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  • General Chemistry  (2,015)
  • Theoretical, Physical and Computational Chemistry  (699)
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  • Cell & Developmental Biology  (441)
  • 1995-1999  (3,838)
  • 1997  (3,838)
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  • 1995-1999  (3,838)
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  • 1
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1469-1500 
    ISSN: 0170-4214
    Keywords: radiating solutions ; exterior boundary value problem in elasticity ; variable coefficients ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use Hodge-Helmholtz decompositions of weighted Sobolev spaces to solve time-harmonic exterior-boundary value problems for perturbations of the (aδd+bdδ)-system (δ: the co-differential, a, b〉0). We prove, that a Fredholm alternative holds true, the eigensolutions decay polynomially at infinity, and that the positive eigenvalues do not accumulate. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 2
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1551-1562 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Neumann problem for the Laplace equation in an exterior connected plane region bounded by closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind, which is uniquely solvable. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 3
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1531-1549 
    ISSN: 0170-4214
    Keywords: gratings ; Helmholtz equation ; high frequencies ; geometric theory of diffraction ; transition regions ; finite element method ; error estimates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new numerical method is derived for the calculation of high-frequency asymptotic expansions of the scalar wave scattered by curved periodic structures. Optimal error estimates for this method are established. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 4
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1563-1598 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give a complete classification for breakdown in finite time or global existence of continuously differentiable solutions to hyperbolic systems of two first-order partial differential equations posed on a real bounded interval, with boundary damping and initial data of small magnitude. Structural bounds for the derivatives of the initial data which govern the behavior of the solution are brought to light. We isolate two classes of boundary damping: the strong damping forbids the solution to blow up after a time that we exhibit while the weak damping permits a late breakdown. The results are applied to nonlinear elasticity. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 5
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 31-45 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
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  • 6
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 133-150 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Solutions of linear elliptic partial differential equations in unbounded domains can be represented by boundary potentials if they satisfy certain conditions at infinity. These radiation conditions depend on the fundamental solution chosen for the integral representation. We prove some basic results about radiation conditions in a rather general framework.Fundamental solutions G are considered that are defined only on the complement of a compact set. It turns out, however, and we present examples for this, that the more interesting results only hold if G is defined on all of ∝n or if it is a Green function for an exterior boundary value problem. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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  • 7
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 189-203 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the present paper, we deal with the long time behaviour of solutions for the generalized Benjamin-Bona-Mahony equation. By a priori estimates methods, we show this equation possesses a global attractor in Hk for every integer k≥2, which has finite Hausdorff and fractal dimensions. We also construct approximate inertial manifolds such that every solution enters their thin neighbourhood in a finite time. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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  • 8
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1185-1198 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An explicit factorization of the Fourier symbol matrix functions generated by Sommerfeld diffraction problems with oblique derivatives is obtained. For this purpose a new prefactorization procedure is developed which makes use of factorization through weighted L2 spaces. These results yield a representation of a generalized inverse of the corresponding matrix Wiener-Hopf operator and the asymptotic behaviour of the solution at the edge of the screen. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 9
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1223-1238 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a high-field version of the periodic Schrödinger-Poisson system, for which the Poisson equation includes nonlinear terms corresponding to a field-dependent dielectric constant. Using a Galerkin scheme, we prove global existence and uniqueness, and present the matrix equations for the numerical evaluation of the potential. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 10
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1199-1222 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A generalized Hele-Shaw flow is derived and analysed in injection and compression moulding which contains non-isothermal and non-Newtonian rheological behaviour of the molten polymers as well as non-symmetric effects. The corresponding fixed domain formulations for the flow are investigated from a mathematical point of view. Different approaches for the determination of the temperature and some viscosity models are discussed. Together with an outline of the proposed solution algorithm special finite element techniques are described for the numerical treatment of this complex non-linear moving boundary problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 11
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1239-1256 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Ginzburg-Landau equation which describes nonlinear modulation of the amplitude of the basic pattern does not give a good approximation when the Landau constant (which describes the influence of the nonlinearity) is small. In this paper a derivation of the so-called degenerate (or generalized) Ginzburg-Landau (dGL)-equation is given. It turns out that one can understand the dGL-equation as an example of a normal form of a co-dimension two bifurcation for parabolic PDEs. The main body of the paper is devoted to the proof of the validity of the dGL as an equation whose solution approximate the solution of the original problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 12
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1257-1269 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper deals with the Dirichlet problem for the Stokes linear equation in a domain exterior to an open surface. With the help of the theory of boundary integral (pseudo-differential) equations uniqueness and existence theorems are proved in the Bessel-potential and Besov spaces and Cα-smoothness (with α〈1/2) of solution is established in the neighbourhood of the boundary of the open surface. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 13
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1271-1281 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper the authors consider the initial boundary value problem of the ferromagnetic spin chain equation and prove the existence of the global attractor and finiteness of the Hausdorff and the fractal dimensions of the attractor. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 14
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1283-1312 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We regard the Schrödinger-Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrödinger operator, the Fermi level and the quantum mechanical electron density operator for square integrable electrostatic potentials. On bounded sets of potentials the Fermi level is continuous and bounded, and the electron density operator is monotone and Lipschitz continuous. As a tool we develop a Riesz-Dunford functional calculus for semibounded self-adjoint operators using paths of integration which enclose a real half-axis. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 15
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1313-1323 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate an initial-value problem modelling fragmentation processes where particles split into two or more pieces at a rate, γ, that not only depends on the sizes of the particles involved but also on time. The existence of non-negative, mass-conserving solutions is established by considering a truncated version of an associated non-autonomous abstract Cauchy problem. The latter has solutions of the form u(t)=Un(t,t0)f, t≥t0, where f is the known data at some fixed time t0≥0 and {Un(t,s)}t0≤s≤t≤T is a uniformly continuous evolution system. A limit evolution system {U(t,s)}t0≤s≤t≤T is shown to exist. Depending on the form of the known data f at time t0, the scalar-valued function u, obtained from the limit evolution system via u(x, t)=[U(t, t0)f](x) for a.e. x〉0, t≥t0, is a solution of either the original initial-value problem or an integral version of this problem. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 16
