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  • 1995-1999  (1,933)
  • 1997  (1,933)
  • Biochemistry and Biotechnology  (1,317)
  • Numerical Methods and Modeling  (616)
  • Engineering General
  • Nuclear reactions
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  • 1995-1999  (1,933)
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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
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    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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    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 5 Ill.
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  • 4
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    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 4 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    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
    Type of Medium: Electronic Resource
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  • 6
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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 3 Ill.
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  • 11
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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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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    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 7 Ill.
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  • 19
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    Chichester, West Sussex : Wiley-Blackwell
    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.
    Additional Material: 4 Ill.
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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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    Chichester, West Sussex : Wiley-Blackwell
    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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  • 23
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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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  • 24
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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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  • 25
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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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  • 26
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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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  • 27
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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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  • 28
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1163-1169 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 29
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1171-1183 
    ISSN: 0170-4214
    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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  • 30
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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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  • 31
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1427-1448 
    ISSN: 0170-4214
    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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  • 32
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1411-1425 
    ISSN: 0170-4214
    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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  • 33
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1459-1468 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 34
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1501-1530 
    ISSN: 0170-4214
    Keywords: radiating solutions ; exterior boundary value problems in elasticity ; asymptotic expansions ; low-frequency behaviour ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 35
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1599-1616 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 36
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 1617-1624 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 37
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 79-94 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 38
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 95-119 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 39
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 205-217 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 40
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 219-243 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 41
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 271-289 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 42
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 245-269 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 43
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 44
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 369-381 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 45
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 315-346 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 46
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 47
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 425-448 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 48
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 49
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 449-459 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 50
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 51
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
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  • 52
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 54
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 56
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 583-597 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 57
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 617-623 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 66
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 767-782 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 67
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 805-812 
    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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  • 68
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 841-854 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 69
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 813-840 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 71
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 867-883 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 72
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 885-890 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 73
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 891-903 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 76
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 933-943 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we consider the Cauchy problem:(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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  • 77
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 945-958 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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  • 78
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    Mathematical Methods in the Applied Sciences 20 (1997), S. 959-978 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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    Biotechnology and Bioengineering 55 (1997), S. 252-260 
