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  • 1
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 481-505 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we provide a theory of the asymptotic expansion for an abstract kinetic equation. We show that the modified Chapman-Enskog procedure, introduced in [19], gives the error of order of ε2, uniformly in time, on the second level of approximation and in particular that the zeroth moment of the solution (the spatial density of particles) can be approximated by the solution of the diffusion-type equation with the same accuracy. The theory is applied to several types of kinetic equations with the Fokker-Planck collision operator.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 555-569 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A mathematical approach to the concept of shape of a submanifold M of a Euclidean space had previously been given by means of ‘measuring functions’ (e.g. diameter or volume) and of the derived ‘size functions’. This paper relates the study and the computation of any such size function to the structure of critical points of the associated measuring function.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 593-605 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on Clifford analysis. Applications to the quantum field theory are described.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 699-716 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the system of elastic waves in three dimensions under the presence of an impurity of the medium which we represent by a real-valued function q(x) (or q(x,t)). The medium is assumed to be isotropic and occupies the whole space Ω = ∝3. We study the location of the scattering frequencies associated with such phenomenon. We conclude that there is a large region on the complex plane which is free of scattering frequencies. In the remaining region they are discrete provided that q satisfies suitable assumptions concerning its behaviour at infinity.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 717-736 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider parabolic systems defined on cylindrical domains close to the threshold of instability, in which the Fourier modes with positive growth rates are concentrated at a non-zero critical wave number. In particular, we consider systems for which a so-called Ginzburg-Landau equation can be derived. Due to the presence of continuous spectrum, classical bifurcation theory is not available to describe bifurcating solutions. Thus, we consider a modified system with artificial spectral gap, which possesses an infinite-dimensional centre manifold. The amplitude equation on this manifold is called a generalized Ginzburg-Landau equation. From previous work [18] it is known that the Fourier modes are exponentially concentrated at integer multiples of the critical wave number. Hence, the error made by this modification is exponentially small in powers of the bifurcation parameter. The approximations obtained via the generalized Ginzburg-Landau equation are valid on a much longer time scale than those obtained by using the classical Ginzburg-Landau equation as an amplitude equation.
    Additional Material: 2 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 825-845 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A review of exact solutions of discrete velocity models is given. Different methods of constructing the solutions are discussed. New methods are proposed for the stationary Broadwell model, and new class of solutions is obtained. Two-dimensional flows in channel are studied on the basis of exact solutions and analogy with the Carleman model. Explicit example of non-unique solution to a boundary value problem is given. Exact hydrodynamic equations are derived for the stationary Broadwell model. A role of the Navier-Stokes approximation is discussed in detail by comparison with these exact equations.
    Additional Material: 2 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1-13 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The albedo and scattering operators are central objects in the time-dependent transport theory. Their mutual relationship has recently been established by Arianfar and Emamirad for the case of transparent boundaries. In this paper, we extend the result to general boundary conditions. To allow for this extension, the scattering theory for a transport-like equation is generalized to include partially reflecting boundary conditions. The existence of the wave and scattering operators is directly inferred from the properties of the evolution operators that are determined, in turn, by the physics of collisions within and at the boundaries of the scattering domain.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 257-285 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of determining bilinear combinations of holomorphic and antiholomorphic generalized hypergeometric type integrals left invariant under the action of the monodromy groups of the integrals is studied. In the special cases of simple Pochhammer type integrals and of twofold hypergeometric type integrals the existence and uniqueness of the bilinear invariants are proved, and the bilinear invariants are explicitly computed. Preparing the tools it is shown how to linearize and iterate representations of the braid group Bn as automorphism groups of certain free subgroups of the braid group Bn+1, and how the resulting iterated linear representations of the braid group in a natural way provide an algorithm to compute the monodromy group of generalized hypergeometric type integrals. Explicit formulae for different types of integration contours are given in the case of simple and twofold integrals.
    Type of Medium: Electronic Resource
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 255-255 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 363-374 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Periodic solutions of arbitrary period to semilinear partial differential equations of Zabusky or Boussinesq type are obtained. More generally, for a linear differential operator A(y,∂), the equation A(y,∂)u = (-1)∣γ∣∂γf(y,∂γu), y = (t,x)∊∝k×G is studied, where homogeneous boundary conditions on ∂G and periodicity conditions on t are imposed. The solutions are obtained by variational methods in anisotropic Sobolev spaces.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 401-424 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The quasi-hydrodynamic carrier transport equations for semiconductors extended to Fermi-Dirac statistics are considered. It is shown that in the high injection case, these equations reduce to a drift-diffusion model with non-linear diffusion terms. The limiting procedure is proved rigorously and error estimates are shown. We compute numerically static voltage-current characteristics of a forward biased pn-junction diode and compare the curves with the corresponding characteristics obtained from the standard drift-diffusion model based on Boltzmann statistics. It turns out that there exists a so-called threshold voltage at which the behaviour of the characteristic changes. Under high injection conditions, the dependence of the current on the bias appears to be approximately polynomial. The characteristics are studied analytically for a unipolar device.
    Additional Material: 6 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 529-554 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 639-649 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for discontinuous initial perturbations this solution is infinitely differentiable with respect to time t and space co-ordinates for t〉0 on a bounded time interval.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 679-697 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a non-linear generalized initial-boundary value problem of a scalar conservation law which models the sedimentation of an ideal suspension.
    Additional Material: 7 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 761-772 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For a linear coagulation kernel and a constant fragmentation kernel we prove the existence of equilibrium solutions and examine asymptotic properties for time-dependent solutions which are proved to converge to the equilibria. The rate of the convergence is estimated. It is shown also that all time-dependent solutions with the same density can tend to only one particular steady-state solution. In this sense the equilibrium solution is proved to be unique. Existence, uniqueness and mass conservation of time-dependent solutions has been proved in a previous paper by the authors [10].
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 847-856 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Using the invariance principle in a Banach space with less restriction, we discuss the asymptotic behaviour of an integro-differential equation with infinite delay which is an infection disease model. It is proved that the equilibria are globally asymptotic stable if the parameters fit some relation and the integral kern satisfies a convergence condition.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 897-907 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a non-linear plate equation of Bernoulli-Euler type with a locally distributed damping term. Our main result asserts that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially. The method we use is a combination of multiplier techniques and of a compactness-uniqueness argument.
    Type of Medium: Electronic Resource
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 287-312 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Child-Langmuir asymptotics of the Vlasov-Poisson system provides a model for vacuum diodes which operate under large biases. In these conditions the energy of the injected particles at the cathode is very small compared with the applied external bias. From the mathematical view point, this leads to an interesting and non-standard asymptotic problem for the Vlasov-Poisson equation, which has already been investigated in the one-dimensional Cartesian case, in [7]. The purpose of this paper is to extend the analysis to the cylindrically or spherically symmetric case. Surprisingly, the behaviour of the solutions of the model is somehow different than in the Cartesian case. This feature had not been noticed by the physicists before. Furthermore, the mathematical analysis is much more involved than in [7] because of the geometrical effects, and the techniques that are used are quite different. They mainly rely on the use of supersolutions in the spirit of [18, 19]. This work is divided in two parts. In this first part, we state the problem and establish the basic estimates which are needed for the asymptotic analysis.
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  • 23
    Electronic Resource
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 375-380 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper an asymptotic result concerning the interface for some problems connected with radially symmetric non-linear diffusion is presented.
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  • 24
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 425-450 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Van Roosbroeck's bipolar drift diffusion equations cover the qualitative behaviour of many semiconductor devices. The complexity of the model equations however prevents efficient implementations needed in circuit simulations. Under close-to-thermal-equilibrium biasing conditions (zero space charge assumption, low injection limit) the van Roosbroeck system can be replaced by a system of coupled non-linear Volterra integral equations of the second kind. Involving only the macroscopic quantities current, applied voltage and serial resistance this Volterra system can be handled with comparably little effort. Volterra integral equations models are formulated for a large class of semiconductor devices with abrupt pn-junctions. The model equations are made explicit for diodes, transistors and thyristors. A survey on various results concerning Volterra models describing the switching behaviour of pn-diodes is given. The integral equation model allows to recover all relevant properties of the voltage-current characteristics.
