Central configurations of the collinear three-body problem and singular surfaces in the mass space

This Letter is to provide a new approach to study the phenomena of degeneracy of the number of the collinear central configurations under geometric equivalence. A direct and simple explicit parametric expression of the singular surface H₃ is constructed in the mass space (m₁,m₂,m₃)∈³(R⁺). The construction of H₃ is from an inverse respective, that is, by specifying positions for the bodies and then determining the masses that are possible to yield a central configuration. It reveals the relationship between the phenomena of degeneracy and the inverse problem of central configurations. We prove that the number of central configurations is decreased to 3!/2−1=2, m₁, m₂, and m₃ are mutually distinct if m∈H₃. Moreover, we know not only the number of central configurations but also what the nonequivalent central configurations are.     

Fluorescent Triphenyl Substituted Maleimide Derivatives: Synthesis,Spectroscopy and Quantum Chemical Calculations

In this paper we describe a semi-empirical quantum method for predicting the wavelength of maximum fluorescence excitation and emission for several known and new maleimide derivatives. All new maleimides, containing a N-Benzyl attachment, were successfully synthesised via a tandem Suzuki reaction with aryl boronic acids containing either an electron donating, electron withdrawing functional groups. Absorption and emission spectra calculated using the semi-empirical AM1 method with excited state ZINDO calculations proved more reliable than either Hartree-Fock Configuration interaction or time dependent density functional methods. Calculated absorption and emission wavelengths were compared with 26 experimental spectra from known or newly synthesised maleimides and found to have provide reasonable predictions, with an average deviation of less the 6% for absorption maxima and less than 4% for emission peaks. The described method provides a strong benchmark for the accuracy that can be expected from theoretical predictions of fluorescence spectra.     

Effect of Injection Parameters and Addition of Nanoscale Materials on the Shrinkage of Polypropylene Copolymer

The effect of variation of injection conditions and addition of nano-calcium carbonate (CaCO₃), nano-silicon dioxide (SiO₂) and full-vulcanized nano-powdered styrene butadiene rubber (PSBR) on the shrinkage of injection-molded polypropylene-ethylene copolymer (90/10, co-PP) were investigated. The results showed that the shrinkage was different for different locations along the flow path. The shrinkage in the length direction of the injection-molded sample varied with the adjustment of the processing parameters, while the shrinkage in the width and thickness direction was almost unchanged. The addition of nano-CaCO₃ and PSBR decreased the shrinkage of co-PP, while the shrinkage of co-PP/ SiO₂ composite was almost unchanged.     

Changes in the Structural Dimensionality of Selenidostannates in Ionic Liquids: Formation,Structures, Stability,and Photoconductivity

In situ transformations of selenidostannate frameworks in ionic liquids (ILs) were initiated by treatment of the starting phase K₂[Sn₂Se₅] and the consecutive reaction products by means of temperature increase and/or amine addition. Along the reaction pathway, the framework dimensionalities of the five involved selenidostannate anions develop from 3D to 1D and back, both in top‐down and bottom‐up style. Addition of ethane‐1,2‐diamine (en) led to the reversion of the 2D→1D step from 2D‐{[Sn₂₄Se₅₆]^16?} to 1D‐{[Sn₆Se₁₄]^4?}. As rationalized by DFT investigations, the 2D anion is thermodynamically favored. Photoconductivity measurements reveal that all samples show Schottky contact behavior with absolute thresholds below 10 V. One of the samples exhibits conductive states within the energy range of visible photons.     

Synthesis and optical behaviour of hydrogen-bonded liquid crystals based on a chiral pyridine derivative

Three series of cholesteryl-containing supramolecular hydrogen-bonded (H-bonded) liquid crystal (LC) complexes with different number of fluoro-substituent were synthesised and characterised. Cholesteryl isonicotinate as proton acceptor and 4-n-alkoxybenzoic acids with or without fluoro-substituent as proton donor had been mixed in tetrahydrofuran to obtain H-bonded LC complexes. The effect of lateral substitution and the length of terminal chain in the H-bonded precursors on the formation of the supramolecular complexes had been examined. It was found that the introduction of fluoro substituent on the induced mesogens could widen the molecular width and thus reduce the molecular aspect ratio of the complexes, therefore it could lead to compress the formation of the LCs. However, the fluoro substituent played a positive role in enhancing the intermolecular interactions and stabilising the H-bond structure of the complexes. The influence of terminal length on the mesogenic behaviours is also discussed. On increasing the spacer length, the clear point and the thermal range of induced mesophase-like cholesteric phase decreased, and an induced chiral smectic phase began to appear in some complexes with long terminal tails.     

Entanglement between two atoms in a damping Jaynes-Cummings model

The entanglement between two atoms in a damping Jaynes-Cummings model is investigated with different decay coefficients of the atoms from the upper level to other levels under detuning between the atomic frequency and the quantized light field frequency. The results indicate that the larger the decay coefficient is, the more quickly the entanglement decays. The detuning enhances the entanglement’s average value at long times. More importantly, the results show that the so-called sudden death effect can be avoided by enhancing the detuning or the decay coefficient.