    ISSN: 0006-3592
    Keywords: lipase ; chemical modification ; stability ; esterification ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Semipurified lipase of Candida rugosa (CRSL) was subjected to chemical modification, and the activities of the modified lipase, in hydrolysis and esterification reactions, were examined. The esterification reactions were carried out in the absence and presence of isooctane. When the enzyme was modified with polyethylene glycol (PEG), two methodologies were studied. The activation of PEG with p-NO2-phenylchloroformate gives better biocatalysts than those obtained with cyanuric chloride-PEG. The chemical modification with PEG increases the stability of pure lipases in isooctane at 50°C (extreme conditions). The chemically modified enzymes are useful for biotransformations in organic solvents. In addition the nitration of tyrosines with tetranitromethane was also studied. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 252-260, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 565-570 
    ISSN: 0006-3592
    Keywords: hybridoma ; hypoosmotic stress ; specific antibody productivity ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: To investigate the response of hybridoma cells to hypoosmotic stress, S3H5/γ2bA2 and DB9G8 hybridomas were cultivated in the hypoosmolar medium [Dulbecco's modified Eagle's medium (DMEM) supplemented with 10% serum] resulting from sodium chloride subtraction. Both hybridomas showed similar responses to hypoosmotic stress in regard to cell growth and antibody production. The cell growth and antibody production at 276 mOsm/kg were comparable to those at 329 mOsm/kg (standard DMEM). Both cells grew well at 219 mOsm/kg, though their growth and antibody production were slightly decreased. When the osmolality was further decreased to 168 mOsm/kg, the cell growth did not occur. When subjected to hyperosmotic stress, both cells displayed significantly enhanced specific antibody productivity (qAb). However, the cells subjected to hypoosmotic stress did not display enhanced qAb. Taken together, both hyperosmotic and hypoosmotic stresses depressed the growth of S3H5/γ2bA2 and DB9G8 hybridomas. However, their response to hypoosmotic stress in regard to qAb was different from that to hyperosmotic stress. © 1997 John Wiley & Sons, Inc. Biotechnol Biong 55: 565-570, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 547-555 
    ISSN: 0006-3592
    Keywords: ethanol ; cellulose ; hemicellulose ; endoglucanase ; cellulase ; lignocellulose ; biomass ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This study demonstrates a new approach to reduce the amount of fungal cellulase required for the conversion of cellulose into ethanol. Escherichia coli KO11, a biocatalyst developed for the fermentation of hemicellulose syrups, was used to produce recombinant endoglucanase as a co-product with ethanol. Seven different bacterial genes were expressed from plasmids in KO11. All produced cell-associated endoglucanase activity. KO11(pLOI1620) containing Erwinia chrysanthemi celZ (EGZ) produced the highest activity, 3,200 IU endoglucanase/L fermentation broth (assayed at pH 5.2 and 35°C). Recombinant EGZ was solubilized from harvested cells by treatment with dilute sodium dodecyl sulfate (12.5 mg/ml, 10 min, 50°C) and tested in fermentation experiments with commercial fungal cellulase (5 filter paper units/g cellulose) and purified cellulose (100 g/L). Using Klebsiella oxytoca P2 as the biocatalyst, fermentations supplemented with EGZ as a detergent-lysate of KO11(pLOI1620) produced 14%-24% more ethanol than control fermentations supplemented with a detergent-lysate of KO11(pUC18). These results demonstrate that recombinant bacterial endoglucanase can function with fungal cellulase to increase ethanol yield during the simultaneous saccharification and fermentation of cellulose. © 1997 Wiley & Sons, Inc. Biotechnol Bioeng 55: 547-555, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 577-580 
    ISSN: 0006-3592
    Keywords: mRNA stability ; hairpins ; gene expression control ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An expression system has been developed for the introduction of DNA cassettes into the region between the transcription and translation start sites of a gene of interest. This cassette system was used to engineer mRNA stability through the introduction of hairpins at the 5′ end. A synthetic DNA cassette was designed so that the resulting mRNA hairpin would be positioned one nucleotide from the 5′ mRNA end. The hairpin-containing mRNA exhibited a half-life 3 times that of the mRNA with no hairpin, resulting in increases in both mRNA and protein levels. These results indicate that it is possible to engineer mRNA stability as an additional means of controlling gene expression. © 1997 John Wiley & Sons Inc. Biotechnol Bioeng 55: 557-580, 1997
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    Biotechnology and Bioengineering 55 (1997), S. 581-591 
    ISSN: 0006-3592
    Keywords: adsorptive membranes ; oscillatory flow ; integrated processes ; in situ product recovery ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Preferential transport in adsorptive membranes can be used to selectively remove biochemicals directly from fermentation broths. During preferential transport, an adsorbing solute is selectively transported across the membrane while nonadsorbing solutes and cells are retained by the membrane. This technique was used to separate lysozyme directly from a feed containing lysozyme, myoglobin, and yeast cells. We found that because the oscillatory flows used in preferential transport involve strokes that are close to symmetric, they are very efficient in alleviating cake formation due to cell deposition on the membrane surface. Theoretical results suggest that, by optimizing process variables, preferential transport can lead to a continuous concentrated stream of the adsorbing protein. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 581-591, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 592-608 
    ISSN: 0006-3592
    Keywords: Saccharomyces cerevisiae ; metabolic modeling ; sensitivity analysis ; glycolysis ; compartmentation ; transient response ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model of glycolysis in Saccharomyces cerevisiae is presented. The model is based on rate equations for the individual reactions and aims to predict changes in the levels of intra- and extracellular metabolites after a glucose pulse, as described in part I of this study. Kinetic analysis focuses on a time scale of seconds, thereby neglecting biosynthesis of new enzymes. The model structure and experimental observations are related to the aerobic growth of the yeast. The model is based on material balance equations of the key metabolites in the extracellular environment, the cytoplasm and the mitochondria, and includes mechanistically based, experimentally matched rate equations for the individual enzymes. The model includes removal of metabolites from glycolysis and TCC for biosynthesis, and also compartmentation and translocation of adenine nucleotides. The model was verified by in vivo diagnosis of intracellular enzymes, which includes the decomposition of the network of reactions to reduce the number of parameters to be estimated simultaneously. Additionally, sensitivity analysis guarantees that only those parameters are estimated that contribute to systems trajectory with reasonable sensitivity. The model predictions and experimental observations agree reasonably well for most of the metabolites, except for pyruvate and adenine nucleotides. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 592-608, 1997.
