Gauge and Bäcklund transformations for the generalized sine-Gordon equation and its η-dependent modified equation

We study the generalized sine-Gordon hierarchy and its associated-dependent modified sine-Gordon hierarchy. Two Bäcklund transformations for these two families are constructed. One of them is a generalization of the Bäcklund transformations of Wadatiet al. and the other one is new. Gauge transformations of a relevant AKNS system are employed to reduce the integration of these equations via the Bäcklund transformations to quadratures. Three generations of explicit solutions of the sine-Gordon equation are presented.     

A rhodium‐catalyzed route for oxidative coupling and cyclization of 2‐aminobenzyl alcohol with ketones leading to quinolines

2‐Aminobenzyl alcohol undergoes oxidative cyclization with aryl(alkyl), alkyl(alkyl) and cyclic ketones in dioxane at 80° in the presence of a catalytic amount of RhCl(PPh₃)₃ along with KOH to afford the corresponding quinolines in good yields. The catalytic pathway seems to be proceeded via a sequence involving initial oxidation of 2‐aminobenzyl alcohol to 2‐aminobenzaldehyde by a rhodium catalyst, cross aldol reaction between 2‐aminobenzaldehyde and ketones, and cyclodehydration.     

Light-emitting tridentate cyclometalated platinum(II) complexes containing sigma-alkynyl auxiliaries: tuning of photo- and electrophosphorescence

The synthesis and structural, photophysical, electrochemical, and electroluminescent properties of a class of platinum(II) complexes bearing sigma-alkynyl ancillary ligands, namely [(C/N/N)Pt(C[triple bond]C]nR] [H(C/N/N) = 6-aryl-2,2'-bipyridine; n = 1-4; R = aryl, alkyl, or trimethylsilyl], have been studied. Substituents with different steric and electronic properties were introduced into the tridentate cyclometalating and arylacetylide ligands, and the pi-conjugation length of the oligoynyl moiety was homologously extended from ethynyl to octatetraynyl. The X-ray crystal structures of several derivatives confirm the Pt-(CC) ligation and reveal various intermolecular interactions, such as pi-pi, Pt...Pt, and C-H...F-C. The complexes display good thermal stability and intense phosphorescence in fluid and glassy solutions with high quantum yields and microsecond lifetimes. Their emission energies are sensitive to solvent polarity, the electronic affinities of the substituents on both the cyclometalating and arylacetylide groups, and the length of the oligoynyl ligand. By choosing appropriate cyclometalating and sigma-alkynyl ligands, the emission color of this class of platinum(II) complexes can be tuned from green-yellow to saturated red. In addition to (3)MLCT [Pt(5d) --> pi*(C/N/N)] and (3)IL(C/N/N), intriguing (3)IL(alkynyl) excited states localized on -(C[triple bond]C)(4)- and -(C[triple bond]Cpyrenyl-1) moieties that afford narrow-bandwidth emissions have been observed. Selected Pt(II) complexes were doped into the emissive region of multilayer, vapor-deposited organic light-emitting diodes. The tunable electrophosphorescence energy resembles that recorded in fluid solutions for these emitters, and the devices exhibit high luminance and efficiencies (up to 4.2 cd A(-1)).     

Potential distribution in the solution interface of a scanning tunneling microscope

The linearized Poisson—Boltzmann equation is solved in the region between a sphere and a plane, which is modelling the electrolyte solution interface between the tip and the substrate in a scanning tunneling microscope. A series expansion in modified Bessel functions and Legendre polynomials, which are solutions to the linearized Poisson—Boltzmann equation, is used to fit the boundary conditions. Another numerical method of finite difference is also used with the domain transformed into bispherical coordinates. Results for cases of different potential values on the boundary surfaces and different distances of the sphere from the plane are presented.     