    Additional Material: 4 Ill.
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  • 26
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1317-1333 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give new finite time blow-up results for the non-linear parabolic equations ut-Δu = up and ut-Δu+μ∣∇u∣q = up. We first establish an a priori bound in Lp+1 for the positive non-decreasing global solutions. As a consequence, we prove in particular that for the second equation on ∝N, with q = 2p/(p+1) and small μ〉0, blow-up can occur for any N≥1, p〉1, (N-2)p〈N+2 and without energy restriction on the initial data. Incidentally, we present a simple model in population dynamics involving this equation.
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  • 27
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1397-1407 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
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  • 28
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 15-31 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We analyse the time decay of solutions to the Cauchy problem for the linear hyperbolic system of elasticity for anisotropic media. As an example, we will consider media with hexagonal symmetry. First we derive decay estimates for special initial data using the method of stationary phase in several variables and degenerate phase function based on the Malgrange preparation theorem. Asymptotic expansions are given to prove the sharpness of the weaker time decay found for zinc and beryl than in the isotropic case. A method using Besov spaces leads to Lp-Lq-estimates.
    Additional Material: 4 Ill.
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  • 29
    Electronic Resource
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 63-85 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the effective numerical treatment of elliptic boundary value problems when the solutions contain singularities. The paper deals first with the theory of problems of this type in the context of weighted Sobolev spaces and covers problems in domains with conical vertices and non-intersecting edges, as well as polyhedral domains with Lipschitz boundaries. Finite element schemes on graded meshes for second-order problems in polygonal/polyhedral domains are then proposed for problems with the above singularities. These schemes exhibit optimal convergence rates with decreasing mesh size. Finally, we describe numerical experiments which demonstrate the efficiency of our technique in terms of ‘actual’ errors for specific (finite) mesh sizes in addition to the asymptotic rates of convergence.
    Additional Material: 12 Ill.
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  • 30
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 171-185 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that the non-linear coagulation-fragmentation equation with constant kernels has a unique equilibrium solution. This equilibrium solution is given explicitly in terms of the initial data and the kernels. Weak L1 convergence of time-dependent solutions to the unique equilibrium is demonstrated via an invariance principle employing a suitable lower semicontinuous Lyapunov functional.
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  • 31
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 217-233 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The mixed-Neumann problem for the non-linear wave equation □u-a(u)(∣∂tu)∣2-∣∇u∣2 = fε(z) is studied. The function fε(z) = ∑k∊Kfk(z,ε-1φk(z),ε), ε∊[0,1], K is finite, fk(z,θk,ε) are 2π-periodic with respect to θk. The existence of solution uε on a domain z = (t,x,y)∊[0,T]×∝+×∝d, d = 1 or 2, is proved when ε is sufficiently small; T does not depend on ε. By the non-linear geometric optics method the asymptotic (with respect to ε→0) solution ũ ε is constructed. The estimation for the rest ε2rε = uε-ũε is derived and the limit rε, ε→0, is studied.
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  • 32
    Electronic Resource
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 33
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper analyses the Child-Langmuir asymptotics of the Vlasov-Poisson problem in cylindrical or spherical symmetry. The problem was stated in the first part of this paper [2]. We recall that the Child-Langmuir asymptotics concerns the boundary value problem for the Vlasov-Poisson system in the situation where the thermal energy of the injected particles at the boundary is small compared with the external applied bias.In the first part, we derived the set of estimates which allow us to pass to the limit in the asymptotic problem. In the present part, we analyse the limit (or ‘reduced’) problem, which leads us to a characterization of the limit or ‘Child-Langmuir’ current which flows through the system.
    Additional Material: 8 Ill.
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  • 34
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 341-361 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Lyapunov stability is analysed for a class of integro-differential equations with unbounded operator coefficients. These equations arise in the study of non-conservative stability problems for viscoelastic thin-walled elements of structures. Some sufficient stability conditions are derived by using the direct Lyapunov method. These conditions are formulated for arbitrary kernels of the Volterra integral operator in terms of norms of the operator coefficients. Employing these conditions the supersonic flutter of a viscoelastic panel is studied and explicit expressions for the critical gas velocity are derived. Dependence of the critical flow velocity on the material characteristics and compressive load is analysed numerically.
    Additional Material: 5 Ill.
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  • 35
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 381-400 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The equations describing the dynamics and steady states of a tubular reactor are studied in the region where an arbitrary number of steady-state solutions exist. The stability of these solutions is examined and their persistence for increases in the parameter values is determined. The physical implications of these solutions are examined.
    Additional Material: 3 Ill.
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  • 36
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 451-461 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use the implicit function theorem to prove an existence of a heteroclinic orbit to a system of two non-linear second-order ODEs. The perturbation is carried out around infinite value of a ‘coupling parameter’. The form of the system which is considered in this paper is related to the system defining travelling wave solutions in a two temperature model of the laser sustained plasma.
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  • 37
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 33-51 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we generalize the abstract results of Mock and Marcowich [13, 12] for convergence of discrete Van Roosbroeck systems [12, 13, 17], to the case when the solutions are typically in W1,4-ε and not in H2. These conditions are verified on finite element discretizations. Error estimates are derived when the solution is unique. Due to the singularity at the flat angles, these estimates in the H1 norm are only O(h1/2). The techniques that are presented are broad and may be applied to other type of discretizations.
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  • 38
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 39
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 40
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1335-1347 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Explicit a priori continuous dependence estimates are derived for the Brinkman equations for non-isothermal flow in porous media. Continuous dependence on the cooling coefficient is shown when a boundary condition of Newton cooling type is employed. Continuous dependence on the model itself is proved when the Boussinesq model is allowed to change to one appropriate to penetrative convection. The final result derives an a priori continuous dependence estimate for the heat supply and body force.
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  • 41
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1349-1395 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Lie's theory in its current formulation is linear, local and canonical. As such, it is not applicable to a growing number of non-linear, non-local and non-canonical systems which have recently emerged in particle physics, superconductivity, astrophysics and other fields. In this paper, which is written by a physicist for mathematicians, we review and develop a generalization of Lie's theory proposed by the Italian-American physicist R. M. Santilli back in 1978 when at the Department of Mathematics of Harvard University and today called Lie-Santilli isotheory. The latter theory is based on the so-called isotopies which are non-linear, non-local and non-canonical maps of any given linear, local and canonical theory capable of reconstructing linearity, locality and canonicity in certain generalized spaces and fields. The emerging Lie-Santilli isotheory is remarkable because it preserves the abstract axioms of Lie's theory while being applicable to non-linear, non-local and non-canonical systems. After reviewing the foundations of the Lie-Santilli isoalgebras and isogroups, and introducing seemingly novel advances in their interconnections, we show that the Lie-Santilli isotheory provides the invariance of all infinitely possible (well-behaved), non-linear, non-local and non-canonical deformations of conventional Euclidean, Minkowskian or Riemannian invariants. We also show that the non-linear, non-local and non-canonical symmetry transformations of deformed invariants are easily computable from the linear, local and canonical symmetry transforms of the original invariants and the given deformation. We then briefly indicate a number of applications of the isotheory in various fields. Numerous rather fundamental and intriguing, open mathematical and physical problems are indicated during the course of our analysis.
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  • 42
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 13-20 
    ISSN: 1069-8299
    Keywords: open channel flows ; Riemann solver ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient numerical method is developed for the one-dimensional open channel flow equations. The scheme is a modification of one presented recently, but with an improvement in the efficiency made through the use of the arithmetic mean as an average of flow variables across the interface between adjacent states. Numerical results are shown for two problems, and an indication of the efficiency gained is given.
    Additional Material: 6 Ill.
