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  • 1995-1999  (1,288)
  • 1998  (1,288)
  • Engineering  (644)
  • General Chemistry  (643)
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  • 1995-1999  (1,288)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Space science reviews 84 (1998), S. 199-206 
    ISSN: 1572-9672
    Keywords: Nuclear reactions ; Nucleosynthesis ; Abundances ; Stars:Evolution ; Interior ; Rotation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We first recall the observational and theoretical facts that constitute the so-called 3He problem. We then review the chemical anomalies that could be related to the destruction of 3He in red giants stars. We show how a simple consistent mechanism can lead to the destruction of 3He in low mass stars and simultaneously account for the low 12C/13C ratios and low lithium abundances observed in giant stars of different populations. This process should both naturally account for the recent measurements of 3He/H in galactic HII regions and allow for high values of 3He observed in some planetary nebulae. We propose a simple statistical estimation of the fraction of stars that may be affected by this process.
    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 21 (1998), S. 1-24 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the large time asymptotics of solutions u(x, t) of the wave equation with time-harmonic force density f(x)e-iωt, ω≥0, in the semi-strip Ω= (0, ∞)×(0, 1) for a given f∊C∞0(Ω). We assume that u satisfies the initial condition u=(∂/∂t)u=0 for t=0 and the boundary conditions u=0 for x2=0 and x2=1, and (∂/∂x1)u=αu for x1=0, with given α, -π≤α〈∞. Let Dα be the self-adjoint realization of -Δ in Ω with this boundary condition. For -π≤α〈0, Dα has eigenvalues λj=π2j2-α2, j=1, 2, … For j≥2 these eigenvalues are embedded in the continuous spectrum of Dα, σc(Dα)=[π2, ∞]. For α≥0, Dα has no eigenvalues. We consider the asymptotic behaviour of u(x, t), t→∞, as a function of α. In the case α=0 resonances of order √t at ω=πj, j=1, 2, …, were found in References 5 and 10. We prove that for α=-π there is a resonance of order t2 for ω=0 and resonances of order t for every ω〉0 (note that 0 is an eigenvalue of D-π). Moreover, for -π〈α〈0 there are resonances of order t at ω=√λj. The resonance frequencies are continuous functions of α for -π〈α〈0 and tend to πj, j=1, 2, … as α goes to zero.On the contrary in the case α〉0 there are no real resonances in the sense that the solution remains bounded in time as t→∞. Actually in this case, the limit amplitude principle is valid for all frequencies ω≥0. This rather striking behaviour of the resonances is explained in terms of the extension of the resolvent R(κ)=(Dα-κ2)-1 as a meromorphic function of κ into an appropriate Riemann surface. We find that as α crosses zero the real poles of R(κ) associated with the eigenvalues remain real, but go into a second sheet of the Riemann surface. This behaviour under perturbation is rather different from the case of complex resonances which has been extensively studied in the theory of many-body Schrödinger operators where the (real) eigenvalues embedded in the continuous spectrum turn under a small perturbation into complex poles of the meromorphic extension of the resolvent, as a function of the spectral parameter κ2. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Type of Medium: Electronic Resource
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  • 3
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 117-128 
    ISSN: 0170-4214
    Keywords: third-grade fluid ; existence ; uniqueness ; classical solution ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The global existence and uniqueness of classical solution of steady motions of a third-grade fluid provided assumptions on positivness of μ (coefficient of viscosity) and α1, γ (material coefficients) is proved. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 4
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 227-249 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Integral equations associated with the basic boundary value problems for the Laplace and Stokes equations are considered. The integral operators for these integral equations are interpreted as the pseudodifferential operators, and their principal symbols are calculated. The symbols are obtained in terms of the principal curvatures and the coefficients of the first quadratic form of the boundary. As a consequence, the initial approximation is suggested for the iterative methods solving the integral equations. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 5
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 327-359 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The boundary integral equation method is used to prove the convergence of the Drude-Born-Fedorov equations with variable coefficients, possibly non-smooth, to Maxwell's equations as chirality admittance tends to zero. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 6
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 565-588 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: New explicit stability conditions are derived for a linear integro-differential equation with periodic operator coefficients. The equation under consideration describes oscillations of thin-walled viscoelastic structural members driven by periodic loads. To develop stability conditions two approaches are combined. The first is based on the direct Lyapunov method of constructing stability functionals. It allows stability conditions to be derived for unbounded operator coefficients, but fails to correctly predict the critical loads for high-frequency excitations. The other approach is based on transforming the equation under consideration in such a way that an appropriate ‘differential’ part of the new equation would possess some reserve of stability. Stability conditions for the transformed equation are obtained by using a technique of integral estimates. This method provides acceptable estimates of the critical forces for periodic loads, but can be applied to equations with bounded coefficients only. Combining these two approaches, we derive explicit stability conditions which are close to the Floquet criterion when the integral term vanishes. These conditions are applied to the stability problem for a viscoelastic bar compressed by periodic forces. The effect of material and structural parameters on the critical load is studied numerically. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 5 Ill.
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  • 7
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 653-664 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In order to maintain spectrally accurate solutions, the grids on which a non-linear physical problem is to be solved must also be obtained by spectrally accurate techniques. The purpose of this paper is to describe a pseudospectral computational method of solving integro-differential systems with quadratic performance index. The proposed method is based on the idea of relating grid points to the structure of orthogonal interpolating polynomials. The optimal control and the trajectory are approximated by the m th degree interpolating polynomial. This interpolating polynomial is spectrally constructed using Legendre-Gauss-Lobatto grid points as the collocation points, and Lagrange polynomials as trial functions. The integrals involved in the formulation of the problem are calculated by Gauss-Lobatto integration rule, thereby reducing the problem to a mathematical programming one to which existing well-developed algorithms may be applied. The method is easy to implement and yields very accurate results. An illustrative example is included to confirm the convergence of the pseudospectral Legendre method, and a comparison is made with an existing result in the literature. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 2 Tab.
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  • 8
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 701-718 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article establishes the existence of a trapped-mode solution to a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls; the forces of gravity and surface tension are operative. A trapped mode corresponds to an eigenvalue of the composition of an inverse differential operator and a Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by extending previous results dealing with the case when surface tension is absent. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
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  • 9
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 501-517 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper an initial-boundary-value problem in one-space dimension is studied for the Broadwell model extended to a gas mixture undergoing bimolecular reactions. Techniques of semigroup of bounded positive operators in a suitable Banach space are used to prove existence and uniqueness of the solution on bounded time intervals whose length depends on the initial data. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 10
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 685-700 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the present work, the problem of electromagnetic wave propagation in three-dimensional stratified media is studied. The method of decoupling the electric and magnetic fields is implemented, and the spectral approach is adopted, componentwise, to the vector equation involving the electric field. Operational calculus of self-adjoint, positive operators in suitable Hilbert spaces is used to solve the corresponding initial value problems. The spectral families of these operators for the cases of the whole space and of a finite layer are constructed. A discussion on the applicability of the obtained results to physical problems is also included. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 11
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 757-780 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove under the assumption of small initial data the global existence of a classical solution to the equations in viscoelasticity, associated with a free damping boundary condition. We also show that if we choose the initial data large enough, blow up will occur in finite time. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 12
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 797-821 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the thermoelastic plate system,utt-γΔutt+Δ2u+αΔθ=0,θt-κΔθ-αΔut=0 and we make a comparison between the models in which γ=0 and γ〉0. We conclude that in the first case the plate system is of a parabolic type, while when γ〉0 the corresponding system has a hyperbolic behaviour. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 13
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 883-894 
    ISSN: 0170-4214
    Keywords: solitary wave ; stability ; long wave-short wave resonance equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper concerns the orbital stability for solitary waves of the Long Wave-Short Wave resonance equations. Since the abstract results of Grillakis et al. [7, 8] cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 14
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1049-1066 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider particle transport in a three-dimensional convex region V, bounded by the regular surface ∂V. We assume that particles are specularly reflected by ∂V and that a source q is assigned on ∂V; more general non-homogeneous boundary conditions are also discussed. The problem is non-linear because the boundary condition is not homogeneous. We prove existence of a unique strict solution and by using the theory of semigroups we derive the explicit expression of such a solution in terms of the boundary source q. In the appendix, we indicate how some properties of affine operators can be used to derive the solution. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 15
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1085-1105 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A phase-field model based on the Coleman-Gurtin heat flux law is considered. The resulting system of non-linear parabolic equations, associated with a set of initial and Neumann boundary conditions, is studied. Existence, uniqueness, and regularity results are proved. An asymptotic analysis is also carried out, in the case where the coefficient of the interfacial energy term tends to 0. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 16