New C2-symmetric 2,2′-bipyridine crown macrocycles for enantioselective recognition of amino acid derivatives

A series of new C₂-symmetric 2,2′-bipyridine-contaning crown macrocycles 1-4 has been developed for enantiomeric recognition of amino acid derivatives. These new macrocycles have been showed to be strong complexing agents for primary organic ammonium salts (with K up to 4.83×10⁵ M⁻¹ and −ΔG₀ up to 32.4 kJ mol⁻¹) and also useful chromophores for UV-vis titration studies. These macrocyclic hosts exhibited enantioselective binding towards the (S)-enantiomer of phenylglycine methyl ester hydrochloride (Am1) with K_(S)/K_(R) up to 2.10 (ΔΔG₀=−1.84 kJ mol⁻¹) in CH₂Cl₂ with 0.25% CH₃OH. The structure-binding relationship studies showed that the aromatic subunit and the ester group of the ammonium guests are both important for good enantioselectivity. In addition, the host-guest complexes have been studied using various NMR experiments.     

Colloidal adhesion of phospholipid vesicles: high-resolution reflection interference contrast microscopy and theory

High-resolution reflection interference contrast microscopy (HR-RICM) was developed for probing the deformation and adhesion of phospholipid vesicles induced by colloidal forces on solid surfaces. The new technique raised the upper limit of the measured membrane–substrate separation from 1 to 4.5 μm and improved the spatial resolution of the heterogeneous contact zones. It was applied to elucidate the effects of wall thickness, pH and osmotic stress on the non-specific adhesion of giant unilamellar vesicles (ULV) and multilamellar vesicles (MLV) on fused silica substrates. By simultaneous cross-polarization light microscopy and HR-RICM measurements, it was observed that ULV with the wall thickness of a single bilayer would be significantly deformed in its equilibrium state on the substrate as the dimension of its adhesive–cohesive zone was 29% higher than the theoretical value of a rigid sphere with the same diameter. Besides, electrostatic interaction was shown as a significant driving force for vesicle adhesions since the reduction in pH significantly increased the degree of deformation of adhering ULV and heterogeneity of the adhesion discs. The degree of MLV deformation on the solid surfaces was significantly less than that of ULV. When the wall thickness of vesicle increased, the dimension of contact zone was reduced dramatically due to the increase of membrane bending modulus. Most important, the adhesion strength of colloidal adhesion approached that of specific adhesion. Finally, the increase of osmotic stress led to the collapse of adhering vesicles on the non-deformable substrate and raised the area of adhesive contact zone. To interpret these results better, the equilibrium deformation of adhering vesicle was modeled as a truncated sphere and the adhesion energy was calculated with a new theory.     

Nuclear orientation of156Tb in gadolinium matrix

The anisotropy of the angular distribution of gamma-rays from the decay of¹⁵⁶Tb, oriented in a gadolinium matrix at low temperatures, has been measured at the angles of 0 and π/2 with respect to the applied magnetic field direction in the range of temperatures from 14·6 to 68·4 mK. The temperature dependence of anisotropy was measured for the first time. The parameters of hyperfine magnetic dipole and electric quadrupole splittings have been determined and the values of the magnetic dipole moment ¦Μ¹⁵⁶¦=(9·6±1·3)×10^?27 J/T and the electric quadrupole momentQ ¹⁵⁶=(2·9±0·9)×10^?28 m² of the¹⁵⁶Tb ground state have been calculated. Multipole mixing ratios andB(E2) branching ratios of many gamma-ray transitions occurring in¹⁵⁶Gd have been found and the results have been discussed in terms of the rotational-vibration and pairing-plus-quadrupole models.     

Mathematical theory of reduction of physical parameters and similarity analysis

The method of similarity analysis in the study of differential equations is extended to study the variability of parameters in a physical system. The analysis provides an insight into the meaning of physical similarity, which usually means the possibility of a reduction in the number of physical parameters characterizing the system. Theorems relating similarities to groups of invariant transformations are proved and employed to show how the number of parameters can be reduced.