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  • 1
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 199-208 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we investigate the direct problem associated with the scattering of ‘plane waves’ from an object submerged in an ocean of finite depth. An integral representation for the Dirichlet problem is found, from which a formula for the far-field pattern evolves.A density theorem is established concerning the set of all far-field patterns. This theorem is essential for the reconstruction of the submerged object, the ‘inverse’ problem [2], [4], [5].
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  • 2
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 267-273 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that solutions of the equations of thermoelasticity in general will develop singularities in finite time.
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  • 3
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 315-339 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove a local existence result for a coupled hyperbolic-parabolic initial boundary value problem.
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  • 4
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 5
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 393-404 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A body Ω floating in a fluid is subjected to small periodic displacement. Under idealized conditions the resulting wave pattern can be described by a linear boundary value problem for the Laplacian in an unbounded domain with a non-coercive boundary condition on part of the boundary. Nevertheless uniqueness can be shown if Ω is confined to certain subsets of the fluid which can be described explicitly. This extends a result of V. G. Maz'ja saying that uniqueness holds provided that the exterior normal for ∂Ω avoids certain directions.
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  • 6
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 413-427 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper applies the technique of the h-p version to the boundary element method for boundary value problems on non-smooth, plane domains with piecewise analytic boundary and data. The exponential rate of convergence of the boundary element Galerkin solution is proved when a geometric mesh refinement towards the vertices is used.
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  • 7
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 8
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 471-487 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we investigate the non-linear Vlasov-Fokker-Planck (VFP) equation, a both physically and mathematically interesting modification of Vlasov's equation, which describes a plasma in a thermal bath. We prove existence, uniqueness and representation results for steady states of the VFP equation both in the case of a mollified interaction potential and for the VFP-Poisson system. The uniqueness and representation results are of special interest since they distinguish special solutions of the Vlasov equation.
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  • 9
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 533-548 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present the control of continuous sedimentation in an ideal thickener as an initial and boundary value problem and construct the entropy solution.
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  • 10
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 69-76 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The scattering of a ‘plane wave’ off a submerged body situated in an ocean of finite depth is investigated. The index of refraction is considered to be depth-independent. It is shown that the far field is not unique; hence, the problem of determining the shape of an object from its far field is not well-posed. If solutions are sought among a restricted class of problems the ‘dense set’ property implies that the problem can be made well-posed.
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  • 11
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 95-103 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Dissipative perturbations of hyperbolic equations such as utt + But + A2u = 0 with positive operators A, B are considered. The rates of decay and partition of energy theorems are established for solutions of these equations.
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  • 12
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 105-128 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with the three-dimensional homogeneous isotropic elastostatic boundary-value problem. Global basis vector fields are shown to be constructive structures for approximating the solution. The theoretical tool is a regularity condition developed from the classical integral equation approach. The paper ends with some reflections on the practical computability and numerical applicability.
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  • 13
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 139-151 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A linear stability condition is dervied for explicit Runge-Kutta methods to solve the compressible Navier-Stokes equations by central second-order finite-difference and finite-volume methods. The equations in non-conservative form are simplified to quasilinear form, and the eigenvalues of the resulting coefficient matrices are determined for general co-ordinates. Assuming a well-posed Cauchy problem with constant coefficients, the von Neumann stability analysis yields sufficient stability conditions for viscous-inviscid operator-splitting schemes. They have been applied in computational aerodynamics to solve the compressible Navier-Stokes equations by an unsplit explicit Runge-Kutta finite-volume method.
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  • 14
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 177-182 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For certain unbounded domains the Laplace operator with Dirichlet condition is shown to have an unbounded sequence of eigenvalues which are embedded into the essential spectrum. A typical example of such a domain is a locally perturbed cylinder with circular cross-section whose diameter in some bounded subset is greater than at infinity.
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  • 15
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 365-368 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let u be a vector field on a bounded Lipschitz domain in ∝3, and let u together with its divergence and curl be square integrable. If either the normal or the tangential component of u is square integrable over the boundary, then u belongs to the Sobolev space H1/2 on the domain. This result gives a simple explanation for known results on the compact embedding of the space of solutions of Maxwell's equations on Lipschitz domains into L2.
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  • 16
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 405-412 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The electric potential u in a solution of an electrolyte around a linear polyelectrolyte of the form of a cylinder satisfies \documentclass{article}\pagestyle{empty}\begin{document}$$ \left({ru'} \right)^\prime = rf\left(u \right),\;0 〈 a 〈 r 〈 R, $$\end{document} \documentclass{article}\pagestyle{empty}\begin{document}$$ u'\left(a \right) = - \sigma /a,\;u\left(R \right) = 0. $$\end{document} We study the problem when R → ∞.
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  • 17
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 439-461 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The fundamental solutions of non-decomposable evolution operators are represented by multi-dimensional parameter integration formulae. The method is applied to operators occurring in the theories of elasticity, magnetohydrodynamics and heat conduction.
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  • 18
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 489-502 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the following two integral equations the latter subject to the condition ∫-11v(y)dy = 0, arising from the same problem of determining the distribution of stress in a thin elastic plate in the vicinity of a cruciform crack. In particular, we prove existence and uniqueness of the solutions of the two equations above in C[0, 1]. We also analyse the behaviour of φ(x) near the end-point x = 0.The therotical result obtained in the first part are then used in the last section to derive optimal rates of convergence for numerical methods, such as Galerkin, collocation and Nyström, applied to equation (1).
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  • 19
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We discuss the solution of the boundary value problem in a duct with a centered septum [9]. On the lower wall of the duct a Neumann condition is applied while on the upper wall a Dirichlet condition is applied. On the septum we apply a Dirichlet condition on the lower side and a Neumann condition on the upper one. This problem is formulated as a pair of integral equations of the Wiener-Hopf type for which we supply solutions for two modes of excitation as well as real and complex wave number. A critical examination is made of the construction, which reduces the problem to one in complex analysis. For real wave number, the physical parameters are provided in very simple forms.
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  • 20
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 387-392 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let Ωi ⊂ ∝N, i = 0, 1, be two bounded separately star-shaped domains such that \documentclass{article}\pagestyle{empty}\begin{document}$ \Omega _0 \supset \bar \Omega _1 $\end{document}. We consider the electrostatic potential u defined in \documentclass{article}\pagestyle{empty}\begin{document}$ \Omega : = \Omega _0 \backslash \bar \Omega _1 $\end{document}: \documentclass{article}\pagestyle{empty}\begin{document}$$ \Delta u = 0\,{\rm in}\,\Omega,\,u = 0\,{\rm on}\,\Gamma _{\rm 0} : = \partial \Omega _0,\,u = 1\,\Gamma _1 : = \partial \Omega _1. $$\end{document} The geometry of the two boundary components Γ0 and Γ1 is not given, but instead the electrostatic potential u is supposed to satisfy the further boundary conditions Using a best possible maximum principle, we show that this free boundary problem has a unique solution which is radially symmetric.
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  • 21
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 429-438 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the Cauchy problem for the quasilinear parabolic equation where p 〉 1 is a parameter and ψ is a smooth, bounded function on (1, ∞) with - ≤ sψ′(s)/ψ(s) ≤ θ for some θ 〉 0. If 1 〈 p 〈 1 + 2/N, there are no global positive solutions, whereas if p 〉 1 + 2/N, there are global, positive solutions for small initial data.
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 463-470 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the solutions of the Navier-Stokes equations when the initial vorticity is concentrated in small disjoint regions of diameter ∊. We prove that they converge, uniformily in ∊. for vanishing viscosity to the corresponding solutions of the Euler equations and they are connected to the vortex model.