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  • 43
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 21-29 
    ISSN: 1069-8299
    Keywords: finite element systems ; elliptic partial differential equations ; approximate LU factorization ; explicit matrix inversion ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new class of explicit generalized approximate inverse finite element matrix algorithmic methods, based on the concept of LU-sparse factorization procedures, without inverting the decomposition factors, has recently been introduced. The large sparse unsymmetric coefficient matrix of irregular structure is factorized approximately and, in conjunction with approximate inverse matrix techniques, yields explicit preconditioned methods for the finite element (FE) and finite difference (FD) method. The numerical implementation of these algorithms is presented and Fortran subroutines for the efficient solution of the sparse unsymmetric linear systems are given.
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  • 44
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 147-148 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 45
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 149-150 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 46
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 63-73 
    ISSN: 1069-8299
    Keywords: asymptotic solution ; natural frequencies ; membrane vibrations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper an asymptotic formula has been developed to correct the discretization error for the finite element predicted natural frequencies of membrane transverse vibration problems. The general idea behind deriving this asymptotic formula is that, when the finite element size approaches zero, a discretized finite element system approaches a continuous system and the predicted natural frequencies of the system from the finite element analysis therefore approach the exact solutions of the system. Without losing generality, several different finite element mesh patterns have been considered and the same asymptotic formula for correcting the finite element predicted natural frequency has been obtained for all the different mesh patterns because of the uniqueness of the exact solution to the natural frequency of a real structure. The usefulness, effectiveness and efficiency of the present asymptotic formula have been assessed by a simple but critical problem, for which the exact solution is available for comparison. In order to investigate the applicability of the asymptotic formula to practical engineering problems, two challenging membrane vibration problems of irregular shapes, an L-shape and a tapered shape with a circular hole in the centre, have also been analysed. The related numerical results have demonstrated that the asymptotic formula provides a very useful post-processing error corrector for the finite element predicted natural frequencies of membrane transverse vibration problems, even though the problem domains are of irregular shape. The greatest advantage in using the present asymptotic formula is that it yields a solution of higher accuracy, by simply using the formula to correct the rough solution obtained from a much coarser finite element mesh with fewer degrees of freedom, without any further finite element calculation.
    Additional Material: 7 Ill.
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  • 47
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 181-190 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper develops an electrical analogue for a gearbox suitable for use in the time-domain modelling of many electromechanical systems, with tensor methods being used to define the changing conditions in the gearbox brought about by backlash. Unlike most existing models it is compatible with the time-varying and discontinuous models often used to describe the electrical items of a typical system, and it allows for the effects of these items of mechanical non-linearities and discontinuities such as friction and backlash.
    Additional Material: 9 Ill.
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  • 48
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 271-294 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Recently, a new method has been presented for the discrete simulation of multidimensional systems, which are described by linear partial differential equations with constant coefficients. It is based on methods customary in linear systems theory and digital signal processing and uses a frequency-domain representation of the continuous system to be simulated. A proper choice of functional transformations for each independent variable allows us to treat the influence of initial conditions, boundary conditions and excitation functions separately by suitable transfer functions. From these, corresponding discrete transfer functions and the structure of a discrete system for the simulation of the continuous problem are derived. The application of this method to wave propagation problems on uniform transmission lines is presented here. At first, the continuous problem is characterized by transfer functions; then the derivation of a discrete system is shown, and finally, some simulation results and a comparison with other methods are given.
    Additional Material: 12 Ill.
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  • 49
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 325-325 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
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  • 50
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 335-344 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The first part of the paper presents the implementation and performance of a new absorbing boundary condition (ABC) for truncating finite element meshes. This ABC can be applied conformally to the surface of the structure for scattering and antenna radiation calculations. Consequently, the computational domain is reduced dramatically, thus allowing the simulation of much larger structures, and results are presented for three-dimensional bodies. The latter part of the paper discusses optimization issues relating to the solver's CPU speed on parallel and vector processors. It is shown that a jagged diagonal storage scheme leads to a four-fold increase in the FLOP rate of the code, and a standard matrix profile reduction algorithm substantially reduces the inter-processor communication.
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  • 51
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996) 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
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  • 52
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 405-415 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: An improved combined fine-coarse mesh (CFCM) method for two transmission line models of diffusion is described. The method allows regular cells of different sizes to be connected and solved simultaneously. The CFCM method is applied to (a) a finite difference algorithm, (b) a conventional transmission line model and (c) a lossy transmission line model. The latter model is shown to be the most accurate. The proposed CFCM method is also compared with the graded mesh and the multigrid techniques.
    Additional Material: 9 Ill.
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  • 53
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 445-457 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The paper reviews some discrete probabilistic numerical techniques with particular emphasis on heat flow in inhomogeneous materials. The effects of different nodal configurations on the development of suitable algorithms are outlined and we suggest a new and consistent description for the discrete apparent effusivity. Our approach is then discussed in the context of TLM, and analogues are presented for flux relaxation time and effusivity.
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  • 54
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 459-461 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: We show that the general boundary condition D∂Φ/∂x + αΦ = 0 (D is the diffusion coefficient and α is a constant) in TLM diffusion modelling can be expressed accurately in terms of a voltage reflection coefficient ρ = (Δx - αΔt)/(Δx + αΔt), where Δx is the spatial resolution and Δt is the time step. Based on this general expression, the special cases of short-circuit (ρ = -1), open-circuit (ρ = 1) and matched-load (ρ = 0) boundaries can be described succinctly by α → ∞, α → 0 and α = Δx/Δt, respectively. This formulation allows for straightforward treatment of mixed boundary conditions found, for example, in diffusion-drift systems.
    Additional Material: 1 Ill.
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  • 55
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 45-57 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The paper gives an overview on mathematical optimization techniques specially suited to problems in electromagnetism. It is described how efficient optimization procedures consist of decision making, treatment of non-linear constraints, and an algorithm for minimizing the objective function. The optimization of a rectangular waveguide branching, a permanent magnet synchronous machine, and the iron cross-section of a superconducting magnet are given as examples. Optimization routines are used for the tracing of manufacturing errors in the production of superconducting coils. Finally the application of a genetic algorithm to a dipole coil design is discussed as an example for field synthesis.
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  • 56
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 81-98 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The vector and scalar variables describing electromagnetic fields with different requirements of continuity can be identified to four different degrees of differential forms. The association of differential forms with finite elements leads to a set of differential forms based elements (Whitney elements); they are naturally adapted to the discretization of different vector and scalar variables. With the help of a Tonti diagram, Maxwell equations can be classified by two dual sequences together with the constitutive laws of materials. The application of Whitney elements to the two dual sequences leads to two dual approximation schemes. As an example, two dual formulations for eddy current computation using potential variables and the hybrid finite element - boundary element method are derived, where Whitney 3-D and 2-D elements are employed. A numerical application is given at the end of the paper, where the dual features of the two formulations are reported.
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  • 57
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 125-143 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The paper proposes an iterative procedure, called current iteration, for the finite element solution of two-dimensional steady-state skin effect problems in open boundaries. In the procedure a fictitious boundary is introduced enclosing all the conductors. On it, the magnetic vector potential is first guessed and then iteratively updated according to the current density computed in the conductors. Conditions are obtained implying convergence to the exact solution of the unbounded problem whatever the initial guess. The choice of the fictitious boundary and the selection of the relaxation parameter in such a way that computational efficiency is obtained are discussed. The greatest advantage of the procedure is its ease of implementation in a pre-existing finite element code for bounded problems. An axisymmetric version of the procedure is also described since implementation only involves minor changes as compared with the 2-D one. Examples are provided in order to clarify and validate the procedure and compare it with other techniques.
    Additional Material: 11 Ill.
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  • 58
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 145-158 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: For the interpretation of human neuromagnetic data it is necessary to compute the magnetic field of a source (e.g. a dipole) in a volume conductor (e.g. a homogeneous conducting sphere or a homogeneous head model). The Multiple Multipole (MMP) method, which is a semianalytical field calculation method, is applied to neuromagnetic field calculation for the first time. The unique feature of the MMP method is that multipole expansions are used for the description of the electromagnetic field. First a validation of the MMP method is done with the help of a spherical model and an analytical solution. Then the MMP method is applied to a realistically shaped one compartment head model. The results are compared to results obtained with the Boundary Element Method (BEM). The results suggest that it is possible to solve the neuromagnetic forward problem faster with the help of the MMP method than with the conventional numerical field calculation methods for realistic shaped volume conductor models. Further investigations are necessary to tackle the inverse problem of biomagnetism with the MMP method.
