Coherent-mode representation of supercontinuum

We apply the coherent-mode expansion to correlation functions used to describe the coherence properties of supercontinuum generated in nonlinear ?bers. We show that the leading term of the expansion represents the quasi-coherent part of the ?eld while the quasi-stationary part is embedded into the higher-order modes. The evolution of the modal expansion and the number of modes needed to describe the supercontinuum ?eld are also discussed.     

Enthalpies of formation of olefinic ethers by G3(MP2)//B3LYP calculations

The gas‐phase enthalpies of formation at 298.15 K of a number of acyclic and cyclic olefinic ethers (mainly α,β‐unsaturated ethers), together with those of a few cyclic mono‐ and dienes, have been estimated by G3(MP2)//B3LYP calculations. In most cases, the computational and experimental data (if available) are in good mutual agreement. Whenever significant deviations between the experimental and computational data were found, the experimental enthalpies of formation arise from a single data source, and it appears that small experimental errors are embedded therein. A marked error was found in the experimental enthalpy of formation of 2‐chloroethyl ethyl ether, used in this work as a reagent for estimation of the enthalpy of formation of 2‐chloroethyl vinyl ether by an isodesmic reaction. Moreover, significant errors were also found in the literature values for the computational (B3LYP/6‐311G**) enthalpies of formation of several Me‐substituted derivatives of methyl vinyl ether. The present computational method, besides providing acceptable enthalpies of formation for unsaturated ethers, was also found to give accurate Δ_fH(g) values for cyclic mono‐ and dienes. Thus, the G3(MP2)//B3LYP computational method proved to be a valuable tool for investigating the energetics of olefinic ethers and hydrocarbons. Copyright © 2008 John Wiley & Sons, Ltd.     

Unifications,deunifications, and their complexity

The execution of a Prolog program can be viewed as a sequence of unifications and backtracks over unifications. We study the time requirement of executing a sequence of such operations (the unify-deunify problem). It is shown that the well-known set union problem is reducible to this problem, even in the case when no function symbols are allowed (the Datalog unify-deunify problem). As the set union problem requires nonlinear time on a large class of algorithms, the same holds for the unify-deunify problem. Thus the linearity of single unifications does not give a complete picture of the time complexity of Prolog primitives. We discuss the methods for executing sequences of Datalog unifications used in Prolog interpreters and show that some of them require even quadratic time in the worst case. Complementing these results, we show that if the number of variables occurring in one clause is bounded by a constant, then the Datalog unify-deunify problem can be solved in linear time.A preliminary version of this paper appeared in the Third International Conference on Logic Programming, London, July 1986. This work was supported by the Academy of Finland and by TEKES.     

Relative thermodynamic stabilities of isomeric 1,2-dialkoxyethenes

The relative thermodynamic stabilities of the geometrical isomers of a number of 1,2-dialkoxyethenes have been determined by chemical equilibration in the neat liquid and in 1,4-dioxane solution with mercuric acetate as catalyst. From the variation of the value of the equilibrium constant with temperature, the thermodynamic parameters G , H , and S of theE Z isomerization were evaluated. In all cases theZ isomer proved to be thermodynamically the more stable species, its favor increasing with the bulkiness of the alkoxy groups. The thermodynamic data obtained for theEZ isomerization of 1,2-dimethoxyethene differ significantly from those reported in the literature. An attempt to correlate the experimental thermodynamic data with MM2 calculations for the title compounds as well as for 1,2-dimethoxypropenes is presented.     

An Ab Initio Study of the Relative Stabilities and Molecular Structures of 3-Substituted 2,5-Dihydrofurans and 4-Substituted 2,3-Dihydrofurans

The geometry optimized structures and total energies of 3-substituted (R) 2,5-dihydrofurans (a) and their isomers, 4-substituted 2,3-dihydrofurans (b), have been determined by ab initio calculations at the MP2/6-31G^*//HF/6-31G^* level. The nature of the moiety R has a marked effect on the relative total energies of the isomeric forms: at the calculation level cited, the reaction enthalpies for the a b isomerization range from +4.7 kJ mol^–1 for R = MeO to –30.5 kJ mol^–1 for both R = COOMe and R = NO₂. The reaction enthalpies appear to be controlled by the electronic effect of R on the strength of p- conjugation in b. The a isomer has a planar ring, independent of R (excluding NH₂), whereas the planarity of b depends on the electronic nature of R: the 2,3-dihydrofuran ring is planar for both R = COOMe and R = NO₂, but nonplanar for less conjugation-enhancing substituents.     

Dendrimer-like PEO glycopolymers exhibit anti-inflammatory properties

A new class of high molecular weight polysulfated PEO dendrimer-like glycopolymer has been synthesized by a combination of arm-first and core-first methodologies followed by trichloroacetimidate glycosidation as a facile bioconjugation strategy. An L-selectin antagonist was identified that exhibits 103-fold greater activity than other multivalent sLex glycopolymers and 20-50 times greater potency than other linear heparinoids. A significant reduction in inflammatory cell recruitment was observed in vivo.     