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  • 23
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 519-531 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An exothermic binary chemical reaction of first order is studied, assuming that one of the reactants can undergo a change of phase. In the limit of low activation energy, a one-dimensional problem is considered and the well-posedness of the corresponding system of two parabolic equations with a free boundary is proved in a classical sense.
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 503-518 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the scattering of a plane time-harmonic electromagnetic wave by a perfectly conducting infinite cylinder with axis in the direction k, where k is the unit vector along the z axis. Suppose the incident wave propagates in a direction perpendicular to the cylinder. For a given observation angle θ, let FD(θ, α)k be the far-field pattern of the electric field corresponding to an incident wave with direction angle α polarized perpendicular to the axis and let FN(θ; α)k be the far-field pattern of the magnetic field corresponding to an incident wave with direction angle α polarized parallel to the z axis. Let {αn}n=1∞ be a distinct set of angles in [ - π, π] and μ a complex number. Then, necessary and sufficient conditions are given for the set {(1 - μ)FD(θ;αn) + μFN(θ;αn)}n = 1∞ to be complete in L2[ - π, π]. Applications, together with numerical examples, are given to the inverse scattering problem of determining the shape of the cylinder from a knowledge of the far-field data.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 385-390 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the stability properties of the one-dimensional Schrödinger equation with boundary conditions that involve the derivative in the direction of propagation (or time). We show that this type of boundary condition might cause a strong growth of the amplitude of the solution. Such a model is not useful for numerical computations. One example is the parabolic wave equation in underwater acoustics for wave propagation in a downsloping duct with the normal derivative condition ∂u/∂n =0 at the bottom.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 431-439 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The coronal loop problem is characterized by mixed boundary conditions and the loop length condition, which is global. Using singular perturbation methods one can identify and construct two boundary layers at the base of the loop.Extending this to a combined asymptotic-numerical treatment it is possible to construct two static solutions satisfying the same conditions; this unusual feature arises from the presence of the first boundary layer, which corresponds with a steep temperature gradient and an energy balance dominated by conduction and radiation losses.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 453-465 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Consider the partial differential equation: wt + bw + a· ∇w = g in ∝n × [0, T] (x1 〈0) and if the function a1 is positive, then, in the left half-space, the solution w is an O (ν) for small Viscosity ν.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 493-514 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider initial-boundary value problems for systems with a small parameter ∊. The problems are mixed hyperbolic-parabolic when ∊ 〉 0 and hyperbolic when ∊ = 0. Often the solution can be expanded asymptotically in ∊ and to first approximation it consists of the solution of the corresponding hyperbolic problem and a boundary layer part. We prove sufficient conditions for the expansion to exist and give estimates of the remainder. We also examine how the boundary conditions should be choosen to avoid O(1) boundary layers.
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 77-90 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the effect of perturbing Burgers' equation by a small term ∊2 Utt. It is shown by means of an energy estimate that the solution of Burgers' equation provides a uniform O (∊) approximation of the solution of the full hyperbolic problem. Existence and uniqueness of classical solutions for both problems is proved. A related linear problem is first addressed using the Faedo-Galerkin method to obtain key estimates. Important for the hyperbolic problem is the introduction of an ∊-dependent energy in order to track the order-∊ behaviour of various higher-order derivatives. Subsequent use of Schauder technique and Banach contraction mapping principle yields solutions of the semilinear problems.
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 153-165 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of global solutions to the Cauchy problem for Yang-Mills-Higgs systems in the temporal gauge is examined. The results apply to the self-coupling of the Higgs field. Results from other works are strengthened.
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 167-176 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper concerns the properties of global solutions to the Cauchy problem of Yang-Mills-Higgs systems in the temporal gauge. The following properties are considered: global analyticity of solutions, an approximation property, conservation of the topological class of solutions, scattering of a part of the energy of solutions through a light cone.
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 183-197 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A conducting dusty gas flow in the presence of a given applied magnetic field is modelled by an initial boundary value problem. The continuous dependence of solutions backward in time to this model is studied. The electric and induced magnetic fields are assumed to be negligible and the dust particles are non-conducting. A uniqueness result is also derived.
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 91-93 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that there exist domains Ω ⊂ ∝N, which outside of some ball coincide with the strip ∝N - 1 × (0, π) and for which the Dirichlet Laplacian - Δ has eigenvalues within the subinterval (1, 4) of the essential spectrum (1, ∞).
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 129-138 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the recent paper [13] we have answered the question of stability for the linear circular plate which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. In this case there are radially symmetric solutions and the contact region is a disk of a smaller radius. This simplified the determination of the critical parameter values for which the plane jumps to another state. For the rectangular plate continuation has to be applied to the variational inequality in order to determine the contact region and evalute the stability criterion. A numerical method is developed for a discretization of the problem and is used to compute the critical load both in the simply supported and the clamped case.
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    Mathematical Methods in the Applied Sciences 12 (1990) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 221-228 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article we present the solution of linear partial differential equations of the form ∂tf = L̂f, for initial value problems. Also the solution of some diffusion equations will be discussed.
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    Mathematical Methods in the Applied Sciences 12 (1990), S. 229-249 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solution of the three-dimensional mixed boundary value problem for the Laplacian in a polyhedral domain has special singular forms at corners and edges. A ‘tensor-product’ decomposition of those singular forms along the edges is derived. We present a strongly elliptic system of boundary integral equations which is equivalent to the mixed boundary value problem. Regularity results for the solution of this system of integral equations are given which allow us to analyse the influence of graded meshes on the rate of convergence of the corresponding boundary element Galerkin solutions. We show that it suffices to refine the mesh only towards the edges of the surfaces to regain the optimal rate of convergence.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 137-141 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A system of equations is investigated which models a reacting mixture of viscous fluids acted upon by an external body force. Through logarithmic convexity arguments the solution is shown to be unique when either the initial or the final data are given.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 181-188 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Some remarks complementary to the work of N. Dencker in [1] concerning the wave front of polarization are given. The theorem due to N. Dencker about the propagation of a wave front of polarization is applied to solutions for the evolution of the three-dimensional Lame system. The propagation of polarized solutions is established.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 189-203 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: A new class of computational far-field boundary conditions for hyperbolic partial differential equations was recently introduced by the authors. These boundary conditions combine properties of absorbing conditions for transient solutions and properties of far-field conditions for steady states. This paper analyses the properties of the wave equation coupled with these new boundary conditions: well-posedness, dissipativity and convergence in time.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 249-261 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The non-linear contact problem for the parabolic system of second order in the sense of Pietrovski, which is the generalization of the problem considered in Part I (preceding paper), is formulated. The matrix of fundamental solutions for parabolic systems of second order with coefficients containing unknown functions and their first-order derivatives is constructed and used to reduce the problem to the equivalent system of integral equations which is then reduced to a system of Volterra type of the second kind. The existence of the solution of the system obtained is proved by using the Schauder fixed-point theorem.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 263-272 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a mathematical model of neutron multiplication in a slab S, by taking into account temperature feedback effects and considering one group of delayed neutrons. The thickness 2a of S is time dependent because of temperature variations due to the energy released by fissions.Starting from a quite detailed picture of the physical phenomena occurring in S, we derive a system of three coupled ordinary differential equations for the total number of neutrons F̂ = F̂(t), for the total number of precursors Ĉ = Ĉ(t), and for the half-thickness of S, a = a(t).We finally examine some stability properties of such a system of ordinary differential equations.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 291-303 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A weakly singular integral equation of the first kind on a plane surface piece Γ is solved approximately via the Galerkin method. The determination of the solution of this integral equation (with the single-layer potential) is a classical problem in physics, since its solution represents the charge density of a thin, electrified plate Γ loaded with some given potential. Using piecewise constant or piecewise bilinear boundary elements we derive asymptotic estimates for the Galerkin error in the energy norm and analyse the effect of graded meshes. Estimates in lower order Sobolev norms are obtained via the Aubin-Nitsche trick. We describe in detail the numerical implementation of the Galerkin method with both piecewise-constant and piecewise-linear boundary elements. Numerical experiments show experimental rates of convergence that confirm our theoretical, asymptotic results.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 373-383 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that the solution to the boundary-initial value problem for a heat-conducting viscous fluid depends continuously on changes in the heat supply function, for the improperly posed backward in time problem. A non-linear convection threshold is also determined for the problem of a layer of fluid heated internally (non-uniformly), with zero neat flux on the lower boundary and constant-temperature upper surface.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 421-430 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: In this paper we consider the inverse problems of identifying some space-dependent unknown coefficients in parabolic equations subject to initial boundary value conditions along with an overspecified condition at the final time t = T. We use the overspecified information to transform the problems into non-linear parabolic equations involving a functional of the solution with respect to the time variable. This transformation allows us to establish existence theorems for these inverse problems by employing the Schauder fixed-point theorem.