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1325-1333 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the boundedness and a priori bounds of global solutions of the problem Δu=0 in Ω×(0, T), (∂u/∂t) + (∂u/∂ν) = h(u) on ∂Ω×(0, T), where Ω is a bounded domain in ∝N, ν is the outer normal on ∂Ω and h is a superlinear function. As an application of our results we show the existence of sign-changing stationary solutions. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 17
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1335-1344 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this note we investigate spatial bounds for the heat conduction equation with three relaxation times. We use energy methods similar to those considered in the study of the backward parabolic heat equation. Finally, we show that for any positive choice of the coefficients we may take initial data for which the solution is unstable when we suppose that the body is bounded. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 18
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1345-1364 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Continuous sedimentation of solid particles in a liquid takes place in a clarifier-thickener unit, which has one feed inlet and two outlets. The process is vital in a waste water treatment plant, where the particles consist of several biological components. The concentrations of these are modelled by a one-dimensional system of conservation laws with source term. It is shown how a unique solution can be obtained, and how analytical solutions are used to form a conservative numerical algorithm. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 19
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1389-1410 
    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 existence and uniqueness of the steady-state solution of hydrodynamic model for semiconductor devices. Boundary conditions are prescribed by vorticity on inflow boundary as well as by electron density, temperature, and normal component of electron velocity on whole boundary. If the ambient temperature is large, and if both vorticity on inflow boundary and the variation of density on boundary are small, a unique subsonic solution exists. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 20
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1379-1388 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The theory of high-frequency waves has been used to calculate first and second-order asymptotic solutions for the propagation of non-linear waves in a cylindrical symmetric flow of an electron plasma. The behaviour of acceleration waves and weak shock waves has been analysed through these solutions and Whitham's rule for a weak shock wave on any wavelet has been confirmed through the first-order solution. The appearance of a weak shock wave on any wavelet has been determined and its strength, the location, and the speed of propagation have been found from the asymptotic solution presented in this paper. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 21
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1449-1457 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Of concern are factored Euler-Poisson-Darboux equations of the type∏Nj=1(d2/dt2+(ρ/t)d/dt+Aj)u(t)=0,where, for example, Aj=-cjΔ, Δ being the Dirichlet Laplacian acting on L2(Ω), Ω⊂∝n, and 0〈c1〈…〈cN. More generally -Aj can be the square of the generator of a (C0) group on a Banach space. When the constant ρ is negative, the initial value problem for the factored EPD equation is ill-posed. Nevertheless, we determine how many initial conditions are necessary to guarantee uniqueness of a solution. This number jumps up as ρ crosses a negative integer from right to left. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 22
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 151-177 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study on the initial-boundary value problem for some degenerate non-linear wave equations of Kirchhoff type with a strong dissipation:\documentclass{minimal} \begin{document} \[ u_{tt}=\left\| \nabla u\right\| ^{2\gamma }\Delta u-\Delta u_t=\left| u\right| ^\alpha u,\quad u(0)=u_0,\;u_t(0)=u_1,\;u|_{\partial \Omega }=0. \] \end{document}When the initial energy $E(u_0,u_1)\equiv \left\| u_1\right\| ⁁2+\frac 1{\gamma +1}\left\| \nabla u_0\right\| ⁁{2(\gamma +1)}-\frac 2{\alpha+2}\left\| u_0\right\| _{\alpha +2}⁁{\alpha +2}$ associated with the equations is non-negative and small, a unique (weak) solution exists globally in time and has some decay properties. When the initial energy E(u0,u1) is negative, the solution blows up at some finite time. In the proof we use the ‘modified potential well’ and ‘Concavity’ methods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 179-187 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove existence, in a small time interval, of a classical solution having a regular free boundary, (i.e. the level set {u=0}) of a multidimensional filtration problem. The key point to get the regularity of the level set {u=0} is the proof of an a priori estimate for the L∞-norm of ut. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 667-677 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study stationary solutions of the relativistic Vlasov-Maxwell system of plasma physics which have a special form introduced (in the classical setting) by Rudykh, Sidorov and Sinitsy and establish their existence under suitable assumptions on the ansatz functions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 667-677 (1997).
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 679-688 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper addresses the question: when the frequency of collisions vanishes, will the solutions of the Landau system converge to the solutions of the Vlasov system? We give a positive answer to the question for solutions satisfying certain regularity conditions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 679-688 (1997).
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 783-803 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers the non-linear stability of a non-hyperbolic system of conservation laws with both relaxation and diffusion, which is commonly used for the modeling of two-phase fluid flows. Global existence in time is proved for initial data with a sufficiently small H1 norm. This result heavily depends on the nice structure of the relaxation system, derived from the initial system by setting the relaxation variables to zero. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1045-1068 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The goal of this paper is to establish that even for strongly non-linear Darcy's laws and strongly non-linear leaky boundary conditions on the bottom of the reservoirs the fluid flow through a porous dam is a well-posed problem for which existence of a solution can be established. In a simple case we provide also the exact solution to the problem. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1163-1169 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: Consider the problem of heat flow in a convex domain in ∝n with Dirichlet boundary condition and constant initial temperature. We show that the solution has a fixed hot spot if the domain is invariant under the action of an essential symmetry group. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1171-1183 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers a particular type of closed-loop for the wave equation in one space dimension with damping acting at an arbitrary internal point, for which the uniform stabilization with exponential decay rate is shown. Applications to chains of coupled strings are also discussed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1365-1377 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper is concerned with optimal control problem for a non-linear parabolic equation with non-homogenous boundary condition and quadratic cost. The control is acting in a nonlinear equation. We derive some results on the existence of optimal controls. Then we treat optimal control problem by Galerkin method and we prove the convergence of optimal values for approximated control problems to the one for the original problem. Finally, we apply the results to give a simple example. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1427-1448 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is proved that there is a (weak) solution of the equationut=a*uxx+b*g(ux)x+f,on ∝+ (where * denotes convolution over (-∞, t)) such that ux is locally bounded. Emphasis is put on having the assumptions on the initial conditions as weak as possible. The kernels a and b are completely monotone and if a(t)=t-α, b(t)=t-β, and g(ξ)∼sign(ξ)∣ξ∣γ for large ξ, then the main assumption is that α〉(2γ+2)/(3γ+1)β+(2γ-2)/(3γ+1). © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1411-1425 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article treats the initial-boundary-value problem of viscoplasticity using unified constitutive models without a yield surface. Semi-discretization with the finite element method (FEM) leads to a system of differential-algebraic equations (DAE) with strongly non-linear evolution equations for the internal state variables. A special family of partitioned Runge-Kutta methods is introduced which allows an efficient time integration of the semidiscrete system. Coefficients for methods of order one, two, and three are given. Finally, numerical results for some two- and three-dimensional examples using the model of Hart are presented. In a second part we will give the theoretical background and state a proof of convergence for the algorithm presented in this paper. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1459-1468 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We prove that any solution of the problem(u+K*u)t+∑ai(u)uxi=0 on (0,∞)×∝Nwith spatially periodic initial data converges to a constant provided some non-degeneracy conditions on the kernel K and the non-linear functions ai,i=1,…,N are imposed. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1501-1530 