17O, 13C, and 1H NMR Studies of p–π Conjugation in 2-Substituted 4-Methylene-1,3-dioxolanes and 4-Methyl-1,3-dioxoles

The ¹⁷O NMR spectra of a number of unsaturated 5-membered cyclic acetals, 2-substituted 4-methylene-1,3-dioxolanes and their endocyclic isomers, 4-methyl-1,3-dioxoles, have been recorded. The ¹⁷O NMR chemical shifts, in comparison with those of similarly 2-substituted 1,3-dioxolanes, were used to explore the variation of the strength of p– conjugation in the unsaturated acetals as a function of the nature of substitution at C2. The ¹⁷O NMR shift data reveal that alkoxy substituents have a significantly more favorable effect on the strength of p– conjugation in 4-methyl-1,3-dioxoles than in 4-methylene-1,3-dioxolanes. This fact appears to be responsible for the previously observed unexpectedly large effect of alkoxy substitution on the relative thermodynamic stabilities of these two classes of isomeric compounds. Additional information of the unexpected charge distribution in 4-methyl-1,3-dioxoles is provided by their ¹H and ¹³C NMR spectra.     

Thermodynamics of Exo–Endo Isomerization of Carbon–Carbon Double Bonds in Five-Membered Ring Compounds. A Quantum Chemical Study

The energies and enthalpies of isomerization of methylenecyclopentane to 1-methylcyclopentene, 1,3-dimethylenecyclopentane to 1-methyl-4-methylenecyclopentene, and 3-methylenecyclopentanone to 3-methylcyclopent-3-en-1-one have been determined by DFT calculations at the B3LYP/6-31G* level of theory. Related studies were also carried out for some structurally related five-membered heterocyclic compounds containing one or two O atoms in the ring. The aim of the work was to study how the energetics of the exo endo isomerization of the C=C bond in methylenecyclopentane, 2-methylenetetrahydrofuran and 4-methylene-1,3-dioxolane is affected by replacement of an sp³ hybridized ring C atom with a trigonal one. This effect turned out to be small—only a few kilojoules per mole in carbocycles, favoring the endo isomer; in the heterocyclic compounds, especially those containing two ring O atoms, the effect is much greater.     

Relative thermodynamic stabilities of isomeric alkyl allyl and alkyl (Z)-propenyl ethers

The relative thermodynamic stabilities of ten allyl ethers (ROCH₂CH=CH₂) and the corresponding isomeric (Z)-propenyl ethers (where R is an alkyl group, or a methoxysubstituted alkyl group) have been determined by chemical equilibration in DMSO solution with t-BuOK as catalyst. From the variation of the equilibrium constant with temperature, the values of the thermodynamic parameters ΔGΘ, ΔHΘ and ΔSΘ of isomerization at 298.15 K were evaluated. The propenyl ethers are highly favored at equilibrium, the values of both ΔGΘ and ΔHΘ for the allyl → propenyl reaction being ca. −18 to −25 kJ mol⁻¹. The favor of the propenyl ethers is increased by bulky alkyl substituents, and decreased by methoxy-substituted alkyl groups. In most cases the entropy contribution is negligible; however, for R = (MeO)₂CH and R = (MeO)₃C the values of ΔSΘ are ca. −5 J K⁻¹ mol⁻¹.     

Ion-induced nucleation of dibutyl phthalate vapors on spherical and nonspherical singly and multiply charged polyethylene glycol ions

Dibutyl phthalate vapor nucleation induced by positive polyethylene glycol (PEG) ions with controlled sizes and charges was experimentally studied. The ions were produced by electrospray ionization, classified in a high-resolution differential mobility analyzer, and studied in a nano condensation nucleus counter of the mixing type. Ionic radii of PEG varied from 0.52 to 1.56 nm, including from singly to quadruply charged ions. Some of these ions are fully stretched chains, other are spherical, and others have intermediate forms, all of them having been previously characterized by mobility and mass spectrometry studies. Activation of PEG1080(+2) requires a supersaturation almost as high as that required for small singly charged ions and higher than for PEG1080(+). This anomaly is explained by the Coulombic stretching of the ion into a long chain, where the two charged centers appear to be relatively decoupled from each other. The critical supersaturation for singly charged spherical ions falls below Thomson's (capillary) theory and even below the already low values seen previously for tetraheptyl ammonium bromide clusters. Spherical PEG4120(+2) falls close to the Thomson curve. The trends observed for slightly nonspherical PEG4120(+3) and highly nonspherical (but not quite linear) PEG4120(+4) are intermediate between those of multiply charged spheres and small singly charged ions.