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    Mathematical Methods in the Applied Sciences 13 (1990) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 441-452 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Let us consider a solution f(x,v,t)∊L1(∝2N × [0,T]) of the kinetic equation where |v|α+1 fo,|v|α ∊L1 (∝2N × [0, T]) for some α〈 0. We prove that f has a higher moment than what is expected. Namely, for any bounded set Kx, we haveWe use this result to improve the regularity of the local density ρ(x,t) = ∫ƒdν for the Vlasov-Poisson equation, which corresponds to g = Eƒ, where E is the force field created by the repartition ƒ itself. We also apply this to the Bhatnagar-Gross-;Krook model with an external force, and we prove that the solution of the Fokker-Pianck equation with a source term in L2 belongs to L2([0, T]; H1/2(∝x,v2N)).
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 467-479 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Hyperthermia is an aid to standard cancer therapy. The aim is to heat up a tumour region inside the patient's body with the help of microwave radiation. The microwayes are generated by some suitable antenna array. Here we investigate the control properties of such antenna configurations and determine their resolution capabilities. We will define the hyperthermia operator, which can produce every field of any antenna array up to any degree of accuracy. We shall see that this operator is compact and we are able to compute a singular system under general assumptions explicitly. This, together with a detailed knowledge of the decay of the singular values, constitutes the tools with which we treat the previously stated problems. We examine the propagation of microwave radiation in homogeneous media and then carry over the results obtained to the case of inhomogeneous media.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 481-491 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a global existence theorem for solutions of utt - ∂iaik (x)∂ku + ut = ƒ(t, x, u, ut, ∇u, ∇ut, ∇2u), u(t = 0) = u0, ut(=0)=u1, u(t, x), t ⋝ 0, x∊Ω.Ω equals ∝3 or Ω is an exterior domain in ∝3 with smoothly bounded star-shaped complement. In the latter case the boundary condition u|∂Ω = 0 will be studied. The main theorem is obtained for small data (u0, u1) under certain conditions on the coefficients aik.The Lp - Lq decay rates of solutions of the linearized problem, based on a previously introduced generalized eigenfunction expansion ansatz, are used to derive the necessary a priori estimates.
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 205-218 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The exponential X-ray transform arises in single photon emission computed tomography and is defined on functions on the plane by Pμf(ϕ,x) = ∫- ∞∞f (x + tϕ)eμt where μ is a constant. In [MMAS(10), 561-574, 1988], we derived analytical formulae for filters K corresponding to a general point spread function E that can be used to invert the exponential X-ray transform via a filtered backprojection algorithm. Here, we use those formulae to derive expressions suitable for numerical computation of the filters corresponding to a specific family of bandlimited point spread functions and give the results of reconstructions of a mathematical phantom using these filters. Also included is an analogue of the Shepp-Logan ellipse theorem, [IEEE Trans. Nucl. Sci. (21), 21-43, 1974], for the exponential X-ray transform.
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    Mathematical Methods in the Applied Sciences 13 (1990) 
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    Mathematical Methods in the Applied Sciences 13 (1990), S. 281-289 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: A hypersingular boundary integral equation of the first kind on an open surface piece Γ is solved approximately using the Galerkin method. As boundary elements on rectangles we use continuous, piecewise bilinear functions which vanish on the boundary of Γ. We show how to compensate for the effect of the edge and corner singularities of the true solution of the integral equation by using an appropriately graded mesh and obtain the same convergence rate as for the case of a smooth solution. We also derive asymptotic error estimates in lower-order Sobolev norms via the Aubin-Nitsche trick. Numerical experiments for the Galerkin method with piecewise linear functions on triangles demonstrate the effect of graded meshes and show experimental rates of convergence which underline the theoretical results.
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    Biotechnology and Bioengineering 35 (1990), S. 103-107 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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    Biotechnology and Bioengineering 35 (1990), S. 408-416 
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    Keywords: Chemistry ; Biochemistry and Biotechnology
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    Notes: The partitioning of vancomycin in polyethylene glycol (PEG)-dextran and PEG-phosphate aqueous two-phase systems was studied at different pHs, at varying concentrations of neutral salts, and with an affinity ligand attached to methoxy polyethylene glycol (MPEG). Vancomycin is found to partition preferentially into the PEG-rich top phase, and its partition coefficient increases nearly exponentially with the addition of water structure-making salts, such as sodium sulfate and sodium chloride, but is independent of sodium phosphate concentration. In the PEG-dextran system the vancomycin partition coefficient increases 3-fold in acidic and neutral solutions, while in the PEG-phosphate system it increases about 30-fold on the addition of the same amount of sodium chloride (1. 5 mol/kg). In basic solution, above its isoelectric point, the vancomycin partition coefficient increases slightly with NaCI concentration in the PEG-dextran system. We also examined the use of the dipeptide D-ala-D-ala as an affinity ligand on MPEG to extract vancomycin into the PEG-rich phase. The vancomycin partition coefficient increased almost 7-fold upon adding the MPEG-ligand in an amount equal to approximately 3% of the total PEG in the system. Finally, fractionation of the polydisperse phase-forming polymers in the two-phase PEG-dextran system was observed. The effect of this polymer fractionation on the partition coefficient of vancomycin is discussed.
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    Biotechnology and Bioengineering 35 (1990), S. 437-453 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Semicontinuous fermentations, in which a fraction of a culture is replaced with fresh media at regular intervals, have been previously used as a means of approximating continuous growth. In most cases deviations from continuous operation were erroneously estimated using Fencl's model, which is only valid when the specific growth rate is independent of the substrate concentration. An approach to modeling Semicontinuous growth that incorporates the same kinetics followed in batch and continuous growth was developed and tested for Monod's expression for the specific growth rate. A dimensionless form of the model was used to simulate Semicontinuous fermentations for comparison to continuous growth. Differences between Semicontinuous and continuous growth were found to depend on three dimensionless variables: feed concentration, replacement rate, and time between replacements. For given values of the dimensionless feed concentration and time between replacements, a range of dimensionless replacement rates can be determined over which semi-continuous cultures are approximately continuous.