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    Keywords: radiating solutions ; exterior boundary value problems in elasticity ; asymptotic expansions ; low-frequency behaviour ; Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We continue the study of the operators of generalized linear elasticity and investigate the behaviour of the solutions as the frequency tends to zero. We identify degenerate operators in terms of special solutions to the static problem which must be added to the usual Neumann series in order to describe the low frequency behaviour adequately. As a byproduct we construct solutions to the homogeneous static operator (‘spherical elastics’) which generalize the spherical harmonics and give rise to a ‘spherical elastics expansion’. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1599-1616 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The Dirichlet initial-boundary-value problem in the half-space ∝t×∝3+ for a non-linear hyperbolic system is studied. About the nonlinearity the null condition structure is imposed. Under the smallness conditions on the initial data the existence of low regularity solutions, on a given interval of time, is proved. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1617-1624 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We develop aspects of Clifford analysis over the sphere and hyperbolae. We focus primarily on the hyperbola lying in the Minkowski type space ∝n,1. We show that in order to give a proper extension of basic results on Clifford analysis in Euclidean space to this context one needs to consider both hyperbolae lying in ∝n,1. We also introduce Bergman spaces of Lp left monogenic sections in this context and consider the decomposition of square integrable sections over suitable bundles constructed over subdomains of spheres and hyperbolae. The results presented here cover the necessary background to enable one to set up and solve boundary value problems for field-type equations over hyperbolae. In particular, one can study analogues of the Dirichlet problem for analogues of the Laplacian over hyperbolae and spheres. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 79-94 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The limiting behaviour of solutions of a system of singularly perturbed equations is studied. The goal is to construct a dissipative feedback control synthesis that stabilizes the prescribed output functional along trajectories of solutions. The results are applied to a singularly perturbed Johnson-Sagelman-Oldroyd model of shearing motions of a piston driven flow of a non-Newtonian fluid. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 95-119 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The three-dimensional steady state oscillation problems of the elasticity theory for homogeneous anisotropic bodies are studied. By means of the limiting absortion principle the fundamental matrices maximally decaying at infinity are constructed and the generalized Sommerfeld-Kupradze type radiation conditions are formulated. Special functional spaces are introduced in which the basic and mixed exterior boundary value problems of the steady state oscillation theory have unique solutions for arbitrary values of the oscillation parameter. Existence theorems are proved by reduction of the original boundary value problems to equivalent boundary integral (pseudodifferential) equations. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 205-217 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The two-dimensional frictionless contact problem of linear isotropic elasticity in the half-space is treated as a boundary variational inequality involving the Poincare-Steklov operator and discretized by linear boundary elements. Quadratic growth of the energy near the solution is shown under weak regularity assumptions if the central axis of external forces intersects the boundary of the domain in a Lebesgue null set. Estimating the numerical range of the discrete Poincare-Steklov operator and properly modifying it, enables the application of an error estimate for semi-coercive variational inequalities. Optimal order of convergence is obtained in the underlying Sobolev space H1/2(∂Ω)2. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 219-243 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The dependence on the small parameter ε of constants in Korn's inequalities is investigated for domains which are obtained by joining thin rods to an elastic spatial body. The external ends of the rods are clamped. The asymptotic accuracy of the derived inequalities is achieved by certain distribution of weight multipliers and powers of ε in L2-norms of displacements and their derivatives while the introduced weights differ for longitudinal and transversal components of displacement fields in the rods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 271-289 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The aim of this paper is to investigate the behaviour as t→∞ of solutions to the Cauchy problem ut-Δut-νΔu-(b, ∇u)=∇⋅F(u), u(x, 0)=u0(x), where ν〉0 is a fixed constant, t≥0, x∊∝n. First, we prove that if u is the solution to the linearized equation, i.e. with ∇⋅F(u)≡0, then u decays like a solution for the analogous problem to the heat equation. Moreover, the long-time behaviour of u is described by the heat kernel. Next, analogous results are established for the non-linear equation with some assumptions imposed on F, p, and the initial condition u0. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 245-269 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The article treats the question of how to numerically solve the Dirichlet problem for the Stokes system in the exterior of a three-dimensional bounded Lipschitz domain. In a first step, the solution of this problem is approximated by functions solving the Stokes system in a truncated domain and satisfying a suitable artificial boundary condition on the outer boundary of this truncated domain. In a second step, this new problem is approximately solved in finite element spaces related to a graded mesh as introduced by Goldstein [Math. Comp., 36, 387-404 (1981)]. The difference between this finite element approximation and the exact solution of the exterior Stokes problem is estimated in the norm of suitable unweighted L2-Sobolev spaces. These estimates are analogous to corresponding results which are known for the Poisson equation. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 291-314 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: Inverse problems for identification of the memory kernel in the linear constitutive stress-strain relation of Boltzmann type are reduced to a non-linear Volterra integral equation using Fourier's method for solving the direct problem. To this equation the contraction principle in weighted norms is applied. In this way global existence of a solution to the inverse problem is proved and stability estimates for it are derived. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 369-381 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We consider exact controllability of a system of two Schrödinger equations. These represent matter waves in adjacent potential wells with different potentials, one zero, the other a positive constant V0. The problem is formulated as a simultaneous boundary controllability problem, with Dirichlet control. Estimates for the controls, including an observability inequality, are proved using multiplier techniques. Then the Hilbert uniqueness method is used to obtain the exact controllability result. If V0 is sufficiently small, there exists a time T^(V0) such that the system is exactly controllable in times T〉T^(V0). © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 315-346 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The Dirichlet problem for the Stokes system in a dihedral angle is considered. An explicit description of special solutions to the homogeneous problem which have the form\documentclass{minimal} \begin{document} \begin{eqnarray*} U(x) &=&\left| x\right| ^\lambda \sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}u^{(k)}(x/\left| x\right|), \\ P(x) &=&\left| x\right| ^{\lambda -1}\sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}p^{(k)}(x/\left| x\right|) \end{eqnarray*} \end{document}is given. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 347-368 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We consider an initial value problem for a system of equations describing the motion and the heat convection in a viscous and incompressible fluid which occupies a smooth region Ωt⊂∝3 depending on time.In the equation for the distribution of temperature in the fluid we take into account not only the convective term but also the term responsible for the dissipation of energy.We prove local in time existence and uniqueness of solutions of the considered problem, and global in time existence for sufficiently small data. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 425-448 
