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  • 1995-1999  (3,008)
  • 1997  (3,008)
  • Biochemistry and Biotechnology  (1,317)
  • Engineering  (683)
  • Cell & Developmental Biology  (441)
  • Industrial Chemistry  (437)
  • crystal structure  (134)
  • Nuclear reactions
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  • 1995-1999  (3,008)
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  • 1
    Electronic Resource
    Electronic Resource
    Synthesis and Characterization of the Isocyanide Ligated Centered Zirconium Halide Cluster [(Zr6Be)Cl12(CNXyl)6] (1997)
    Springer
    Journal of cluster science 8 (1997), S. 521-531 
    Details
    ISSN: 1572-8862
    Keywords: Zirconium clusters ; isocyanide ; synthesis ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The first isocyanide ligated hexanuclear zirconium halide cluster is reported. The unoxidized [(Zr6Be)Cl12(CNXyl)6] (CNXyl = 2,6-dimethylphenyl isocyanide) was obtained from the solid state precursor K3Zr6Cl15Be by dissolution in CH3CN in the presence of CNXyl. The CNXyl ligands occupy all the axial positions on the cluster. The compound was recrystallized from CH2Cl2 and Et2O. [(Zr6Be)Cl12(CNXyl)6].2CH2Cl2 crystallizes in the space group $${\text{P}}\overline {\text{1}} $$ (#2) with a = 12.092(5) Å, b=12.728(5) Å, c = 14.102(8) Å, α = 104.98(4)°, β =107.11°, γ = 100.94°, V = 1919(2) Å3, Z = l, R = 11.3% and R W = 27.0%. For the bound isocyanide ligands, v CN increases to 2140 cm−1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022605113866
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  • 2
    Electronic Resource
    Electronic Resource
    Reactions of the Dirhenium(II) Complexes Re2 X 4(μ-dppm)2 (X=Cl, Br; dppm=Ph2PCH2PPh2) with Isocyanides. Part XV: A Fifth Structural Isomer of the [Re2Cl3(μ-dppm)2(CO)(CNXyl)2]+ Cation (Xyl = 2, 6-Dimethylphenyl) (1997)
    Springer
    Journal of cluster science 8 (1997), S. 547-551 
    Details
    ISSN: 1572-8862
    Keywords: Rhenium ; dirhenium complexes ; rhenium–rhenium multiple bonds ; isocyanide ligands ; carbonyl ligand ; structural isomers ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The reaction of the unsymmetrical, coordinatively unsaturated dirhenium(II) complex [(XylNC)(OC)CIRe(μ-dppm)2ReCl2]O3SCF3 (dppm = Ph2PCH2PPh2) with one equivalent of XylNC in CH2Cl2 affords a fifth structural isomer of the [Re2Cl3(μ-dppm)2(CO)(CNXyl)2] + cation; this is believed to have a CO-bridged structure of the type [(XylNC)ClRe(μ-Cl)(μ-CO)(μ-dppm)2ReCl(CNXyl)]+. The latter complex reacts with a further equivalent of XylNC in the presence of Tl+ to form the [Re2Cl2(μ-dppm)2(CO)(CNXyl)3]2+ cation, which has been shown by IR spectroscopy, and by the X-ray crystallographic characterization of its neutral congener Re2Cl2(μ-dppm)2(CO)(CNXyl)3, to contain a very weak and unsymmetrical CO bridge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022609214775
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  • 3
    Electronic Resource
    Electronic Resource
    Thermal latent coordination compounds (1997)
    Springer
    Journal of thermal analysis and calorimetry 50 (1997), S. 569-586 
    Details
    ISSN: 1572-8943
    Keywords: crystal structure ; metal(II) picolinate and quinaldinate ; thermal degradation of imidazole and pyrazole complexes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Complexes of the type M(Pa)2(HAz)2 and M(QA)2(HAz)2 (M=cobalt(II) and nickel(II); HPa=picolinic acid, HQa=quinaldic acid; HAz=azoles like imidazole (Him), pyrazole (HPz), benzimidazole (HBzIm) etc.) show a similar thermal behaviour. In the first step of decomposition the corresponding azolinium picolinates or quinaldinates (H2AzPa, H2AzQa) are split off with formation of polymeric mixed ligand complexes M(Pa)(Az) or M(Qa)(Az). X-ray analysis of Co(Qa)2(HBzIm)2 XIIIa illustrates a proton transfer and a subsequent thermal removal of benzimidazolinium quinaldinate (H2BzImQa): Hydrogen bridges from pyrrole nitrogen of the benzimidazole to the non-coordinated oxygen of the quinaldinate predetermine the thermal initiated proton transfer. The high volatility of the heterocyclic acids and the nitrogen coordination are responsible for the formation of the mixed ligand complex Co(Qa)(BzIm) XIVa. Exceptions are the complexes M(Pa)2(HPz)2 XIa-b and M(Qa)2(HIm)2 XVIIa-b. Pyrazole is eliminated from the complexes XIa-b with formation of the solvent-free inner complex M(Pa)2 XIIa-b. From compounds XVIIIa-b quinaldic acid or their decomposition products are split off and a high temperature modification of M(Im)2 XVIIIa-b is formed at elevated temperature. XVIIIa-b are decomposed to the cyanides M(CN)2 similarly to the thermal behaviour of Cu(Im). In the first step the thermal degradation of imidazole and pyrazole adducts of copper(II) picolinates and quinaldinates is characterized by the elimination of azoles. The reason for this thermal behaviour is the weaker coordination of the azole heterocycles in copper chelate compounds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01979029
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  • 4
    Electronic Resource
    Electronic Resource
    Structures and tautomeric interconversions of anthraquinone imine derivatives (1997)
    Springer
    Structural chemistry 8 (1997), S. 197-204 
    Details
    ISSN: 1572-9001
    Keywords: Tautomerism ; anthraquinone ; crystal structure ; semiempirical computations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Substituted 1-hydroxy-9,10-anthraquinone-9-imines have been found to exhibit tautomeric interconversions between the 9,10- and 1,10-quinonoid forms in the solid state as well as in solution. Single-crystal X-ray crystallography was used to study the structures of 4-(N-acetyl-p-tolylamino)-9-amino-1,10-anthracenedione and 4-hydroxy-1-phenylamino-10-mesitylimino-9(10H)-anthracenone at ambient and low temperatures. The former compound gave crystals belonging to the monoclinic space group P2l/c and, at 295 K,a=9.684(2),b=16.371(3),c=12.097(2) å,Β=110.41(1)
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02263507
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  • 5
    Electronic Resource
    Electronic Resource
    Synthesis and structure of 5-methoxy-4-methylbenzopsoralen (1997)
    Springer
    Structural chemistry 8 (1997), S. 453-457 
    Details
    ISSN: 1572-9001
    Keywords: Benzopsoralen ; photochemotherapeutic agent ; crystal structure ; molecular mechanics ; AM1 theoretical calculations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract 5-Methoxy-4-methyl-2H-benzofuro[3,2-g]benzo-1-pyran-2-one was synthesized and its crystal structure was determined and compared with the optimal conformation arrived at by MM and AM1 theoretical calculations. The latter indicated that the tetracyclic skeleton is planar with total length (C2–C8) 9.23 å, and that the line joining the conters of the terminal-benzene and furan rings makes an angle of 30.5
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02311704
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  • 6
    Electronic Resource
    Electronic Resource
    The crystal and molecular structures of cellulose I and II (1997)
    Springer