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1115-1148 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We apply the Child-Langmuir asymptotics of the Vlasov-Poisson system to the case of a bipolar diode, i.e. a vacuum diode where two species of particles of opposite electric charge are flowing. This leads to a simplified model which, if at least one of the two injected currents is not too large, has a unique solution. Moreover, in that case, the currents flowing inside the diode are limited by the so-called bipolar Child-Langmuir currents. In the case of large currents, other solutions may appear, and the formation of virtual electrodes may occur inside the diode. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 17
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1107-1113 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the Cauchy problem for the equation∂u/∂t + u ∂u/∂x + u/x = 0 for x 〉 0, t ≥ 0, with u(x, 0) = u0-(x) for x 〈 x0, u(x, 0) = u0+(x) for x 〉 x0, u0-(x0) 〉 u0+(x0). Following the ideas of Majda, 1984 and Lax, 1973, we construct, for smooth u0- and u0+, a global shock front weak solution u(x, t) = u-(x, t) for x 〈 φ(t), u(x, t) = u+(x, t) for x 〉 φ(t), where u- and u+ are the strong solutions corresponding (respectively) to u0- and u0+ and the curve t → φ(t) is defined by dφ/dt (t) = 1/2[u-(φ(t), t) + u+(φ(t), t)], t ≥ 0 and φ(0) = x0.© 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 18
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1195-1206 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A variational approach to a non-linear non-local identification problem related to the non-linear transport equation is studied. Introducing a similarity transformation, the problem is formulated as an identification problem for a non-linear differential equation of second order with an additional non-local condition. For the solution of the forward problem stability in H1-norm with respect to the identification parameter is obtained. Using this result the existence of a solution to the identification problem is proved. Some results of computational experiments are given. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 19
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1233-1267 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the plate equation in a polygonal domain with free edges. Its resolution by boundary integral equations is considered with double layer potentials whose variational formulation was given in Reference 25. We approximate its solution (u, (∂u/∂n)) by the Galerkin method with approximated spaces made of piecewise polynomials of order 2 and 1 for, respectively, u and (∂u/∂n). A prewavelet basis of these subspaces is built and equivalences between some Sobolev norms and discrete ones are established in the spirit of References 14, 16, 30 and 31. Further, a compression procedure is presented which reduces the number of nonzero entries of the stiffness matrix from O(N2) to O(N log N), where N is the size of this matrix. We finally show that the compressed stiffness matrices have a condition number uniformly bounded with respect to N and that the compressed Galerkin scheme converges with the same rate than the Galerkin one. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 20
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1287-1296 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The relativistic Vlasov-Maxwell-Fokker-Planck system is used in modelling distribution of charged particles in plasma. It consists of a transport equation coupled with the Maxwell system. The diffusion term in the equation models the collisions among particles, whereas the viscosity term signifies the dynamical frictional forces between the particles and the background reservoir. In the case of one space variable and two momentum variables, we prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 21
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1415-1439 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider reactive mixtures of dilute polyatomic gases in full vibrational non-equilibrium. The governing equations are derived from the kinetic theory and possesses an entropy. We recast this system of conservation laws into a symmetric conservative form by using entropic variables. Following a formalism developed by the authors in a previous paper, the system is then rewritten into a normal form, that is, in the form of a quasilinear symmetric hyperbolic-parabolic system. Using a result of Vol'pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 22
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1479-1494 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Approximate solutions of the non-linear Boltzmann equation, which have the structure of the linear combination of three global Maxwellians with arbitrary hydrodynamical parameters, are considered. Some sufficient conditions which allow the error between the left- and the right-hand sides of the equation tend to zero, and which are calculated either in the mixed metric or in the pure integral metric, are obtained. The class of the distributions, which minimized this error for the arbitrary Knudsen number, is found. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 23
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1519-1542 
    ISSN: 0170-4214
    Keywords: non-hyperbolic systems ; two-phase flows ; dispersion terms ; symmetrization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers a system of partial differential equations of convection dispersion type, modelling a stratified two-phase fluid flow. Local existence in time is proved for a sufficiently smooth initial data, given in the set of physically admissible states. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 24
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1559-1569 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study the motion of an elastic conducting wire in a magnetic field. The motion of the conductor induces a current in the wire (Faraday's law) which, in turn produces a force on the wire. We consider the linear equation obtained by linearizing the resulting equations of motion about an equilibrium solution. This is a hyperbolic partial differential equation with a non-local term. We prove existence and uniqueness of a weak solution of an initial-boundary value problem for this equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 25
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1637-1654 
    ISSN: 0170-4214
    Keywords: generalized Stokes equations ; incompressible flow ; least-squares ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity-stress-pressure formulation) in six equations and six unknowns together with Riemann-Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H1 product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L2-norm and in the H1-norm. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 26
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1619-1635 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the two-parameter non-linear Sturm-Liouville problems. By using the variational method on general level sets, the variational eigenvalues are obtained. The purpose of this paper is to study the properties of these variational eigenvalues with respect to the parameter of general level sets. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 27
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 187-226 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the limit behaviour of solution of Poisson's equation in a class of thin two-dimensional domains, both simply connected or single-hollowed, as its thickness becomes very small. The method is based on a transformation of the original problem into another posed on a fixed domain, obtention of a priori estimates and convergence results when thickness parameter tends to zero. As an important application of abstract results we obtain the limit expressions for functions appearing in elastic beam theories as torsion and warping functions. In this way, we provide a mathematical justification and a correct definition of torsion, warping and Timoshenko functions and constants that should be used in the open and closed thin-walled elastic beam theories. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 28
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 269-279 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The generalized Möbius function and Möbius inversion formula are applied to a multiplicative semigroup. A general mathematical method based on this Möbius inversion is presented to solve inversion problems of expansions with unequally weighted terms. By this method, all the inverse lattice problems in physics can be solved concisely. The solutions of four inverse lattice problems: the Fibonacci structure, the square lattice structure, the bcc and the hcp lattice structures are given. These are difficult to be solved by other methods. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 361-374 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use the eigenfunction expansion of Green's function of Dirichlet problems to obtain sampling theorems. The analytic properties of the sampled integral transforms as well as the uniform convergence of the sampling series are proved without any restrictions on the integral transforms. We obtain a one- and multi-dimensional versions of sampling theorems. In both cases the sampling series are written in terms of Lagrange-type interpolation expansions. Some examples and the truncation error as well as the stability of the obtained sampling expansions are discussed at the end of the paper. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 393-416 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a dynamical von Kármán system in the presence of thermal effects. Our model includes the possibility of a rotational inertia term in the system. We show that the total energy of the solution of such system decays exponentially as t→+∞. The decay rates we obtain are uniform on bounded sets of the energy space. The main ingredients of our method of proof are suitable properties of a decoupled system, the energy method and the compactness of the nonlinear map associated to the von Kármán system. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 479-488 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This short article discusses the spectrum of the Neumann Laplacian in the infinite domain Ω⊂∝n, n ≥2 created by inserting a compact obstacle P into the uniform cylinder Ω0 =(-∞, ∞)×Ω′. The main result is the existence of at least one embedded eigenvalue when P is an (n -2)-dimensional surface whose unit normal is parallel to Ω′ at each point of P . The special case when P is symmetric about {0}×Ω′ is also treated. It is shown that there is at least one symmetric eigenvector and, when P is sufficiently long, at least one antisymmetric eigenvector. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 551-564 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the existence of solutions to the three-dimensional elastoplastic problem with Hencky's law and Neumann boundary conditions by elliptic regularization and the penalty method, both for the case of a smooth boundary and of an interior two dimensional crack. It is shown, in particular, that the variational solution satisfies all boundary conditions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 251-268 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The propagation of Hölder regularity of the solutions to the 3D Euler equations is discussed. Our method is a special semi-linearization of the vorticity equation combined with the classical Schauder interior estimates. © 1998 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 433-461 