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    Topics: Mathematics
    Notes: The work deals with boundary equations appearing if non-stationary problems for Maxwell system are solved with the help of surface-retarded potentials. The solvability of these equations is proved in some functional spaces of Sobolev type. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 385-401 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We consider the electromagnetic inverse scattering problem of determining the index of refraction of an isotropic inhomogeneous medium from a knowledge of the total electric near field data. We consider both the case of scattering by an infinite inhomogeneous cylinder and a bounded inhomogeneous region in space. We conclude by giving an application of our method to the problem of imaging leukemia in the upper leg by means of microwaves. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 449-459 
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    Topics: Mathematics
    Notes: Here we consider initial boundary value problems for parabolic equations in non-bounded (with respect to time) domains by using the single-layer potential. We discuss the solvability in anisotropic Hölder spaces of the boundary integral equations, to which original parabolic problems are reduced. We construct the special operators (regularizers) for these integral equations which transform them to equivalent integral Volterra equations of the second kind with weakly singular kernels. As a corollary we obtain the theorem about the classical solvability in anisotropic Hölder spaces for initial boundary value parabolic problems. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 403-423 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: In this paper we prove an a posteriori error estimate for the symmetric coupling of finite elements and boundary elements applied to linear parabolic-elliptic interface problems. The discontinuous Galerkin method is used for the discretization in time. We present an adaptive algorithm for choosing the mesh size in space and time and we analyse the Hybrid Modified Conjugate Residual (HMCR) method as a solution method for the linear systems which arise. Computational results show that the number of HMCR-iterations grows slowly with the problem size. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 383-384 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 477-493 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: Implicit one-step difference methods for quasilinear parabolic initial boundary value problems in two space variables and in polar coordinates are considered. Problems of this kind are suitable for the description of diffusion processes in plasma physics. Therefore, because of its special physical interest the dependence of the coefficients both on the solution and on its space derivatives (the fluxes) is included. The first part of this paper deals with proving convergence of the discrete approximations for vanishing step sizes. For this purpose, bounds for the inverse difference operators have to be derived previously. The nonlinear systems arising from the discretizations have exactly one solution for all step sizes being sufficiently small. In the second part of the article numerical tests are performed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 521-545 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: This article establishes the existence of trapped-mode solutions of 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. A trapped mode corresponds to an eigenvalue of a non-local Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by generalizing previous results concerning spectral theory for differential operators to this non-local operator. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 599-616 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The existence of the classical global solutions for the non-linear Klein-Gordon-Schrödinger equations is proved in H1-subcritical cases for space dimensions n≤5. For higher space dimensions 6≤n≤9, we will give a subsequent paper to deal with. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 569-581 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We show that any solution of the scalar conservation law(u+k*u)t+σ(u)x=0starting from spatially periodic initial datum stabilizes to its integral mean as time goes to infinity. No convexity or ‘genuinely non-linear’ like conditions are assumed concerning σ. © 1997 by B. C. Teubner stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 583-597 
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    Topics: Mathematics
    Notes: We consider the initial-boundary value problem for quasi-linear symmetric hyperbolic systems with dissipation and characteristic boundary of constant multiplicity. We investigate the global existence and decay property of small regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary. We also show the existence, uniqueness and stability of the time periodic solutions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 617-623 
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    Topics: Mathematics
    Notes: The uniqueness for unbounded classical solutions of the magnetohydrodynamic (MHD) equations in the whole space is investigated. Under suitable growth condition, it is shown that the solution to the initial value problem is unique. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 625-634 
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    Topics: Mathematics
    Notes: The steady-state problem of the non-linear reaction-diffusion systemut-uxx=u(av-b),vt-vxx=cuis considered. The existence of positive steady-solutions is established by using a fixed point theorem in ordered Banach space. The uniqueness of ordered positive steady-state solutions and an application to the associated reaction-diffusion system are presented. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 635-652 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: A class of diffraction problems for the two-dimensional Helmholtz equation is studied where the boundary conditions on a canonical screen contain oblique derivatives. The problem in weak formulation is reduced to a system of pseudodifferential equations on a half-line. The Fredholm property is characterized in dependence of the parameters, index formulas are given, and, if necessary, a normalization of the problem is implemented. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 653-666 
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    Topics: Mathematics
    Notes: In this paper a time-discrete dynamic model for the process of disarmament is investigated. The state variables of the system are costs and security values. We assume that the costs can be controlled, and we aim at reducing the costs to zero and achieving non-negative security values after a finite number of time steps. In the case where the opponents behave cooperatively this leads to the solution of a linear programming problem. If the opponents behave non-cooperatively, then a Nash equilibrium has to be determined under linear constraints. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 653-666 (1997).
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 689-706 
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    Topics: Mathematics
    Notes: In this paper we prove the existence of a weak solution to the non-stationary drift-diffusion equations (van Roosbroeck's system) of semiconductor theory involving discontinuous permittivities. The proof is based on an approximation of these equations by a system with bounded non-linearities, deriving a priori estimates on the approximate solutions and then carrying out the passage to limit. The discussion is completed by some regularity results for the weak solution under consideration. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 689-706 (1997).
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 717-736 
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    Topics: Mathematics
    Notes: We study the free streaming operator T∧ in a slab domain with boundary conditions described by a linear matrix operator Λ acting between the ‘incoming’ and ‘outgoing’ particle fluxes. Under suitable assumptions on the entries of Λ, it is proved that the resolvent operator of T∧ is positive. It is proved also that T∧ is the generator of a positive strongly continuous semigroup, whose type depends on the norm of the entries of Λ. Some examples are given. In particular the case of Maxwell type boundary conditions is studied and the location of the spectrum of T∧ is improved. © 1997 by B. G. Teubner Stuttgart - John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 717-736 (1997).