    Additional Material: 11 Ill.
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  • 92
    Electronic Resource
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 609-615 
    ISSN: 0006-3592
    Keywords: interacting populations ; membrane reactor ; induced metabolic changes ; elicitation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The design of a reactor in which two interacting cell populations (microorganisms and plants) could grow under controlled conditions was considered. In this reactor, the cell populations are separated by a membrane which permits semi-in vivo study of induced interaction-specific changes in metabolism. In this paper, the interaction of suspension culture of Nicotiana tabacum (tobacco) and the Oomycete, Phytophthora nicotiana was simulated. The results of the computer simulation show the induced metabolic changes as a consequence of the biological interaction. The paper introduces a novel approach in the strategy for the study of interacting population in suspension cultures. This type of system has potential applications in studies of the regulation of secondary metabolism and for the production of high values pharmaceuticals. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 609-615, 1997.
    Additional Material: 3 Ill.
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  • 93
    Electronic Resource
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 616-629 
    ISSN: 0006-3592
    Keywords: cell adhesion ; radial-flow chamber ; hydrodynamic shear ; detachment kinetics ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The strength of adhesion and dynamics of detachment of murine 3T3 fibroblasts from self-assembled monolayers were measured in a radial-flow chamber (RFC) by applying models for fluid mechanics, adhesion strength probability distributions, and detachment kinetics. Four models for predicting fluid mechanics in a RFC were compared to evaluate the accuracy of each model and the significance of inlet effects. Analysis of these models indicated an outer region at large radial positions consistent with creeping flow, an intermediate region influenced by inertial dampening, and an inner region dominated by entrance effects from the axially-oriented inlet. In accompanying experiments patterns of the fraction of cells resisting detachment were constructed for individual surfaces as a function of the applied shear stress and evaluated by comparison with integrals of both a normal and a log-normal distribution function. The two functions were equally appropriate, yielding similar estimates of the mean strength of adhesion. Further, varying the Reynolds number in the inlet, Red, between 630 and 1480 (corresponding to volumetric flow rates between 0.9 and 2.1 mL/s) did not affect the mean strength of adhesion. For these same experiments, analysis of the dynamics of detachment revealed three temporal phases: 1) rapid detachment of cells at the onset of flow, consistent with a first-order homogeneous kinetic model; 2) time-dependent rate of detachment during the first 30 sec. of exposure to hydrodynamic shear, consistent with the first-order heterogeneous kinetic model proposed by Dickinson and Cooper (1995); and 3) negligible detachment, indicative of pseudo-steady state after 60 sec. of flow. Our results provide rigorous guidelines for the measurement of adhesive interactions between mammalian cells and prospective biomaterial surfaces using a RFC. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 616-629, 1997.
    Additional Material: 10 Ill.
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  • 94
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 693-700 
    ISSN: 0006-3592
    Keywords: glucose ; lactate ; real-time determination ; hematopoietic cell culture ; colony-forming cells ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Glucose and lactate metabolic rates were evaluated for cultures of cord blood (CB) mononuclear cell (MNC), peripheral blood (PB) MNC, and PB CD34+ cell cultures carried out in spinner flasks and in T-flasks in both serum-containing and serum-free media. Specific glucose uptake rates (qgluc, in micromoles per cell per hour) and lactate generation rates (qlac) correlated with the percentage of colony-forming cells (CFC) present in the culture for a broad range of culture conditions. Specifically, the time of maximum CFC percentage in each culture coincided with the time of maximum qgluc and qlac in cultures with different seeding densities and cytokine combinations. A two-population model (Qlac = α[CFC] + β([TC] - [CFC]), where [TC] is total cell concentration; Qlac is volumetric lactate production rate in micromoles per milliliter per hour; α is qlac for an average CFC; and β is qlac for an average non-CFC) was developed to describe lactate production. The model described lactate production well for cultures carried out in both T-flasks and spinner flasks and inoculated with either PB or CB MNC or PB CD34+ cells. The values for α and β that were derived from the model varied with both the inoculum density and the cytokine combination. However, preliminary results indicate that cultures carried out under the same conditions from different samples with similar initial CD34+ cell content have similar values for β and β. These findings suggest that it should be possible to use lactate production data to predict the harvest time that corresponds to the maximum number of CFC in culture. The ability to harvest ex vivo hematopoietic cultures for transplantation when CFC are at a maximum has the potential to speed the rate at which immunocompromised patients recover. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 693-700, 1997.