    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 solution of Maxwell equations in the modelling of the scattering of a time-harmonic electromagnetic wave by an obstacle located in a two-layered medium. The use of the Silver-Müller radiation condition in each layer is shown to provide a well-posed scattering problem. The analysis is based on the study of the Green tensor, which allows to relate the radiation condition to an integral representation formula. The analyticity properties of the scattering problem with respect to the frequency are then investigated. This gives rise to a limiting absorption principle and furnishes a characterization of the resonances. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 489-499 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We apply our recently developed distributional technique [2, 3] to study time-domain asymptotics. This enables us to present a rigorous mathematical discussion and extensions of the results given by Chapman [1] and subsequent workers in this field. The present analysis is facilitated by defining functions which are distributionally small at infinity. We find that one of the advantages of using this technique is that multidimensional extensions can be derived very easily. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 519-549 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with a specific finite element strategy for solving elliptic boundary value problems in domains with corners and edges. First, the anisotropic singular behaviour of the solution is described. Then the finite element method with anisotropic, graded meshes and piecewise linear shape functions is investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates for functions from anisotropically weighted spaces are derived. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 605-617 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a general method of analysis for investigating the whirl stability of a rotor-bearing system whose appendage is flexibly attached to the spinning shaft. Sufficient conditions of asymptotic stability involving system different parameters are derived based on Liapunov's theory. An inclusive analysis of the effect of the combined flexibilities of the elastic attachment of the appendage to the shaft and the two end bearings coupled with the other various parameters of the system on the dynamic stability is presented. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 665-684 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the steady compressible Navier-Stokes equations near the equilibrium state v = 0, ρ = ρ0 (v the velocity, ρ the density) corresponding to a large potential force. We introduce a method of decomposition for such equations: the velocity field v is split into a non-homogeneous incompressible part u (div (ρ0u) = (0) and a compressible (irrotational) part ∇φ. In such a way, the original complicated mixed elliptic-hyperbolic system is split into several ‘standard’ equations: a Stokes-type system for u, a Poisson-type equation for φ and a transport equation for the perturbation of the density σ = ρ - ρ0. For ρ0 = const. (zero potential forces), the method coincides with the decomposition of Novotny and Padula [21]. To underline the advantages of the present approach, we give, as an example, a ‘simple’ proof of the existence of isothermal flows in bounded domains with no-slip boundary conditions. The approach is applicable, with some modifications, to more complicated geometries and to more complicated boundary conditions as we will show in forthcoming papers. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 619-651 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider acoustic scattering from an obstacle inside an inhomogeneous structure. We prove in the paper that if the outside inhomogeneity is known then the obstacle and possible inside inhomogeneity are uniquely determined by the fixed energy far field data. The proof is based on new mapping properties of layer potentials in spaces that specify one point. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 939-967 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The linear problem for the velocity potential around a slightly curved thin finite wing is considered under the Joukowskii-Kutta hypothesis. The exponents of possible singularities of solutions at angular points on wing's trailing edge are expressed in terms of eigenvalues of mixed boundary value problems for the Beltrami-Laplace operator on the hemisphere and the semicircle. These singularities have a structure such that the circulation function turns out to be continuous in interior angular points of the trailing edge. In the case of trapezoidal shape of the wing ends there occur square-root singularities of the velocity field at the trailing edge endpoints and the same singularities, of course, are extended along the lateral sides of the wake behind the wing. It is proved that for any angular point on the trailing edge the exponents of all above-mentioned singularities form a countable set in the upper complex half-plane with the only accumulation point at infinity. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 985-1014 
    ISSN: 0170-4214
    Keywords: Vlasov-Poisson-Fokker-Planck ; long-time behaviour ; fundamental solutions ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the long-time behaviour of solutions of the Vlasov-Poisson-Fokker-Planck equation for initial data small enough and satisfying some suitable integrability conditions. Our analysis relies on the study of the linearized problems with bounded potentials decaying fast enough for large times. We obtain global bounds in time for the fundamental solutions of such problems and their derivatives. This allows to get sharp bounds for the decay of the difference between the solutions of the Vlasov-Poisson-Fokker-Planck equation and the solution of the free equation with the same initial data. Thanks to these bounds, we get an explicit form for the second term in the asymptotic expansion of the solutions for large times. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 42
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1067-1084 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An initial-value problem modelling coagulation and fragmentation processes is studied. The results of earlier papers are extended to models where either one or both of the rates of coagulation and fragmentation depend on time. An abstract integral equation, involving the solution operator to the linear fragmentation part, is investigated via the contraction mapping principle. A unique global, non-negative, mass-conserving solution to this abstract equation is shown to exist. The latter solution is used to generate a global, non-negative, mass-conserving solution to the original non-autonomous coagulation and multiple-fragmentation equation. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1185-1194 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove the global existence and study decay property of the solutions to the initial boundary value problem for the quasi-linear wave equation with a dissipative term without the smallness of the initial data. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1207-1226 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Reaction random-walk systems are hyperbolic models to describe spatial motion (in one dimension) with finite speed and reactions of particles. Here we present two approaches which relate reaction random-walk equations with reaction diffusion equations. First, we consider the case of high particle speeds (parabolic limit). This leads to a singular perturbation analysis of a semilinear damped wave equation. A initial layer estimate is given. Secondly, we consider the case of a transcritical bifurcation. We use techniques similar to that of the Ginzburg-Landau method to find a modulation equation for the amplitude of the first unstable mode. It turns out that the modulation equation is Fisher's equation, hence near the bifurcation point travelling wave solutions are obtained. The approximation result and the corresponding estimate is given in terms of the bifurcation parameter. Both results are based on an a priori estimate for classical solutions which follows from explicit representations of the solution of the linear telegraph equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1365-1377 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the article the problem of regulation of the cardiovascular system is investigated from the point of view of control process theory. This problem was reduced to finding the optimal control in the sense of speed in a bilinear system. In the first part of the article the possibility of applying Saburov's method for the solution to bilinear control problems is considered. The second part of the article is devoted to the application of this method to a concrete problem from practical medicine. The method has allowed the complete synthesis of an optimal control to be carried out  -  the sliding mode takes place and it was investigated completely. The results obtained are interesting from the point of view of control process theory, and testify to the high efficiency of the method. The final results allow concrete recommendations about the regulation of the cardiovascular system. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1399-1413 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The steady-state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot be expected for physical reasons. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1343-1363 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider an elastic plate with the non-deformed shape ΩΣ := Ω \ Σ, where Ω is a domain bounded by a smooth closed curve Γ and Σ ⊂ Ω is a curve with the end points {γ1, γ2}. If the force g is given on the part ΓN of Γ, the displacement u is fixed on ΓD := Γ \ ΓN and the body force f is given in Ω, then the displacement vector u(x) = (u1(x), u2(x)) has unbounded derivatives (stress singularities) near γk, k = 1, 2   u(x) = ∑2k, l=1 Kl(γk)r1/2kSCkl(θk) + uR(x)     near γk.Here (rk, θk) denote local curvilinear polar co-ordinates near γk, k = 1, 2, SCkl (θk) are smooth functions defined on [-π, π] and uR(x) ∊ {H2(near γk)}2. The constants Kl(γk),   l = 1, 2, which are called the stress intensity factors at γk (abbr. SIFs), are important parameters in fracture mechanics. We notice that the stress intensity factors Kl(γk) (l = 1, 2;  k = 1, 2) are functionals Kl(γk) = Kl(γk; L, Ω, Σ) depending on the load L, the shape of the plate Ω and the shape of the crack Σ. We say that the crack Σ is safe, if Kl(γk; Ω)2 + K2(γk; Ω)2 〈 RẼ. By a small change of Ω the shape Σ can change to a dangerous one, i.e. we have K1(γk; Ω)2 + K2(γk; Ω)2 ≥ RẼ. Therefore it is important to know how Kl(γk) depends on the shape of Ω.For this reason, we calculate the Gâteaux derivative of Kl(γk) under a class of domain perturbations which includes the approximation of domains by polygonal domains and the Hadamard's parametrization Γ(τ) := {x + τφ(x)n(x);  x ∊ Γ}, where φ is a function on Γ and n is the outward unit normal on Γ. The calculations are quite delicate because of the occurrence of additional stress singularities at the collision points {γ3, γ4} = ΓD ∩ ΓN.The result is derived by the combination of the weight function method and the Generalized J-integral technique (abbr. GJ-integral technique). The GJ-integrals have been proposed by the first author in order to express the variation of energy (energy release rate) by extension of a crack in a 3D-elastic body. This paper begins with the weak solution of the crack problem, the weight function representation of SIF's, GJ-integral technique and finish with the shape sensitivity analysis of SIF's. GJ-integral Jω(u; X) is the sum of the P-integral (line integral) Pω(u, X) and the R-integral (area integral) Rω(u, X). With the help of the GJ-integral technique we derive an R-integral expression for the shape derivative of the potential energy which is valid for all displacement fields u ∊ H1. Using the property that the GJ-integral vanishes for all regular fields u ∊ H2 we convert the R-integral expression for the shape derivative to a P-integral expression. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1543-1558 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that a stochastic system of N interacting particles in a slab approximates, in the Boltzmann-Grad limit, a one-dimensional Boltzmann equation with diffusive boundary conditions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1571-1591 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The asymptotic behaviour of solutions of certain semilinear elliptic Dirichlet boundary value problems defined on a semi-infinite cylinder is investigated by means of energy arguments and maximum principles. Various hypotheses are made on the form of the semilinear term, and in some cases it is found that the rate of decay of solutions is faster than the optimal decay rate for harmonic functions. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1655-1679 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper the problem of collision analysis for a mobile robot operating in a planar environment with moving objects (obstacles) is addressed. The pattern of motion of the potential obstacles cannot be predicted; only a bound on their maximum velocity is available. Based on this information, at its current position the robot constructs the Hazard Region that corresponds to the path it contemplates. If the Hazard Region contains at least one obstacle, then there is a potential for this obstacle to collide with the robot (in which case perhaps another path should be planned). We first derive the solution for Hazard Region for two standard path primitives, a straight line segment and a circular arc segment; the solution is exact, except for one special case (for which the approximation error is estimated). This result is then applied to a more complex case when the path presents a combination of those primitives. Such are, for example, the optimal (shortest) paths with constrained curvature (known as Dubins paths [3]), which connect two points, each with a prescribed direction of motion. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1681-1704 