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    Biotechnology and Bioengineering 35 (1990), S. 870-881 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Characterization of mycelial morphology is important for physiological and engineering studies of filamentous fermentations, and in the design and operation of such fermentations. Image analysis has been developed as a method for this characterization, and has been shown to be faster and generally more accurate than previous methods. A fully automatic system has been developed, in which speed is gained, but with loss of accuracy in some cases. The method has been tested on Streptomyces clavuligerus and Penicillium chrysogenum P1 batch fermentations. It has also been tested on a fed-batch Penicillium chrysogenum P2 fermentation, in which the medium contained solid ingredients. Fully automatic image analysis for morphological characterization of filamentous microorganisms is an important development which will make practical many engineering and physiological studies of such fermentations that have so far not been completely satisfactory.
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    Biotechnology and Bioengineering 35 (1990), S. 907-920 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A general model for aerobic yeast growth in batch culture is presented. It is based on the concept that the aerobic metabolism of all yeasts is determined by the relative sizes of the transport rate of sugar into the cell and the transport rate of respiratory intermediates into the mitochondrion. If the rate of sugar uptake rate exceeds the rate of transport of respiratory intermediates into the mitochondrion (as in Saccharomyces cerevisiae, S. uvarum, and S. pombe), the metabolism exhibits the features of ethanol excretion and limited specific oxygen uptake rate. If the rate of transport of respiratory intermediates into the mitochondrion is of the same order as the transport of sugar into the cell (as in Candida utilis), the metabolism is characterized by little or no ethanol excretion and a much higher specific oxygen uptake rate. Batch data from an extensive range of yeast and carbon sources is used to illustrate the use of this model. The ability of this model to fit such an extensive range of experimental data suggests that it can be used as a generalized model for aerobic yeast growth.
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    Biotechnology and Bioengineering 35 (1990), S. 948-950 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Biotechnology and Bioengineering 35 (1990), S. 955-965 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A novel process has been developed which uses reversed micelles to isolate denatured protein molecules from each other and allows them to refold individually. These reversed micelles are aqueous phase droplets stabilized by the surfactant AOT and suspended in isooctane. By adjusting conditions such that only one protein molecule is present per reversed micelle, it was possible to achieve independent folding without encountering the problem of aggregation due to interactions with neighboring molecules. The feasibility of this process was demonstrated using bovine pancreatic ribonuclease A as a model system. It was shown that denatured and reduced ribonuclease can be transferred from a buffered solution containing guanidine hydrochloride into reversed micelles to a greater extent than native enzyme under the same conditions. The denaturant concentration can then be significantly reduced in the reversed micellar phase, while retaining most of the protein, by means of extractive contacting stages with a denaturant-free aqueous solution. Denatured and reduced ribonuclease will subsequently recover full activity inside reversed micelles within 24 h upon addition of a mixture of reduced and oxidized glutathione to reoxidize disulfide bonds. Extraction of this refolded enzyme from reversed micelles back into aqueous solution can be accomplished by contacting the reversed micelle phase with a high ionic strength (1.0M KCl) aqueous solution containing ethyl acetate.
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    Biotechnology and Bioengineering 35 (1990), S. 15-22 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: α-Galactosidase from soybean (Glycine max) was purified by a five-step procedure. The enzyme's natural substrates, raffinose and stachyose, have Km's of 3. 0 mM and 4. 79 mM, respectively. The products, galactose and sucrose, were measured after separation by liquid chromatography. Galactose is a competitive product inhibitor of stachyose and raffinose hydrolysis with a Ki of 0. 12 mM. We determined these parameters by an integral kinetic approach. Stachyose hydrolysis gives a nearly constant level of raffinose shortly after hydrolysis begins. Thus, cleavage of the first α-(1,6)-bond in the tetrasaccharide is the rate-limiting step. Since the stachyose hydrolysis yields raffinose, soybean α-galactosidase simultaneously hydrolyzes two substrates. We present a novel approach for analyzing simultaneous substrate hydrolysis with competitive product inhibition by a modified integral rate expression. The experimentally found kinetic parameters are confirmed by solving the simultaneous equations which describe the hydrolysis. This technique may be applicable to other hydrolytic enzymes with multiple substrates.
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    Biotechnology and Bioengineering 35 (1990), S. 57-65 
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    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Relatively large activated sludge floes (larger than about 100 μm) were stabilized, using a histological tissue specimen preparation procedure, and then were sliced into sections of 3 to 6 μm thick. The study of these sections, after staining, revealed the internal structure of the activated sludge floes. No uniformity of this structure was found. The distribution of microorganisms and of extracellular polymers (EPs) in the floes varied randomly on the plane of the sections and along the dimension perpendicular to the plane, leaving large water channels and reservoirs in some of the floes. The lack of a characteristic size for the water gaps in the floes and a general self-similar appearance of the sections suggested that the activated sludge floes might be characterized by the fractal concept within a certain size limit. Direct observation of the interior of the floes indicated an abundant presence of extracellular polymers (EPs) in amorphous forms, surrounding microorganisms in most of the floes.
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    Biotechnology and Bioengineering 35 (1990), S. 99-102 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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    Biotechnology and Bioengineering 35 (1990) 
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    Keywords: Chemistry ; Biochemistry and Biotechnology
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    Biotechnology and Bioengineering 35 (1990), S. 138-145 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Pirt's maintenance model has been widely accepted for the effects of growth rate and maintenance on growth yield. However, the interpretation of parameters in Pirt's model as biological constants is difficult for energy-sufficient culture growth. In this study, a mechanistic model for the growth energetics of energy-sufficient chemostat cultures is proposed and verified with literature data. In the model, the overutilization of the energy substrate in energy-sufficient culture growth is attributed to the defective regulation of the energy substrate metabolism and energy uncoupling. The model also uses an “energy surplus” concept to collectively represent the effects of energy excessiveness. The proposed model provides a better quantitative understanding of the maximum growth yield and maintenance of energy-sufficient cultures. It also explains the glucose concentration effect reported in the literature.
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    Biotechnology and Bioengineering 35 (1990), S. 1125-1134 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The extracellular enzymes and cell mass from the pregrown Phanerochaete chrysosporium cultures were used for the degradation of PCP. The use of both extracellular enzymes and cell mass resulted in extensive mineralization of PCP, while the action of only the crude extracellular enzymes led to the formation of a degradation intermediate (TCHD). A kinetic model, which describes the relationship among PCP degradation, initial PCP concentration, dosage of extracellular enzymes, and cell mass concentration, was developed. Based on this model, various effects of initial PCP concentration, dosage of extracellular enzymes, and cell mass concentration were evaluated experimentally. It was found that when initial PCP concentration is lower than 12 μmol/L, the model of a parallel-series first-order reaction is sufficient to describe the degradation process. PCP disappearance and mineralization were enhanced by increasing either the extracellular enzyme concentration or the cell mass concentration. As high as 70% of PCP mineralization could be obtained by using a higher dosage of extracellular enzymes and cell mass. Various parameters of the kinetic model were determined and the model was verified experimentally. Simulation using this model provided the criteria needed to choose rational dosages of extracellular enzymes and cell mass for the degradation of PCP. Data reported allow some insight into the function of the extracellular enzymes and cell mass of P. chrysosporium in degradation processes of toxic pollutants and assist in the design and evaluation of practical bioremediation methods.