    Glycoconjugate journal 14 (1997), S. 677-690 
    Details
    ISSN: 1573-4986
    Keywords: molecular dynamics ; crystal structure ; cellulose I and II
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The paper describes molecular dynamics (MD) simulations on the crystal structures of the Iβ and II phases of cellulose. Structural proposals for each of these were made in the 1970s on the basis of X-ray diffraction data. However, due to the limited resolution of these data some controversies remained and details on hydrogen bonding could not be directly obtained. In contrast to structure factor amplitudes in X-ray diffraction, energies, as obtained from MD simulations, are very sensitive to the positions of the hydroxyl hydrogen atoms. Therefore the latter technique is very suitable for obtaining such structural details. MD simulations of the Iβ phase clearly shows preference for one of the two possible models in which the chains are packed in a parallel orientation. Only the parallel-down mode (in the definition of Gardner and Blackwell (1974) J Biopolym 13: 1975-2001) presents a stable structure. The hydrogen bonding consists of two intramolecular hydrogen bonds parallel to the glycosidic linkage for both chains, and two intralayer hydrogen bonds. The layers are packed hydrophobically. All hydroxymethyl group are positioned in the tg conformation. For the cellulose II form it was found that, in contrast to what seemed to emerge from the X-ray fibre diffraction data, both independent chains had the gt conformation. This idea already existed because of elastic moduli calculations and 13C-solid state NMR data. Recently, the structure of cellotetraose was determined. There appear to be a striking similarity between the structure obtained from the MD simulations and this cellotetraose structure in terms of packing of the two independent molecules, the hydrogen bonding network and the conformations of the hydroxymethyl group, which were also gt for both molecules. The structure forms a 3D hydrogen bonded network, and the contribution from electrostatics to the packing is more pronounced than in case of the Iβ structure. In contrast to what is expected, in view of the irreversible transition of the cellulose I to II form, the energies of the Iβ form is found to be lower than that of II by 1 kcal mol-1 per cellobiose.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018509231331
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  • 7
    Electronic Resource
    Electronic Resource
    The molecular complex of dibenz[a,c]anthracene and trinitrobenzene (1997)
    Springer
    Structural chemistry 8 (1997), S. 141-147 
    Details
    ISSN: 1572-9001
    Keywords: Dibenzanthracene ; trinitrobenzene complex ; trinitrobenzene complex ; π-complex ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The crystal structure of the complex between the polycyclic aromatic hydrocarbon di-benz[a,c]anthracene and 1,3,5-trinitrobenzene is reported. The crystals are triclinic, space group P¯1 with unit cell dimensionsa=7.277(2) å,b=11.237(6) å, andc=13.902(5) å,α= 104.13(4)
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02262849
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  • 8
    Electronic Resource
    Electronic Resource
    Generalized linear elasticity in exterior domains. I: Radiation problems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1469-1500 
    Details
    ISSN: 0170-4214
    Keywords: radiating solutions ; exterior boundary value problem in elasticity ; variable coefficients ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use Hodge-Helmholtz decompositions of weighted Sobolev spaces to solve time-harmonic exterior-boundary value problems for perturbations of the (aδd+bdδ)-system (δ: the co-differential, a, b〉0). We prove, that a Fredholm alternative holds true, the eigensolutions decay polynomially at infinity, and that the positive eigenvalues do not accumulate. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 9
    Electronic Resource
    Electronic Resource
    The 2-D Neumann problem in an exterior domain bounded by closed and open curves (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1551-1562 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Neumann problem for the Laplace equation in an exterior connected plane region bounded by closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind, which is uniquely solvable. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 10
    Electronic Resource
    Electronic Resource
    Numerical methods for scattering problems by curved gratings at high frequencies (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1531-1549 
    Details
    ISSN: 0170-4214
    Keywords: gratings ; Helmholtz equation ; high frequencies ; geometric theory of diffraction ; transition regions ; finite element method ; error estimates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new numerical method is derived for the calculation of high-frequency asymptotic expansions of the scalar wave scattered by curved periodic structures. Optimal error estimates for this method are established. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 5 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    Classification of smooth solutions to 2×2 hyperbolic systems with boundary damping (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1563-1598 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give a complete classification for breakdown in finite time or global existence of continuously differentiable solutions to hyperbolic systems of two first-order partial differential equations posed on a real bounded interval, with boundary damping and initial data of small magnitude. Structural bounds for the derivatives of the initial data which govern the behavior of the solution are brought to light. We isolate two classes of boundary damping: the strong damping forbids the solution to blow up after a time that we exhibit while the weak damping permits a late breakdown. The results are applied to nonlinear elasticity. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Singular Stress Behavior in a Bonded Hereditarily-Elastic Aging Wedge. Part II: General Heredity (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 31-45 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
    Type of Medium: Electronic Resource
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  • 13
    Electronic Resource
    Electronic Resource
    On Representation Formulas and Radiation Conditions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 133-150 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Solutions of linear elliptic partial differential equations in unbounded domains can be represented by boundary potentials if they satisfy certain conditions at infinity. These radiation conditions depend on the fundamental solution chosen for the integral representation. We prove some basic results about radiation conditions in a rather general framework.Fundamental solutions G are considered that are defined only on the complement of a compact set. It turns out, however, and we present examples for this, that the more interesting results only hold if G is defined on all of ∝n or if it is a Green function for an exterior boundary value problem. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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  • 14
