Geometric Formulation and Multi‐dark Soliton Solution to the Defocusing Complex Short Pulse Equation

In the present paper, we study the defocusing complex short pulse (CSP) equations both geometrically and algebraically. From the geometric point of view, we establish a link of the complex coupled dispersionless (CCD) system with the motion of space curves in Minkowski space , then with the defocusing CSP equation via a hodograph (reciprocal) transformation, the Lax pair is constructed naturally for the defocusing CSP equation. We also show that the CCD system of both the focusing and defocusing types can be derived from the fundamental forms of surfaces such that their curve flows are formulated. In the second part of the paper, we derive the defocusing CSP equation from the single‐component extended Kadomtsev‐Petviashvili (KP) hierarchy by the reduction method. As a by‐product, the N‐dark soliton solution for the defocusing CSP equation in the form of determinants for these equations is provided.     

Structural analysis of the phase separation in magnetic semiconductor (Zn,Cr)Te

We have studied the structural properties of the phase separation in Zn_1−xCr_xTe films grown by MBE with a relatively high Cr composition x∼0.2. In the combined analyses using TEM and EELS, it has been revealed that the Cr-aggregated regions are composed of precipitates of the hexagonal structure, which are formed in a particular crystallographic relation with the zinc-blende (ZB) structure of the matrix that the c-plane of the hexagonal structure nearly parallel to the (1 1 1) plane of the ZB structure. In the XRD measurements, the diffraction from the hexagonal precipitates has been detected in the ω-scan. From the measurements on the series of films grown at different temperatures, it has been suggested the hexagonal precipitates were formed in a larger quantity with the increase in growth temperature.     

Observation of temporal vector soliton propagation and collision in birefringent fiber

We report the experimental observation of temporal vector soliton propagation and collision in a linearly birefringent optical fiber. To the best of the authors' knowledge, this is both the first demonstration of temporal vector solitons with two mutually incoherent component fields, and of vector soliton collisions in a Kerr nonlinear medium. Collisions are characterized by an intensity redistribution between the two components, and the experimental results agree with numerical predictions of the coupled nonlinear Schr?dinger equation.     

Inclusion of aliphatic alcohols in pockets of (S)-threonyl-(S)-phenylglycine using grinding method

Inclusion compounds of a dipeptide, (S)-threonyl-(S)-phenylglycine (Thr-Phg), with several aliphatic alcohols were easily prepared by grinding them in a mortar. Thr-Phg molecules arranged in antiparallel to construct a sheet, and guest alcohols were accommodated in a chiral pocket between the sheets. 3-Butyn-2-ol and 2-butanol were included with moderate enantioselectivity, 57% ee (R) and 49% ee (R), respectively. The role of the hydroxy group of Thr-Phg is not only to construct the unique pocket but also to capture guest alcohols by hydrogen bonding.     

Recent development for enantioselective synthesis of aromatic compounds from alkynes via metallacyclopentadienes

Metallacyclopentadiene, which is recognized as a metallo‐heterocycle, is an important intermediate for the formation of aromatic derivatives. In this short review, we summarized the recent advance on construction of axial, central, planar, and helical chirality by transition‐metal‐catalyzed aromatic compounds formation via metallacyclopentadienes. J. Heterocyclic Chem., (2011).     

Novel Flavonoids in Dragon's Blood of Daemonorops draco

The three novel methylene bis[flavonoids] 1 – 3 , the novel 2‐flavene 4 , the new naturally occurring flavan 5 , and the new retro‐dihydrochalcone 6 were isolated from dragon's blood of Daemonorops draco, together with seven known compounds. The structures were elucidated by extensive 1D‐ and 2D‐NMR spectroscopic analysis.     

Trace inequalities for products of matrices

In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.