    ISSN: 0170-4214
    Keywords: stratified medium ; acoustic waves ; self-adjoint operators ; spectrum ; limiting absorption principle ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the acoustic propagator A=-∇·c2∇ in the strip Ω={(x, z)∊∝2∣0〈z〈H} with finite width H〉0. The celerity c depends for large ∣x∣ only on the variable z and describes the stratification of Ω: it is assumed to be in L∞(Ω), bounded from below by cmin〉0, such that there exists M〉0 with c(x, z)=c1(z) if x〈 -M and c(x, z)=c2(z) if x〉M. We look at the propagator A as a ‘perturbation’ of the free propagators Aj in Ω associated to the velocities cj, j=1, 2, and implement a ‘perturbative’ method, adapting ideas of Majda and Vainberg. The spectrum of A is defined in section 2, a limiting absorption principle is proved in section 3 outside of a countable set Γ(A). The points of Γ(A) can only accumulate at the left of the thresholds of the free propagators. The needed material about Aj, j=1, 2, and some technical estimates for A are given in Appendix. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 25-42 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Considered is the rotation of a robot arm or rod in a horizontal plane about an axis through the arm's fixed end and driven by a motor whose torque is controlled. The model was derived and investigated computationally by Sakawa and co-authors in [7] for the case that the arm is described as a homogeneous Euler beam. The resulting equation of motion is a partial differential equation of the type of a wave equation which is linear with respect to the state, if the control is fixed, and non-linear with respect to the control.Considered is the problem of steering the beam, within a given time interval, from the position of rest for the angle zero into the position of rest under a certain given angle.At first we show that, for every L2-control, there is exactly one (weak) solution of the initial boundary value problem which describes the vibrating system without the end condition.Then we show that the problem of controllability is equivalent to a non-linear moment problem. This, however, is not exactly solvable. Therefore, an iteration method is developed which leads to an approximate solution of sufficient accuracy in two steps. This method is numerically implemented and demonstrated by an example. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 59-91 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A time-dependent Ginzburg-Landau-type model of a superconducting-normal-superconducting junction is presented. The existence and the uniqueness of the solutions are proved. When the data of the model are symmetric of some kinds, the solutions turns out to be symmetric of some kinds. In this symmetric case, an approximate model with the small thickness of the normal material in the middle of the junction as coefficients of a differential system is established for the sake of numerical computations. And also the existence and the uniqueness of the solution to this approximate model are set up. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 54
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 165-185 
    ISSN: 0170-4214
    Keywords: boundary integral equations ; boundary finite element ; free edge polygonal plate ; hypersingular kernels ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the problem of a polygonal plate with free edges. It is a boundary value problem for the biharmonic operator on a polygon with Neumann boundary conditions. Its resolution is studied via boundary integral equations. A variational formulation of the boundary problem obtained by a double-layer potential is given. Finally, we implement the method and give numerical results. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 55
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 129-163 
    ISSN: 0170-4214
    Keywords: wavelets on closed surfaces ; Dirichlet's and Neumann's problem ; scaling function ; scale discrete wavelets ; integral formulas ; exact fully discrete wavelet transform ; band-limited harmonic wavelets ; Runge-Walsh approximation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Wavelets on closed surfaces in Euclidean space ∝3 are introduced starting from a scale discrete wavelet transform for potentials harmonic down to a spherical boundary. Essential tools for approximation are integration formulas relating an integral over the sphere to suitable linear combinations of function values (resp. normal derivatives) on the closed surface under consideration. A scale discrete version of multiresolution is described for potential functions harmonic outside the closed surface and regular at infinity. Furthermore, an exact fully discrete wavelet approximation is developed in case of band-limited wavelets. Finally, the role of wavelets is discussed in three problems, namely (i) the representation of a function on a closed surface from discretely given data, (ii) the (discrete) solution of the exterior Dirichlet problem, and (iii) the (discrete) solution of the exterior Neumann problem. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 56
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 417-432 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We state a 1D model with quasi-stationary gas flows approximation for a carbon reactivity test in the production of silicon. The mathematical problem we formulate is a non-linear boundary value problem for a third-order ordinary differential equation with non-linear boundary conditions, which are non-local in time. We prove existence and uniqueness of a classical solution and provide a numerical example. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 4 Ill.
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  • 57
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 281-325 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a bending model for a shallow arch, namely the type of curved rod where the curvature is of the order of the diameter of the cross section. The model is deduced in a rigorous mathematical way from classical tridimensional linear elasticity theory via asymptotic techniques, by taking the limit on a suitable re-scaled formulation of that problem as the diameter of the cross section tends to zero. This model is valid for general cases of applied forces and material, and it allows us to calculate displacements, axial stresses, bending moments and shear forces. The equations present a more general form than in the classical Bernoulli-Navier bending theory for straight slender rods, so that flexures and extensions are proved to be coupled in the most general case. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 58
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 375-392 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system using the technique of sub and supersolutions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 59
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 589-603 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the paper we study the problem of control by means of a heat source g for a thermoelastic system of equationsutt - ρ∇·p(θ, ∇u) - νΔut + DΔ2 u = f, cv(θ, ∇u)θt - κΔθ - ρθ[pθ (θ, ∇u)·∇ut] - ν∣∇ut∣2 = g, in a two-dimensional domain, where both viscosity ν and rigidity D are positive. Such a system has been considered in our former papers, and existence of solutions as well as uniqueness have been obtained. Here we prove the continuity and differentiability of solutions under somewhat stronger assumptions. An example of a control problem and necessary optimality conditions are presented. The system has an interpretation as a plate reinforced with shape memory alloy (SMA) wire mesh. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 60
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 719-731 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations can be obtained by the AKNS class. The technique developed relies on the construction of the wave functions which are solutions of the associated AKNS system; that is, a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Bäcklund transformations (BTs) are employed to generate two new solutions from the old. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 61
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 781-795 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the boundary value problem for a semilinear equation□u(t, x)-μu(t, x)+aum(t, x)=0, μ〉0, a∊ℜ in the interior domain. We find a time global classical solution with exponential decay property by using singular hyperbolic equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 62
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 895-906 
    ISSN: 0170-4214
    Keywords: geometrical inverse problems ; crack detection ; identifiability ; stability ; Lipschitz stability ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with the detection of emergent plane cracks, by using boundary measurements. An identifiability result (uniqueness of the solution) is first proved. Then, we look at the stability of this solution with respect to the measurement. A weak stability result is proved, as well as a Lipshitz stability result for straight cracks, by using domain-derivative techniques. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 63
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1467-1477 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, the existence, both locally and globally in time, the uniqueness of solutions and the non-existence of global solutions to the initial boundary value problem of a generalized Modification of the Improved Boussinesq equation utt-uxx-uxxtt=σ(u)xx are studied and a few examples are discussed. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 64
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1593-1617 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study the following problem:ut-Δu=-f(u) in Ω×(0, T)≡QT,∂u ∂n=g(u) on ∂Ω×(0, T)≡ST,u(x, 0)=u0(x) in Ω, where Ω⊂∝N is a smooth bounded domain, f and g are smooth functions which are positive when the argument is positive, and u0(x)〉0 satisfies some smooth and compatibility conditions to guarantee the classical solution u(x, t) exists. We first obtain some existence and non-existence results for the corresponding elliptic problems. Then, we establish certain conditions for a finite time blow-up and global boundedness of the solutions of the time-dependent problem. Further, we analyse systems with same kind of boundary conditions and find some blow-up results. In the last section, we study the corresponding elliptic problems in one-dimensional domain. Our main method is the comparison principle and the construction of special forms of upper-lower solutions using related equations. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 65
    ISSN: 1434-193X
    Keywords: Photocycloaddition ; Ring opening ; Oxetanes ; 1,2-Diols ; Alkyldealkoxylation ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The ring opening of 3-isopropyl-2-phenyl-3-oxetanol (2a) by various nucleophiles has been studied. In the presence of BF3 as a Lewis acid, a clean reaction at the less substituted C-4 position was observed and the corresponding 1,2-diols 6-11 and 21-23 were isolated in diastereomerically pure form (47-97% yield). Alkyl-, aryl-, alkynyl- and alkenyllithium compounds proved to be suitable carbon nucleophiles. Deprotonated thiols were used as sulfur nucleophiles. An alkoxide derived from benzyl alcohol and an amide derived from benzylamine reacted less readily under these conditions, yielding the 1,2,3-trifunctional compounds 24 (42% yield) and 26 (54% yield). Other 2-phenyl-3-oxetanols such as 2b and 2c can also be employed as electrophiles, whereas 2-anisyl derivatives preferentially undergo rearrangement reactions, as exemplified by the conversion of oxetane 16 to the hydroxy ketone 17 (84% yield). The superior behaviour of 3-oxetanols as compared to their silyl derivatives in reactions with nucleophiles became evident from the reaction of 3-silyloxyoxetane 1a with alkyllithium reagents. A β elimination occurred upon treatment with nBuLi, which, after pericyclic ring opening and addition of nBuLi, yielded the allylic alcohol 20.