    Electronic Resource
    Electronic Resource
    Attractors and Approximate Inertial Manifolds for the Generalized Benjamin-Bona-Mahony Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 189-203 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the present paper, we deal with the long time behaviour of solutions for the generalized Benjamin-Bona-Mahony equation. By a priori estimates methods, we show this equation possesses a global attractor in Hk for every integer k≥2, which has finite Hausdorff and fractal dimensions. We also construct approximate inertial manifolds such that every solution enters their thin neighbourhood in a finite time. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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  • 15
    Electronic Resource
    Electronic Resource
    Factorization of a class of matrices generated by Sommerfeld diffraction problems with oblique derivatives (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1185-1198 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An explicit factorization of the Fourier symbol matrix functions generated by Sommerfeld diffraction problems with oblique derivatives is obtained. For this purpose a new prefactorization procedure is developed which makes use of factorization through weighted L2 spaces. These results yield a representation of a generalized inverse of the corresponding matrix Wiener-Hopf operator and the asymptotic behaviour of the solution at the edge of the screen. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 16
    Electronic Resource
    Electronic Resource
    On quasi-linear Schrödinger-Poisson systems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1223-1238 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a high-field version of the periodic Schrödinger-Poisson system, for which the Poisson equation includes nonlinear terms corresponding to a field-dependent dielectric constant. Using a Galerkin scheme, we prove global existence and uniqueness, and present the matrix equations for the numerical evaluation of the potential. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 17
    Electronic Resource
    Electronic Resource
    A generalized temperature-dependent, non-Newtonian Hele-Shaw flow in injection and compression moulding (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1199-1222 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A generalized Hele-Shaw flow is derived and analysed in injection and compression moulding which contains non-isothermal and non-Newtonian rheological behaviour of the molten polymers as well as non-symmetric effects. The corresponding fixed domain formulations for the flow are investigated from a mathematical point of view. Different approaches for the determination of the temperature and some viscosity models are discussed. Together with an outline of the proposed solution algorithm special finite element techniques are described for the numerical treatment of this complex non-linear moving boundary problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 3 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    On the Validity of the degenerate Ginzburg - Landau equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1239-1256 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Ginzburg-Landau equation which describes nonlinear modulation of the amplitude of the basic pattern does not give a good approximation when the Landau constant (which describes the influence of the nonlinearity) is small. In this paper a derivation of the so-called degenerate (or generalized) Ginzburg-Landau (dGL)-equation is given. It turns out that one can understand the dGL-equation as an example of a normal form of a co-dimension two bifurcation for parabolic PDEs. The main body of the paper is devoted to the proof of the validity of the dGL as an equation whose solution approximate the solution of the original problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 19
    Electronic Resource
    Electronic Resource
    The Dirichlet problem for Stokes equation in a domain exterior to an open surface (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1257-1269 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper deals with the Dirichlet problem for the Stokes linear equation in a domain exterior to an open surface. With the help of the theory of boundary integral (pseudo-differential) equations uniqueness and existence theorems are proved in the Bessel-potential and Besov spaces and Cα-smoothness (with α〈1/2) of solution is established in the neighbourhood of the boundary of the open surface. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 20
    Electronic Resource
    Electronic Resource
    Long-time behaviour of ferromagnetic spin chain equation: global attractor and its dimension (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1271-1281 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper the authors consider the initial boundary value problem of the ferromagnetic spin chain equation and prove the existence of the global attractor and finiteness of the Hausdorff and the fractal dimensions of the attractor. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 21
    Electronic Resource
    Electronic Resource
    On stationary Schrödinger-Poisson equations modelling an electron gas with reduced dimension (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1283-1312 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We regard the Schrödinger-Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrödinger operator, the Fermi level and the quantum mechanical electron density operator for square integrable electrostatic potentials. On bounded sets of potentials the Fermi level is continuous and bounded, and the electron density operator is monotone and Lipschitz continuous. As a tool we develop a Riesz-Dunford functional calculus for semibounded self-adjoint operators using paths of integration which enclose a real half-axis. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 22
    Electronic Resource
    Electronic Resource
    Existence results for non-autonomous multiple-fragmentation models (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1313-1323 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate an initial-value problem modelling fragmentation processes where particles split into two or more pieces at a rate, γ, that not only depends on the sizes of the particles involved but also on time. The existence of non-negative, mass-conserving solutions is established by considering a truncated version of an associated non-autonomous abstract Cauchy problem. The latter has solutions of the form u(t)=Un(t,t0)f, t≥t0, where f is the known data at some fixed time t0≥0 and {Un(t,s)}t0≤s≤t≤T is a uniformly continuous evolution system. A limit evolution system {U(t,s)}t0≤s≤t≤T is shown to exist. Depending on the form of the known data f at time t0, the scalar-valued function u, obtained from the limit evolution system via u(x, t)=[U(t, t0)f](x) for a.e. x〉0, t≥t0, is a solution of either the original initial-value problem or an integral version of this problem. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 23