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 737-744 
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    Topics: Mathematics
    Notes: In the present paper we prove Cα-estimates for ∇u using components of boundary values of u, div u, curl u and quantities given by components of boundary values of u as well as boundary values of elements belonging to de Rhams cohomology modules. The vector field u is defined on a bounded set G¯⊂∝3, meanwhile the cohomology group will be defined with regard to ∝3-G. Our inequalities turn out to be a priori estimates concerning well-known boundary value problems for vector fields. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 759-766 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We consider in this paper a system of equations modelling a steady-state induction heating process for ‘two-dimensional geometries’. Existence of a solution is stated in W1,p(Ω) Sobolev spaces and is derived using the Leray-Schauder's fixed point theory. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 745-757 
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    Topics: Mathematics
    Notes: We extend the recently developed Riesz-Clifford monogenic functional calculus (based on Clifford analysis) for a set of unbounded non-commuting operators. Connections with quantum mechanics are discussed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 767-782 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: Existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions are studied. The answers to some questions concerning a generalization of a problem posed by I. Rubinstein are given. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 805-812 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Notes: No Abstract
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 841-854 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We consider a free boundary value problem arising from a non-symmetric problem of electrochemical machining (ECM). After a conformal mapping of the unknown domain the problem is transformed to a non-smooth non-linear Riemann-Hilbert problem for holomorphic functions in the complex unit disk. A special technique allows to remove the singularities in the boundary condition. Utilizing existence results for smooth non-orientable Riemann-Hilbert problems, existence and uniqueness of a solution are shown. Finally, we propose an iterative method of Newton type for the effective numerical computation of the free boundary of the anode and present some test results. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 813-840 
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    Notes: We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5]. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 855-865 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We prove the existence of a wide collection of finite sets of functionals that completely determine the long-time behaviour of strong solutions to the von Karman evolution equations. This collection contains finite sets of determining modes, nodes and local volume averages. The approach presented relies on the concept of a completeness defect for a set of linear functionals and it involves some ideas from abstract approximation theory. Our method is general enough and also can be applied to other non-linear partial differential equations which are of second order in time. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 867-883 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: In this paper, we study a system of biharmonic equations coupled by the boundary conditions. These boundary conditions contain some combinations of the values, div, curl, and grad. Applications in mathematical physics are possible and the investigations will be done with the help of hypercomplex methods. It is also the aim of the paper to demonstrate the application of Clifford analytic methods to the solution of boundary value problems. The results on a special boundary value problem for the biharmonic equation will be used for the investigation of some first-order systems of partial differential equations. We study a theoretical problem connected with the ∂¯-problem and the solution of a Beltrami system by using a fixed-point iteration. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 885-890 
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    Topics: Mathematics
    Notes: Modified fundamental solutions are used to show that the system of boundary integral equations in a direct method for the interior Dirichlet problem for the two-dimensional biharmonic equation has at most one solution on any smooth closed boundary contour. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 891-903 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The non-homogeneous magnetohydrodynamics equation is studied, with emphasis on the singularities due to Alfvén resonance. It is shown that for any arbitrary function defined on the singular set, there exists a unique solution of the problem coinciding with this function. Then the values on the singular set which correspond to the correct physical solution are determined proving that this is unique except for a discrete set of geometrical configurations. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 905-914 
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    Notes: In this paper we present some new results of symmetry for inhomogeneous Dirichlet eigenvalue problems overdetermined by a condition involving the gradient of the first eigenfunction on the boundary. One specificity of the problem studied is the dependence of the equation and the boundary condition on the distance to the origin. The method of investigation is based on the use of continuous Steiner symmetrization together with some domain derivative tools. An application is given to the study of an overdetermined eigenvalue problem for a wedge-like membrane. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 915-932 
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    Topics: Mathematics
    Notes: We consider the initial-boundary value problem for a linear thermoelastic plate equation and we prove that the energy associated to the system decays exponentially to zero as time goes to infinity. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 933-943 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: In this paper, we consider the Cauchy problem:(ECP)ut-Δu+p(x)u=u(x,t)∫∝3u2(y,t)/∣x-y∣dy; x∊∝3, t〉0,u(x, 0)=u0(x)≥0 x∊∝3, (0.2)The stationary problem for (ECP) is the famous Choquard-Pekar problem, and it has a unique positive solution ū(x) as long as p(x) is radial, continuous in ∝3, p(x)≥ā〉0, and lim∣x∣→∞p(x)=p¯〉0. In this paper, we prove that if the initial data 0≤u0(x)≤(≢)ū(x), then the corresponding solution u(x, t) exists globally and it tends to the zero steady-state solution as t→∞, if u0(x)≥(≢)ū(x), then the solution u(x,t) blows up in finite time. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 945-958 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We consider the incompressible limit of the compressible Euler equation in the half-space ∝n+. It is proved that the solutions of the non-dimensionalized compressible Euler equation converge to the solution of the incompressible Euler equation when the Mach number tends to zero. If the initial data v∞0 do not satisfy the condition ‘∇⋅v∞0=0’, then the initial layer will appear. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 959-978 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We study the linearized stability of planer flows of incompressible, viscous fluid in two-dimensional annular domains. A certain family of steady, explicit solutions which have spiral streamlines are considered. The Navier-Stokes equations are linearized at these solutions and we show analytically or numerically that these solutions are stable to perturbation of steady states, whatever the Reynolds number or the aspect ratio of the annuli may be. Hopf bifurcations from them are also examined numerically. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 979-988 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: The subject of this paper is the study of free oscillations of a composite material consisting of an elastic medium and a large number of elastic piles periodically immersed in a part of the medium. The ends of piles lying on the boundary of the medium are clamped to a force-free rigid plate. Such a partially composite structure arises in pile foundation mechanics. Assuming that the period of pile structure tends to zero, we obtain the macroscopic equations for free oscillations by homogenization method and prove the corresponding convergence result. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 989-1014 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: This paper deals with a famous diffraction problem for a single half-plane Σ: x〉0, y=0 as an obstacle and for some time-harmonic plane incident wave field. Rawlins in 1975 was the first to solve the mixed (Dirichlet/Neumann) boundary value problem for the scalar Helmholtz equation. He also was the first to solve the equivalent pair of coupled Wiener-Hopf equations explicitly by factoring their discontinuous 2×2 Fourier matrix symbol in 1980. Although for real wave numbers k the usual factorization procedure fails it will serve as the basis: Following the lines given by Ali Mehmeti in his habilitation thesis [1] for the (Dirichlet/Dirichlet) boundary value problem we combine the idea of integral path deforming along the branch cuts of the characteristic square root √(ξ2-k2) given in Meister's book [13] with the modern Wiener-Hopf method solution derived by Speck [24] explicitly in a H1+ε, ε≥0, Sobolev space setting. The symmetry of the intermediate spaces Hs, H-s, ∣s∣〈1 2, which is due to generalized factorization, plays a key role in deforming the Fourier integral paths in order to get Laplace transform representations of the generalized eigenfunctions of the problem. As a remarkable fact 0〈ε〈¼ must hold here. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1015-1044 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Consider the two adjacent rectangular wedges K1, K2 with common edge in the upper halfspace of ∝3 and the operator A (=-Laplacian multiplied by different constant coefficients a1, a2 in K1, K2, respectively) acting on a subspace of ∏2j=1L2(Kj). This subspace should consist of those sufficiently regular functions u=(u1,u2) satisfying the homogeneous Dirichlet boundary condition on the bottom of the upper halfspace. Moreover, the coincidence of u1 and u2 along the interface of the two wedges is prescribed as well as a transmission condition relating their first one-sided derivatives. We interpret the corresponding wave equation with A defining its spatial part as a simple model for wave propagation in two adjacent media with different material constants. In this paper it is shown (by Friedrichs' extension) that A is selfadjoint in a suitable Hilbert space. Applying the Fourier (-sine) transformations we reduce our problem with singularities along the z-axis to a non-singular Klein-Gordon equation in one space dimension with potential step. The resolvent, the limiting absorption principle and expansion in generalized eigenfunctions of A are derived (by Plancherel theory) from the corresponding results concerning the latter equation in one space dimension. An application of the spectral theorem for unbounded selfadjoint operators on Hilbert spaces yields the solution of the time dependent problem with prescribed initial data. The paper is concluded by a discussion of the relation between the physical geometry of the problem and its spectral properties. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1069-1087 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We establish local existence and comparison for a model problem which incorporates the effects of non-linear diffusion, convection and reaction. The reaction term to be considered contains a non-local dependence, and we show that local solutions can be obtained via monotone limits of solutions to appropriately regularized problems. Utilizing this construction, it is further shown that, under conditions of either ‘weak reaction’ or ‘sufficiently small’ initial mass, solutions exist for all time. Finally, we provide an alternative analysis of global existence and investigate blow up in finite time for the case of power law diffusion and convection. These results show the extent to which the assumption of weak reaction may be relaxed and still obtain global existence. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1089-1109 
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    Topics: Mathematics
    Notes: By means of the Conley connection index theory we prove existence of travelling wave solutions to a system of equations in a two temperature model of laser maintained plasma. These solutions describe locally the motion of plasma boundaries. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1111-1125 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: We consider characteristic Galerkin methods for the solution of hyperbolic systems of partial differential equations of first order. A new recipe for the construction of approximate evolution operators is given in order to derive consistent methods. With the help of semigroup theory we derive error estimates for classes of characteristic Galerkin methods. The theory is applied to the wave equation and also to the Euler equations of gas dynamics. In the latter case one can show that Fey's genuinely multidimensional method can be reinterpreted as a characteristic Galerkin method. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1127-1134 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
    Notes: This paper proves the uniqueness result for global in time large solutions of quasistatic equations to an inelastic model of material behavior of metals, provided that an a priori L∞-estimation for the Cauchy stress tensor holds. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Journal of Physical Organic Chemistry 10 (1997), S. 305-310 
    ISSN: 0894-3230
    Keywords: non-covalent interactions ; host-guest complexes ; fluorinated phenyl compounds ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Complexation constants with the macrocyclic azoniacyclophane CP44 and phenyl guest compounds with at least four fluorine atoms or alternatively protons at the ring were obtained by NMR shift titrations in water. The fluorinated compounds show free energies of complexation which are smaller by ΔΔG=3·4-7·7 kJ mol-1 in comparison with the protonated compounds. The NMR shifts induced upon 100% complexation (CIS values) were obtained simultaneously from non-linear least-squares fitting and indicate intra-cavity inclusion in all cases. The CIS values agree roughly with screening constants calculated from aromatic ring current and linear electric field effects, the latter resulting from the permanent charges at the host compound. Molecular mechanics calculations (CHARMm) indicate that intracavity inclusion is possible with all compounds with negligible strain induced (〈1 kJ mol-1) in the macrocycle upon complexation. In contrast, α-cyclodextrin can accommodate fluorinated phenyl compounds only at the rim of the cavity without larger strain. Preliminary data with α-cyclodextrin, obtained by competitive UV-visible titration with methyl orange, indicate again a smaller association free energy (ΔΔG=1·-7 kJ mol-1) for pentafluorphenol compared with normal phenol as guest. © 1997 John Wiley & Sons, Ltd.
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    Keywords: hydrophobic cavity characterization ; cyclophanes ; Chemistry ; Theoretical, Physical and Computational Chemistry
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    Topics: Chemistry and Pharmacology , Physics
    Notes: The guest-binding behavior of two different cyclophane hosts, each being capable of providing a three-dimensionally extended hydrophobic cavity toward aromatic guests, was examined in aqueous media: a steroid cyclophane bearing four rigid cholate moieties and an octopus cyclophane having four flexible double-chain segments. Even though the binding constant for 2,7-dihydroxynaphthalene with the steroid cyclophane was comparable to that with the octopus cyclophane, the guest binding modes were very different from each other, as confirmed by 1H NMR spectroscopy. That is, the steroid cyclophane incorporates the guest into its rigid macrocyclic cavity with axial geometry whereas the octopus cyclophane provides a three-dimensional space created by the macrocyclic skeleton and the flexible hydrocarbon chains so that the long axis of the guest becomes more or less perpendicular to the molecular axis of the host upon complexation. Temperature-dependent molecular recognition by these hosts toward 8-anilinonaphthalene-1-sulfonate was examined by means of fluorescence spectroscopy. Characteristic differences in the guest-binding mode between these hosts were sensitively reflected in the thermodynamic entropy change on host-guest complexation and the temperature-dependent microscopic viscosity experienced by the guest at the binding site. © 1997 John Wiley & Sons, Ltd.
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    Journal of Physical Organic Chemistry 10 (1997), S. 254-272 
    ISSN: 0894-3230
    Keywords: π-π interactions ; self-assembly ; catenanes ; cyclophanes ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The recent surge of interest in the control of molecular organization in both the solution state (i.e. self-assembly) and the solid state (i.e. crystal engineering) has led researchers to recognize increasingly the importance of weak non-covalent interactions. The design and synthesis of an efficient molecular construction set are dependent upon a very close interplay between x-ray crystallography and synthetic chemistry. π-π Stacking interactions between π-donors, such as hydroquinone, resorcinol or dioxynaphthalene residues, and π-accepting ring systems, such as bipyridinium or π-extended viologen units, can govern the self-assembly of a variety of complexes and interlocked molecular compounds in both the solid and solution states. Non-covalent bonding interactions (i.e. π-π interactions) can be considered as information vectors: they define and rule the self-assembly processes that lead to the formation of the desired molecular and supramolecular architectures, and thereafter they still govern the dynamic processes occurring within the self-assembled structures and superstructures. The manner in which such molecules and supermolecules can contribute to an understanding of non-covalent interactions at both structural and superstructural levels is described, with reference to numerous examples of self-assembly processes in synthesis, of dynamic processes in the solution state, and of the packing of molecules and molecular complexes in the solid state. © 1997 John Wiley & Sons, Ltd.