    Additional Material: 10 Ill.
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  • 59
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 201-214 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Charged particle motion is incorporated within a transmission line modelling (TLM) field code to establish a new model which allows the investigation of field-particle interactions. The model is validated by using it to predict the trajectory of moving particles and the field and potential distributions inside a planar diode for which analytical solutions are available. The effect of space charge on the operation of the diode is also investigated. The model is then applied to study in detail a practical electron gun design.
    Additional Material: 12 Ill.
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  • 60
    ISSN: 0947-6539
    Keywords: azadienes ; azepines ; cycloadditions ; Fischer carbenes complexes ; reaction mechanisms ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 4-Amino-1-azadienes 1 react with α,β-unsaturated Fischer carbene complexes at -40°C to give stereoselectively a variety of substituted 3H-4,5-dihydroazepines 3; similarly, 1-hydroxy-1-azadienes (α,β-unsaturated oximes) 6 afforded the corresponding azepine derivatives 7. Chiral, nonracemic carbene complexes 11 gave azepines 12-13 (d.e. = 40-44%) upon reaction with oxime 6a; the major isomers were obtained in a diastereomerically and enantiomerically pure form (45-50% overall yield) after crystallization. An X-ray structure of 12a allowed assignment of the absolute stereochemistry. The acid hydrolysis of azepines synthesized provided racemic and enantiomerically pure 1,6-dicarbonyl compounds (±)-5, (±)-9, and (-)-14, as well as diol (-)-15. The mechanism of the reaction of 1 and 2 was investigated by multinuclear (1H, 13C, 15N, and 183W) NMR characterization of four intermediates (A, B, C, and D) at low temperature. The experimental sequence of events involves: i) 1,2-nucleophilic addition of the unsubstituted imine nitrogen of 1 to the metal carbene function (zwitterion A, -60°C), ii) cyclization to the seven-membered ring with 1,2-migration of the pentacarbonyl metal (zwitterion B, -40°C), iii) reductive elimination and coordination of the metal to the amine nitrogen (intermediate C, -40°C), and iv) thermal decomplexation and tautomerization (intermediate D and compound 3, above -20°C).
    Additional Material: 6 Ill.
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  • 61
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    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996), S. cpi 
    ISSN: 0947-6539
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 62
    Electronic Resource
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    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996) 
    ISSN: 0947-6539
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 63
    ISSN: 0947-6539
    Keywords: homolytic cleavage ; organometallic compounds ; photochemistry ; rhenium complexes ; time-resolved spectroscopy ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: MLCT excitation of the complexes [Re(R)(CO)3(α-diimine)] (R = Me, Et, benzyl (Bz); α-diimine = iPr-PyCa, R′-DAB) results in the homolysis of the Re-R bond leading to the formation of radicals R. and [Re(CO)3(α-diimine)]. as primary photoproducts. The quantum yield of this photoprocess is dependent on the alkyl group used. For R = Me, the quantum yield is low (10-2) and depends on the temperature and excitation wave-length, whereas for R = Et and Bz the quantum yield is near unity and independent of T and λexc. The reaction is shown to proceed via a σ(Re-R)π* excited state that is rapidly (〈 20 ps) populated by a nonradiative transition from the optically excited MLCT state. Time-resolved IR and UV/Vis absorption spectra studied in the ns-μs and ps-μs time domains, respectively, show that the σπ* excited state is rather long-lived (τ ≈ 250 ns) in noncoordinating solvents; the dissociation of the Re-R bond from this state is strongly accelerated by polar or coordinating solvents (τσπ*〈 20 ps). The σπ* excited state is spectroscopically characterized by a (presumably σπ* → MLCT) transition at approximately 500 nm and by CO stretching frequencies closely resembling their ground-state values. The relative energies of the MLCT and reactive σπ* states, controlled by the nature of the alkyl lig-and, determine the photoreactivity of the complexes.
    Additional Material: 8 Ill.
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  • 64
    ISSN: 0947-6539
    Keywords: dendrimers ; high-spin molecules ; photochemistry ; polycarbenes ; solid solutions ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A “starburst”-type nonadiazo compound was designed and synthesized by using the cyclotrimerization of 3,5-dibenzylphenyl ethynyl ketone as a key step. The diazo compound was photolyzed in methyltetrahydrofuran solid solution at cryogenic temperatures and analyzed by means of Faraday magnetometry and EPR spectroscopy. While the m-phenylene-connected nonacarbene was predicted to have a nonadecet (S = 9) ground state, the magnetic data of the photoproduct was more consistent with a pentadecet (S = 7) species. The result was interpreted in terms of the intramolecular cross-linking between the carbene centers by the determination of both the amount and the multiplicity of the spin. In the “starburst”-type polycarbenes with extended branching, the reactive carbene centers are able to approach one another and thus appear to readily recombine. This study highlights one of the limitations of the extension of the carbene network by way of flexible “starburst”-type structures.
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  • 65
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    Chemistry - A European Journal 2 (1996), S. 382-384 
    ISSN: 0947-6539
    Keywords: asymmetric synthesis ; chirality ; enolates ; hydrogen bonds ; structure elucidation ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The reaction of acetophenone with tetrabutylammonium hydroxide affords the tetrabutylammonium enolate of phenyl (2-hydroxy-2-phenyl)propyl ketone. The crystal structure of this chiral enolate shows intramolecular hydrogen bonding between the hydroxyl group and the enolate oxygen atom. Furthermore, the α-methylene units of the ammonium counterion form hydrogen bonds to the basic enolate C and O atoms and to the O atom of the hydroxy group. This three-point bonding occurs selectively on the Re,Re side, a phenomenon which may be responsible for the direction of diastereo-selectivity in the epoxide-forming reaction of the enolate with N-bromosuccinimide.
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  • 66
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    Chemistry - A European Journal 2 (1996), S. 390-397 
    ISSN: 0947-6539
    Keywords: band structures ; hypervalent bonding ; semiempirical calculations ; tellurium compounds ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The bonding in the recently reported Cs3 Te22 phase, which contains both Te8 rings and remarkable Te6 sheets, is studied by approximate molecular orbital theory. Our focus is on the geometric and electronic features of the unique 2,3-connected Te net found as a substructure in this phase. The calculations show that both the linear and T-shaped Te geometries in the 2,3-connected Te net of Cs3 Te22 are determined by their particular electron count. Both types of tellurium atoms are hypervalent; we make connections to other well known hypervalent molecules, such as XeF2, I3-, and BrF3. Several possible variations and distortions of this net are discussed, all of which are found to be less stable. The discrete crown-shaped Te8 units that appear in the phase show normal covalent bonding and should occur in smaller molecular entities, too. According to our computations, Cs3 Te22 should be metallic. Two structurally related phases, CsTe7 and Cs2 Te15, are suggested.
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  • 67
    ISSN: 0947-6539
    Keywords: carbon-carbon coupling ; carbonyl complexes ; hafnium complexes ; ketenylidene complexes ; zirconium complexes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The biscyclopentadienyldicarbonyl derivatives of zirconium(II) and hafnium(II) ([MCp2(CO)2]; M=Zr, Hf) promote the reductive coupling of coordinated carbon monoxide to give, in the presence of N,N-dialkylcarbamtes of the tetravalent metals [M(O2CNR2)4], the ketenylidene complexes [M3Cp2(μ2-CCO)-(μ3-O)(O2CNR2)6] (1 a: M=Zr, R=Et; 1 b: M=Zr, R=iPr; 2: M=Hf, R=iPr). The yields of the isolated zirconium complexes are as high as 60%, while that of the hafnium derivative is 40%. The X-ray crystal structure analysis of 1 b shows that it consists of trinuclear molecules, with the three zirconium atoms held together by the bidentate C2O ligand, by the tridentate bridging oxide and by the bidentate carbamato groups. Labelling experiments with [ZrCp2(13CO)2] show that the ketenylidene ligand originates from the coordinated CO groups. These ketenylidene complexes, which are rare examples of compounds containing a CCO but no CO ligand, are characterized by an intense IR band at about 2015 cm-1, associated with the bridging C2O ligand. The ketenylidene group of 1 b was readily removed and replaced by a bidentate μ-oxo ligand of the same hapticity by reaction with carbon dioxide or acetone or by thermal decomposition. The resulting product [Zr3Cp2(μ-O)(μ3-O)-(O2CNiPr2)6] (3) crystallizes in the same space group as 1 b and with similar cell constants and bond parameters.