    Electronic Resource
    Electronic Resource
    Global solutions of the Laplace equation with a nonlinear dynamical boundary condition (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1325-1333 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the boundedness and a priori bounds of global solutions of the problem Δu=0 in Ω×(0, T), (∂u/∂t) + (∂u/∂ν) = h(u) on ∂Ω×(0, T), where Ω is a bounded domain in ∝N, ν is the outer normal on ∂Ω and h is a superlinear function. As an application of our results we show the existence of sign-changing stationary solutions. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 24
    Electronic Resource
    Electronic Resource
    Spatial bounds and growth estimates for the heat equation with three relaxation times (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1335-1344 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this note we investigate spatial bounds for the heat conduction equation with three relaxation times. We use energy methods similar to those considered in the study of the backward parabolic heat equation. Finally, we show that for any positive choice of the coefficients we may take initial data for which the solution is unstable when we suppose that the body is bounded. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Continuous sedimentation of multi-component particles (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1345-1364 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Continuous sedimentation of solid particles in a liquid takes place in a clarifier-thickener unit, which has one feed inlet and two outlets. The process is vital in a waste water treatment plant, where the particles consist of several biological components. The concentrations of these are modelled by a one-dimensional system of conservation laws with source term. It is shown how a unique solution can be obtained, and how analytical solutions are used to form a conservative numerical algorithm. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Subsonic solutions of hydrodynamic model for semiconductors (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1389-1410 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the existence and uniqueness of the steady-state solution of hydrodynamic model for semiconductor devices. Boundary conditions are prescribed by vorticity on inflow boundary as well as by electron density, temperature, and normal component of electron velocity on whole boundary. If the ambient temperature is large, and if both vorticity on inflow boundary and the variation of density on boundary are small, a unique subsonic solution exists. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Asymptotic solution of a non-linear wave motion in an electron plasma (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1379-1388 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The theory of high-frequency waves has been used to calculate first and second-order asymptotic solutions for the propagation of non-linear waves in a cylindrical symmetric flow of an electron plasma. The behaviour of acceleration waves and weak shock waves has been analysed through these solutions and Whitham's rule for a weak shock wave on any wavelet has been confirmed through the first-order solution. The appearance of a weak shock wave on any wavelet has been determined and its strength, the location, and the speed of propagation have been found from the asymptotic solution presented in this paper. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    The amount of non-uniqueness for factored equations with Euler-Poisson-Darboux factors (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1449-1457 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Of concern are factored Euler-Poisson-Darboux equations of the type∏Nj=1(d2/dt2+(ρ/t)d/dt+Aj)u(t)=0,where, for example, Aj=-cjΔ, Δ being the Dirichlet Laplacian acting on L2(Ω), Ω⊂∝n, and 0〈c1〈…〈cN. More generally -Aj can be the square of the generator of a (C0) group on a Banach space. When the constant ρ is negative, the initial value problem for the factored EPD equation is ill-posed. Nevertheless, we determine how many initial conditions are necessary to guarantee uniqueness of a solution. This number jumps up as ρ crosses a negative integer from right to left. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On Global Existence, Asymptotic Stability and Blowing Up of Solutions for Some Degenerate Non-linear Wave Equations of Kirchhoff Type with a Strong Dissipation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 151-177 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study on the initial-boundary value problem for some degenerate non-linear wave equations of Kirchhoff type with a strong dissipation:\documentclass{minimal} \begin{document} \[ u_{tt}=\left\| \nabla u\right\| ^{2\gamma }\Delta u-\Delta u_t=\left| u\right| ^\alpha u,\quad u(0)=u_0,\;u_t(0)=u_1,\;u|_{\partial \Omega }=0. \] \end{document}When the initial energy $E(u_0,u_1)\equiv \left\| u_1\right\| ⁁2+\frac 1{\gamma +1}\left\| \nabla u_0\right\| ⁁{2(\gamma +1)}-\frac 2{\alpha+2}\left\| u_0\right\| _{\alpha +2}⁁{\alpha +2}$ associated with the equations is non-negative and small, a unique (weak) solution exists globally in time and has some decay properties. When the initial energy E(u0,u1) is negative, the solution blows up at some finite time. In the proof we use the ‘modified potential well’ and ‘Concavity’ methods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Existence of a Classical Solution for a Multidimensional Filtration Problem (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 179-187 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove existence, in a small time interval, of a classical solution having a regular free boundary, (i.e. the level set {u=0}) of a multidimensional filtration problem. The key point to get the regularity of the level set {u=0} is the proof of an a priori estimate for the L∞-norm of ut. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    On Stationary Solutions of the Relativistic Vlasov-Maxwell System (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 667-677 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study stationary solutions of the relativistic Vlasov-Maxwell system of plasma physics which have a special form introduced (in the classical setting) by Rudykh, Sidorov and Sinitsy and establish their existence under suitable assumptions on the ansatz functions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 667-677 (1997).
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    Convergence of Solutions of the Landau Equations in the Collisionless Limit (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 679-688 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper addresses the question: when the frequency of collisions vanishes, will the solutions of the Landau system converge to the solutions of the Vlasov system? We give a positive answer to the question for solutions satisfying certain regularity conditions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 679-688 (1997).
