Periodicity of Two-Dimensional Bonding of Main Group Elements

In the periodic table the position of each atom follows the ‘aufbau’ principle of the individual electron shells. The resulting intrinsic periodicity of atomic properties determines the overall behavior of atoms in two-dimensional (2D) bonding and structure formation. Insight into the type and strength of bonding is the key in the discovery of innovative 2D materials. The primary features of 2D bonding and the ensuing monolayer structures of the main-group II–VI elements result from the number of valence electrons and the change of atom size, which determine the type of hybridization. The results reveal the tight connection between strength of bonding and bond length in 2D networks. The predictive power of the periodic table reveals general rules of bonding, the bonding-structure relationship, and allows an assessment of published data of 2D materials.     

Three-dimensional Schwarzschild spacetimes

In the following we find all of the three-dimensional flat spacetimes which are static and rotationally symmetric.     

Ueber die Biegung und Drillung eines unendlich dünnen elastischen Stabes,dessen eines Ende von einem Kräftepaar angegriffen wird

Ohne ZusammenfassungMit einer lithographirten Tafel.Ein Auszug aus dieser Untersuchung ist erschienen in den Sitzungsberichten der bayer. Acad. d. Wissensch. 1883, 82–110.     

Iterative regularization methods for atmospheric remote sensing

In this paper we present different inversion algorithms for nonlinear ill-posed problems arising in atmosphere remote sensing. The proposed methods are Landweber's method (LwM), the iteratively regularized Gauss-Newton method, and the conventional and regularizing Levenberg-Marquardt method. In addition, some accelerated LwMs and a technique for smoothing the Levenberg-Marquardt solution are proposed. The numerical performance of the methods is studied by means of simulations. Results are presented for an inverse problem in atmospheric remote sensing, i.e., temperature sounding with an airborne uplooking high-resolution far-infrared spectrometer.     

2,4,6‐Trifluoropyrimidine. Reactions with nitrogen nucleophiles

In a continuation of our studies involving the nucleophilic displacement of one of the chlorines from 2,4,6‐trichloropyrimidine, we now report the initial displacement of one of the fluorine atoms from 2,4,6‐trifluoropyrimidine using both aliphatic and aromatic amines. The monosubstitution products favor 2‐substitution with ammonia and ethanolamine while aniline gave the 4‐substituted derivative as the preferred product.