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    Biotechnology and Bioengineering 35 (1990), S. 1161-1163 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
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    Biotechnology and Bioengineering 35 (1990), S. 287-295 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A two-stage continuous system in combination with a temperature-sensitive expression system were used as model systems to maximize the productivity of a cloned gene and minimize the problem associated with the plasmid instability for a high-expression recombinant. In order to optimize the two-stage fermentation process, the effects of such operational variables as temperature and dilution rate on productivity of cloned gene were studied using the model systems and a recombinant, Escherichia coli K12 ΔH1 Δtrp/pPLc23trp A1. When the expression of cloned gene is induced by raising the operating temperature above 38°C, a significant decrease in the colony-forming-units (CFU) of the plasmid-harboring cell was observed, and the decrease was related to the product concentration. In order to describe this phenomenon, a new kinetic parameter related to the metabolic stress (metabolic stress factor) was introduced. It is defined as the ratio of the rate of change of pheno-type from colony-forming to non-colony-forming cells to the product accumulation per unit cell mass. At a fixed temperature of 40°C, the varying dilution rate D in the range of 0.35-0.90 h-1 did not affect the metabolic stress factor significantly. At a fixed dilution rate of D = 0.35 h-1, this factor remained practically constant up to 41°C but increased rapidly beyond 41°C. The effects of temperature and dilution rate in the second stage on the specific production rate were also studied while maintaining the apparent specific growth rate (μ2app) of the second stage constant at or near μ2app = 0.26 h-1. Under a constant dilution rate, D2 = 0.35 h-1, the maximum specific production rate obtained was about qp, max = 38 units TrpA/mg cell/h at 41°C. At a constant temperature, T2 = 40°C, specific production rate increased with decreasing dilution rate with in the dilution rate range of D2 = 0.35-0.90 h-1. Based on the results of our study, the optimal operating conditions found were dilution rate D2 = 0.35 h-1 and operating temperature T2 = 41°C at the apparent specific growth rate of 0.26 h-1. Under the optimal operating conditions, about threefold increase in productivity was achieved compared to the best batch culture result. In addition, the fermentation period could be extended for more than 100 h.
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  • 68
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    Biotechnology and Bioengineering 35 (1990), S. 349-355 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: It is shown that, in a mixed culture, under realistic assumptions, the optimal temperature profile maximizing the final biomass production under the constraint of the final relative proportions of the two populations is constant. This result is illustrated with a simulation experiment on a lactic fermentation model.
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  • 69
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    Biotechnology and Bioengineering 35 (1990), S. 395-407 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The reg 1 mutation will allow the expression of a cloned gene on a plasmid under the control of a GAL promoter in the presence of glucose. The metabolism of wild-type and reg l mutant strains was examined by in vivo 31P nuclear magnetic resonance (NMR) spectroscopy. Transient profiles of glucose 6-phosphate, fructose 6-phosphate, fructose 1, 6-diphosphate, and 3-phosphoglycerate indicated that glucose was processed differently for the reg 1 strain despite similar cytoplasrnic pH values and ATP levels. Intracellular phosphate became depleted in the transition to quasi-steady state and limited glycolysis in the reg 1 strain. The glucose uptake step or hexokinase step appears to be altered in the reg 1 strain. The reg 1 strain utilized galactose faster than the wild-type strain under the conditions used for NMR analysis. These results are consistent with the hypothesis that the REG 1 product operates early in the regulatory circuitry for glucose repression. This study illustrates the usefulness of transient information provided by NMR in understanding changes in the metabolism of genetically manipulated organisms.
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  • 70
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    Biotechnology and Bioengineering 35 (1990), S. 427-435 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Limitations of oxygen transfer in fermentation can be solved using auxiliary liquids immiscible in the aqueous phase. The liquids (called oxygen-vectors) used in this study were hydrocarbon (n-dodecane) and perfluorocarbon (forane F66E) in which oxygen is highly soluble (54.9 mg/L in n-dodecane and 118 mg/L in forane F66E at 35°C in contact with air at atmospheric pressure). It has been demonstrated that the use of n-dodecane emulsion in a culture of Aerobacter aerogenes enabled a 3. 5-fold increase of the volumetric oxygen transfer coefficient(kLa) calculated on a per-liter aqueous phase basis. The droplet size of the vector played a crucial role in the phenomena. When a static contact between gas bubble and vector droplet was established in water, the vector covered the bubble, in agreement with positive values of the spreading coefficient for these fluids. The determination of the oxygen transfer coefficients (kL) in a reactor with a definite interfacial area enabled the main resistance to be located in the boundary layer of the waterside either for a gas-water or a vector-water interface. Because oxygen consumption by weakly hydrophobic cells can only occur in the aqueous phase, the oxygen transfer is achieved according to the following pathway: gas-vector-water-cell. Finally, a mechanism for oxygen transfer within this four-phased system is proposed.
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  • 71
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    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A thermodynamic model was used in this study to predict the adhesion of Phanerochaete chrysosporium INA-12 as conidiospores or mycelium to various solid carriers. Theoretical predictions were closely reflected by experimental results. Amount of immobilized mycelium was higher for hydrophobic (polypropylene and polyurethane) than for hydrophilic carrier (stainless steel and grey). Lignin peroxidase production was stimulated in the same way. However, better results were obtained with polyurethane than with polypropylene and with grey than with stainless steel. These results were attributed to roughness effects of solid surfaces. Surface morphology characterization showed that the surface roughness parameter RA was higher for polyurethane and grey as compared to polypropylene and stainless steel, respectively. On the other hand, polyurethane is not simply rugous; it has an intraparticle porosity as well as a higher total surface area as compared to polypropylene.
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  • 72
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    Biotechnology and Bioengineering 35 (1990), S. 518-524 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Water-insoluble proteases were prepared by immobilizing papain and chymotrypsin onto the surface of polyacrolein microspheres with and without oligoglycines as spacer. The activity of immobilized proteases was found to be still high toward small ester substrates, but very low toward casein, a high-molecular-weight substrate. The relative activity of the immobilized proteases without spacer decreased gradually with the decreasing surface concentration of the immobilized proteases on the microspheres. On the contrary, the immobilized proteases with oligoglycine spacers gave an almost constant activity for the substrate hydrolysis within the surface concentration region studied and gave a much higher relative activity than those without any spacer. With the longer spacer, the immobilized enzymes showed a higher activity toward casein hydrolysis, whereas there was an optimum length for the spacer when hydrolysis was carried out toward the low-molecular-weight substrate. The thermal stability of the immobilized proteases was higher than that of the respective native proteases. The initial enzymatic activity of the immobilized proteases maintained almost unchanged without any elimination and inactivation of proteases, when the batch enzyme reaction was performed repeatedly, indicating the excellent durability.
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  • 73
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    Biotechnology and Bioengineering 35 (1990), S. 540-546 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A simple model for prediction of liquid velocity in external-loop airlift bioreactors has been developed. Theoretical correlations for friction factor of gas-non-Newtonian two-phase flows and for liquid velocity in the riser were derived using the concept of an eddy diffusivity. The predictions of the proposed model were compared with the available experimental data for the friction factor and the liquid velocity in the riser of external-loop airlift contactors. Satisfactory agreement was obtained.
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  • 74
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    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Spray columns can be used to isolate and purify proteins using the two-phase aqueous extraction technique based on polyethylene glycol (PEG) and dextran. The fractional dispersed phase (PEG) holdup and overall mass transfer coefficients were measured in a 9.7 mm i.d. spray column. We found that the dispersed phase holdup increased with increasing PEG phase velocity. The overall mass transfer coefficients for bovine serum albumin, normalized for the PEG holdup, were found to be independent of the PEG phase velocity. This result was expected, since true mass transfer coefficients do not vary with phase velocity.