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    Journal of Physical Organic Chemistry 10 (1997), S. 323-334 
    ISSN: 0894-3230
    Keywords: redox-switched amphiphiles ; ferrocene derivatives ; vesicles ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: ---Thirty ferrocene derivatives were prepared and their ability to form vesicles in aqueous solution when oxidized was assessed. The compounds included alkyl ferrocenylmethyl ether derivatives of the form C10H9FeCH2OR in which R=octyl, dodecyl, tetradecyl, hexadecyl, octadecyl and eicosanyl. One single-tailed amine derivative, C10H9FeCH2NR2, R=octadecyl, was studied. Alkylferrocene derivatives had the form C10H9FeR in which R=butyl, decyl, tetradecyl, hexadecyl, octadecyl, eicosanyl and docosanyl. Sixteen symmetrical 1,1′-disubstituted ferrocenes were also studied. Three ethers were of the form C10H8Fe-1,1′-(CH2OR),2, R=tetradecyl, hexadecyl and octadecyl. Four corresponding dialkyl derivatives of the form C10H8Fe-1,1′-R2, R=decyl, tetradecyl, hexadecyl and octadecyl, were assessed. Finally, a range of 1,1′-disubstituted ferrocene derivatives were analyzed. These all had the form C10H8Fe-1,1′-(COR)2, for which R has the following identities: octyl, tridecyl, pentadecyl and heptadecyl (ketones); heptadecyloxy, 3-cholesteryl and 3-cholestanyl (esters); and two amides, R=NHC18H37 and N(C18H37)2. The alkyl and ether derivatives could be readily oxidized and formed vesicular aggregates upon sonication. The ketones, esters and amides could be oxidized but the ferricenium derivatives did not form stable aggregates. An interesting observation is that the aggregates formed were vesicular whether the ferrocene derivative had one or two alkyl tails. © 1997 John Wiley & Sons, Ltd.
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    Journal of Physical Organic Chemistry 10 (1997), S. 273-285 
    ISSN: 0894-3230
    Keywords: cation-π interactions ; calix[n]arenes ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Non-covalent intermolecular forces have been recognized as a very important part of molecular interactions in complex biological systems. The fundamental functions of living matter such as transcription of genetic information in DNA, spatial arrangement of protein molecules, enzymatic functions or immunity system response are enabled owing to the presence of weak non-covalent forces based on hydrogen bonding interactions, van der Waals interactions, electrostatic interactions, hydrophobic effects, etc. Recently, among them so-called "cation-π" interactions have been proved to contribute to the overall binding process in various artificial or biological systems. Calix[n]arenes have emerged as an important family of molecules with promising applications in many branches of chemistry. Because of their suitable molecular preorganization with aromatic units being "concentrated' in a relatively small space, calix[n]arenes represent interesting compounds exhibiting an enhanced ability for cation-π interactions. The importance of such forces in calix[n]arene chemistry is demonstrated here on several recent examples. © 1997 John Wiley & Sons, Ltd.
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    Journal of Physical Organic Chemistry 10 (1997), S. 335-342 
    ISSN: 0894-3230
    Keywords: hydrophobic interactions ; aqueous solutions ; living systems ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: ---Evidence is provided for the enormous role of hydrophobic interactions in aqueous solutions. It is concluded that complementary functions of hydrophilic and of hydrophobic species are in continuous operation and that these are a conditio sine qua non for the existence of the liquid. With regard to the supermolecular aggregations, hydrophobic interactions are operative on the highest hierarchic levels of the system organization, i.e. at the interface and at the holes around dissolved hydrophobic species. It is further emphasized that water is essential both for the unity and for the differentiation of each living organism. With regard to its role for the differentiation of the body, the hydrophobic interactions are of paramount importance, notably those provided by amphipathic solutes. The cell membrane is considered to be the result of interactions between the highest hierarchic levels of intracellular and extracellular water. The hydrophobic double layer provides the barriers for the separation of intracellular and extracellular water and at the same time the connections for recognition and for exchange of information between them. The DNA structures obtain conservative boundary conditions for their surrounding water systems which do not freeze at -60 °C. These water systems are dynamically superior to all other parts of the water system of the organism. It is suggested that more knowledge about the abilities of liquid water can be obtained by giving appropriate attention to its properties within the living body. © 1997 John Wiley & Sons, Ltd.
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  • 92
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    Journal of Physical Organic Chemistry 10 (1997), S. 343-346 
    ISSN: 0894-3230
    Keywords: charge-transfer complexes ; intrinsic (gas-phase) basicities ; stability ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: ---The standard Gibbs energy changes for the formation of 1:1 charge-transfer complexes between molecular iodine and several bases in solution at 25·0 °C [ΔG0l2(soln)] were determined experimentally. The bases were 2,2,2-trifluoro- ethylamine, cyclopropylamine and 1,1,3,3-tetramethylguanidine. These [ΔG0l2(soln)] values, determined in n-heptane, and also that for the formation of the 1:1 complex between 2,2,2-trifluoroethanethiol and molecular iodine in dichloromethane, were found to follow with excellent precision the correlation equations linking ΔG0l2(soln) and the intrinsic (gas-phase) basicities of N(sp3), N(sp2) and S(sp3) bases. These findings strongly support previous conclusions regarding the relationship between gas-phase and solution reactivity data. © 1997 John Wiley & Sons, Ltd.
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  • 93
    ISSN: 0894-3230
    Keywords: molecular recognition ; non-aqueous titration ; hydrogen bonding ; proton transfer ; pKa shifts ; acid-base catalysis ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Whenever hydrogen bonding is involved in molecular recognition, the possibility of a proton transfer from the donor to the acceptor arises. In most cases the pKa of the donor is far enough above the pKa of the conjugate acid of the acceptor for it to be clear that no proton transfer will occur. However, as the difference between the donor and acceptor pKas decreases, it can become difficult to predict whether a proton transfer will occur. Since most hydrogen bond-driven molecular recognition is studied in low dielectric solvents, non-aqueous titrations can be used to measure the pKas and therefore predict proton transfers. In this paper three studies which involved non-aqueous titrations are summarized. The first deals with distinguishing simple proton transfer from host-guest complex formation. The second involves measuring pKa shifts upon host-guest complex formation. The last is a study of the catalysis of a phosphoryl transfer. In all three scenarios the non-aqueous titration method gave results which would have been difficult to obtain by other means, and which proved crucial for a complete understanding of the molecular recognition process. © 1997 John Wiley & Sons, Ltd.
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  • 94
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    Journal of Physical Organic Chemistry 10 (1997), S. 347-350 
    ISSN: 0894-3230
    Keywords: benzene · · · hexafluorobenzene ; supramolecular synthon ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The benzene · · · hexafluorobenzene stacking interaction was evaluated at several levels of theory. At the MP2/6-31G** level, it is estimated that the interaction is stabilizing by approximately 3.7 kcal mol-1. Lower levels of theory perform poorly on this system. This is a fairly strong non-covalent interaction, suggesting this motif may be a valuable supramolecular synthon. © 1997 John Wiley & Sons, Ltd.
