Elliptic Linear Problem for Painlevé VI Equation with Spectral Parameter

We introduce a linear problem with a spectral parameter for the elliptic form of the Painlevé VI equation. The corresponding nonautonomous version produces the Lax pair with spectral parameter for the Calogero-Inozemtsev model with a single degree of freedom.     

超声复合振动系统中的“局部共振”现象实验研究

本从实验的角度出发,对超声复合振动系统中细长杆的“局部共振”现象进行了较为精确的测量,主要研究了细杆长度与谐振频率之间的关系,超声振子对“局部共振”的影响,以及“局部共振”中细杆长度对振幅的影响,从而为深入研究“局部共振”现象产生的机理提供了更多的依据。     

Efficient transport of saccharides through a liquid membrane mediated by a cyclodextrin dimer

A new efficient system for transporting saccharides through a liquid membrane has been constructed. The transport rates of saccharides were accelerated greatly by the cyclodextrin dimer 2; by contrast, the corresponding cyclodextrin monomer 1 was not effective at mediating saccharide transport. The transport rate of D-ribose through a chloroform liquid membrane was 17 times faster when the cyclodextrin dimer 2 was used as the transporter than when the cyclodextrin monomer 1 was used. Similarly the transport rate of methyl D-galactopyranoside was 16 times faster by 2 than by 1.     

The Order Parameter and Phase Transformations in Compounds with Ionic Stoichiometry

The paper considers instability of a symmetric linear ion chain against a spontaneous distortion that orders ions of opposite charge without a multiple change in the spacing. Transverse deformation in dense chains is observed. The dipolar interaction responsible for 3D ordering of similar structures of Cu—O chains in yttrium perovskites has been assessed. The superclose ion packing in Cu—O chains is explained by the existence of an oriented hole orbital in the electronic structure of bivalent copper. The possible role of this orbital as an additional degree of freedom leading to thermodynamic singularities at intermediate temperatures below the tetra–ortho transition temperature has been investigated.     

Selective rearrangements of quadruply hydrogen-bonded dimer driven by donor-acceptor interaction

A general method has been developed to control the selective rearrangement of Meijer's AADD quadruply hydrogen-bonded homodimers by introducing an additional donor-acceptor interaction. Therefore, one donor-assembling monomer, 1, in which the electron-rich bis(p-phenylene)-34-crown-10 moiety is connected to the hydrogen-bonding moiety, and two acceptor-assembling monomers, 2 and 3, in which the electron-deficient pyromellitic diimide or naphthalene diimide group is incorporated, respectively, are synthesized and characterized. 1H NMR and 2D-NOESY studies show that all these compounds exist as stable homodimers in chloroform. Mixing 1 equiv of 1 with 1 equiv of 2 in chloroform leads to the formation of heterodimers 1.2 in approximately 60 % yield, as a result of the electrostatic interaction between the bis(p-phenylene)-34-crown-10 moiety of 1 and the pyromellitic diimide group of 2. Selective formation of heterodimer 1.3 (>97 %) was achieved by mixing 1 equiv of 1 with 1 equiv of 3 in chloroform which resulted in a strengthened electrostatic interaction between the bis(p-phenylene)-[34]crown-10 moiety of 1 and the naphthalene diimide group of 3. The structures of heterodimers 1.2 and 1.3, which have been characterized by 1H NMR and UV/Vis experiments, reveal a remarkable promoting effect between the donor-acceptor interaction and intermolecular hydrogen-bonding. 1H NMR studies also reveal that heterodimers 1.2 and 1.3 can be fully and partially dissociated by addition of heterocycle 29, leading to the formation of new more robust heterodimers 1.29 and 2.29, or 3.29,respectively, and partially regenerated by subsequent addition of heterocyclic compound 30 through the formation of a new heterodimer 29.30. Heterodimers 1.2 and 1.3 represent a novel class of pseudo[2]rotaxanes constructed by two different noncovalent interactions.     

Complexation behavior of a highly preorganized 7,7-diphenylnorbornane-derived macrocycle: towards the design of molecular clocks

The syntheses of two new cyclophane hosts, 4 and 6, are described. The main difference between them is the higher degree of preorganization of 4 as a consequence of the inclusion of the 7,7-diphenylnorbornane (DPN) subunit. The inner cavity of 4 adopts a belt-shaped structure, while 6 has a twisted geometry. In the solid state, the molecules of macrocycle 6 are stacked along an axis to form nanotubular structures. Compounds 4 and 6 form two of the strongest complexes between arene cyclophanes and Ag(+) reported up to date. The silver cation is located inside the cavity of the macrocycles. The stability of 4.Ag(+) is considerably higher than that of 6.Ag(+). The additional stabilization of 4.Ag(+) is attributed to higher preorganization of macrocycle 4. DNMR experiments as well as theoretical calculations carried out with 4.Ag(+) show evidence of Ag(+)-hopping between two different binding sites inside the macrocycle. This phenomenon could be the basis for the design of molecular clocks.     

An Open Question on Cyclic Relaxation

The problem discussed in this note is highly interesting. It is related to several dual iterative methods, such as the methods proposed by Kaczmarz, Hildreth, Agmon, Cryer, Mangasarian, Herman, Lent, Censor, and others. Cast as row-action methods these algorithms have been proved as useful tools for solving large convex feasibility problems that arise in medical image reconstruction from projections, in inverse problems in radiation therapy, and in linear programming.The question that we want to answer is how these algorithms behave when the feasible region is empty. It is shown that under certain conditions the primal sequence still converges while the dual sequence {y _k } obeys the rule y _k =u _k +k v, where {u _k } is a converging sequence and v is a fixed vector that satisfies A ^T v=0,v0,and,b ^T v>0. It is conjectured that these properties hold whenever the feasible region is empty. However, the validity of this claim remains an open question.This revised version was published online in October 2005 with corrections to the Cover Date.