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  • 75
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    Biotechnology and Bioengineering 36 (1990), S. 135-141 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A technique for enzyme reuse and product recovery from enzymatic catalysis in microemulsions is demonstrated. The enzymatic reaction is performed in a homogeneous isotropic microemulsion; AOT (sodium bis-(2-ethyl- hexyl)sulfosuccinate)/isooctane/buffer or C12E5(penta ethylene glycol dodecyl ether)/heptane/buffer. By small temperature changes the systems are shifted to two phase regions, where an oil-rich phase, containing the product, coexists with a water-rich phase containing surfactant and enzyme. The oil-rich phase may be replaced by an oil solution containing new substrate. Thus, the reaction may be continued and the enzyme reused. This procedure was repeated nine times in the present study. Data on phase behavior in presence and in absence of protein, partitioning of the components and a radioactive-labelled protein between the phases, and the repeated use of horse liver alcohol dehydrogenase (HLADH) in the microemulsions are presented.
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  • 76
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    Biotechnology and Bioengineering 36 (1990), S. 149-154 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The concept of a charged membrane bioreactor (CMBR) has been proposed for continuous reactions of enzymatic reduction dependent upon the nicotinamide coenzyme NADP(H). It was found that a composite membrane with a negative charge, NTR 7410, could retain NADP(H) selectively without any chemical modification. Several permeation experiments have revealed that the retainment of a coenzyme is based on electrostatic repulsion of negative charges between the membrane and the phosphate moiety of NADP(H). The retainment ratio was reduced by the addition of inorganic salt, although it could be restored to 0.8 in the presence of albumin. A reactor equipped with a charged membrane as the coenzyme separator module was constructed and used in the continuous production of sorbitol. NADPH-dependent aldose reductase isolated from Candida tropicalis IAM 12202 was used for the production of sorbitol from glucose. The coenzyme oxidized in this reaction was enzymatically regenerated by conjugation with glucose dehydrogenase, together with the coproduction of gluconic acid from glucose. With a substrate conversion of 85%, 100 g/L sorbitol was produced and equimolar gluconic acid was coproduced for more than 800 h, indicating that the reaction was efficiently coupled to the enzymatic regeneration. The initial high retainment ratio of the membrane was almost maintained throughout the entire reaction. Consequently, the turnover number of the coenzyme reached 106,000.
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  • 77
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    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A theoretical model was constructed in order to study charged membrane bioreactors (CMBRs). In this model, it was postulated that a native nicotinamide coenzyme NADP(H) can be partially retained by a charged membrane in continuous operation. A multienzyme system composed of NADPH-dependent aldose reductase (AR) and glucose dehydrogenase (GDH) was used for the production of sorbitol and gluconic acid from glucose and for the conjugated enzymatic regeneration of NADP(H). Both enzymes were studied with respect to their reaction kinetics. AR was determined to obey the Theorell-Chance mechanism. GDH reaction was approximated by the initial velocity equation of the sequential Bi-Bi mechanism since the reverse reaction could be neglected. Significant inhibitions of both enzymes by sorbitol, gluconic acid, and glucose were observed, and the mode of inhibition was estimated to modify the velocity equations. The differential equation system for each component was derived and numerically analyzed according to the model. The theoretical model elucidated several features of the CMBR. (1) When compared at the same productivity, higher retainment was found to bring about a higher coenzyme turnover number, indicating that the feed coenzyme concentration can be reduced. (2) Under constant conversion, a contradictory relationship between turnover number and residence time arises if the feed concentration of a coenzyme varies. The theoretical model predicts that there is a practically optimal concentration for using NADP(H) efficiently. This concentration was consistent with that yielding the estimated minimum total cost. (3) In this system, excess-GDH-to-AR activity was required because of differences in their kinetic constants. The amount of regeneration enzyme required can be reduced by the accumulation of excels NADPH due to coenzyme retainment. (4) Comparison with an ideal repeated batch reaction revealed that the continuously operated CMBR was vastly superior with respect to productivity as well as operation ability.
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  • 78
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    Biotechnology and Bioengineering 36 (1990), S. 207-217 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Acetone-butanol-ethanol (ABE) fermentation was performed continuously in an immobilized cell, trickle bed reactor for 54 days without, degeneration by maintaining the pH above 4.3. Column clogging was minimized by structured packing of immobilization matrix. The reactor contained two serial glass columns packed with Clostridium acetobutylicum adsorbed on 12- and 20-in.-long polyester sponge strips at total flow rates between 38 and 98.7 mL/h. Cells were initially grown at 20 g/L glucose resulting in low butanol (1.15 g/L) production encouraging cell growth. After the initial cell growth phase a higher glucose concentration (38.7 g/L) improved solvent yield from 13.2 to 24.1 wt%, and butanol production rate was the best. Further improvement in solvent yield and butanol production rate was not observed with 60 g/L of glucose. However, when the fresh nutrient supply was limited to only the first column, solvent yield increased to 27.3 wt% and butanol selectivity was improved to 0.592 as compared to 0.541 when fresh feed was fed to both columns. The highest butanol concentration of 5.2 g/L occurred at 55% conversion of the feed with 60 g/L glucose. Liquid product yield of immobilized cells approached the theoretical value reported in the literature. Glucose and product concentration profiles along the column showed that the columns can be divided into production and inhibition regions. The length of each zone was dependent upon the feed glucose concentration and feed pattern. Unlike batch fermentation, there was no clear distinction between acid and solvent production regions. The pH dropped, from 6.18-6.43 to 4.50-4.90 in the first inch of the reactor. The pH dropped further to 4.36-4.65 by the exit of the column. The results indicate that the strategy for long term stable operation with high solvent yield requires a structured packing of biologically stable porous matrix such as polyester sponge, a pH maintenance above 4.3, glucose concentrations up to 60 g/L and nutrient supply only to the inlet of the reactor.
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  • 79
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    Biotechnology and Bioengineering 36 (1990), S. 224-232 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: If a microorganism has a growth coupled production or consumption of acid or alkali, it is possible to use the pH-auxostat as a means of control in continuous fermentation. In using the pH-auxostat, it is possible to separate the inlet substrate flow in two different streams. These will both be pH controlled, with one main flow, consisting of nutrients and a second minor but concentrated flow, of acid or alkali. Hereby, it is possible to vary the difference in pH between the fermentor and the inlet medium. This pH difference is proportional to the steady-state cell mass concentration.1,2 It is shown that by separating the inlet flow in two different streams and cultivating without any substrate limitation, the maximum growth rate may be obtained while the cell mass concentration will be controlled. This will also give the possibility to reach high cell mass concentrations at μmax without the risk of wash-out. A modified expression, based on hydrogen, of the steady-state bio-mass concentration, X, is developed as \documentclass{article}\pagestyle{empty}\begin{document}$$ X = Y_{X/H} \cdot [F_{{\rm Hin}} /(F_{{\rm Hin}} + F_{{\rm Min}} )] \cdot (C_{{\rm Hin}} - C_{{\rm HFERM}} ) $$\end{document} where YX/H is the yield coefficient of cell mass per acid produced. The indexes Hin and Min refer to the inflows of alkali and medium, respectively; CHin is the inlet concentration of hydrogen ions. The boundary condition for the cell mass shows that Sin 〉 X/YX/S, where Sin is the medium substrate concentration and YX/S is the yield of biomass per consumed substrate. It is shown that when the cell mass concentration exceeds this value, the flow stops. The applicability of the pH-auxostat method is then verified from different experiments. It is hereby used to detect a deviation from the maximal growth rate showing effects on the microbial physiology. With Escherichia coli used as the model organism, the effect on the growth rate of temperature and high concentration of ammonia were investigated.