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  • 95
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    Journal of Physical Organic Chemistry 10 (1997), S. 358-368 
    ISSN: 0894-3230
    Keywords: hydrogen bonding ; RP-HPLC C18 stationary phases ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The linear free energy equationlogk′ = c + rR2 + sπ2H + a∑α2H + b∑β2 + vVxwas applied to the capacity factors for various sets of solutes on C18 stationary phases with aqueous methanol and acetonitrile eluents. Here, k′ are the capacity factors for a series of solutes with a given C18 phase and a given eluent, and R2, π2H, ∑α2H, ∑β2, Vx are parameters or descriptors of the solutes as follows: R2 is an excess molar refraction, π2H is the solute polarizability/dipolarity, ∑α2H and ∑β2 are the solute hydrogen-bond acidity and basicity and Vx is the solute volume. It is shown that although the regression coefficients r, s, a, b and v vary widely within the C18 column and mobile phase used, the ratios r/v, s/v, a/v and b/v are remarkably constant. Thus, for the retention of 25 series of solutes on six different C18 columns with 30-90% aqueous methanol as the eluent, all the 25 LFER equations can be combined into one general equation:logk′ = c + v(0.13 R2 - 0.32 π2H - 0.22 ∑α2H - 0.90 ∑β2O + 1.00 Vx)where only c and v vary from system to system. For 11 other phases for which data are available, the ratios v/A and (v + c)/A are constant, where A is the quantity of stationary phase per unit surface area. Similar results were found with C18 phases and aqueous acetonitrile as eluents. Although a first examination of equations based on the first equation above suggests that various C18 phases behave differently, for example the v coefficient, that is related to the observed hydrophobicity of a stationary phase relative to the mobile phase, varies considerably from phase to phase with the same eluent, a detailed analysis led to the conclusion that all the C18 phases examined have roughly the same hydrophobicity, when the v coefficients are corrected for the quantity of stationary phase per unit surface area. It is suggested that these corrected v coefficients, v/A and (v + c)/A, can be regarded as the ‘intrinsic’ phase hydrophobicity. © 1997 John Wiley & Sons, Ltd.
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  • 96
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    Journal of Physical Organic Chemistry 10 (1997), S. 286-291 
    ISSN: 0894-3230
    Keywords: chiral recognition ; cyclodextrins ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: ---The mechanisms for chiral recognition by cyclodextrins (CDxs) are discussed. Examples of host-guest systems where the "lock-and-key mechanism" and the "three-point rule" are applicable are cited and discussed. Most results reported so far suggest that the ability of native CDxs and chemically modified CDxs to discriminate between enantiomers of guests having a central chirality is low in aqueous solutions. Small ΔΔG values for enantioselective complexation of CDxs with amino acids seem to be due to unpredictably small changes in the structures of the complexes of the guest enantiomers. Therefore, it is very difficult to prove the participation of hydrogen bonding in chiral recognition through the "three-point rule" in these systems. The use of the Coulomb interaction and the coordinate bonds as point interactions is discussed. CDxs might be good hosts to recognize axial chirality or helicity of guests. Hydrogen bonding in water is assumed in the recognition of the helicity of bilirubin. Very large ΔΔG values have been reported for the chiral recognition of the binaphthyl derivatives. Such a system seems to be a suitable model system to study the mechanism of chiral recognition by CDxs. © 1997 John Wiley & Sons, Ltd.
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  • 97
    ISSN: 0894-3230
    Keywords: aryliminodimagnesium ; condensation with NO2 and CO groups ; addition to CN group ; single electron transfer efficiency ; σ-complexation ability ; inter- and intramolecular competition ; bifunctional substrates ; positional effect of functional groups ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: ---The reactions of aryliminodimagnesium [ArN(MgBr)2, IDMg] with p′-substituted p-cyanobenzophenones, 1-cyano-9-fluorenone, o-, m- and p-dicyanobenzenes and o-, m- and p-nitrobenzonitriles were examined, and the relative yields of products were referred to the previous results of electron spin resonance studies. The products of condensation with carbonyl and nitro groups and of addition to cyano groups were formed. From the variations of the yields caused by the molar ratio of the magnesium reagent versus substrates and by the substituents of both reactants, the preferred groups were determined. The groups of p- and m-substrates are consistent with the position of highest density of free electrons in the anion radicals, whereas those of the o-substrates are inconsistent. The consistency indicates competition of functional groups reflecting the relative ability of single electron acceptance from the reagent, whereas the inconsistency is ascribed to cooperation of neighbouring groups for σ-complexation with the Mg atom of the reagent. The categories of competition and cooperation are discussed in relation to fundamental features and general governing factors proposed for the IDMg reactions of monofunctional substrates. © 1997 John Wiley & Sons, Ltd.
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  • 98
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    Journal of Physical Organic Chemistry 10 (1997), S. 383-395 
    ISSN: 0894-3230
    Keywords: hydrogen bond strength ; organic groups ; isotopic substitution ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Although the electronic contribution to the strength of a H-bond is unaffected by isotopic substitution, the heavier mass of deuterium compared with protium lowers some of the vibrational frequencies in the complex. The binding energy of the complex, which includes zero-point and thermal vibrational energies, can thus be altered by several tenths of a kcal mol-1 by H/D substitution. Ab initio calculations are used to analyze this phenomenon in a number of common organic functional groups that are prone to form H-bonds: hydroxyl, carboxyl and amide, both self-complexing as homodimers and with water molecules as partners. It is found that any site of D-substitution increases the complexation energy; however, the bridging sites show a stronger preference for D over H than do the non-bridging, or terminal, sites. Hence D-bonding can be considered to be stronger than H-bonding in these functional groups. Of the groups considered, the energetic preference for D over H is greater in the hydroxyl group, so deuterium would be expected to gravitate toward solvent water molecules in isotopic scrambling experiments. The increments in H-bonding energy resulting from each site of substitution are addititve in cases of multiple substitution. © 1997 John Wiley & Sons, Ltd.
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  • 99
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    Journal of Physical Organic Chemistry 10 (1997), S. 253-253 
    ISSN: 0894-3230
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 100
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    Journal of Physical Organic Chemistry 10 (1997), S. 405-413 
    ISSN: 0894-3230
    Keywords: non-covalent interactions ; thermodynamic hydrogen bond parameter ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: ---This paper describes how empirical free energy and/or enthalpy values for hydrogen binding strength are derived from thousands of corresponding measurements between H-bond donors and acceptors, mostly in carbon tetrachloride, and how they can be used to construct common scales or factor values (increments) also for other reactions involving electron donor and acceptor ability of functions. The corresponding databases and programs (HYBOT) allow one to predict thermodynamic values for experimentally unknown equilibria, including also ionophore complexes with crown ethers or cryptands. Applications in QSAR involve the prediction of lipophilicity from any structure on the basis of only two variables, e.g. 234 systems are described this way with a correlation coefficient r=0·96. Similarly, permeabilities and some biological properties such as narcotic activities of chemicals and anti-HIV-1 activity of some porphyrins are evaluated. © 1997 John Wiley & Sons, Ltd.
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