Bispectral KP solutions and linearization of Calogero-Moser particle systems

Rational and soliton solutions of the KP hierarchy in the subgrassmannianGr ₁ are studied within the context of finite dimensional dual grassmannians. In the rational case, properties of the tau function, , which are equivalent to bispectrality of the associated wave function, , are identified. In particular, it is shown that there exists a bound on the degree of all time, variables in if and only if is a rank one bispectral wave function. The action of the bispectral involution, , in the generic rational case is determined explicitly in terms of dual grassmannian parameters. Using the correspondence between rational solutions, and particle systems, it is demonstrated that is a linearizing map of the Calogero-Moser particle system and is essentially the map introduced by Airault, McKean and Moser in 1977 [2].Research supported by NSA Grant MDA904-92-H-3032     

Inclusion-exclusion: Exact and approximate

It is often required to find the probability of the union of givenn eventsA ₁ ,...,A _n . The answer is provided, of course, by the inclusion-exclusion formula: Pr(A _i )= _i – _i<j Pr(A _i A _j )±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A _i ), from the above data with an additive error of exp . In the present article we develop an expression that can be computed in polynomial time, that, given the sums _|S|=j Pr( _iS A _i ) forj=1,...k, approximates Pr(A _i ) with an additive error of exp . This error is optimal, up to the logarithmic factor implicit in the notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v _l ^m C _i is an instance of the general problem that had been extensively studied [7]. HereA _i is the set of assignments that satisfyC _i , and Pr( _iS A _i )=a _S /2ⁿ where _iS C _i is satisfied bya _S assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa _S for, say, all cardinalities . Quite surprisingly, already the numbersa _S over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation.     

Charge separation versus recombination in dye-sensitized nanocrystalline solar cells: the minimization of kinetic redundancy

In this paper we focus upon the electron injection dynamics in complete dye-sensitized nanocrystalline metal oxide solar cells (DSSCs). Electron injection dynamics are studied by transient absorption and emission studies of DSSCs and correlated with device photovoltaic performance and charge recombination dynamics. We find that the electron injection dynamics are dependent upon the composition of the redox electrolyte employed in the device. In a device with an electrolyte composition yielding optimum photovoltaic device efficiency, electron injection kinetics exhibit a half time of 150 ps. This half time is 20 times slower than that for control dye-sensitized films covered in inert organic liquids. This retardation is shown to result from the influence of the electrolyte upon the conduction band energetics of the TiO2 electrode. We conclude that optimum DSSC device performance is obtained when the charge separation kinetics are just fast enough to compete successfully with the dye excited-state decay. These conditions allow a high injection yield while minimizing interfacial charge recombination losses, thereby minimizing "kinetic redundancy" in the device. We show furthermore that the nonexponential nature of the injection dynamics can be simulated by a simple inhomogeneous disorder model and discuss the relevance of our findings to the optimization of both dye-sensitized and polymer based photovoltaic devices.     

Full multinuclear resonance analysis of 4-amino-1,1,2,2,9,9,10,10-octafluoro[2.2]paracyclophane

The complete assignment of 19F, 1H and 13C NMR spectra for a monosubstituted octafluoro[2.2]paracyclophane derivative is described for the first time. The unambiguous assignments were achieved through the combination of 19F--1H HOESY, 1H COSY and 19F COSY techniques and then further confirmed employing a complementary approach using a Karplus-dependent 3JCF interaction. Interesting aspects of the coupling patterns for various JHH, JHF, JCF and JFF interactions are also discussed.     

Evaluation of cellulase preparations for hydrolysis of hardwood substrates

Seven cellulase preparations from Penicillium and Trichoderma spp. were evaluated for their ability to hydrolyze the cellulose fraction of hardwoods (yellow poplar and red maple) pretreated by organosolv extraction, as well as model cellulosic substrates such as filter paper. There was no significant correlation among hydrolytic performance on pretreated hardwood, based on glucose release, and filter paper activity. However, performance on pretreated hardwood showed significant correlations to the levels of endogenous β-glucosidase and xylanase activities in the cellulase preparation. Accordingly, differences in performance were reduced or eliminated following supplementation with a crude β-glucosidase preparation containing both activities. These results complement a previous investigation using softwoods pretreated by either organosolv extraction or steam explosion. Cellulase preparations that performed best on hardwood also showed superior performance on the softwood substrates.     

Photochemische Reaktionen 81. Mitteilung [1] Notiz zur UV.-Bestrahlung von γ, δ-Epoxy-eucarvon und dessen Reaktivität gegenüber Botrifluorid-äthylätherat

UV.-irradiation (λ ≥ 327 nm) of the α,β-unsaturated γ,δ-epoxy ketone 2 in pentane gives the isomers oxidoketone 3 and diketone 4, in high yield. On treatment with BF₃O(C₂H₅)₂, 2 undergoes rearrangement to the diketone 4 and the isomeric lactone 8 and yields also the dimer 9.     

On assignment of fundamental vibrational modes of hypophosphite anion and its deuterated analogue

Results of ab initio and density functional theory calculations on the structure and vibrational frequencies of hypophosphite anion indicate earlier experimental assignments of the fundamental vibrational modes are correct while the recent reassignments of several modes proposed by Bickley et al. are inconsistent with the calculated results.     

Intermolecular coupling in nanometric domains of light-harvesting dendrimer films studied by photoluminescence near-field scanning optical microscopy (PL NSOM)

Near-field scanning optical microscopy (NSOM) has been used to investigate the photophysical characteristics of first- to fourth-generation (G1 to G4) light-harvesting dendrimer thin films containing coumarin-343 and coumarin-2 as the core and peripheral chromophores, respectively. Thin film photoluminescence (PL) spectra exhibit a significant red shift in the lower generations (G1, G2, and G3) as compared to their respective solution PL spectra, implying the formation of excimers. Spatially resolved PL NSOM images exhibit pronounced nanoscopic domains in G1, which become more homogeneous in higher generations due to site-isolation of the core chromophore. G4 exhibits complete site-isolation for these light-harvesting dendrimer films.     

Chiral induction in self-assembled helicates: CHIRAGEN type ligands with ferrocene bridging units

The aim of this work was the preparation of enantiomerically pure bis(pinene-bipyridine) ligands containing the ferrocenyl moiety. Several such ligands (1-3) were synthesized and completely characterized. These molecules can be diastereoselectively deprotonated at the acidic methylene group of the pinene moiety using a strong and sterically hindered base such as LDA. Subsequent reaction of the formed anion with alkyl halides yield the family of C(2)-symmetric enantiopure compounds (1a-c). Copper(I), silver(I), or zinc(II) complexes with several ligands (C1-C8) were prepared and structurally characterized in the solid state and in solution. Self-assembled helical species are formed in several cases. It became evident that the chiral groups present in the ligand do not completely determined the helical configuration of the assemblages. Diastereoselectivity is thus not complete with this type of ligands, contrary to other, similar ligands studied before.