    Additional Material: 4 Ill.
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  • 68
    Electronic Resource
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    Chemistry - A European Journal 2 (1996), S. 458-461 
    ISSN: 0947-6539
    Keywords: ab initio calculations ; barbaralanes ; borabarbaralanes ; Cope rearrangement ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The reaction of MgCOT(thf)x with tBuBF2 or PhBCl2 affords the first 9-borabarbaralanes 2 (C8H8BR, a: R = tBu; b: R=Ph). With the aminoboron dihalides BCl2NiPr2 and BCl2N(SiMe3)tBu 9-borabicyclo[4.2.1]-nona-2,4,7-trienes 3 (a: R=NiPr2, b: R=N(SiMe3)tBu) and the trans-9-borabicyclo[4.3.0]nona-2,4,7-triene 4 are obtained. The bicyclic compounds 3a and 3 b are converted into 9-borabarbaralanes 2c and 2 d, respectively, by irradiation in solution as well as by heating. All 9-borabarbaralanes 2 are fluxional in solution. In the crystalline state, the B-phenyl derivative 2b displays a well-ordered van der Waals crystal structure. The theoretical prediction that the degenerate Cope rearrangement in barbaralanes will be retarded by π-acceptor groups in the 9 position has been verified. Quantum chemical calculations employing density functional theory support and help interpret the experimental findings. The isoelectronic 9-barbaralyl cations, in contrast, have such high Cope barriers that other rearrangement pathways are followed instead.
    Additional Material: 1 Ill.
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  • 69
    ISSN: 0947-6539
    Keywords: density-functional theory ; liquid water ; molecular dynamics simulations ; NMR chemical shifts ; solvent effects ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The solvent effect on the NMR chemical shielding in liquid water is calculated from a combination of molecular dynamics simulations and quantum chemical calculations for protons and 17O. The simulations are performed with three different potentials, ab initio as well as empirical ones, to study the influence of the force field. From the liquid configurations obtained in these simulations, molecules are randomly chosen together with neighbouring molecules to give clusters of water typical for the liquid at the selected temperature and density. Different cluster sizes are studied. The clusters are treated as supermolecules in quantum chemical calculations of chemical shifts by sum-over-states density functional perturbation theory with individual gauge for localised orbitals. The influence of the quantum chemical method is studied with an ab initio coupled Hartree-Fock gauge including atomic orbitals calculations with different basis sets for a selected cluster. An average over clusters yields the chemical shielding in the liquid at the selected temperature and density. The calculated values for the gas-liquid shift, which are in best agreement with experiment, are -3.2 ppm (exp. -4.26 ppm) for the proton and -37.6 ppm (exp. -36.1 ppm) for 17O, but the results depend strongly on the chosen interatomic potential.
    Additional Material: 1 Ill.
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  • 70
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    Chemistry - A European Journal 2 (1996), S. 1053-1059 
    ISSN: 0947-6539
    Keywords: chalcogenides ; periodic trends ; redox reactions ; soft chemistry ; transition metals ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The increase in energy of the sp anionic band on going from oxides to the less electronegative sulfides, selenides, or tellurides (with a similar trend in neighboring columns) facilitates anion-cation redox interactions involving the d levels of transition metal cations and the sp levels of anionic species. The interactions can induce phase transitions or gradual change within a given structural model. When a cation is reduced by electron transfer to its d levels from the sp band, holes appear at the top of the latter. Interesting soft chemistry can be carried out based on redox processes that neutralize the holes with electrons. This approach also allows particular structural types to be stabilized. Three structural domains can be recognized amongst the transition elements: 1) on the left-hand side of the periodic table layered structures are observed involving M4+ and (chalcogen)2- ions; 2) formation of sets of metal-metal bonds is then observed, the geometry of which depends on both the initial electron population and the electron transfer to the metal; 3) on the right-hand side the metals in their highest oxidation state are no longer active, and the holes at the top of the sp band are taken up by a catenation of the anions, which can lead to full polymerization of the anionic sublattice.
    Additional Material: 8 Ill.
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  • 71
    ISSN: 0947-6539
    Keywords: cyclic voltammetry ; dendrimers ; metallodendrimers ; terpyridine ; X-ray photoelectron spectroscopy ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of iron-containing metallodendrimers from the zeroth to the third generation was synthesized and characterized. The iron(II) ion of these metal complexes is encapsulated within a hydrophobic polyether dendritic envelope. X-ray photoelectron spectroscopy analysis revealed that the bonding environment of the iron atom was essentially ronment of the iron atom was essentially the same in dendrimers of different generations. However, cyclic voltammetry studies indicated that the reversibility of the metal redox process decreased in the higher-generation dendrimers. These observations were similar to those of a related electrochemical study conducted on the redox protein cytochrome C, in which the decrease in electron transfer reversibility was explained as a result of the increasing remoteness of the metal ion of the higher-generation dendrimers from the electrode surface.
    Additional Material: 6 Ill.
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  • 72
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    Chemistry - A European Journal 2 (1996), S. 1112-1114 
    ISSN: 0947-6539
    Keywords: coordination ; crystal structure ; halogen compounds ; magnesium compounds ; structure elucidation ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: MgBr2·OEt2 (1), which is commercially available and has been examined by different methods in the past, was obtained in crystalline form as a by-product of the reaction of amine-stabilised A1C1 solution with mesitylene magnesium bromide. The following unexpected structure was obtained by X-ray techniques: five-coordinate magnesium centres form trigonal bipyramids, which are connected by two common bromine atoms into chains. Structural details and especially the relationship with solid MgBr2, MgBr2·(OEt2)2 and MgI2·(OEt2)2 (2) are discussed in order to illuminate the unusual bonding in 1.
    Additional Material: 2 Ill.
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  • 73
    ISSN: 0947-6539
    Keywords: iron complexes ; magnetic susceptibility ; Mössbauer spectroscopy ; phasetransitions ; spin crossover ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The iron(II) complex [Fe(bpp)2]-(CF3SO3)2 H2O (bpp = 2,6-bis(pyrazolyl-3-yl)pyridine) shows a thermal spin transition associated with a hysteresis of approximately 140 K width. The transition temperatures T1/2 (where the fraction of HS species γHS = 0.5) are 147 K and ≍285 K in the cooling and heating directions, respectively. The compound shows the LIESST and reverse-LIESST effects at low temperatures. The relaxation of the metastable HS states generated by LIESST was observed quantitatively at temperatures between 77.5 and 85 K by Mössbauer spectroscopy. Metastable HS states can also be generated by rapid cooling of the sample. The relaxation of the metastable HS states formed by thermal spin-state trapping was monitored at temperatures between 104 and 118 K by magnetic susceptibility measurements. The relaxation mechanisms of the HS states generated by LIESST and thermal spinstate trapping are completely different. We suggest that the HS → LS relaxation after thermal spin-state trapping is triggered by an additional structural phase transition of the system.
    Additional Material: 8 Ill.
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  • 74
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    Chemistry - A European Journal 2 (1996), S. 1164-1172 
    ISSN: 0947-6539
    Keywords: allylations ; allylsilanes ; double stereodifferentiation ; ephedrine ; homoallylic alcohols ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Enantiopure homoallylic alcohols 5, which are important building blocks in organic synthesis, are obtained with an ee of greater than 99% and a yield of 75-95% by cleavage of the secondary homoallylic ethers 4 using sodium in liquid ammonia. The ethers 4 are formed with excellent diastereoselectivity and in 52-89% yield by treatment of the aldehydes 1 with the trimethylsilyl ether of N-trifluoroacetylnorpseudoephedrine (2) in the presence of a catalytic amount of TMS triflate or TMS borontriflate, followed by addition of allylsilane 3. Nearly all achiral aliphatic aldehydes employed gave a diastereoselectivity of over 99:1. With the chiral aldehydes 24, the difference between matched and mismatched pairs was low; this reveals that there is strong reagent control.
