应用双相角结构不变量概率值分辨相角双银问题

分析了Harker作图法中在几何上不可分辨的双解的对称性, 将衍射的物理性质(双相角结构不变量的概率性质)附加到对称的双解上时, 发现它具有可能分辨的彩色对称性。因此, 把Hauptman 1982年的概率式同Harker作图法相结合, 得到了蛋白细胞色素C550的大约1000个相角的估计值, 并对误差来源及其影响做了计算。     

Optical Space of the Reissner-Nordström Solutions

We present an exhaustive discussion of the embedding diagrams for the optical geometry of the Reissner-Nordström solutions. Whereas in the black hole sector there are no qualitative differences with respect to the Schwarzschild case, the diagrams are considerably different if naked singularities are present. Our treatment is sufficiently general that it can be applied also to any other static spherically symmetric spacetime.     

Origin of Classical Singularities

We briefly review some results concerning theproblem of classical singularities in generalrelativity, obtained with the help of the theory ofdifferential spaces. In this theory one studies a givenspace in terms of functional algebras defined on it.Then we present a generalization of this methodconsisting in changing from functional (commutative)algebras to noncommutative algebras. By representingsuch an algebra as a space of operators on a Hilbertspace we study the existence and properties of variouskinds of singular space-times. The results obtainedsuggest that in the noncommutative regime, supposedly reigning in the Planck era, there is nodistinction between singular and non-singular states ofthe universe, and that classical singularities areproduced in the transition process from thenoncommutative geometry to the standard space-timephysics.     

New minimal hypersurfaces in and

We find a class of minimal hypersurfaces as the zero level set of Pfaffians, resp. determinants of real dimensional antisymmetric matrices. While and are congruent to the quadratic cone resp. Hsiang's cubic invariant in , (special harmonic ‐invariant cones of degree ⩾4) seem to be new.