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  • 66
    ISSN: 1434-193X
    Keywords: Azoalkanes ; DBO ; Fluorescence quenching ; Exciplexes ; Hydrogen transfer ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The fluorescence of the DBO derivatives 1-3 is efficiently quenched by olefins and arenes, exciplex formation and hydrogen transfer operate as quenching mechanisms. The electron-accepting ester groups in the azoalkanes 1-3 promote significantly more effective quenching compared to the parent DBO. Steric hindrance accounts for the differences in the quenching efficiencies, but electronic effects dominate
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  • 67
    ISSN: 1434-193X
    Keywords: Mannich bases ; γ-Amino alcohols ; Grob fragmentation ; (Z)-Alkenes ; Oxetanes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Quaternized γ-amino alcohols 5 derived from ternary iminium salts 2 are stereospecifically converted into both unsaturated aldehydes/ketones 6 with a (Z)-C—C double bond in a Grob-type fragmentation and highly functionalized oxetanes 7 by intramolecular substitution.
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  • 68
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    Liebigs Annalen 1998 (1998), S. 2201-2207 
    ISSN: 1434-193X
    Keywords: Antibiotics ; Asymmetric synthesis ; β-Lactams ; Michael additions ; Multicomponent reactions ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Lithium dialkylcuprates react either in a sequential one-pot or in a domino “three-component” fashion with chiral Michael acceptors, like Oppolzer's N-enoyl-2,10-camphorsultams 7 and 11 or ‘Evans’ N-enoyl-4-phenyl-1,3-oxazolidin-2-ones 8 and 13, and N-(methoxycarbonylmethylidene)(4-methoxyphenyl)amine 9 to afford the corresponding cis-3-alkyl-4-methoxycarbonyl-1-(4-methoxyphenyl)azetidin-2-ones 10, 14-15 in overall yields of 40-67% and enantiomeric excesses of 91-99%.
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  • 69
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    Liebigs Annalen 1998 (1998), S. 2229-2235 
    ISSN: 1434-193X
    Keywords: 3-Nitro-ω-benzylideneacetophenone ; Carbanions ; Michael addition ; Intramolecular vicarious nucleophilic substitution of hydrogen ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 3-Nitro-ω-benzylideneacetophenone (1) reacts with carbanions containing leaving groups to give addition products to the electrophilic side chain. As a result of conjugated addition and subsequent intramolecular vicarious nucleophilic substitution of hydrogen (VNS) in the nitroaromatic ring of 1 in the position para to the nitro group, 4-cyano-7-nitro-3-phenyl-1,2,3,4-tetrahydronaphthalen-1-one and 4-cyano-7-nitro-3-phenylnaphth-1-ol are obtained. Smooth intramolecular VNS in the position para to the nitro group was observed for 4-chloro-1-(3-nitrophenyl)-3-phenyl-4-(p-tosyl)butanol.
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  • 70
    ISSN: 1434-193X
    Keywords: Conformation analysis ; Electrochemistry ; Nitrogen heterocycles ; Dimerization ; Mechanism ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In aqueous media the one-electron reduction of the title compounds on a mercury pool generally gives rise to three dimers, which are distinguishable by HPL chromatography. From spectroscopic analyses it has been possible to propose a structure for these conformers and their stability has been studied. Two conformers are unstable, yielding the third conformer. A mechanism is proposed for this transformation.
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  • 71
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    Liebigs Annalen 1998 (1998), S. 837-846 
    ISSN: 1434-193X
    Keywords: AZT ; cycloSal-pro-nucleotide ; Prodrugs ; Nucleotide delivery ; HIV chemotherapy ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The application of our cycloSaligenyl- (cycloSal) pronucleotide concept to the approved anti-HIV dideoxynucleoside 3′-azido-3′-deoxythymidine AZT (1) is reported. This pro-nucleotide concept has been designed to deliver the corresponding 3′-azido-3′-deoxythymidine monophosphate AZTMP (2) by selective chemical hydrolysis from the lipophilic precursors cycloSal-AZTMP 4a-h. All derivatives 4a-h were synthesized using differently substituted salicyl alcohols 7a-h as starting materials. In hydrolysis studies, compounds 4 decomposed selectively releasing AZTMP (2) and the salicyl alcohols 7 following the designed tandem reaction. Furthermore, due to the electronic properties introduced by substituents, the half-lives of the triesters 4 could be ajusted over a wide range. Phosphotriesters 4 exhibited considerable biological activity in HIV-1 and HIV-2 infected wild-type human T-lymphocyte (CEM/O) cells, whereas, contrary to our expectations, nearly all activity was lost in HIV-2 infected thymidine-kinase-deficient CEM cells.
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  • 72
    ISSN: 1434-193X
    Keywords: N-Alkylation ; Diketopiperazine building block ; Peptidomimetics ; RGD analogues ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: As a new scaffold for peptidomimetic synthesis, a highly constrained bifunctional diketopiperazine, 4, has been prepared by smooth N-alkylation with tert-butyl bromoacetate. As a first application, we describe herein the synthesis of new peptidomimetics of the Arg-Gly-Asp (RGD) sequence. The product 30, which shows a selective platelet-aggregation inhibiting activity, can be used as a lead for the preparation of more potent products.
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  • 73
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    Liebigs Annalen 1998 (1998), S. 871-876 
    ISSN: 1434-193X
    Keywords: Dioxirane ; Homolysis, induced ; Aminoxyl ; Oxidation ; Spin-trapping ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In the reactions of dimethyldioxirane (1a) and methyl(trifluoromethyl)dioxirane (1b) with 2,2,6,6-tetramethylpiperidinyl-1-oxyl (2) (TEMPO) in acetone, the corresponding methoxyamine 1-methoxy-2,2,6,6-tetramethylpiperidine (5) is produced in ≥98% yield, both in air and under N2, and in the absence or presence of a hydrocarbon (adamantane). Kinetic experiments show that aminoxyl 2 triggers the radical decomposition of the dioxirane, in addition to scavenging methyl radicals derived therefrom. The reactions of an aminoxyl less prone to oxidation, namely 1,2-dihydro-2-methyl-2-phenyl-3H-indol-3-one-1-oxyl (4), with dioxiranes 1a and 1b in acetone have also been studied. In these cases, not only is the corresponding methoxyamine 8a produced (yield 12-16%), but quinoneimine-N-oxides 10 (yield 12-21%) and 11 (yield 18-19%) are also formed. Furthermore, significant amounts (8-14%) of the amine 9 (the product of deoxygenation of 4) can be isolated. These observations provide useful information concerning the free-radical mechanism that follows the initial attack by the aminoxyl at the dioxirane.
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  • 74
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    Liebigs Annalen 1998 (1998), S. 2373-2377 
    ISSN: 1434-193X
    Keywords: Charge-transfer fluorescence ; Fluorogenic probe ; Fluorescence labelling ; Maleimide group ; Solvatochromism ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Structural modification of the highly fluorescent donor-bridge-acceptor molecule “Fluoroprobe” (FP) is shown to extend the excitation window to longer wavelengths. The resulting “Fluorotrope” (FT) shows appreciable absorption in the 350-420-nm range, so that visible (blue) light can be used for excitation. Further functionalization with a maleimide group results in the novel fluorogenic reagent MaleimidoFluorotrope (MFT) which yields fluorescent adducts with amines, thiols and other reactive groups that add to the double bond of the maleimide. The fluorescence wavelength of these adducts is extremely sensitive to the polarity and mobility of the medium.
    Additional Material: 4 Ill.
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  • 75
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    Liebigs Annalen 1998 (1998), S. 2379-2387 
    ISSN: 1434-193X
    Keywords: β-Peptides ; Polylithiation of peptides ; Li-enolates of peptides ; Back-bone alkylation of β-peptides ; Diastereoselective alkylation of β-peptide enolates ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of N-Boc-protected β-tripeptide derivatives with or without N-methyl groups and with free or Me-ester-protected C terminus has been prepared (8-14, 16, 17). As with α-peptides (→ A), the β-peptide derivatives can be polylithiated (→ B, C). No epimerization of stereogenic centers and no β elimination (exception 17 → 24) is observed upon treatment with bases as strong as tBuLi. The C terminal ester Li-enolate moiety of tetralithio β-tripeptides (cf. C) can be selectively alkylated with methyl, benzyl and allyl halides, and with tert-butyl bromoacetate in yields ranging from 35-80% (8 → 18, 14 → 20-23).