    Additional Material: 2 Tab.
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  • 75
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    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996) 
    ISSN: 0947-6539
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 76
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    Chemistry - A European Journal 2 (1996), S. 1201-1203 
    ISSN: 0947-6539
    Keywords: alkali metals ; hydrogen ; metallic hydrogen ; metallization densities ; periodicity ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We examine the density-dependent metal-nonmetal transition (MNMT) for the Group 1 elements hydrogen, rubidium and caesium. Remarkably, the experimentally observed metallization densities agree closely with those predicted from the 1927 classical theory of K. F. Herzfeld, which outlines the critical conditions necessary for the metallization of any element of the periodic system. The metallization densities of the alkali metal elements are also consistent with the quantum mechanical theory of the MNMT, as first set out by Sir Nevill Mott.
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  • 77
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    Chemistry - A European Journal 2 (1996) 
    ISSN: 0947-6539
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 78
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    Chemistry - A European Journal 2 (1996), S. 1514-1517 
    ISSN: 0947-6539
    Keywords: calcium compounds ; calorimetry ; nitrides ; ternary metal nitrides ; zinc compounds ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energetics of ternary oxide formation is reasonably well understood, but little is known of the energetics of ternary nitride formation. We have developed new procedures for high-temperature oxide melt solution calorimetry on metal nitrides and employed them to study compounds in the Ca/Zn/N system. The calorimetry utilized the easy reduction of MoO3 in the solvent to supply a pathway for rapid oxidation of “N3-” to N2 gas. These experiments represent the first high-temperature solution calorimetry of ternary metal nitrides. The results indicate that Ca3N2 acts as a basic nitride analogous to CaO in oxide systems, while Zn3N2 acts as an acidic nitride (“N3-” acceptor) in this ternary nitride system.
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  • 79
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    Chemistry - A European Journal 2 (1996), S. 1509-1513 
    ISSN: 0947-6539
    Keywords: ab initio calculations ; binding studies ; crystal packing ; drug design ; hydrogen bonds ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In the design of novel protein ligands one of the major challenges is the replacement of functional groups to modify and improve the binding characteristics. Often nitrogen- and oxygen-containing groups are exchanged, or both atoms occur in a competitive situation. We have investigated the hydrogen-bonding abilities of oxygen atoms covalently bound to two non-hydrogen atoms of which at least one is formally assigned to an sp2-type hybridization. In particular, examples in which such oxygen atoms compete with nitrogen atoms in the same molecular segment have been studied. Based on interaction energies obtained from ab initio calculations for complexes of these molecules with water, the oxygen atoms can be classified as rather weak hydrogen-bond acceptors; nitrogen atoms present in the same fragment exhibit much stronger interaction energies. The ab initio results are confirmed by the relative frequencies with which oxygen and nitrogen atoms are found to be involved in hydrogen bonding in the crystal structures of organic molecules containing the fragments of interest.
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  • 80
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    Chemistry - A European Journal 2 (1996), S. 1533-1536 
    ISSN: 0947-6539
    Keywords: catalysis ; dehydrogenations ; oxidations ; ruthenium complexes ; secondary alcohols ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Highly efficient ruthenium-catalyzed Oppenauer-type oxidations of secondary alcohols to ketones have been developed. The catalytic system consists of [(PPh3)3RuCl2] (1) and K2CO3 or [(C4Ph4COHOCC4Ph4)(μ-H)(CO)4Ru2] (2) in refluxing acetone. The catalytic reaction is of high efficiency and permits a catalyst: substrate ratio of 1:1000 at 56 °C. In some cases the initial turnover rate exceeds 1500 h-1. The reaction was found to be general and compatible with double bonds and oxidation-sensitive aromatics. With some allylic alcohols, isomerization to saturated ketones took place. The reaction proceeds by ruthenium-catalyzed dehydrogenation of the alcohol and subsequent hydrogen transfer to acetone. No primary kinetic isotope effect was observed for the catalytic reaction when α-deuterated 1-phenylethanol was employed as substrate (kH/kD=1.1); this shows that β-hydride elimination from a ruthenium alkoxide intermediate is not the rate-limiting step.
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  • 81
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    Chemistry - A European Journal 2 (1996), S. 4-6 
    ISSN: 0947-6539
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 82
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    Chemistry - A European Journal 2 (1996), S. 7-8 
    ISSN: 0947-6539
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 83
    ISSN: 0947-6539
    Keywords: carbon ligands ; diynes ; iridium compounds ; metallacumulenes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The reaction of [IrH2Cl(PiPr3)2] (2) with the pentadiyne derivative HC≡C—C≡C—CPh2OH (1) yields the five-coordinate compound [IrH(C≡C—C≡CPh2OH)Cl(PiPr3)2] (3), which photochemically rearranges to give the vinylidene-substituted isomer trans-[IrCl(=C=CH-C≡CPh2OH)(PiPr3)2] (4). On treatment of 3 with pyridine, the octahedral complex [IrH (C≡C—C≡CPh2OH)Cl(py)(PiPr3)2] (5) is formed. While attempts to eliminate water from 4 (or 5) failed, the reaction of 3 with one equivalent of trifluorosulfonic acid anhydride and two equivalents of triethylamine led to the formation of trans-[IrCl(=C=C=C=C=CPh2)(PiPr3)2] (6), which is the first neutral transition-metal complex containing a C5R2 ligand. The X-ray structural analysis of 6 reveals a perfect square-planar coordination geometry around the metal centre and an almost linear IrC5 chain with Ir-C—C and C—C—C bond angles of 174-179°.
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  • 84
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    Chemistry - A European Journal 2 (1996), S. 45-49 
    ISSN: 0947-6539
    Keywords: exchange processes ; kinetics ; NMR spectroscopy ; zirconium complexes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have shown that it is possible to inhibit the transfer of magnetization in a system with several exchanging sites in dynamic equilibrium, as in a mixture of cis- and trans-ZrCl4L2 with excess free ligand L (L = (CH3O)3PO). The forward and backward reaction rates involving two selected sites can be studied while the effect of competing exchange processes is “quenched”. This can be achieved either by selective inversion of the magnetization of the two chosen sites in the course of the reaction interval, or alternatively by inversion of the magnetization of all other sites in the exchange network. The rate of exchange from the free to the cis site was determined to be kcis←free = 0.018 s-1. In the usual methods, this process would tend to be overshadowed by the almost two hundred times faster competing exchange process from the cis to the trans site (Ktrans←cis = 3.32 s-1).
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  • 85
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    Chemistry - A European Journal 2 (1996), S. cpi 
    ISSN: 0947-6539
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 86
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    Chemistry - A European Journal 2 (1996), S. 9-18 
    ISSN: 0947-6539
    Keywords: ab initio calculations ; azaenolates ; NMR chemical shifts ; peptides ; Ramachandran maps ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Structures and conformations of the azaenolate lithium salts of amides (formamide, acetamide, and N-methylacetamide) and of the dipeptide model N-formylalaninamide were investigated by means of ab initio MO theory. Four possible structures of the lithiated C-enolates of acetamide were also included in the study. All structures were calculated at the HF/6-31+G(d) and MP2(fc)/6-31 + G(d)/HF/6-31 + G(d) levels; the lithiated azaenolates of formamide were also investigated at higher theoretical levels (up to MP4(fc)/6-311 + G(d,p)/MP2(fc)/6-311 + G(d,p)). For the lithiated azaenolates of all amides investigated, the most stable structure contains a four-membered ring in which the lithium ion is complexed by the oxygen and nitrogen atoms; the substituents attached to the carbon and nitrogen atoms of the azaenolate are in a cis arrangement. The lithiated azaenolates of acetamide are predicted to be more stable than the corresponding C-enolates. To simulate solvation, calculations on complexes of the lithiated azaenolates of formamide with up to three molecules dimethyl ether were also performed, and all azaenolates of amides were also reoptimized by ab initio reaction-field calculations. Both solvation models reduce the preference for lithium-chelated cis structures. The Ramachandran maps of the dilithiated bis(azaenolate) of N-formylalaninamide (having cis or trans arrangements of the azaenolate substituents) were scanned by MNDO calculations for conformational accessible regions. Thirteen stable structures were subsequently optimized at the HF/6-31 + G(d) ab initio level. The global minimum resembles a peptide in C7 conformation, but other conformations, not known for peptides, are close in energy. The structures of dimers of the lithiated azaenolates of N-methylacetamide and of glycinaldehyde were also calculated. The NMR chemical shielding of carbon, nitrogen, and oxygen atoms in all structures were predicted ab initio by using the gauge-including atomic orbital (GIAO) method.
