Duality and quantum-algebra symmetry of the AN−1 open spin chain with diagonal boundary fields

We show that the transfer matrix of the A_N−1⁽¹⁾ open spin chair with diagonal boundary fields has the symmetry U_q(SU(l)) × U_q(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.     

The modified nonlinear Schrödinger equation: facts and artefacts

We argue that the integrable modified nonlinear Schr?dinger equation with the nonlinearity dispersion term is the true starting point to analytically describe subpicosecond pulse dynamics in monomode fibers. Contrary to the known assertions, solitons of this equation are free of self-steepening and the breather formation is possible. Received 29 September 2001 / Received in final form 25 January 2002 Published online 2 October 2002 RID="a" ID="a"doktorov@dragon.bas-net.by     

超广义Burgers方程族的非线性可积耦合及其Bargmann对称约束

基于李超代数,构造了超广义Burgers方程族的非线性可积耦合,并且利用超级恒等式得到了它的超Hamilton结构.此外,该文计算出超广义Burgers方程族的非线性可积耦合的Bargmann对称约束.     

On Neumann eigenfunctions in lip domains

A ``lip domain' is a planar set lying between graphs of two Lipschitz functions with constant 1. We show that the second Neumann eigenvalue is simple in every lip domain except the square. The corresponding eigenfunction attains its maximum and minimum at the boundary points at the extreme left and right. This settles the ``hot spots' conjecture for lip domains as well as two conjectures of Jerison and Nadirashvili. Our techniques are probabilistic in nature and may have independent interest.

     

Temperature dependence of proton–proton residual dipolar couplings in adenosine dissolved in charged phospholipid bicelles. Application of a two‐dimensional selective refocusing method

¹H NMR spectra of nucleoside adenosine were recorded in 7.5% (w/v) DMPC/DHPC bicelles doped with CTAB. Despite the small size of adenosine in comparison with the distances between discoidal bicelles, intramolecular ¹H,¹H residual dipolar couplings D were observed at 29.5–38°C. The absolute values of ¹H,¹H spin interactions Δ (sum of J‐ and D‐couplings) were measured selectively by a series of 2D SERF experiments as a function of temperature. At lower temperatures dipolar couplings are scaled down, which leads to simplification of the ¹H NMR spectra. For some pairs of protons, which are simultaneously J‐ and D‐coupled, the exact values of D can be determined from temperature dependence of Δ. Copyright © 2002 John Wiley & Sons, Ltd.     

Residual Dipolar Couplings in 31P MAS Spectra of PPh 3 Substituted Cobalt Complexes

Summary.  Residual dipolar couplings between ³¹P–⁵⁹Co spin pairs were studied in ³¹P MAS spectra of mono- and dinuclear cobalt-triphenylphosphine complexes. These spectra can provide important informations such as the scalar coupling between the dipolar phosphorus and the quadrupolar cobalt nuclei normally not available from solution phase studies. In case of complementary (NQR or X-ray) data even the relative orientation of the interacting shielding, dipolar, scalar couplings, and electric field gradient tensors or internuclear distances can be determined. Examples are shown both for well resolved and practically unresolved cases, factors which possibly control the spectral resolution are discussed in detail. E-mail: gabor.szalontai@sparc4.mars.vein.hu Received June 7, 2002; accepted June 29, 2002     

TRAVELINGWAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS

The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations. By using the bifurcation theory of dynamical systems to do qualitative analysis, all possible phase portraits in the parametric space for the traveling wave systems are obtained. It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied. The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.     

ADJOINT SYMMETRY CONSTRAINTS OF MULTICOMPONENT AKNS EQUATIONS

A soliton hierarchy of multicomponent AKNS equations is generated from an arbitraryorder matrix spectral problem,along with its bi-Hamiltonian formulation.Adjoint symmetryconstraints are presented to manipulate binary nonlinearization for the associated arbitraryorder matrix spectral problem.The resulting spatial and temporal constrained fiows are shownto provide integrable decompositions of the multicomponent AKNS equations.