Catalytic N-sulfonyliminium ion-mediated cyclizations to alpha-vinyl-substituted isoquinolines and beta-carbolines and applications in metathesis

[reaction: see text] Catalytic Sn(OTf)2-induced cyclization of linear, aryl-containing allylic N,O-acetals produced vinyl-substituted tetrahydroisoquinolines and tetrahydro-1H-beta-carbolines. The usefulness of the vinyl moiety in the resulting products was demonstrated via the synthesis of various key building blocks for alkaloid structures. The alpha-vinyl moiety was utilized in a [2,3] sigmatropic rearrangement, in ring-closing metathesis and a cross-metathesis-based synthesis of vincantril, an antianoxia agent, and a synthetic member of the vincamine type natural products.     

Linear electric field (LEF) effects in 13C NMR. Some model calculations on 5-chloro-1-pentene

The usefulness and some of the limitations of the linear electric field (LEF) effect in ¹³C NMR are illustrated by means of model calculations on the ¹³C NMR chemical shifts of C-1 and C-2 in 5-chloro-1-pentene in nine different conformations. Two different concepts are used in order to calculate the electric fields near C-1 and C-2 caused by the C-5? Cl dipole. It is also demonstrated that, when using charges calculated by CNDO/2, the influences of the hydrogen atoms at C-5 cannot be neglected. The use of the dipole–dipole interaction formula is advocated. The consequences of taking into account the additional contributions of the vinylic bonds to the accumulated charges at C-1 and C-2 are described. The results with the dipole–dipole formula show that the same signs and similar magnitudes of the LEF effects are calculated in seven out of nine conformations of 5-chloro-1-pentene. This reduces the LEF to a means of confirming, rather than deducing, conformational equilibria in acylic flexible compounds. The usefulness of some recently published applications of the LEF concept to explain some short range substituent effects is critically discussed, mainly in view of the inhomogeneities of the calculated electric fields.     

Kinetic theory of hydrodynamic flows. I. The generalized normal solution method and its application to the drag on a sphere

We consider the flow of a dilute gas around a macroscopic heavy object. The state of the gas is described by an extended Boltzmann equation where the interactions between the gas molecules and the object are taken into account in computing the rate of change of the distribution function of the gas. We then show that the extended Boltzmann is equivalent to the usual Boltzmann equation, supplemented by boundary conditions imposed on the distribution function at the surface of the object. The remainder of the paper is devoted to a study of the solution of the extended Boltzmann equation in the case that the mean free path of a gas molecule is small compared to some characteristic dimension of the macroscopic object. We show that the Chapman-Enskog normal solution of the ordinary Boltzmann equation is not in general a solution of the extended equation near the surface of the object and must be supplemented by a boundary layer term. We then introduce a projection operator method which allows us to decompose the solution of the extended equation into a normal solution part and a boundary layer part when the gas flow is sufficiently slow. As a specific example of the method we consider the flow around a sphere, and derive the Stokes-Boussinesq form for the frequency-dependent force on the sphere for arbitrary slip coefficient. This derivation is the first one that starts from the Boltzmann equation for a general dilute gas and incorporates the effect of the boundary layer on the drag force.Work supported by the National Science Foundation.     

Alkylsilver(I) induced 1,5-substitution in functionally conjugated enynes. a novel route to cumulated trienes

Functionally conjugated enynes, H₂CC(R¹)CCCR²R₃OS(O)Me, undergo 1,5-substitution with alkylsilver(I) reagents, RAGG ☆ 3 LiBr. The purity of the produced alkylated butatrienes, RCH₂C(R¹)CCCR²R³ depends on the nature of R in RAg ☆ 3 LiBr and on the substituents R¹, R² and R³ in the substrate.     

