1910) 265 - 277) but no positive phototaxis was found (A. A. Schaeffer, Biol. Bull., 32 (1917) 45 - 74). Absorption spectra of suspensions of whole cells have an absorption band with a similar spectral peak. The response follows the Bunsen-Roscoe law and the sensitivity appears to be greater at low oxygen tension. The photomechanical link in this response, i.e. conversion of a light stimulus to a change in motion, suggests a primitive mechanism of avoidance that may have evolutionary implications (R. M. Eakin, Evol. Biol., 2 (1968) 194 - 242; L. von Salvini-Plawen and E. Mayr, Evol. Biol., 10 (1977) 207 - 263).     

On Riemannian coverings of manifolds admitting locally splitting actions

By studying the structure of certain covering manifolds, associated with a series of subgroups of ₁(M), we approximate the structure of the Riemannian manifoldM, provided that it admits a locally splitting action. The above series arises because of the local splitting of the action and the study is carried out via initial data. Also, we indicate how manifolds without conjugate points can be investigated using locally splitting actions of abelian Lie groups.     

Progress on Detection of Metals Ions by Functional Nucleic Acids Biosensor

Functional nucleic acids are natural or artificial nucleic acid sequences with specific functions and special structures. A part of metal ions are essential trace elements of human health, but excessive metal ions will be harmful to human health. The functional nucleic acids are widely used for detection of metal ions because of its advantages such as easy modification, low price, high stability and strong specificity. This paper detailed the interaction between functional nucleic acids and metal ions, mainly including cutting type, link type, metal ion-mediated base pairing, click chemistry type, conformational change type, and other types. The biosensors based on the combination of functional nucleic acid with different signal output were then introduced. Finally, the research significance and existing problems of functional nucleic acid for metal ion detection were discussed. The future development trends and applications of functional nucleic acid biosensor were prospected.     

氯水的漂白作用原理探究

首先,通过对氯水体系中存在的化学过程进行全面深入地综合分析,旨在厘清氯水是由多种分子﹑多种离子和多种自由基组成的复杂的氧化还原系统;其次,通过设计6个实验对氯水在不同条件下的漂白作用进行科学探究,并对实验结果给予科学合理的解释;最后,科学地归纳出氯水的漂白作用是一个多种成分协同作用的过程,影响因素很多,但“主角”仍是次氯酸,并对其漂白作用的化学原理给予科学阐释。     

Physicochemical and antibacterial properties of polyurethane coatings modified by ZnO

The synthesis of polyurethane nanocomposite coatings containing 1% to 5% suitably dispersed ZnO by 1‐stage polyaddition process in the bulk using 4,4′‐methylenebis(cyclohexyl isocyanate), poly(ε‐caprolactone)diol, and 1,4‐butanediol was performed. Infrared and nuclear magnetic resonance spectra confirmed the structure of obtained polyurethanes. Scanning electron microscope and energy dispersive X‐ray analyzer methods showed randomly distributed ZnO in a polyurethane matrix. The differential scanning calorimetry and wide‐angle X‐ray diffraction patterns were used for the microstructural assessment of the obtained materials. Antimicrobial properties of ZnO and the effect of this modifier on the hydrophobicity of the coatings were demonstrated. The obtained coatings were characterized in terms of the mechanical properties and changes during incubation in a Baxter saline solution.