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  • 76
    ISSN: 1434-193X
    Keywords: Natural products ; Steroids ; Chenodeoxycholic acid ; Brassinosteroid analogues ; Biological activity ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The synthesis and spectroscopic characterization of two new bioactive analogues of brassinosteroids with a 24-hydroxylated cholanic side chain, an A/B ring cis-junction and oxygenated functions in C-7 is described.
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  • 77
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    Liebigs Annalen 1998 (1998), S. 2409-2416 
    ISSN: 1434-193X
    Keywords: Sulfur heterocycles ; Rearrangements ; Reductions ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The syntheses of 1,2-benzodithiino[5,4,3-cde][1,2]benzodithiin-2,7-diamine (1) and dithio-bridged benzidine 2 have been achieved. The starting material for the synthesis of 1 was 1,3-diiodo-5-nitrobenzene (15) which was transformed by conventional means into 1,2-bis[3,5-bis(ethylthio)phenyl]diazane (19). The benzidine rearrangement of 19 in the presence of HBF4 at -30 °C yielded 4,4′-diamino-2,2′,6,6′-tetraethylthiobiphenyl (20) in 50 % yield. Treatment of 20 with sodium in ammonia and work-up in the presence of air yielded 1. The latter compound could be reduced with LiAlH4 to the tetrathiol 20a. The starting material for the preparation of 2 was 3-chloro-1-iodo-5-nitrobenzene (23), a side product of the preparation of 15. It was transformed analogously to the preparation of 1 into 1,2-bis(3-ethylthiophenyl)diazane (28). The benzidine rearrangement of 28 in presence of HBF4 at -30 °C afforded 4,4′-diamino-2,2′-bis(ethylthio)biphenyl (29) in 49 % yield. Treatment of 29 with sodium in ammonia and work-up under aerobic conditions yielded 2. Quantitative reduction of 2 to the thiol 29a could be achieved with LiAlH4. The reversible electrochemical reduction of 1 on unmodified glassy carbon electrodes leads to a product to which the structure of 3 was assigned.
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  • 78
    ISSN: 1434-193X
    Keywords: N-Heterocycles ; Porphyrins ; Radical cations ; N-Dealkylation ; Stereoelectronic effects ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Evidence for a stereoelectronic inhibition of deprotonation of the radical cation of N-benzylpiperidine is presented. This stereoelectronic effect, which is due to the cyclic structure of the precursor, provides a tool to differentiate hydrogen-atom- versus electron-transfer routes in the biomimetic oxidative N-dealkylation of tertiary amines: the electron-transfer route appears to be the operating mechanism.
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  • 79
    ISSN: 1434-193X
    Keywords: Colchicine ; 10-Ethylthiocolchicide, diene properties of ; π-Facial diastereoselectivity ; Consecutive [4+2],[3+2] cycloadditions ; Atropisomerism ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Cycloaddition reactions of the facially dissymmetric diene moiety of (-)-(M,7S)-colchicine (5) and (-)-(M,7S)-10-ethylthiocolchicide (9) to various alkynes have been studied. With 5 and the dienophilic benzyne (3), dimethyl acetylenedicarboxylate (DMAD) (4) and cyclooctyne (6) as starting materials all cycloadditions could be realized with high regioselectivity at the 8,12-positions of the alkaloid. The approach of the dienophiles preferentially occurred toward the syn π-face of the diene. In contrast to the cycloaddition mode of 5 the ethylthiocolchicide 9 surprisingly reacted in a different manner. With benzyne as starting material a novel [3+2] cycloaddition of the thioenol ether moiety of 9 towards the dipolarophilic benzyne is supposed, affording the unexpected colchicide 10 after [1,5]H shift of the primarily formed cycloadduct followed by cleavage of the C-S linkage. With DMAD (4) and cyclooctyne (6) the reaction course is more complex. In a consecutive [4+2]/[3+2] cycloaddition (or vice versa) followed by a thermally induced cycloreversion of a not identified intermediate DMAD (4) gives rise to the polycyclic thiophene derivative 13 and the novel allocolchicinoid 14. In a similar way cyclooctyne (6) yielded three products, the thiophene-annulated homobarrelenones 18 and 19 and the tetracyclic allocolchicinoid 21. The structures of the novel colchicine derivatives were assigned on the basis of spectral data, those of the cycloadducts 1 and 19 were verified by X-ray crystallography. For the unprecedented formation of the various allocolchicinoids by consecutive [4+2]/[3+2] cycloadditions plausible reaction pathways are suggested, as far as possible. In addition the inhibitory effects on the tubulin polymerization reaction in vitro of 10, 14, and 21 are reported.
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  • 80
    ISSN: 1434-193X
    Keywords: Paclitaxel (Taxol®) ; Paclitaxel CD-ring ; High-pressure Diels-Alder reactions ; Furan cycloadditions ; Ether cleavage in 7-oxabicyclo[2.2.1]heptanes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The high-pressure promoted Diels-Alder reactions between several furans and citraconic anhydride have been studied and the cycloadducts obtained have been explored in new straightforward routes to the CD-ring fragment of paclitaxel. The reaction between furan and citraconic anhydride afforded the exo cycloadduct diastereoselectively, whereas a variety of 2-substituted furans afforded approximate 1:1 mixtures of exo regioisomers. Separation of both regioisomers was accomplished after either diastereoselective esterification or regioselective reduction of the anhydride function. Ether cleavage of the bicyclic compounds by either high-pressure promoted ether cleavage or Boord elimination afforded several potential CD-ring precursors which can be used in the total synthesis of paclitaxel analogues.
    Additional Material: 2 Ill.
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  • 81
    ISSN: 1434-193X
    Keywords: Camphoracetyl chloride ; Lactols, fused ; Lactones, fused ; Pseudoacid chlorides ; Reagents, stereoselective ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: endo-Fused lactone 3 was obtained in high yield from the camphoracetic acid 2 with thionyl chloride and a subsequent reduction of intermediate 5 with tributyltin hydride. The structure of 5 was elaborated and some aspects of the mechanism of its formation and reactivity were investigated. Lactone 3 serves as key intermediate for lactol 1 which is a useful reagent in racemate resolution and asymmetric synthesis.
    Additional Material: 1 Ill.
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  • 82
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 2609-2615 
    ISSN: 1434-193X
    Keywords: Supramolecular chemistry ; Domino reactions ; Bipyridines ; 1,x-Cyclohexanediones ; Mannich bases ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A one-pot reaction using 1,x-cyclohexanediones, a Mannich base (or its hydrochloride), and ammonium acetate delivers novel pyridines or 3,3′-bridged bipyridine compounds 8, 16, 18, 20, and 22. This strategy offers a great flexibility in the design of new building blocks, e.g. in supramolecular chemistry and underlines the efficiency of domino reactions.
    Additional Material: 1 Ill.
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  • 83
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 2603-2607 
    ISSN: 1434-193X
    Keywords: Fluoro analogs of vitamin A ; Horner-Wittig reaction ; Fluoroisoprenoid building blocks ; Stereoselectivity ; Hydrolysis of chlorofluorocyclopropanes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An improved method for the preparation of ethyl 2-fluoro-3-methyl-2-butenoate (3) is described. The two stereoisomers [(E)-4 and (Z)-4] obtained after γ-bromination can be separated and can be individually converted into the corresponding diethyl phosphonates. The PO-ylides generated by α-deprotonation of the latter lose their stereochemical integrity by rapid torsional equilibration of the ester tail. Thus, Horner-Wittig reactions accomplished with benzaldehyde and (Z)- or (E)-(β-ionylidene)-acetaldehyde lead inevitably to stereorandomization at the terminal, ethoxycarbonyl-bearing double bond affording (E)- and (Z)-isomers in 50:50 to 15:85 ratios, depending on the reaction conditions. The new double bond, however, is formed with perfect trans-selectivity.
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  • 84
    ISSN: 1434-193X
    Keywords: Alkaloids ; Total synthesis/Pumiliotoxin ; PTX-C ; PTX isomers ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method is described for the synthesis of pumiliotoxin C (1a) and related stereoisomeric compounds 1c-1f. Starting from (+)- or (-)-3-methylcyclohexanone (6a,b), the oxo esters 7a and 7b were prepared. Condensation with (+)- or (-)-3-aminohexanol (8a,b) gave the stereoisomeric 3-aminoacrylates 9a, 9b and 9c. The hydroxy group of the amino-acrylates was transformed into bromide using the tosylate method. Cyclization of the bromides led to unsaturated quinoline ring systems. Finally, decarboxylation and catalytic hydrogenation gave the different cis- and trans-fused stereoisomeric alkaloids of the pumiliotoxin C type. The structures were verified by X-ray analysis.