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    Analysis of a Non-hyperbolic System Modeling Two-phase Flows Part 1: The Effects of Diffusion and Relaxation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 783-803 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers the non-linear stability of a non-hyperbolic system of conservation laws with both relaxation and diffusion, which is commonly used for the modeling of two-phase fluid flows. Global existence in time is proved for initial data with a sufficiently small H1 norm. This result heavily depends on the nice structure of the relaxation system, derived from the initial system by setting the relaxation variables to zero. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    The dam problem for non-linear Darcy's laws and non-linear leaky boundary conditions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1045-1068 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The goal of this paper is to establish that even for strongly non-linear Darcy's laws and strongly non-linear leaky boundary conditions on the bottom of the reservoirs the fluid flow through a porous dam is a well-posed problem for which existence of a solution can be established. In a simple case we provide also the exact solution to the problem. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Convex domains with stationary hot spots (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1163-1169 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Consider the problem of heat flow in a convex domain in ∝n with Dirichlet boundary condition and constant initial temperature. We show that the solution has a fixed hot spot if the domain is invariant under the action of an essential symmetry group. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Exponential decay for the one-dimensional wave equation with internal pointwise damping (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1171-1183 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers a particular type of closed-loop for the wave equation in one space dimension with damping acting at an arbitrary internal point, for which the uniform stabilization with exponential decay rate is shown. Applications to chains of coupled strings are also discussed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A non-linear parabolic control problem with non-homogeneous boundary condition - convergence of Galerkin approximation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1365-1377 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper is concerned with optimal control problem for a non-linear parabolic equation with non-homogenous boundary condition and quadratic cost. The control is acting in a nonlinear equation. We derive some results on the existence of optimal controls. Then we treat optimal control problem by Galerkin method and we prove the convergence of optimal values for approximated control problems to the one for the original problem. Finally, we apply the results to give a simple example. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On a fractional partial differential equation with dominating linear part (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1427-1448 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is proved that there is a (weak) solution of the equationut=a*uxx+b*g(ux)x+f,on ∝+ (where * denotes convolution over (-∞, t)) such that ux is locally bounded. Emphasis is put on having the assumptions on the initial conditions as weak as possible. The kernels a and b are completely monotone and if a(t)=t-α, b(t)=t-β, and g(ξ)∼sign(ξ)∣ξ∣γ for large ξ, then the main assumption is that α〉(2γ+2)/(3γ+1)β+(2γ-2)/(3γ+1). © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Numerical solution of viscoplastic constitutive equations with internal state variables Part I: algorithms and implementation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1411-1425 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article treats the initial-boundary-value problem of viscoplasticity using unified constitutive models without a yield surface. Semi-discretization with the finite element method (FEM) leads to a system of differential-algebraic equations (DAE) with strongly non-linear evolution equations for the internal state variables. A special family of partitioned Runge-Kutta methods is introduced which allows an efficient time integration of the semidiscrete system. Coefficients for methods of order one, two, and three are given. Finally, numerical results for some two- and three-dimensional examples using the model of Hart are presented. In a second part we will give the theoretical background and state a proof of convergence for the algorithm presented in this paper. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Asymptotic spatial homogeneity of solutions to conservation laws with memory in several space dimensions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1459-1468 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove that any solution of the problem(u+K*u)t+∑ai(u)uxi=0 on (0,∞)×∝Nwith spatially periodic initial data converges to a constant provided some non-degeneracy conditions on the kernel K and the non-linear functions ai,i=1,…,N are imposed. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Generalized linear elasticity in exterior domains. II: low-frequency asymptotics (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1501-1530 
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    ISSN: 0170-4214
    Keywords: radiating solutions ; exterior boundary value problems in elasticity ; asymptotic expansions ; low-frequency behaviour ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We continue the study of the operators of generalized linear elasticity and investigate the behaviour of the solutions as the frequency tends to zero. We identify degenerate operators in terms of special solutions to the static problem which must be added to the usual Neumann series in order to describe the low frequency behaviour adequately. As a byproduct we construct solutions to the homogeneous static operator (‘spherical elastics’) which generalize the spherical harmonics and give rise to a ‘spherical elastics expansion’. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Half-space Fourier transform in application to non-linear hyperbolic initial-boundary-value problem: low regularity solutions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1599-1616 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Dirichlet initial-boundary-value problem in the half-space ∝t×∝3+ for a non-linear hyperbolic system is studied. About the nonlinearity the null condition structure is imposed. Under the smallness conditions on the initial data the existence of low regularity solutions, on a given interval of time, is proved. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Clifford analysis on spheres and hyperbolae (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1617-1624 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We develop aspects of Clifford analysis over the sphere and hyperbolae. We focus primarily on the hyperbola lying in the Minkowski type space ∝n,1. We show that in order to give a proper extension of basic results on Clifford analysis in Euclidean space to this context one needs to consider both hyperbolae lying in ∝n,1. We also introduce Bergman spaces of Lp left monogenic sections in this context and consider the decomposition of square integrable sections over suitable bundles constructed over subdomains of spheres and hyperbolae. The results presented here cover the necessary background to enable one to set up and solve boundary value problems for field-type equations over hyperbolae. In particular, one can study analogues of the Dirichlet problem for analogues of the Laplacian over hyperbolae and spheres. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Dissipative Feedback Synthesis for a Singularly Perturbed Model of a Piston Driven Flow of a Non-Newtonian Fluid (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 79-94 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The limiting behaviour of solutions of a system of singularly perturbed equations is studied. The goal is to construct a dissipative feedback control synthesis that stabilizes the prescribed output functional along trajectories of solutions. The results are applied to a singularly perturbed Johnson-Sagelman-Oldroyd model of shearing motions of a piston driven flow of a non-Newtonian fluid. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Boundary Integral Equation Method in the Steady State Oscillation Problems for Anisotropic Bodies (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 95-119 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The three-dimensional steady state oscillation problems of the elasticity theory for homogeneous anisotropic bodies are studied. By means of the limiting absortion principle the fundamental matrices maximally decaying at infinity are constructed and the generalized Sommerfeld-Kupradze type radiation conditions are formulated. Special functional spaces are introduced in which the basic and mixed exterior boundary value problems of the steady state oscillation theory have unique solutions for arbitrary values of the oscillation parameter. Existence theorems are proved by reduction of the original boundary value problems to equivalent boundary integral (pseudodifferential) equations. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Error Estimates for the Boundary Element Approximation of a Contact Problem in Elasticity (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 205-217 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The two-dimensional frictionless contact problem of linear isotropic elasticity in the half-space is treated as a boundary variational inequality involving the Poincare-Steklov operator and discretized by linear boundary elements. Quadratic growth of the energy near the solution is shown under weak regularity assumptions if the central axis of external forces intersects the boundary of the domain in a Lebesgue null set. Estimating the numerical range of the discrete Poincare-Steklov operator and properly modifying it, enables the application of an error estimate for semi-coercive variational inequalities. Optimal order of convergence is obtained in the underlying Sobolev space H1/2(∂Ω)2. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Korn's Inequalities for Junctions of Spatial Bodies and Thin Rods (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 219-243 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The dependence on the small parameter ε of constants in Korn's inequalities is investigated for domains which are obtained by joining thin rods to an elastic spatial body. The external ends of the rods are clamped. The asymptotic accuracy of the derived inequalities is achieved by certain distribution of weight multipliers and powers of ε in L2-norms of displacements and their derivatives while the introduced weights differ for longitudinal and transversal components of displacement fields in the rods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Asymptotic Behaviour of Solutions to some Pseudoparabolic Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 271-289 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The aim of this paper is to investigate the behaviour as t→∞ of solutions to the Cauchy problem ut-Δut-νΔu-(b, ∇u)=∇⋅F(u), u(x, 0)=u0(x), where ν〉0 is a fixed constant, t≥0, x∊∝n. First, we prove that if u is the solution to the linearized equation, i.e. with ∇⋅F(u)≡0, then u decays like a solution for the analogous problem to the heat equation. Moreover, the long-time behaviour of u is described by the heat kernel. Next, analogous results are established for the non-linear equation with some assumptions imposed on F, p, and the initial condition u0. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Finite Element Methods for the Stokes System in Three-Dimensional Exterior Domains (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 245-269 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The article treats the question of how to numerically solve the Dirichlet problem for the Stokes system in the exterior of a three-dimensional bounded Lipschitz domain. In a first step, the solution of this problem is approximated by functions solving the Stokes system in a truncated domain and satisfying a suitable artificial boundary condition on the outer boundary of this truncated domain. In a second step, this new problem is approximately solved in finite element spaces related to a graded mesh as introduced by Goldstein [Math. Comp., 36, 387-404 (1981)]. The difference between this finite element approximation and the exact solution of the exterior Stokes problem is estimated in the norm of suitable unweighted L2-Sobolev spaces. These estimates are analogous to corresponding results which are known for the Poisson equation. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Inverse Problems for Identification of Memory Kernels in Viscoelasticity (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 291-314 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Inverse problems for identification of the memory kernel in the linear constitutive stress-strain relation of Boltzmann type are reduced to a non-linear Volterra integral equation using Fourier's method for solving the direct problem. To this equation the contraction principle in weighted norms is applied. In this way global existence of a solution to the inverse problem is proved and stability estimates for it are derived. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Control of Matter Waves in Adjacent Potential Wells (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 369-381 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider exact controllability of a system of two Schrödinger equations. These represent matter waves in adjacent potential wells with different potentials, one zero, the other a positive constant V0. The problem is formulated as a simultaneous boundary controllability problem, with Dirichlet control. Estimates for the controls, including an observability inequality, are proved using multiplier techniques. Then the Hilbert uniqueness method is used to obtain the exact controllability result. If V0 is sufficiently small, there exists a time T^(V0) such that the system is exactly controllable in times T〉T^(V0). © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On ‘Power-logarithmic’ Solutions to the Dirichlet Problem for the Stokes System in a Dihedral Angle (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 315-346 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Dirichlet problem for the Stokes system in a dihedral angle is considered. An explicit description of special solutions to the homogeneous problem which have the form\documentclass{minimal} \begin{document} \begin{eqnarray*} U(x) &=&\left| x\right| ^\lambda \sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}u^{(k)}(x/\left| x\right|), \\ P(x) &=&\left| x\right| ^{\lambda -1}\sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}p^{(k)}(x/\left| x\right|) \end{eqnarray*} \end{document}is given. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the Heat Convection Equations with Dissipation Term in Regions with Moving Boundaries (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 347-368 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider an initial value problem for a system of equations describing the motion and the heat convection in a viscous and incompressible fluid which occupies a smooth region Ωt⊂∝3 depending on time.In the equation for the distribution of temperature in the fluid we take into account not only the convective term but also the term responsible for the dissipation of energy.We prove local in time existence and uniqueness of solutions of the considered problem, and global in time existence for sufficiently small data. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    The Solvability of Boundary Equations in Mixed Problems for Non-stationary Maxwell's System (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 425-448 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The work deals with boundary equations appearing if non-stationary problems for Maxwell system are solved with the help of surface-retarded potentials. The solvability of these equations is proved in some functional spaces of Sobolev type. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A New Algorithm in Electromagnetic Inverse Scattering Theory with an Application to Medical Imaging (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 385-401 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the electromagnetic inverse scattering problem of determining the index of refraction of an isotropic inhomogeneous medium from a knowledge of the total electric near field data. We consider both the case of scattering by an infinite inhomogeneous cylinder and a bounded inhomogeneous region in space. We conclude by giving an application of our method to the problem of imaging leukemia in the upper leg by means of microwaves. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Parabolic Problems and Boundary Integral Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 449-459 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Here we consider initial boundary value problems for parabolic equations in non-bounded (with respect to time) domains by using the single-layer potential. We discuss the solvability in anisotropic Hölder spaces of the boundary integral equations, to which original parabolic problems are reduced. We construct the special operators (regularizers) for these integral equations which transform them to equivalent integral Volterra equations of the second kind with weakly singular kernels. As a corollary we obtain the theorem about the classical solvability in anisotropic Hölder spaces for initial boundary value parabolic problems. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Adaptive Coupling and Fast Solution of FEM-BEM Equations for Parabolic-Elliptic Interface Problems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 403-423 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove an a posteriori error estimate for the symmetric coupling of finite elements and boundary elements applied to linear parabolic-elliptic interface problems. The discontinuous Galerkin method is used for the discretization in time. We present an adaptive algorithm for choosing the mesh size in space and time and we analyse the Hybrid Modified Conjugate Residual (HMCR) method as a solution method for the linear systems which arise. Computational results show that the number of HMCR-iterations grows slowly with the problem size. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Editorial: G. C. Hsiao on his 60th birthday (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 383-384 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
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    Difference Methods for Quasilinear 2D-diffusion Problems in Toroidal Configurations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 477-493 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Implicit one-step difference methods for quasilinear parabolic initial boundary value problems in two space variables and in polar coordinates are considered. Problems of this kind are suitable for the description of diffusion processes in plasma physics. Therefore, because of its special physical interest the dependence of the coefficients both on the solution and on its space derivatives (the fluxes) is included. The first part of this paper deals with proving convergence of the discrete approximations for vanishing step sizes. For this purpose, bounds for the inverse difference operators have to be derived previously. The nonlinear systems arising from the discretizations have exactly one solution for all step sizes being sufficiently small. In the second part of the article numerical tests are performed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the Existence of Trapped Modes in Channels of Arbitrary Cross-section (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 521-545 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article establishes the existence of trapped-mode solutions of a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls. A trapped mode corresponds to an eigenvalue of a non-local Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by generalizing previous results concerning spectral theory for differential operators to this non-local operator. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Classical Global Solutions for Non-linear Klein-Gordon-Schrödinger Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 599-616 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of the classical global solutions for the non-linear Klein-Gordon-Schrödinger equations is proved in H1-subcritical cases for space dimensions n≤5. For higher space dimensions 6≤n≤9, we will give a subsequent paper to deal with. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the Long-time Behaviour of Solutions to a Conservation Law with Memory (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 569-581 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show that any solution of the scalar conservation law(u+k*u)t+σ(u)x=0starting from spatially periodic initial datum stabilizes to its integral mean as time goes to infinity. No convexity or ‘genuinely non-linear’ like conditions are assumed concerning σ. © 1997 by B. C. Teubner stuttgart-John Wiley & Sons Ltd.
