Isospectral theory of Euler equations

Isospectral problem of both 2D and 3D Euler equations of inviscid fluids, is investigated. Connections with the Clay problem are described. Spectral theorem of the Lax pair is studied.     

激发对相干态的等阶Y压缩效应

用数值计算法研究了激发对相干态|ζ;m〉＝a^+mb^+m|ζ〉的等阶Y压缩效应.结果表明:对于态a^+mb^+m|ζ〉,光场存在着等阶K(＝2,3,4,5,…)次方Y压缩效应,但是随着场模上光子增加数m的增大,等阶K次方Y压缩效应减弱.     

NMR studies on a palladium(II) complex containing an incompletely coordinated facultative pentadentate Schiff base ligand

Palladium(II) dichloride reacts with 1,10‐bis(2‐pyrrolyl)‐2,5,9‐triaza‐1,9‐decadiene to give a [Pd(C₁₅H₂₀N₅)]Cl complex in which the ligand is four‐coordinated, leaving one pyrrole group dangling. By using COSY, gHSQC, gHMBC connectivities and NOE experiments it has been concluded that one linkage isomer exists in DMSO solution, in spite of the fact that different sets of N atoms of potentially pentadentate ligand might be involved in coordination, and that the three chelate rings in the complex cation are arranged in a sequence: five‐membered, six‐membered, five‐membered which is different from that (5–5–6) found by x‐ray studies on the related [Ni(C₁₅H₂₀N₅)]Cl compound. NMR studies allowed an unambiguous assignment of all ¹H and ¹³C NMR resonances for the complex. Results of x‐ray structural analysis of [Pd(C₁₅H₂₀N₅)](CH₃COO)H₂O supported the five‐membered, six‐membered, five‐membered ring sequence in the [Pd(C₁₅H₂₀N₅)]⁺ complex cation and show an E (trans) orientation of the dangling pyrrole group with respect to the metal center. Copyright © 2002 John Wiley & Sons, Ltd.     

Weak Attractive Ligand–Polymer and Related Interactions in Catalysis and Reactivity: Impact,Applications, and Modeling

The notion of weak attractive ligand–polymer interactions is introduced, and its potential application, importance, and conceptual links with “cooperative” ligand–substrate interactions are discussed. Synthetic models of weak attractive ligand–polymer interactions are described, in which intramolecular weak C? H???F? C interactions (the existence of which remains contentious) have been detected by NMR spectroscopy and neutron and X‐ray diffraction experiments. These C? H???F? C interactions carry important implications for the design of catalysts for olefin polymerization, because they provide support for the practical feasibility of ortho‐F???H_β ligand–polymer contacts proposed for living Group 4 fluorinated phenoxyimine catalysts. The notion of weak attractive noncovalent interactions between an “active” ligand and the growing polymer chain is a novel concept in polyolefin catalysis.     

Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension, at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross–Pitaevskii scaling included, a less-than-100% condensation into a single-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.     

Sn/Ge(1 1 1) α-phase: characterization of image resonances by specular electron reflection and selective electron scattering

Image potential resonances on the Sn/Ge(1 1 1) α-phase are investigated by two closely related methods: specular electron reflection and so-called selective electron scattering. Electrons from image resonances are detected on this surface at 120 and 300 K, i.e. below and above the phase transition at about 200 K. The dispersion of the image resonances reveals at these two temperatures equivalent effective electron masses, which are characteristic for this type of electronic surface states. The results of the two methods are consistent according to the similarity of the scattering processes. Changes in the loss peak intensity with the annealing temperature are assigned to the surface quality and are reflected by characteristic photoemission intensities.     

The intramolecular hydrogen bond in ortho-hydroxy acetophenones

The crystal structures of two ortho-hydroxy ketones (5-chloro-2-hydroxyacetophenone (I K) and 3,5-dichloro-2-hydroxyacetophenone (II K)) have been determined with X-ray diffraction at 100 K. A comparison of steric effects on properties of pseudoaromatic hydrogen bonds in ortho-hydroxy acetophenone and ortho-hydroxy ketimines have been carried out with the application of crystallographic data.

Nuclear quadrupole resonance (NQR) spectra have been measured and interpreted.     

The structure of multi-electrode-pair pulse laser and discharge pulse time selection

Applying multi-electrode-pair pulse TEA CO₂ laser to one optical resonance cavity will have several advantages over traditional method, including higher gain, shorter pulse discharge time interval, and in particular, continuous adjustable time interval of multi-pulse laser output can be achieved without high vacuum condition. To improve laser's working stabilization, we proposed new approaches to optimize laser structure design and discharge pulse time interval selection.     

A minimal pair joining to a plus cupping Turing degree

A computably enumerable (c.e.) degree a is called nonbounding, if it bounds no minimal pair, and plus cupping, if every nonzero c.e. degree x below a is cuppable. Let NB and PC be the sets of all nonbounding and plus cupping c.e. degrees, respectively. Both NB and PC are well understood, but it has not been possible so far to distinguish between the two classes. In the present paper, we investigate the relationship between the classes NB and PC , and show that there exists a minimal pair which join to a plus cupping degree, so that PC ? NB . This gives a first known difference between NB and PC . (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Configurational and conformational preferences in stereoselective acylations of <Emphasis Type="Italic">N</Emphasis>-methyl-1,3-diaminopropane with acyl chlorides

Evidence for a stereoinduction profile of the reaction of N-methyl-1,3-diaminopropane with acyl chlorides has been provided. A possibility to engage in intramolecular CH₂⋯HN and Cl⋯H-N interactions and the proton migration process to the methylamino group leads to the E secondary amides carrying the N⋯H⁺⋯N or N-H⋯N bridges, that show unusual spectroscopic images. Empirical relations between the Δδ _C chemical shift differences, the polarizability of the CO(S) groups and hydrogen bonding strength have been found. Both ¹H-¹⁵N-GHSQC and GHMBC experiments provide insight into the nature of hydrogen bonding and confirm the cyclic array of atoms.