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  • 85
    ISSN: 1434-193X
    Keywords: Lawesson's reagent ; Thiolation of cyclic ketones ; Anchimeric effect ; cis-Bicyclo[3.3.0]octane-3,7-diones ; 9-Thiatricyclo[3.3.1.03,7]nonane ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A simple and efficient approach to the 9-thiatricyclo[3.3.1.03,7]nonane ring system (5) has been found by treating cis-bicyclo[3.3.0]octane-3,7-diones (1) with Lawesson's reagent or phosphorus pentasulfide. When dione 1 is treated with Lawesson's reagent tetramethyl 3(4aH)oxo-1,4-dihydrophenanthro[9,10-a]pentalene-1,2,4,4a-tetracarboxylate (6) is obtained as a by-product as shown by X-ray structural analysis.
    Additional Material: 1 Ill.
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  • 86
    ISSN: 1434-193X
    Keywords: Pyrazolidin-3-ones ; Optical activity ; Asymmetric synthesis ; Ring transformation ; Hydrazines ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Enantiopure α-alkylidenelactones 7 were prepared by a Wittig reaction from α-bromolactones 4 and chiral aldehydes 6. Compounds 7 react with hydrazines 9 by stereoselective Michael-like addition and ring-chain transformation affording optically active 4-(ω-hydroxyalkyl)pyrazolidin-3-ones 11.
    Additional Material: 5 Ill.
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  • 87
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 2673-2676 
    ISSN: 1434-193X
    Keywords: Aromatic aldehydes ; Pinacol coupling ; Radical reactions ; Reagent control ; Titanium ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A novel concept for conductingtransition-metal-catalyzed radical reactions that allows highly diastereoselective titanocene-catalyzed pinacol couplings is described.
    Additional Material: 4 Ill.
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  • 88
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 2677-2682 
    ISSN: 1434-193X
    Keywords: Terpenoid lactones ; Antifeedants ; Limonene ; Claisen rearrangement ; Iodolactonization ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Four enantiomeric pairs of spirolactones were obtained in a four step synthesis from (+) and (-) limonene. The Claisen rearrangement and iodolactonization were the key steps of the syntheses presented. The structures of products were confirmed by X-ray crystallography of 11, 18b, and 19.
    Additional Material: 3 Ill.
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  • 89
    ISSN: 1434-193X
    Keywords: Phosphole ; Phosphanorbornadiene ; Stille cross-coupling ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The reaction of alkynylstannanes with 1-phenyl-3,4-dimethylphosphole at 150 °C affords the corresponding 2-stannyl-1-phosphanorbornadienes (2a, b), in fair yield. Oxidation under mild conditions affords the corresponding phosphane oxides (3a, b), whereas more drastic conditions (H2O2, 15% in toluene at 80 °C) induce the oxidative cleavage of the P-CH2 bond of the bridge to give a bicyclic phosphinate such as 4. Treatement of 4 by iodine leads to a tin → iodine exchange. The X-ray crystal structure analysis of the resulting 1-phospha-2-oxabicyclo[2.2.2]octa-5,7-diene 1-oxide confirms the functionalisation at the α-position and the relief of ring strain taking place upon insertion of oxygen into the P-CH2 bond of the norbornadiene. The 2-stannyl-1-phosphanorbornadiene 1-oxides (3a, b) readily undergo tin → iodine exchange. The resulting 2-iodo derivatives (6a, b) can be cross-coupled with 2-furyl-, 2-thienyl-, 2-pyrrolyl-, phenylethynyl-, and vinyl-tributylstannanes to give the corresponding 2-functional 1-phosphanorbornadiene 1-oxides in excellent yields (80-95%)
    Additional Material: 1 Ill.
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  • 90
    ISSN: 1434-193X
    Keywords: Asymmetric synthesis ; Density functional calculations ; Cycloadditions ; Dihydropyrans ; Enantioselective oxidations ; Sulfur heterocycles ; Sulfoxides ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The 4-benzylidene-3-oxo[1,3]oxathiolan-5-ones 13-15, which were derived from the 3-oxo[1,3]oxathiolan-5-ones 9-11 by Knoevenagel condensation with the aldehydes 12, cyclize in an intramolecular hetero Diels-Alder reaction with high yield and excellent endo/exo as well as induced diastereoselectivity to give the hetero Diels-Alder adducts 16-18. The preferred formation of the Knoevenagel products 13-15 with a (Z) configuration was predicted with DFT calculations (B3LYP-6-311+G*) using the model systems 28 and 29. In addition B3LYP-6-31G*/sB3LYP/3-21G(*) calculations on transition structures for the hetero Diels-Alder reaction of 29 and 30 allowed a good correlation with the experimental results, which show that an endo attack of the dienophile syn to the S-O group in 13-15 leads to the main products.
    Additional Material: 2 Ill.
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  • 91
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 2759-2767 
    ISSN: 1434-193X
    Keywords: Phosphorus phthalocyanines ; Triazatetrabenzcorroles ; Dihydroxyphosphorus(V) phthalocyanine hydroxides ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The previously reported reaction of phthalocyanines [H2(pc)] with PBr3, which was claimed to give a phosphorus(III) phthalocyanine “(PcPIII)”, has been reinvestigated in detail with both unsubstituted and alkyl-substituted phthalocyanines, 1-4. The products exhibit unusual electronic and mass spectra compared to normal phthalocyanines and have been identified as oxophosphorus(V) triazatetrabenzcorroles 5-8. The corresponding dihydroxyphosphorus(V) phthalocyanine hydroxides 9-12 have also been synthesized for the first time by insertion of phosphorus(V) into phthalocyanines and have been characterized in detail. The different reactivities of PBr3 and POX3 (X = Cl, Br) toward phthalocyanines are discussed.
    Additional Material: 3 Ill.
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  • 92
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1998 (1998), S. 2769-2773 
    ISSN: 1434-193X
    Keywords: Rubicenes ; Cyclization ; Polycyclic aromatic hydrocarbons ; Arenes ; Synthetic methods ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The synthesis of novel disubstituted rubicenes 1a-k is described. Starting from 1,5-dichloroanthraquinone and aryllithium reagents 3, the diol adducts 4 are reduced and the resulting diarylanthracenes 5 are cyclized to afford the title compounds in fair to good overall yield.
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  • 93
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 37-41 
    ISSN: 1434-1948
    Keywords: Tripodal P ligands ; Rhodium ; Water-soluble complexes ; Immobilization ; Biphasic hydroformylation ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The synthesis of the water-soluble tripodal phosphane ligand cis,cis-1,3,5-(PPh2)3-1,3,5-[CH2(OCH2CH2)xOCH3]C6H6 (x = 30-160) (5) has been achieved in a four-step reaction sequence. The alcohol Mo(CO)3[cis,cis-1,3,5-(PPh2)3-1,3,5-(CH2OH)3C6H6] (1) is converted to the corresponding alcoholate 2, which forms the polyethylene glycol derivative 3 in a polyaddition reaction with oxirane. After methylation of the end groups of 3, the ligand 5 is obtained by a combined photochemical/oxidative demolybdenation reaction. The water-soluble tripodal phosphane 5 and the methoxymethyl functionalized tripodal ligand 6 react with Rh(PPh3)3(CO)H to form the water-soluble and water-insoluble rhodium carbonyl hydrido complexes 5a and 6a, respectively. The catalytic activity of the rhodium complex 5a in the hydroformylation of 1-hexene was found to be comparable in a single-phase system (1-hexene/methanol) with that in the biphasic system (1-hexene/water). Only traces of alcohol were found, which demonstrates that the catalyst 5a displays higher selectivity in hydroformylation than in hydrogenation.
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  • 94
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 55-59 
    ISSN: 1434-1948
    Keywords: Arsaalkenes ; Arsenic ligands ; Carbonyl complexes ; Chromium ; Iron ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Reaction of equimolar amounts of the metalloarsaalkene [(η5-C5Me5)(CO)2FeAs=C(NMe2)2] (1) with the carbonyl complexes [Ni(CO)4], [Fe2(CO)9], and [{(Z)-cyclooctene}Cr(CO)5], respectively, affords the adducts [(η5-C5Me5)(CO)2FeAs{M(CO)n}=C(NMe2)2] with [M(CO)n] = [Ni(CO)3] (2); [Fe(CO)4] (3), and [Cr(CO)5] (4). These feature η1 coordination of the arsaalkene ligand via the arsenic atom. The molecular structures of the complexes 3 and 4 have been determined by X-ray diffraction analyses.