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  • 87
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    Chemistry - A European Journal 2 (1996), S. 50-57 
    ISSN: 0947-6539
    Keywords: alkenes ; catalysis ; dihydroxylations ; electrophilicity ; ruthenium compounds ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Oxidative ruthenium catalysis (0.07 molequiv RuCl3·(H2o)3, 1.5 molequiv NaIO4, EtOAc/CH3CH3CN/H2O 3:3:1), beyond the usual C—C bond cleavage to give dicarbonyls, has been shown to syn-dihydroxylate a wide range of alkenes (except for strained bicyclic alkenes, sterically hindered trisubstituted alkenes, and most tetrasubstituted alkenes) to give vicinal diols rapidly (within minutes) and efficiently. The minor products are the usual oxidative fission products, namely, ketones and aldehydes or carboxylic acids, and sometimes ketols. Longer reaction times lower the yields of most diols, probably owing to oxidative glycol cleavage. Reactions with substrates containing one or more electron-with-drawing groups in conjugation with or adjacent to the alkene moiety are generally slower but give better yields. The diastereoselectivity of the present “flash” dihydroxylation, anti to the existing α-stereogenic center, with cycloalkenes is excellent whereas that with acyclic alkenes is moderate to poor. Sodium metaperiodate is still the best co-oxidant for the catalytic reaction. Aqueous acetonitrile (approximately 86%) as an alternative solvent system was found to give better yields of 1,2-diols than the original solvent system in some cases.
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  • 88
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    Chemistry - A European Journal 2 (1996), S. 475-475 
    ISSN: 0947-6539
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Ill.
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  • 89
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    Chemistry - A European Journal 2 (1996), S. 502-510 
    ISSN: 0947-6539
    Keywords: alkynes ; C-glycosides ; cobalt complexes ; cyclizations ; enzyme inhibitors ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Reaction of gluconolactone 2 with allylmagnesium bromide at low temperatures afforded ketopyranose 3, which could easily be converted into open-chain ketoses (R)-6 and (S)-6. Their reaction with lithioacetylide 9 afforded propargylic alcohol derivatives (R)-10 and (S)-10, which could not be cyclized directly to the desired C-ketosides. They were converted by standard procedures into (R)-14 and (S)-14 and then into dicobalthexacarbonyl complexes (R)-16 and (S)-16. A facile acid-catalyzed ring closure gave the desired C-ketosides (R)-18 α/β and (S)-18α/β, respectively, in different ratios. In order to demonstrate that removal of the protective groups and hydrogenation of the CC triple bond proceed smoothly, (R)-18 α was transformed into the deprotected target molecule (R)-1 α. For the assignment of the new chiral centers at C-2/2′ and at C-8, (S)-18α was transformed into azido derivative (S)-22α, which underwent intramolecular cycloaddition to afford the spiro derivative (S)-25α. Because of the conformational constraints in this molecule, unequivocal configurational assignment was possible with the help of NMR data.
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  • 90
    ISSN: 0947-6539
    Keywords: carbonyl complexes ; chiral ligands ; iron complexes ; phosphorus ligands ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Secondary phosphines such as HPPh2 and to the cationic iron dienyl complex [η5-(1R)-ethylnopadienyl)Fe-(CO)3]+ (1) by nucleophilic addition. The phosphonium salt initially formed is readily deprotonated to yield an optically active tertiary phosphine [(n4-(1 R)-ethylnopadienePPh2)Fe(CO)3] (2b). A similar reaction also occurs with [C6H7Fe-(CO)3]+ (3) and [C7H9Fe(CO)3]+ (4) to give [(C6H7PPh2)Fe(CO)3] (5) and [(C7H9PPh2)Fe(CO)3] (6) in good yields. The mechanism of formation of these novel phosphines is discussed. Complex 2 b crystallizes in the space group P212121 (no. 19); 5 crystallizes in the space group P21/c (no. 14). Like other monodentate optically active phosphines, 2 b is capable of coordinating to transition metal complexes. It forms palladium complexes on reaction with [{μ-chloro(allyl)palladium}2] as well as with [{μ-chloro[(N,N-dimethylamino-kN-2-methyl)phenyl-kC]palladium}2] (11). The latter reaction product crystallizes in the space group P31 (no. 144).
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  • 91
    ISSN: 0947-6539
    Keywords: carbohydrates ; cyclodextrin analogues ; cyclooligomerizations ; glycosylations ; nanotubes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An efficient polycondensation-cyclization approach to the synthesis of cyclodextrin analogues is demonstrated by the preparation of cyclohexaoside 1 and cyclooctaoside 2. The key intermediate, disaccharide 3, bearing the cyanoethylidene group as a glycosyl donor function and the trityloxy group as a glycosyl acceptor function was prepared in 15 steps starting from L-rhamnose and D-mannose. The crucial cyclooligomerization of the disaccharide monomer 3 was carried out in the presence of TrClO4 as a promoter with the use of ultra-dry conditions at normal concentrations. This reaction led to formation of the cyclic oligosaccharides 28 and 29 (in 34 and 31% yield, respectively), which were deprotected to afford 1 and 2, respectively. The X-ray crystal structural analysis of the cyclooctaoside 2 reveals a cylindrical shape for the cyclic oligosaccharide with C4 symmetry. Individual molecules of 2 are arranged perfectly in stacks that form nanotubes in the solid state.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 92
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996) 
    ISSN: 0947-6539
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 93
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996), S. 624-633 
    ISSN: 0947-6539
    Keywords: catenanes ; macrocycles ; rotaxanes ; self-assembly ; tetrathiafulvalenes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A general stepwise approach is described for the preparation of tetrathiafulvalene (TTF)-based linear and monoand dimacrocyclic compounds incorporating one or two 1,4-dioxyphenylene, 9,10-dioxyanthrylene, or 1,5- or 2,6-dioxynaphthylene units from readily available starting materials. By utilizing the π-π stacking interactions of the TTF unit with the dipyridinium dication of 1,1′-[1,4-phenylenebis (methylene)] bis-4,4′-bipyridinium bis(hexafluorophosphate), a rotaxane and two [2]catenanes were synthesized starting from the linear and monomacrocyclic compounds, respectively. From the dioxyphenylene-based dimacrocycle, three [3]pseudocatenanes (trans, cis, and a mixture of cis/trans isomers) were obtained with the trans compound as the major product. From the dioxyanthrylene dimacrocycle, only the trans-[3]pseudocatenane was obtained. Catenane products were formed quantitatively from the 1,5-dioxynaphthylene dimacrocycle in a template-directed reaction, affording a trans-[3]pseudo-catenane together with a [4]pseudocatenane (mixture of cis/trans isomers). From the 2,6-dioxynaphthylene dimacrocycle, a cis-[3]pseudocatenane was obtained as the major product and a trans-[3]pseudocatenane as the minor one. For the [3]pseudocatenanes (i.e., both the cis and trans catenanes), in which the TTF units were clamped by the tetracationic macrocycle, isomerizations were completely prevented even in the presence of trifluoroacetic acid. All new rotaxanes and catenanes were characterized by electrospray mass spectrometry, and the cis- and trans- [3]pseudocatenanes were additionally investigated by 1H NMR spectroscopy. The electrochemical and spectral properties of the rotaxane and the catenanes are reported. Catenane formation increases the redox potentials of the TTF unit. The results demonstrate the versatility of TTF as a building block in the construction of supramolecular structures.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 94
    ISSN: 0947-6539
    Keywords: chemoselectivity ; cinchona alkaloids ; clathrates ; osmium tetroxide ; spiro compounds ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Hydrobromination of quinidine (1) with fuming HBr furnished diastereomeric secondary bromides 2a and 2b in 82% yield. After acetylation the resulting bromides 2a-Ac and 2b-Ac could be separated na dconverted stereospecifically into ethylidene rubanes Z)-4 and (E)-4, respectively. cis-Dihydroxylation of (Z)-olefin 4 with OsO4 was shown to be feasible by two catalytic variants, giving the two diastereomeric diols 5a and 5b, separable by chromatography. A simple onepot procedure was developed for converting the sterically hindered 1,2-secondary, tertiary diols stereospecifically into spiroepoxides (5a 6a-Ac; 5b 6b-Ac). Our procedure involves overall inversion of configuration. The procedure complements the Kolb-Sharpless route to epoxides from 1,2-disecondary diols with overall retention of configuration. The other two diastereomeric spiroepoxides 6c and 6d were prepared in one pot under different conditions (chloramine T, then alkali). Two unprecedented tricyclic allylic N,O-acetals (Z)-7 and (E)-7 were also obtained. The structure of spiroepoxide 6c (as a CH2Cl2 monosolvate) and of tricyclic olefinic N,O-acetal (E)-7 was corroborated by X-ray crystallography.
