Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.     

The Wigner–Yanase information can increase under phase sensitive incoherent operations

We found that the Wigner-Yanase skew information, which has been recently proposed as a measure of coherence in Girolami (2014), can increase under a class of operations which may be interpreted as incoherent following the framework of Baumgratz et al., while being phase sensitive.     

Nondestructive rare earth element imaging of fish teeth from deep‐sea sediments

X‐ray fluorescence computed tomography is an emerging imaging modality that allows for the nondestructive reconstruction of the internal distribution of elements within a sample. The common use of X‐ray excitation energy (up to approximately 20 keV) has necessitated the use of l ‐shell fluorescence for heavy elements. In this study, based on high energy X‐ray at BL13W1 of the Shanghai Synchrotron Radiation Facility, we employed high‐energy excitation for tomographic imaging of the heavy metals (rare earth elements) in fish teeth from deep‐sea sediments on the micrometer scale using K‐shell X‐ray fluorescence. The virtual cross‐sectional distribution of La, Ce, Pm, Pr, Nd, and Sm were obtained, thereby providing a feasible approach for analyzing the enrichment mechanism of rare earth elements. Copyright © 2015 John Wiley & Sons, Ltd.     

Black phosphorus saturable absorber for ultrafast mode‐locked pulse laser via evanescent field interaction

Black phosphorus, or BP, has found a lot of applications in recent years including photonics. The most recent studies have shown that the material has an excellent optical nonlinearity useful in many areas, one of which is in saturable absorption for passive mode‐locking. A direct interaction scheme for mode‐locking, however, has a potential to optically cause permanent damage to the already delicate material. Evanescent field interaction scheme has already been proven to be a useful method to prevent such danger for other 2‐dimensional nanomaterials. In this report, we have utilized the evanescent field interaction to demonstrate that the optical nonlinear characteristics of BP is sufficiently strong to use in such an indirect interaction method. The successful demonstration of the passive mode‐locking operation has generated pulses with the pulse duration, repetition rate, and time bandwidth product of 2.18 ps, 15.59 MHz, and 0.336, respectively.     

One-Pot Synthesis and Fungicidal Activities of Derivatives of Imidazo [2,1-b]-1,3,4-thiadiazol-5(6H)-one

The isothiocyanates 2, obtained from aza-Wittig reactions of vinyliminophosphoranes 1 with CS ₂ , reacted with hydrazine to give 3-amino-2-thioxo-4-imidazolidinones 4. One-pot reactions of 4, aromatic isocyanates, Ph ₃ P, C ₂ Cl ₆ , and Et ₃ N generated imidazo[2,1-b]-1,3,4-thiadiazol-5(6H)-ones 7. Compound 7 exhibited good fungicidal activities, especially against Sclerotinia sclerotiorum de Bary and Botrytis Cinerea Pers.     

The Synthesis and 31P NMR Spectral Studies of Cyclophosphazenes

A modified method for preparing large-scale quantities of pure hexachlorocyclophosphazene (N₃P₃Cl₆) and octachlorocyclotetraphosphazene (N₄P₄Cl₈), phosphorus pentachloride with ammonium chloride, in the presence of zinc chloride, has been developed. The time of the reaction and the quantities of the catalyst are also studied. It is found that the optimum reaction time is 1.5 h and by-products are remarkably reduced by addition of 10% zinc chloride. As indicated by the ³¹ P NMR spectra, the synthesis and separation of cyclophosphazenes can be accomplished in moderate yield of tetramer (39%) and good yield of trimer (83%).