Effect of power-law nonlinearity on ${ \mathcal P }{ \mathcal T }$-symmetric optical system with fourth-order diffraction

Gaussian-type soliton solutions of the nonlinear Schrödinger (NLS) equation with fourth order dispersion, and power law nonlinearity in the novel parity-time (${ \mathcal P }{ \mathcal T }$)-symmetric quartic Gaussian potential are derived analytically and numerically. The exact analytical expressions of the solutions are obtained in the first two-dimensional (1D and 2D) power law NLS equations. By means of the linear stability analysis, the effect of power law nonlinearity on the stability of Gauss type solitons in different nonlinear media is carried out. Numerical investigations do confirm the stability of our soliton solutions in both focusing and defocusing cases, specially around the propagation parameters.     

Parallel and totally geodesic hypersurfaces of non-reductive homogeneous four-manifolds

We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.     

The differentiation operator in the space of uniformly convergent Dirichlet series

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half-planes for each . The properties of the formal inverse of the differentiation are also investigated.     

The powder X-band electron paramagnetic resonance spectroscopy of septet pyridyl-2,4,6-trinitrene

The first X-band EPR spectrum containing only non-overlapping signals of septet pyridyl-2,4,6-trinitrene and triplet pyridylnitrenes is reported. This spectrum was recorded after photolysis of 2,4,6-triazidopyridine in solid argon at 5 K. The zero-field splitting (ZFS) parameters of this trinitrene as well as of intermediate triplet mononitrenes and quintet dinitrenes formed at early stages of the photolysis were determined using the combination of modern computer line-shape spectral simulations and density functional theory (DFT) calculations. It was found that septet pyridyl-2,4,6-trinitrene has the record negative parameter D_S = −0.1031 cm⁻¹ among all known to date septet pyridyl-2,4,6-trinitrenes and may be of interest as a model multi-qubit spin system for investigations of quantum computation processing.     

Mechanically strong and stiff supramolecular polymers enabled by fiber reinforced long-chain alkane matrix

Fiber-reinforced-concrete (FRC) mechanism refers short discrete fibers that are uniformly distributed and randomly oriented, which offers an effective way to improve the mechanical performance of concrete. In the design of supramolecular polymers, an analogous concept of FRC appears to have been considered very rarely-although fibrous structure has been frequently observed/generated during the supramolecular polymerization. In this work, we apply the alkane thermosets, octadecane (C₁₈H₃₈) and tetracosane (C₂₄H₅₀), taking the role of “concrete”, and the low-molecular-weight monomer with long alkyl chains as the essential “fiber” component, to fabricate the “fiber reinforced supramolecular polymer”. Very much like FRC mechanism in material science, the resulting fiber reinforced supramolecular polymer thus exhibit unusually high mechanical strength and stiffness, which is unprecedented in the conventional supramolecular strategy.