    Additional Material: 1 Ill.
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  • 95
    ISSN: 0947-6539
    Keywords: asymmetric alkylations ; chiral auxiliaries ; kinetics ; organolithium compounds ; stereoselective syntheses ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Complexation of the configurationally labile α-phenylselenoalkyllithium compound 8 with 1,2-bisdimethylaminocyclohexane 15 led to two diastereomeric complexes 13 and 14 in a 7:3 ratio. Owing to ligand acceleration the complexes 13 and 14 added more rapidly to benzaldehyde than the uncomplexed organolithium compound 8. Trapping of complexes 13 and 14 by benzaldehyde was shown to occur more rapidly than their equilibration. This corresponds to non-Curtin-Hammett kinetics, in which enantiomeric enrichment in the products reflects the equilibrium ratio of the complexes 13 and 14.
    Additional Material: 1 Ill.
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  • 96
    ISSN: 0947-6539
    Keywords: amphiphiles ; cytomimetic chemistry ; phosphitylation ; polyprenols ; vesicles ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Identical- and mixed-chain di(polyprenyl) phosphates, derived from 3-methyl-2-buten-1-ol, (E)-geraniol, (E,E)-farnesol, (E,E,E)-geranylgeraniol, (R)-citronellol, or (R)-tetrahydrogeraniol have been synthesized by phosphitylation and oxidation with iodine/water. These phosphates gave organized systems in water, in particular vesicles, the physical properties of which were studied by photon correlation spectroscopy, electron microscopy, entrapment of a fluorescent dye (calcein), 31P NMR, stopped-flow/light-scattering studies, and fluorescence polarization with lipophilic probes. Interdigitation of mixed-length phosphates was not found to have any favorable effect on the stability of the vesicles. The C〉15 vesicles were formed despite the fact that they are composed of only one molecular species and are devoid of any reinforcer, but those with two geranyl chains appeared to be rather fragile. Phosphates containing C5 chains are soluble in water. The results obtained lend weight to the hypothesis that polyprenyl phosphates might have been primitive membrane constituents, and stimulate the search for appropriate reinforcers.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 97
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996), S. 812-814 
    ISSN: 0947-6539
    Keywords: alkanes ; cracking ; isomerizations ; sulfur compounds ; superacids ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A novel family of inorganic aprotic superacids has been found. Oxochlorides and chloride of sulfur combined with aluminium halides (SOCl2·n AlX3, SO2Cl2·n AlX3, MeSO2Cl·n AlX3, CF3SO2Cl·n AlX3, S2Cl2·n AlX3; n = 2 or 3, X = Br or Cl) are found to be effective promoters for the cracking and isomerization of alkanes at room temperature.
    Additional Material: 2 Tab.
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  • 98
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996), S. 832-837 
    ISSN: 0947-6539
    Keywords: cyclophanes ; macrocyclisations ; molecular ribbons ; nanostructures ; repetitive syntheses ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The longest molecular ribbons known to date (3-10), composed of a series of [3.3]metacyclophane units, have been synthesised by means of a repetitive synthetic strategy. These multiple ring systems with up to nine bridged benzene rings in a row are the longest structurally perfect cyclophane sequences known to date. The synthetic strategy comprises three steps: ester reduction to a tetrakis(hydroxymethyl) compound, derivatisation to the corresponding tetrakis(bromomethyl) derivative, and double cyclisation with the new key building block 14, which was especially developed for this sequence. Single-crystal X-ray analyses (3 a-7 a) and 1H NMR spectroscopy (3-10) show that, regardless of their length, these molecules adopt zigzag folded all-syn conformations. π-Stacks of nanometre dimensions are thus formed.
    Additional Material: 3 Ill.
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  • 99
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996), S. 869-876 
    ISSN: 0947-6539
    Keywords: ab initio calculations ; silaguanidinium cations ; silylium cations ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Quantium mechanical calculations at the MP2/6-31 G(d) level are reported for the silaguanidinium cation Si(NH2)3+ (1) and derivatives thereof. The equilibrium structure 1a has D3 symmetry with planar amino groups rotated out of the SiN3 plane by 19.60. The Si-N bond length of 1 a (1.658 Å) is intermediate between a single and a double bond. Isodesmic reactions show that the stabilization of the silylium cation 1 a by the amino groups (63.5 kcal mol-1) is about 40% of the resonance stabilization of the guanidinium cation (159.3 kcal mol-1), but 1 a is clearly better stabilized than alkyl-substituted silylium cations. The electronic stabilization of 1 a by the amino groups is also made obvious by the calculated complexation energy with one molecule of water. The calculated stabilization through complexation of water at HF/6- 31 G(d) is markedly lower for Si(NH2)3-(H2O)+ (6) (28.8 kcal mol-1) than for SiMe3(H2O)+ (40.6 kcal mol-1). The tris(dimethylamino) silylium cation Si(N-Me2)3+ (8) is even more stable than 1 a. The complexation energy of Si(NMe2)3-(H2O)+ (10) is only 17.3 kcal mol-1. IGLO calculations of the 29Si N M R chemical shifts predict that 1 a and 8 should not show the same extremely low shielding that is calculated for alkyl-sub-stituted silylium ions. The calculated 29Si resonances for 8 are in reasonable agreement with the experimental N M R spectrum of (Me2N)3 SiB(C6F5)4. AM 1 calculations predict that the substituted tripyrrolidino silylium cation 12 would be an even better candidate for a stable tricoordinate silylium cation in condensed phases. One of the pyrrolidine rings of 12 has tert-butyl groups in the 2 and 5 positions, which serve as a steric fence around the silicon atom.
    Additional Material: 3 Ill.
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  • 100
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemistry - A European Journal 2 (1996), S. 894-900 
    ISSN: 0947-6539
    Keywords: aza-Claisen rearrangement ; azoniones ; indolizidinones ; ring contractions ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The zwitterionic aza-Claisen rearrangement of optically active 3-pyrrolidine acryl esters and various acid chlorides to generate optically active azoninones proceeds with high simple diastereoselectivity (internal asymmetric induction) and a complete 1,3-chirality transfer. The reaction path observed depends on the subsitution pattern of the allylic system: while the more electron-rich alkylated allyl amine fromed predominantly von Braun type products, the α,β-unsaturated esters could be rearranged with high yields. The azoniones thus obtained were treated with electrophiles, inducing regio- and diastereoselective transannular ring contractions. The resulting indolizidinones should be useful key intermediates in alkaloid synthesis.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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