Boundary relations and their Weyl families

The concepts of boundary relations and the corresponding Weyl families are introduced. Let be a closed symmetric linear operator or, more generally, a closed symmetric relation in a Hilbert space , let be an auxiliary Hilbert space, let

and let be defined analogously. A unitary relation from the Krein space to the Krein space is called a boundary relation for the adjoint if . The corresponding Weyl family is defined as the family of images of the defect subspaces , , under . Here need not be surjective and is even allowed to be multi-valued. While this leads to fruitful connections between certain classes of holomorphic families of linear relations on the complex Hilbert space and the class of unitary relations , it also generalizes the notion of so-called boundary value space and essentially extends the applicability of abstract boundary mappings in the connection of boundary value problems. Moreover, these new notions yield, for instance, the following realization theorem: every -valued maximal dissipative (for ) holomorphic family of linear relations is the Weyl family of a boundary relation, which is unique up to unitary equivalence if certain minimality conditions are satisfied. Further connections between analytic and spectral theoretical properties of Weyl families and geometric properties of boundary relations are investigated, and some applications are given.

     

Monte Carlo study of supramolecular polymer fractionation: selective removal of chain stoppers by phase separation

Supramolecular polymers consist of bifunctional monomers that join and break reversibly. Supramolecular polymer solutions are often polluted by monofunctional contaminants, which drastically reduce the chain-forming capabilities of the system. Unfortunately, the monofunctional contaminants are difficult to remove due to the physical and chemical resemblance with the bifunctional counterparts. In this paper, we present a method to specifically remove the monofunctional contaminants from a supramolecular polymer solution. The general idea is to induce phase separation by decreasing the solvent quality and to remove the most dilute phase. This concept is explored by means of a recently developed Monte Carlo scheme to calculate the compositions of the coexisting liquid phases. The simulations provide a proof of principle that the proposed purification method is suitable to remove the monofunctional contaminants efficiently. The calculations indicate that, at the right experimental conditions, the vast majority of the monofunctional contaminants can be removed in this way while retaining most of the bifunctional monomers. Because of the general nature of the arguments presented here, it is to be expected that the results are applicable to a large variety of supramolecular systems. Moreover, the method is very suitable for large-scale applications because only solvent is added and no tedious chromatographic steps are required.     

Correlated Fractal Percolation and the Palis Conjecture

Let F ₁ and F ₂ be independent copies of one-dimensional correlated fractal percolation, with almost sure Hausdorff dimensions dim?_H(F ₁) and dim?_H(F ₂). Consider the following question: does dim?_H(F ₁)+dim?_H(F ₂)>1 imply that their algebraic difference F ₁?F ₂ will contain an interval? The well known Palis conjecture states that ‘generically’ this should be true. Recent work by Kuijvenhoven and the first author (Dekking and Kuijvenhoven in J. Eur. Math. Soc., to appear) on random Cantor sets cannot answer this question as their condition on the joint survival distributions of the generating process is not satisfied by correlated fractal percolation. We develop a new condition which permits us to solve the problem, and we prove that the condition of Dekking and Kuijvenhoven (J. Eur. Math. Soc., to appear) implies our condition. Independently of this we give a solution to the critical case, yielding that a strong version of the Palis conjecture holds for fractal percolation and correlated fractal percolation: the algebraic difference contains an interval almost surely if and only if the sum of the Hausdorff dimensions of the random Cantor sets exceeds one.     

Persistence Properties of Normally Hyperbolic Tori

Near-resonances between frequencies notoriously lead to small denominators when trying to prove persistence of invariant tori carrying quasi-periodic motion. In dissipative systems external parameters detuning the frequencies are needed so that Diophantine conditions can be formulated, which allow to solve the homological equation that yields a conjugacy between perturbed and unperturbed quasi-periodic tori. The parameter values for which the Diophantine conditions are not fulfilled form so-called resonance gaps. Normal hyperbolicity can guarantee invariance of the perturbed tori, if not their quasi-periodicity, for larger parameter ranges. For a 1-dimensional parameter space this allows to close almost all resonance gaps.     

Suppression of thermally excited capillary waves by shear flow

We investigate the thermal fluctuations of the colloidal gas-liquid interface subjected to a shear flow parallel to the interface. Strikingly, we find that the shear strongly suppresses capillary waves, making the interface smoother. This phenomenon can be described by introducing an effective interfacial tension that increases with the shear rate. The increase of sigma(eff) is a direct consequence of the loss of interfacial entropy caused by the flow, which affects especially the slow fluctuations. This demonstrates that the interfacial tension of fluids results from an intrinsic as well as a fluctuation contribution.