    Additional Material: 10 Ill.
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  • 95
    ISSN: 0006-3592
    Keywords: tubular photobioreactors ; light distribution ; average solar irradiance ; light attenuation ; microalgae mass culture ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model to estimate the solar irradiance profile and average light intensity inside a tubular photobioreactor under outdoor conditions is proposed, requiring only geographic, geometric, and solar position parameters. First, the length of the path into the culture traveled by any direct or disperse ray of light was calculated as the function of three variables: day of year, solar hour, and geographic latitude. Then, the phenomenon of light attenuation by biomass was studied considering Lambert-Beer's law (only considering absorption) and the monodimensional model of Cornet et al. (1900) (considering absorption and scattering phenomena). Due to the existence of differential wavelength absorption, none of the literature models are useful for explaining light attenuation by the biomass. Therefore, an empirical hyperbolic expression is proposed. The equations to calculate light path length were substituted in the proposed hyperbolic expression, reproducing light intensity data obtained in the center of the loop tubes. The proposed model was also likely to estimate the irradiance accurately at any point inside the culture. Calculation of the local intensity was thus extended to the full culture volume in order to obtain the average irradiance, showing how the higher biomass productivities in a Phaeodactylum tricornutum UTEX 640 outdoor chemostat culture could be maintained by delaying light limitation. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 701-714, 1997.
    Additional Material: 15 Ill.
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  • 96
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 715-726 
    ISSN: 0006-3592
    Keywords: fungal morphology ; pellets ; hyphae ; hair of pellets ; agitation intensity ; fermentation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Both parallel fermentations with Aspergillus awamori (CBS 115.52) and a literature study on several fungi have been carried out to determine a relation between fungal morphology and agitation intensity. The studied parameters include hyphal length, pellet size, surface structure or so-called hairy length of pellets, and dry mass per-wet-pellet volume at different specific energy dissipation rates. The literature data from different strains, different fermenters, and different cultivation conditions can be summarized to say that the main mean hyphal length is proportional to the specific energy dissipation rate according to a power function with an exponent of -0.25 ± 0.08. Fermentations with identical inocula showed that pellet size was also a function of the specific energy dissipation rate and proportional to the specific energy dissipation rate to an exponent of -0.16 ± 0.03. Based on the experimental observations, we propose the following mechanism of pellet damage during submerged cultivation in stirred fermenters. Interaction between mechanical forces and pellets results in the hyphal chip-off from the pellet outer zone instead of the breakup of pellets. By this mechanism, the extension of the hyphae or hair from pellets is restricted so that the size of pellets is related to the specific energy dissipation rate. Hyphae chipped off from pellets contribute free filamentous mycelia and reseed their growth. So the fraction of filamentous mycelial mass in the total biomass is related to the specific energy dissipation rate as well.To describe the surface morphology of pellets, the hyphal length in the outer zone of pellets or the so-called hairy length was measured in this study. A theoretical relation of the hairy length with the specific energy dissipation rate was derived. This relation matched the measured data well. It was found that the porosity of pellets showed an inverse relationship with the specific energy dissipation rate and that the dry biomass per-wet-pellet volume increased with the specific energy dissipation rates. This means that the tensile strength of pellets increased with the increase of specific energy dissipation rate. The assumption of a constant tensile strength, which is often used in literature, is then not valid for the derivation of the relation between pellet size and specific energy dissipation rate. The fraction of free filamentous mycelia in the total biomass appeared to be a function of the specific energy dissipation in stirred bioreactors. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 715-726, 1997.
    Additional Material: 13 Ill.
