A matrix integral solution to [P,Q]=P and matrix laplace transforms

In this paper we solve the following problems: (i) find two differential operatorsP andQ satisfying [P, Q]=P, whereP flows according to the KP hierarchy P/t _n =[(P ^n/p )₊,P], withp:=ordP2; (ii) find a matrix a integral representation for the associated -function. First we construct an infinite dimensional spaceW= span{ ₀(z, ₁(z,...)} of functions ofz invariant under the action of two operators, multiplication byz ^p andA _c :=z/z–z+c. This requirement is satisfied, for arbitraryp, if ₀ is a certain function generalizing the classical Hänkel function (forp=2); our representation of the generalized Hänkel function as adouble Laplace transform of a simple function, which was unknown even for thep=2 case, enables us to represent the -function associated with the KP time evolution of the spaceW as a double matrix Laplace transform in two different ways. One representation involves an integration over the space of matrices whose spectrum belongs to a wedge-shaped contour ^-+ ^- defined by ^± = ₊e^±i/p. The new integrals above relate to matrix Laplace transforms, in contrast with matrix Fourier transforms, which generalize the Kontsevich integrals and solve the operator equation [P, Q]=1.The support of a National Science Foundation grant #DMS-95-4-51179 is gratefully acknowledged.The hospitality of the Volterra Center at Brandeis University is gratefully acknowledged.The hospitality of the University of Louvain and Brandeis University is gratefully acknowledged.The support of a National Science Foundation grant #DMS-95-4-51179, a Nato, an FNRS and a Francqui Foundation grant is gratefully acknowledged.     

A theoretical study of alcohol oxidation by ferrate

The conversion of methanol to formaldehyde mediated by ferrate (FeO(4)2-), monoprotonated ferrate (HFeO4-), and diprotonated ferrate (H2FeO4) is discussed with the hybrid B3LYP density functional theory (DFT) method. Diprotonated ferrate is the best mediator for the activation of the O-H and C-H bonds of methanol via two entrance reaction channels: (1) an addition-elimination mechanism that involves coordination of methanol to diprotonated ferrate; (2) a direct abstraction mechanism that involves H atom abstraction from the O-H or C-H bond of methanol. Within the framework of the polarizable continuum model (PCM), the energetic profiles of these reaction mechanisms in aqueous solution are calculated and investigated. In the addition-elimination mechanism, the O-H and C-H bonds of ligating methanol are cleaved by an oxo or hydroxo ligand, and therefore the way to the formation of formaldehyde is branched into four reaction pathways. The most favorable reaction pathway in the addition-elimination mechanism is initiated by an O-H cleavage via a four-centered transition state that leads to intermediate containing an Fe-O bond, followed by a C-H cleavage via a five-centered transition state to lead to formaldehyde complex. In the direct abstraction mechanism, the oxidation reaction can be initiated by a direct H atom abstraction from either the O-H or C-H bond, and it is branched into three pathways for the formation of formaldehyde. The most favorable reaction pathway in the direct abstraction mechanism is initiated by C-H activation that leads to organometallic intermediate containing an Fe-C bond, followed by a concerted H atom transfer from the OH group of methanol to an oxo ligand of ferrate. The first steps in both mechanisms are all competitive in energy, but due to the significant energetical stability of the organometallic intermediate, the most likely initial reaction in methanol oxidation by ferrate is the direct C-H bond cleavage.     

Phenolic constituents of licorice. VIII. Structures of glicophenone and glicoisoflavanone, and effects of licorice phenolics on methicillin-resistant Staphylococcus aureus

Two new phenolic compounds, glicophenone (1) and glicoisoflavanone (2), were isolated from commercial licorice, and their structures were elucidated on the basis of spectroscopic data. Antibacterial assays of licorice phenolics for Staphylococcus aureus, including four strains of methicillin-resistant S. aureus (MRSA), and also for Escherichia coli K12 and Pseudomonas aeruginosa PAO1, were then examined. Two compounds among them, 8-(gamma,gamma-dimethylallyl)-wighteone (21) and 3'-(gamma,gamma-dimethylallyl)-kievitone (28), showed remarkable antibacterial effects [minimum inhibitory concentrations (MICs), 8 microg/ml on the MRSA strains and methicillin-sensitive S. aureus. Licochalcone A (14), gancaonin G (20), isoangustone A (24), glyasperins C (30) and D (31), glabridin, (32), licoricidin (33), glycycoumarin (34) and licocoumarone (40) showed antibacterial effects on the MRSA strains with MIC values of 16 microg/ml. Effects on the beta-lactam resistance of the MRSA strains were also examined, and licoricidin (33) noticeably decreased the resistance of the MRSA strains against oxacillin, as shown by the reduction in the MICs of oxacillin (lower than 1/128-1/1000 in the presence of 8 microg/ml of 33, and 1/8-1/32 in the presence of 4 microg/ml of 33). Mechanistic study suggested that 33 does not inhibit the formation of penicillin-binding protein 2' (PBP2'), but affects the enzymatic function of PBP2'.     