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  • 80
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    Biotechnology and Bioengineering 36 (1990), S. 377-386 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In Part I of this series,1 we derived a model and made simulations for a multistage fluidized bed reactor (MFBR). It was concluded that the MFBR can be an attractive alternative for a fixed bed reactor when operated with a deactivating biocatalyst. In Part II of this series, the design of a laboratory-scale MFBR and its evaluation to investigate the practical feasibility of this reactor type, will be described. Experiments with a duration as long as 10 days were carried out successfully using immobilized glucose isomerase as a model reaction system. The results predicted by the model are in good agreement with the measured glucose concentration and biocatalyst activity gradients, indicating perfect mixing of the particles in the reactor compartments.The diameters of the biocatalyst particles used in the experiments showed a large spread, with the largest being 1.7 times the smallest. Therefore, an additional check was carried out, to make sure that the particles were not segregating according to size. Particles withdrawn from the reactor compartments were investigated using an image analyzer. Histograms of particle size distribution do not indicate segregation and it is concluded that the particles used have been mixed completely within the compartments. As a result, transport of biocatalyst is nearly plug flow.
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    Biotechnology and Bioengineering 36 (1990), S. 965-969 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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    Biotechnology and Bioengineering 36 (1990) 
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    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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  • 83
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    Biotechnology and Bioengineering 36 (1990), S. 993-1001 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The effect of reduced nutritional levels (particularly nitrogen source) for immobilized K. fragilis type yeast were studied using a trickle flow, “differential” plug flow type reactor with cells immobilized by adsorption onto an absorbant packing matrix. Minimizing nutrient levels in a feed stream to an immobilized cell reactor (ICR) might have the benefits of reducing cell growth and clogging problems in the ICR, reducing feed preparation costs, as well as reducing effluent disposal costs. In this study step changes in test feed medium nutrient compositions were introduced to the ICR, followed by a return to a basal medium. Gas evolution rates were monitored and logged on a continuous basis, and effluent cell density was used as an indicator of cell growth rate of the immobilized cell mass. Startup of the reactor using a YEP medium showed a rapid buildup of cells in the reactor during the initial 110 h operation. The population density then stabilized at 1.6 × 1011 cells/g sponge. A defined medium containing a complex mix of essential nutrients with an inorganic nitrogen source (ammonium sulfate) was able to maintain 90% of the productivity in the ICR as compared to the YEP medium, but proved unable to promote growth of the immobilized cell mass during startup. Experiments on reduced ammonium sulfate in the defined medium, and reduced yeast extract and peptone in YEP medium indicated that stable productivity could be maintained for extended periods (80 h) in the complete absence of any nutrients besides a few salts (potassium phosphate and magnesium sulfate). It was found that productivity rates dropped by 35-65% from maximal values as nitrogenous nutrients were eliminated from the test mediums, while growth rates (as determined by shed cell density from the reactor) dropped by 75-95%. Thus, nutritional deficiencies largely decoupled growth and productivity of the immobilized yeast which suggests productivity is both growth- and non-growth-associated for the immobilized cells. A yeast extract concentration of 0.375 g/L with or without 1 g/L ammonium sulfate was determined to be the minimum level which gave a sustained increase in productivity rates as compared to the nutritionally deficient salt medium. This represents a 94% reduction in complex nitrogenous nutrient levels compared to standard YEP batch medium (3 g/L YE and 3.5 g/L peptone).
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    Biotechnology and Bioengineering 36 (1990), S. 1041-1048 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This article presents an introduction to the use of neural network computational algorithms for the dynamic modeling of bioprocesses. The dynamic neural model is used for the prediction of key fermentation variables. This relatively hew method is compared with a more traditional prediction technique to judge its performance for prediction. Illustrative simulation results of a continuous stirred tank fermentor are used for this comparison. It is shown that neural network models are accurate with a certain degree of noise immunity. They offer the distinctive ability over more traditional methods to learn very naturally complex relationships without requiring the knowledge of the model structure.
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    Biotechnology and Bioengineering 36 (1990), S. 1070-1082 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A method is presented for the estimation of the standard Gibbs energies of formation of biochemical compounds (and hence the Gibbs energies and equilibrium constants of biochemical reactions) from the contributions of groups. The method employs a large set of groups and special corrections. The contributions were estimated via multiple linear regression, using screened and weighted literature data. For most of the data employed, the error is less than 2 kcal/mol. The method provides a useful first approximation to Gibbs energies and equilibrium constants in biochemical systems.
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    Biotechnology and Bioengineering 36 (1990), S. 1105-1109 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: It was observed that about 90% of free-swimming Thiobacillus ferrooxidans in 9 K medium was adsorbed on added activated carbon when the concentration of the cultivated bacteria reached about 4 × 1013 cells m-3. The oxidation of ferrous iron and the leaching of copper ore were carried out in shake flasks and in aerated columns. The rates of oxidation and leaching increased when bacteria adsorbed on activated carbon were used. However, the evaluation of the reaction rates by eliminating the catalytic effect of activated carbon showed that the contribution to the reaction by the adsorbed microorganism was very small.
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    Biotechnology and Bioengineering 36 (1990), S. 1133-1140 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In order to develop an efficient process for large-scale production of recombinant protein, various factors were studied which affect the productivity of Sf-9 (Spodoptera frugiperda) insect cells when using the baculovirus expression system. It was shown that upon infection with the Bac-BRV6L recombinant baculovirus, the level per cell of VP6 (a bovine rotavirus nucleocapsid protein) would drop 10-fold when host cell density at the time of infection increased from 2 × 106 to 3 × 106 cells/mL. The decrease was found to be totally reversible by culture medium renewal after infection, even when cells were infected at the stationary phase. Recombinant protein production was 4-6 times higher using TNMFH medium supplemented with 10% fetal bovine serum (FBS) than in IPL/41 serum-free medium. Fine-tuning of infection parameters in a 4-L surface-aerated bioreactor resulted in the production of typically 350 mg/L of VP6 protein, representing more than 25% of total cell proteins.
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    Biotechnology and Bioengineering 36 (1990), S. 717-722 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Cells of an in vitro culture system are not the same as for an in vivo system, metabolically and physiologically; ineffective utilization of nutrients occurs by cells in vitro. Therefore, a simpler approach is needed to examine closely and overcome differences between in vivo and in vitro cells.Recognizing the ineffectiveness of nutrient utilization in vitro, we have constructed, a balanced, fortified high-density medium based on RPMI 1640 medium previously optimized for relatively low-density cell culture. The high-density medium was used to cultivate a hybridoma line in a batch spinner flask culture. In this fortified medium, a hybridoma cell line 2c3.1 was cultivated to near 1 × 107 cells/mL in batch suspension culture. During the culture, glucose, glutamine, and 10 essential amino acids of concentrations five times richer than normal in the medium were almost thoroughly consumed. Combined analysis of these consumption profiles reveals that the balanced, fortified nutrient supply contributes much to cellular activity to overcome the limitations of in vitro cellular growth. Intermediate metabolites, such as ammonium ion and lactic acid, were produced over concentrations reported until now to be inhibitory. This observation suggests that the major conclusive factor against cellular growth over the critical cell density is not so-called inhibitory metabolites. As a result of the high-density culture, 5-8 times higher production of a monoclonal antibody for hepatitis B surface antigen (anti-HBs) was obtained.Active cellular consumption of all the essential nutrients and the corresponding production of MAb strongly support the potential of our approach to overcome the growth limitation of cells in vitro and to obtain high-density hybridoma cell culture.