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  • 97
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 921-926 
    ISSN: 0006-3592
    Keywords: green fluorescent protein ; sensor ; on-line monitoring ; quantitation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: We present an intensity based sensor designed for on-line monitoring of green fluorescent protein, a revolutionary marker of protein expression. The device consisted of a blue light emitting diode as the excitation source. A band pass excitation filter cut off light longer than 490 nm. The light was directed into a bifurcated optical fiber bundle with the common end inserted into a stainless steel housing equipped with a quartz window. The fiber bundle and stainless steel housing are steam sterilizable. The emission radiation was collected through a long wave pass filter to reject the excitation light shorter than 505 nm and was detected by a photomultiplier tube. The signal was amplified and sent to a computer for recording time course data. The sensor was tested in an Escherichia coli fermentation of JM105 transformed with pBAD-GFP. The on-line signal was compared to off-line fluorescence spectrophotometer measurements. The on-line profile closely followed the off-line. Western blot data showed that with a time shift, the sensor was able to both continuously and quantitatively monitor expression of green fluorescent protein on-line in real time. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55:921-926, 1997.
    Additional Material: 6 Ill.
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  • 98
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 909-920 
    ISSN: 0006-3592
    Keywords: baculovirus ; insect cells ; metabolism ; Sf-9; high five™ ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Nutrient utilization and byproduct accumulation were monitored in Spodoptera frugiperda Sf-9 and Trichoplusia ni BTI-Tn-5B1-4 (High Five™) cell lines during growth and following viral infection in suspension cultures in order to develop a better understanding of cell metabolism and to acquire information relevant to large scale fed-batch bioreactors. The utilization of glucose, dissolved oxygen, and amino acids were monitored in Sf-9 cell cultures grown in Sf-900 II serum-free medium (SFM) and in High Five™ cell cultures grown in both Sf-900 II and Express Five SFM. Using the optimal medium for each cell line, i.e., Sf-900 II SFM for Sf-9 cells and Express Five SFM for High Five™ cells, the cell growth rate, maximum cell density, specific glucose and glutamine utilization rates, and specific alanine production rate were comparable during cell growth. In addition, the expression level of recombinant human tissue plasminogen activator was comparable in the two cell lines on a per cell basis. It was found, however, that lactate and ammonia accumulated in High Five™ cell cultures, but not in Sf-9 cell cultures. In addition, High Five™ cells utilized asparagine more rapidly than glutamine, whereas Sf-9 cells consumed only minimal asparagine, and the oxygen utilization rate was significantly higher in High Five™ cell cultures. It was also found that the medium had a significant effect on High Five™ cell metabolism, e.g., the specific glucose utilization rate and the specific lactate and alanine production rates were significantly higher in Sf-900 II SFM than in Express Five SFM. In addition, the maximum cell density and specific asparagine utilization rate were significantly higher in Express Five SFM. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55:909-920, 1997.
    Additional Material: 9 Ill.
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  • 99
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 940-940 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: No abstract.
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 56 (1997), S. 1-8 
    ISSN: 0006-3592
    Keywords: transesterification ; hydrolysis ; water activity ; cutinase ; gas ; bioreactor ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Fusarium solani cutinase supported onto Chromosorb P was used to catalyze transesterification (alcoholysis) and hydrolysis on short volatile alcohols and esters in a continuous gas/solid bioreactor. In this system, a solid phase composed of a packed enzymatic preparation was continuously percolated with carrier gas which fed substrates and removed reaction products simultaneously. A kinetic study was performed under differential operating conditions in order to get initial reaction rates. The effect of the hydration state of the biocatalyst on the kinetics was studied for 3 conditions of hydration (aw = 0.2, aw = 0.4 and aw = 0.6), the alcoholysis of propionic acid methyl ester with n-propanol, and for 5 hydration levels (from aw = 0.2 to aw = 0.6) for the hydrolysis of propionic acid methyl, ethyl or propyl esters. F. solani cutinase was found to have an unusual kinetic behavior. A sigmoid relationship between the rate of transesterification and the activity of methyl propionate was observed, suggesting some form of cooperative activation of the enzyme by one of its substrate. For the hydrolysis of short volatile propionic acid alkyl esters, threshold effects on the reaction rate, highly depending on the water activity and the substrate polarity, are reported. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 1-8, 1997.
    Additional Material: 6 Ill.
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