Complete Photochromic Structural Changes in Ruthenium(II)?Diimine Complexes,Based on Control of the Excited States by Metalation

The thermal and photochemical reactions of a newly synthesized complex, [Ru^II(TPA)(tpphz)]²⁺ ( 1 ; TPA=tris(2‐pyridylmethyl)amine, tpphz=tetrapyrido[3,2‐a:2′,3′‐c:3′′,2′′‐h: 2′′′,3′′′‐j]phenazine), and its derivatives have been investigated. Heating a solution of complex 1 (closed form) and its derivatives in MeCN caused the partial dissociation of one pyridylmethyl moiety of the TPA ligand and the resulting vacant site on the Ru^II center was occupied by a molecule of MeCN from the solvent to give a dissociated complex, [Ru^II(η³‐TPA)(tpphz)(MeCN)]²⁺ ( 1′ , open form), and its derivatives, respectively, in quantitative yields. The thermal dissociation reactions were investigated on the basis of kinetics analysis, which indicated that the reactions proceeded through a seven‐coordinate transition state. Although the backwards reaction was induced by photoirradiation of the MLCT absorption bands, the photoreaction of complex 1′ reached a photostationary state between complexes 1 and 1′ and, hence, the recovery of complex 1 from complex 1′ was 67 %. Upon protonation of complex 1 at the vacant site of the tpphz ligand, the efficiency of the photoinduced recovery of complex 1 +H⁺ from complex 1′ +H⁺ improved to 83 %. In contrast, dinuclear μ‐tpphz complexes 2 and 3 , which contained the Ru^II(TPA)(tpphz) unit and either a Ru^II(bpy)₂ or Pd^IICl₂ moiety on the other coordination edge of the tpphz ligand, exhibited 100 % photoconversion from their open forms into their closed forms ( 2′ → 2 and 3′ → 3 ). These results are the first examples of the complete photochromic structural change of a transition‐metal complex, as represented by complete interconversion between its open and closed forms. Scrutinization by performing optical and electrochemical measurements allowed us to propose a rationale for how metal coordination at the vacant site of the tpphz ligand improves the efficiency of photoconversion from the open form into the closed form. It is essential to lower the energy level of the triplet metal‐to‐ligand charge‐transfer excited state (³MLCT*) of the closed form relative to that of the triplet metal‐centered excited state (³MC*) by metal coordination. This energy‐level manipulation hinders the transition from the ³MLCT* state into the ³MC* state in the closed form to block the partial photodissociation of the TPA ligand.     

Spontaneous racemization and epimerization behavior in solution of chiral nitroxides

[reaction: see text] Enantiomerically enriched samples of chiral cyclic nitroxides with a 4-hydroxyphenyl group on the stereogenic center bearing the NO radical group undergo unprecedented spontaneous racemization and/or epimerization in aprotic solvents, which can be well accounted for by the multistep equilibrations involving planar quinoid intermediates.     

Improvement of Targeted Gene Delivery to Human Cancer Cells by a Novel Trifunctional Crosslinker

A facile method for the construction of an immunoconjugate which displays targeting ligands, such as antibody fragments, with a high density is reported. For this purpose, we synthesized a novel trifunctional crosslinking reagent. By the use of this reagent, ligands targeting the specific cell can be displayed on the surface of the drug carrier with a high density. In this study, we display HER2 (human epidermal growth‐factor receptor‐2) binding ligands on branched polyethylenimine (PEI), which can form polyplexes with plasmid DNA. Kinetic analysis of the binding to the extracellular domain of HER2 show the PEI displaying a high density of ligands binds to the target more strongly compared to the PEI displaying ligands at a low density. The increased density of HER2 ligands displayed on the gene carrier contributes to the improved transfection efficiency. This approach can be applied to other drug delivery systems, including liposome, micelle, and so on.     

Theoretical study of the mechanism of valence tautomerism in cobalt complexes

Valence tautomerism is studied in the [Co(II-HS)(sq)(2)(bpy)]/[Co(III-LS)(sq)(cat)(bpy)] mononuclear cobalt complex by using DFT methods (HS, high spin; LS, low spin; cat, catecholate; sq, semiquinone; bpy, 2,2'-bipyridine). Calculations at the B3LYP* level of theory reproduce well the energy gap between the Co(II-HS) and Co(III-LS) forms giving an energy gap of 4.4 kcal/mol, which is comparable to the experimental value of 8.9 kcal/mol. Potential energy surfaces and crossing seams of the electronic states of the doublet, quartet, and sextet spin states are calculated along minimum energy paths connecting the energy minima corresponding to the different spin states. The calculated minimum energy crossing points (MECPs) are located at 8.8 kcal/mol in the doublet/sextet surfaces, at 10.2 kcal/mol in the doublet/quartet surfaces, and at 8.4 kcal/mol in the quartet/sextet surfaces relative to the doublet ground state. Considering the energy of the three spin states and the crossing points, the one-step relaxation mechanism between the Co(II-HS) and Co(III-LS) forms is the most probable. This research shows that mapping MECPs can be a useful strategy to analyze the potential energy surfaces of systems with complex deformation modes.     

Thermal [2+2] cycloaddition of morpholinoenamines with C60 via a single electron transfer

The thermal reaction of C(60) with five- and six-membered morpholinocycloalkenes in refluxing toluene exclusively gave the [2+2] cycloadducts in high yields. However, a seven-membered homologue sluggishly reacted with C(60) because of the increasing steric hindrance. This cycloaddition reaction is likely to proceed via a single electron transfer (SET), a radical-coupling, and subsequent ion cyclization rather than the prior proton transfer between the radical ions.