Room squares with sub-squares

Suppose there is a Room square of side r. Then there is a Room square of side 4r + 1 with a sub-square of side r which is isomorphic to the original square.No example was known previously of a Room square of side s with a subsquare of side r where s ? 6r.     

Molecular distortions in crystalline 2-phenylethynylbenzoic acid

2-Phenylethynylbenzoic acid shows a short intramolecular 1,5 C=O···spC contact with no significant in-plane distortion of bonding geometry at the sp C atom. However, there are angular distortions at the second sp C atom and the adjacent ipso C atom of the benzene ring, most likely because of optimization of the packing arrangement. Crystal data: C₁₅H₁₀O₂, Mr = 222.23, a = 6.1890(10), b = 9.791(2), c = 18.849(4) Å, = 97.14(2)°, monoclinic, P2₁/n, Z = 4.     

Interactions between Functional Groups Part IV. The responses of four diazonium groups to adjacent electron-rich atoms in peri-substituted naphthalene and quinoline derivatives

Four peri-substituted naphthalene-1-diazonium cations all show short attractive interactions between an electron-rich atom of the peri-substituent and the α -N-atom of the diazonium group. These are interpreted as models for incipient nucleophilic attack on a N?N bond. The diazonium group is a better acceptor of electron density ‘through space’ than the NO₂ group, which parallels their relative ‘through-σ-bond’ inductive effects.     

Enhanced backscattering in a magnetic field

By means of numerical simulations the authors study the scattering of a beam of p-polarized light from a small RMS slope one-dimensional random surface on a semi-infinite metal or n-type semiconductor to which a constant magnetic field is applied. The surface is defined by the equation x₃=ξ(x₁), where the surface profile function ξ(x₁) is a stationary stochastic Gaussian process. The plane of incidence is the x₁x₃ plane, and the magnetic field is directed along the x₂-axis. In the presence of the magnetic field the dispersion curve for the surface polaritons supported by the surface in the absence of the random roughness becomes non-reciprocal, i.e. the wavenumber k₊(ω) for a surface polariton of frequency ω propagating in the +x₁-direction is unequal to the (magnitude of the) wavenumber k_-(ω) for a surface polariton of the same frequency propagating in the -x₁-direction. As a consequence of this they find that the peak in the angular distribution of the intensity of the incoherent component of the scattered light that is observed in the retroreflection direction in the absence of the magnetic field—enhanced backscattering—is shifted in the direction of larger scattering angles with increasing magnetic field strength. At the same time the width of the peak increases and its amplitude decreases. When the frequency of the incident light is high enough that the dispersion curve for surface polaritons on the planar surface becomes completely non-reciprocal, i.e. the surface polariton propagates only in the +x₁-direction but not in the -x₁-direction, the enhanced backscattering is completely suppressed. These results are interpreted as being due to the breakdown of the coherency between a given light/surface polariton path that contributes to backscattering and its time-reversed partner, caused by the removal of time-reversal symmetry from the scattering system by the application of the external magnetic field. They provide strong evidence for the fundamenlal role played by surface polaritons in the enhanced backscattering of light from small RMS slope random surfaces.     

The effect of high magnetic fields on degenerate band excitons in InSb

A variational technique is used to calculated the binding energy of degenerate band excitons in InSb as a function of magnetic field. the nonparabolicity of the conduction bands is taken into account and standard perturbation theory is used for deviation of the valence bands from the spherical. A comparison of the theoretical results and available experimental results is made.     

Nonlinear matrix solution of the Kohn-Hohenberg-Sham equation for electrons in a jellium slab

A new method is presented for the numerical solution of the Kohn- Hohenberg-Sham equation for the one-electron wavefunctions and energies for electrons in the presence of a jellium slab of finite thickness.     

Construction of skew Room squares

It is shown that the question of existence of skew Room squares is solved in all but finitely many cases.