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    Biotechnology and Bioengineering 36 (1990), S. 338-345 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In batch fermentation Leuconostoc mesenteroides immobilized in calcium alginate beads produced a total dextransucrase activity equal to about 93% of that by free, suspended bacterial cells under comparable conditions in a bubble column reactor. Continuous sucrose feeding (5 g/L h) to the immobilized-cell culture in the airlift bioreactor increased production of enzymatic activity by about 107% compared with ordinary batch operation of this reactor. About 14% of the enzymatic activity produced by the immobilized cells appears as soluble activity in the cell-free broth compared with about 40% in case of free cells. In an airlift bioreactor, both the soluble and the intact (sorbed and entrapped) enzymatic activity produced by the immobilized bacterial cells was about 34% greater under automatic pH control, compared to that produced in a bubble column reactor with only manual pH control. During formation of dextran by intact enzyme within cells and beads, declines are observed in apparent enzymatic activity.
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  • 90
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    Biotechnology and Bioengineering 36 (1990), S. 411-416 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: As much as 84% of the thermostable serine protease from Thermomonospora fusca strain YX was covalently attached to silanized glass using glutaraldehyde. The immobilized protease exhibited a higher temperature optimum (86°C) and pH optimum (9.4) for activity compared to soluble YX-protease (80°C and pH 9.0, respectively). Immobilization improved enzyme thermo-stability above 90°C and reduced inactivation during prolonged storage (9% loss of activity after 90 days at 12°C). A continuous-flow column reactor packed with immobilized protease readily hydrolyzed casein over broad ranges of temperature and pH.
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  • 91
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    Biotechnology and Bioengineering 35 (1990), S. 31-42 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A model is proposed for enzymatic lysis of microbial cells based on number balances over the distribution of cell-wall mass in a population of cells. Analytical solutions to the population balance equations were obtained by the method of characteristics for simple reaction kinetics. The model has been used to analyze the following cases of lysis in a nonhomogeneous cell population: wall hydrolysis with cell rupture and product release, the effect of a distribution of lysis rates, and lysis of two-layer cell walls. Rate expressions for the reactions of lysis can be derived from bulk-phase experiments; the distributions of cell size and product content can be measured independently by flow cytometric techniques. The population model also provides an explanation for the initial lag seen in lysis kinetics for virtually any initial distribution. The model demonstrates patterns of lysis and product recovery for heterogeneous populations of cells and also applies to the more general problem of soluble-enzyme reactions with heterogeneous solid substrates.
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  • 92
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 35 (1990), S. 66-72 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Viable hybridoma cells were encapsulated. The capsules were formed in one step by placing a drop of cell suspension mixed with negatively charged carboxymethylcellulose (CMC) into a positively charged chitosan solution through the interpolymeric ionic interaction between two oppositely charged polymers. These capsules were found to have a mean diameter of about 1. 5 mm and wall thickness of 3 μm. The cells grew in the capsules using supplemented DMEM/F12 (four kinds of growth factor). The maximum cell density in encapsulating cell culture reached 1 × 107 cells/ml, 10 times higher than that obtained in the free cell culture. The maximum monoclonal antibody concentration in the free cell culture was 15μg/mL, but that in the capsule was 45μg/mL The antibody produced by the cell was concentrated about four times higher inside than outside of the capsules.
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  • 93
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    Biotechnology and Bioengineering 35 (1990), S. 132-137 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Six different types of materials including PVC, chitosan, chitin, agarose, Sepharose, and Trisacryl were evaluated for their lipase-coupling efficiencies. Among those tested, chitosan yielded the highest amount of lipase (79 mg/mL packed gel) immobilized but with lowest oil hydrolytic activity (0.03 mg eq/mL gel). The amount of lipase immobilized was affected by the length of the hydrocarbon chain attached to the PVC matrix but not by the pore size of the supports used. On the other hand, the specific activity of the immobilized lipase was affected by the pore size but not by the chain length of the hydrocarbon attached to the support. After immobilization, the optimal reaction pH was shifted from 7.5 to 8.5 and the optimal reaction temperature from 35 to 45-55°C. Lipase immobilized on PVC exhibited higher thermal stability than that on agarose. The half-life of the PVC immobilized lipase operating at 30°C in a packed-bed reactor was estimated to be about 400 h.
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  • 94
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    Biotechnology and Bioengineering 35 (1990), S. 160-184 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model for the growth process of the bacterium Bacillus subtilis is described. The model is a highly structured one. The driving motivation for development of the model and explicit accounting of major interactions of metabolic networks in the model is related to our eventual goal that the model will be used in the analysis of complex biological patterns. Bacillus subtilis was chosen in our study due to the interesting sporulation process that these cells undergo in response to adverse environmental conditions including nutrient limitation. Sporulation process in B. subtilis represents a primordial prototype of cellular differentiation in higher cellular systems. Thus a model for the B. subtilis growth process should prove extremely useful for understanding questions of developmental biology. The model is capable of simulating the transition between the exponential and stationary phase of growth in a batch culture. Since during the transition period the growth process and the metabolism become decoupled and many transient processes are taking place, such predictions are a severe test for the validity of any model. A strategy to examine the leading hypothesis on B. subtills sporulation implementing GTP as a component which signals sporulation initiation is described.
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  • 95
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    Biotechnology and Bioengineering 35 (1990), S. 185-194 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model of the tryptophan operon is analyzed to investigate the regulatory effects of feedback repression and the demand for tryptophan in the cell. In this model, feedback repression is considered to be a two-step process. First, the endproduct tryptophan combines with the inactive repressor produced by the regulatory genes to yield an active complex. This complex subsequently binds to the operator and prevents transcription of the structural genes into mRNA. The demand for tryptophan in the cell is modeled by a hyperbolic saturation function of the Michaelis-Menten type. Results are obtained for the expression of the tryptophan operon in Escherichia coli and their applicability to tryptophan production by microbial fermentation is discussed. It is shown that, depending on the strain level of the operon and the rate of utilization of tryptophan in the cell, an overproduction of tryptophan can be achieved under stable operating conditions; in other circumstances, the operon may become stable or unstable, and may lead to a periodic synthesis.
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  • 96
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    Biotechnology and Bioengineering 35 (1990), S. 211-216 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 4 Ill.
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  • 97
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    Biotechnology and Bioengineering 35 (1990), S. 305-311 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 9 Ill.
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  • 98
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 35 (1990), S. 320-325 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 5 Ill.
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  • 99
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 35 (1990) 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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  • 100
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    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 35 (1990), S. 454-468 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Batch xanthan fermentations by Xanthomonas campestris NRRL B-1459 at various temperatures ranging between 22°C and 35°C were studied. At 24°C or lower, xanthan formation lagged significantly behind cell growth, resembling typical secondary metabolism. However, at 27°C and higher, xanthan biosynthesis followed cell growth from the beginning of the exponential phase and continued into the stationary phase. Cell growth at 35°C was very slow; the specific growth rate was near zero. The specific growth rate had a maximum value of 0.26 h-1 at temperatures between 27°C and 31°C. Cell yield decreased from 0.53 g/g glucose at 22°C to 0.28 g/g glucose at 33°C, whereas xanthan yield increased from 54% at 22°C to 90% at 33°C. The specific xanthan formation rate also increased with increasing temperature. The pyruvate content of xanthan produced at various temperatures ranged between 1.9% and 4.5%, with the maximum occurring between 27°C and 30°C. These results suggest that the optimal temperatures for cell growth are between 24°C and 27°C, whereas those for xanthan formation are between 30°C and 33°C. For single-stage batch fermentation, the optimal temperature for xanthan fermentation is thus dependent on the design criteria (i. e., fermentation rate, xanthan yield, and gum qualities). However, a two-stage fermentation process with temperature shift-up from 27°C to 32°C is suggested to optimize both cell growth and xanthan formation, respectively, at each stage, and thus to improve overall xanthan fermentation.
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