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  • 95
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 155-157 
    ISSN: 1434-1948
    Keywords: Bite angle ; Catalysis ; P ligands ; Palladium ; Cross-coupling ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The effect of the natural bite angle (βn) of diphosphane ligands on catalyst selectivity and activity in the palladium-catalyzed cross-coupling of sec-butyl magnesium chloride with bromobenzene was investigated. The calculated natural bite angles range from 78° for dppe (1,2-bisdiphenylphosphanoethane) to 110° for Xantphos. The natural bite angle of diphosphane ligands has a large effect on catalyst selectivity and activity. Both rate and selectivity of the cross-coupling reaction increase with increasing bite angle and reach a maximum value with DPEphos (βn = 102.7° ). Larger bite angles of the diphosphane ligands result in a decreased selectivity and activity.
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  • 96
    ISSN: 1434-1948
    Keywords: Ligand field spectra ; Phosphonate complexes ; X-ray structures ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The synthesis and characterization of transition-metal coordination compounds containing the ligand diethyl 2-quinolylmethylphosphonate (2-qmpe) is described. Complexes of CoII, MnII, NiII, CdII, and ZnII were found to be mutually isomorphous according to their X-ray powder diffraction patterns and IR spectra. The new coordination compounds were identified and characterized by elemental analysis, magnetic measurements, infrared and ligand-field spectra. The crystal structures of the complexes [M(2-qmpe)4(H2O)2](ClO4)2 (M = Ni, 1; Mn, 2) reveal six-coordinate [M(2-qmpe)4(H2O)2] cations with the qmpe ligand coordinating via the oxygen rather than via the nitrogen atom, as well as lattice perchlorate anions. The metal ion is octahedrally surrounded by the four oxygen atoms of the four organic ligands. The non-participation of the pyridine nitrogen atom is unusual. The two water molecules occupy the fifth and the sixth coordination sites in a trans configuration. The coordinated water molecules are strongly hydrogen-bonded to the pyridine nitrogen atom of the 2-qmpe, further stabilizing the solid-state structure. The geometry of the metal ion can be described as distorted octahedral. For the CuII complex, a hydroxo-bridged dinuclear structure of the type [Cu(2-qmpe)2(OH)(H2O)2]2(ClO4)2 is proposed, based on its spectroscopic and magnetic properties. Ligand-field spectra of the Co and Ni compounds were found to be in agreement with the tetragonally distorted octahedral geometry.
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  • 97
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 191-202 
    ISSN: 1434-1948
    Keywords: Polynuclear complexes ; Carbene complexes ; Bridging ligands ; Alkynyl complexes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The sequential reaction of two equivalents of the dimethylamino(ethynyl)carbene complexes [(CO)5M=C(NMe2)C≡CH] [M = W (1a), Cr (1b)] with two equivalents of nBuLi and one equivalent of a transition metal dichloride, [Cl2M′(Ln)], affords trinuclear biscarbene complexes of the type [(CO)5M=C(NMe2)C≡C-M′(Ln)-C≡CC(NMe)2=M(CO)5] [M′(Ln) = Ni(PEt3)2 (2a, b), Pd(PEt3)2 (3a, b), Pt(PEt3)2 (4a, b), Fe(dmpe)2 (6a), Hg (8a), Ti(η5-C5H5)2 (9a, b)] [dmpe = 1,2-bis(dimethylphosphino)ethane]. Treatment of 1a with equimolar amounts of first nBuLi and then [Cl2M′(Ln)] results in the formation of the monosubstitution products [(CO)5W=C(NMe2)C≡CM′(Ln)] [M′(Ln) = trans-Pd(PEt3)2Cl (5a), trans-Fe(dmpe)2Cl (7a)]. Additionally, the synthesis of the heterobimetallicethynylcarbene complex [(CO)5W=C(NMe2)C≡CPd(PEt3)2C≡CH] (10a), starting from 1a and [ClPd(PEt3)2C≡CH], is described. When three equivalents of 1a are treated, first with three equivalents of nBuLi and then with one equivalent of the trihalides PCl3 or BBr3, the novel tris(ethynylcarbene) complexes [{(CO)5W=C(NMe2)C≡C}3E] [E = B (11a), P (12a)] are obtained. The reaction of four equivalents of 1a,b with four equivalents of nBuLi, followed by addition of one equivalent of a group 14 tetrachloride [M′Cl4], yields the novel tetrakis(ethynylcarbene) complexes [{(CO)5M=C(NMe2)C≡C}4M′] [M′ = Si (13a, b), Ge (14a), Sn (15a, b)]. The complexes 8a, 9a, 12a, and 15a were characterized by X-ray structural analyses. All spectroscopic and structural data suggest that the carbene fragments and the central transition metal or heteroatom in these new bis-, tris-, and tetrakis(ethynylcarbene) complexes interact only weakly.
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  • 98
    ISSN: 1434-1948
    Keywords: Rhenium ; Oxacyclocarbene complexes ; Vinylidene comlexes ; Alkynols ; Tripodal ligands ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Various β-, γ-, and δ-alkynols have been reacted with the 16e- fragment [(triphos)Re(CO)2]+ generated in situ by H2 elimination from [(triphos)Re(CO)2(η2-H2)]BF4 [triphos = MeC(CH2PPh2)3]. Irrespective of the length of the alkyl chain between the C≡C and OH functional groups in the ω-alkynol, 2-oxacyclocarbene complexes are obtained. These include the 2-oxacyclopentylidene derivatives [(triphos)Re(CO)2{=CCH2CH2CH2O}]BF4 and [(triphos)Re(CO)2{=CCH2CH2CH(Me)O}]BF4, the 2-oxacyclohexylidene dervivatives [(triphos)Re(CO)2{=CCH2CH2CH2CH2O}]BF4 and[(triphos)Re(CO)2{=CCH2CH2CH2CH(Me)O}]BF4, and the 2-oxacycloheptylidene complex [(triphos)Re(CO)2{=CCH2CH2- CH2CH2CH2O}]BF4. The latter compound contains a unprecedented seven-membered oxacarbene ring. The rhenium-assisted δ-alkynol to 2-oxacyloheptylidene rearrangement proceeds via the hydroxybutylvinylidene kinetic intermediate [(triphos)Re(CO)2{C=C(H)CH2CH2CH2CH2OH}]BF4, which has been characterized in both the solid state and solution. An X-ray analysis has been carried out on a single crystal of [(triphos)Re(CO)2{=CCH2CH2CH(Me)O}]BF4. The structure of this complex consists of [(triphos)Re(CO)2{=CCH2CH2CH(Me)O}]+ cations and tetrafluoroborate anions with no interspersed solvent molecules. A facial triphos ligand, two cis-disposed carbonyl groups and a 2-oxacyclopentylidene ligand coordinate the Re centre in a slightly distorted octahedral environment.
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  • 99
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 237-244 
    ISSN: 1434-1948
    Keywords: Titanium complexes ; Amido-cyclopentadienyl ligand ; Titanium alkyl ; Intramolecular coordination ; Ethene polymerization ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Titanium complexes containing a linked isopropyl- or benzylamido(tetramethylcyclopentadienyl) ligand C5Me4SiMe2NR (R = iPr, CH2Ph,) and one bidentate organyl group C6H4(CH2NMe2)-2, CH2C6H4(NMe2)-2, and {η5-C5H3(CH2NMe2)-2}Fe(η5-C5H5) were prepared by salt metathesis of the corresponding dichloro complex Ti(η5:η1-C5Me4SiMe2NR)Cl2 with the lithium organyl. Single crystal X-ray structural analysis of Ti(η5:η1-C5Me4SiMe2NCH2Ph)- {C6H4(CH2NMe2)-2}Cl and of Ti(η5:η1-C5Me4SiMe2NiPr){CH2C6H4(NMe2)-2}Cl revealed the presence of intramolecular coordination with square pyramidal geometry around titanium. In the ferrocenyl derivative Ti(η5:η1-C5Me4SiMe2NCH2Ph)[{η5-C5H3(CH2NMe2)-2}Fe(η5-C5H5)]Cl the NMe2 group is not bonded at the titanium atom. Ethene polymerization catalyzed by these complexes upon activation with methylaluminoxane was examined.
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  • 100
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 271-274 
    ISSN: 1434-1948
    Keywords: Zinc complexes ; Pyrazolylborate ligands ; Hydrolytic cleavage ; Diphosphate ; Sulfonatophosphate ; Disulfonate ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Three (pyrazolylborate)zinc hydroxide complexes Tp*Zn-OH were used as hydrolytic reagents to cleave the P-O-P, P-O-S, and S-O-S linkages of organic diphosphates, sulfonatophosphates, and disulfonates. The resulting complexes of the types Tp*Zn-OPO(OR)2 and Tp*Zn-OSO2R could also be obtained by condensation reactions between Tp*Zn-OH and HO-PO(OR)2 or HO-SO2R. Two of them were characterized by structure determinations.
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