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    Characteristic Symmetric Hyperbolic Systems with Dissipation: Global Existence and Asymptotics (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 583-597 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the initial-boundary value problem for quasi-linear symmetric hyperbolic systems with dissipation and characteristic boundary of constant multiplicity. We investigate the global existence and decay property of small regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary. We also show the existence, uniqueness and stability of the time periodic solutions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Uniqueness for Unbounded Classical Solutions of the MHD Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 617-623 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The uniqueness for unbounded classical solutions of the magnetohydrodynamic (MHD) equations in the whole space is investigated. Under suitable growth condition, it is shown that the solution to the initial value problem is unique. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Positive Steady-state Solutions of a Non-linear Reaction-Diffusion System (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 625-634 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The steady-state problem of the non-linear reaction-diffusion systemut-uxx=u(av-b),vt-vxx=cuis considered. The existence of positive steady-solutions is established by using a fixed point theorem in ordered Banach space. The uniqueness of ordered positive steady-state solutions and an application to the associated reaction-diffusion system are presented. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Sommerfeld Diffraction Problems with Oblique Derivatives (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 635-652 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A class of diffraction problems for the two-dimensional Helmholtz equation is studied where the boundary conditions on a canonical screen contain oblique derivatives. The problem in weak formulation is reduced to a system of pseudodifferential equations on a half-line. The Fredholm property is characterized in dependence of the parameters, index formulas are given, and, if necessary, a normalization of the problem is implemented. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Control and Game-Theoretical Treatment of a Cost-Security Model for Disarmament (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 653-666 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a time-discrete dynamic model for the process of disarmament is investigated. The state variables of the system are costs and security values. We assume that the costs can be controlled, and we aim at reducing the costs to zero and achieving non-negative security values after a finite number of time steps. In the case where the opponents behave cooperatively this leads to the solution of a linear programming problem. If the opponents behave non-cooperatively, then a Nash equilibrium has to be determined under linear constraints. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 653-666 (1997).
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    On Weak Solutions to the Non-stationary van Roosbroeck's System with Discontinuous Permittivities (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 689-706 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove the existence of a weak solution to the non-stationary drift-diffusion equations (van Roosbroeck's system) of semiconductor theory involving discontinuous permittivities. The proof is based on an approximation of these equations by a system with bounded non-linearities, deriving a priori estimates on the approximate solutions and then carrying out the passage to limit. The discussion is completed by some regularity results for the weak solution under consideration. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 689-706 (1997).
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    Study of the Free Streaming Operator in Slab Geometry in Dependence of the Boundary Conditions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 717-736 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the free streaming operator T∧ in a slab domain with boundary conditions described by a linear matrix operator Λ acting between the ‘incoming’ and ‘outgoing’ particle fluxes. Under suitable assumptions on the entries of Λ, it is proved that the resolvent operator of T∧ is positive. It is proved also that T∧ is the generator of a positive strongly continuous semigroup, whose type depends on the norm of the entries of Λ. Some examples are given. In particular the case of Maxwell type boundary conditions is studied and the location of the spectrum of T∧ is improved. © 1997 by B. G. Teubner Stuttgart - John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 717-736 (1997).
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    Estimating ∇u in terms of div u, curl u, either (ν, u) or ν×u and the topology (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 737-744 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the present paper we prove Cα-estimates for ∇u using components of boundary values of u, div u, curl u and quantities given by components of boundary values of u as well as boundary values of elements belonging to de Rhams cohomology modules. The vector field u is defined on a bounded set G¯⊂∝3, meanwhile the cohomology group will be defined with regard to ∝3-G. Our inequalities turn out to be a priori estimates concerning well-known boundary value problems for vector fields. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Two-dimensional Stationary Induction Heating Problem (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 759-766 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider in this paper a system of equations modelling a steady-state induction heating process for ‘two-dimensional geometries’. Existence of a solution is stated in W1,p(Ω) Sobolev spaces and is derived using the Leray-Schauder's fixed point theory. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Functional Model for Quantum Mechanics: Unbounded Operators (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 745-757 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We extend the recently developed Riesz-Clifford monogenic functional calculus (based on Clifford analysis) for a set of unbounded non-commuting operators. Connections with quantum mechanics are discussed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Singular Problem in Electrolytes Theory (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 767-782 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions are studied. The answers to some questions concerning a generalization of a problem posed by I. Rubinstein are given. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Asymptotics as t → + ∞ of a Solution to the Periodic Cauchy Problem for the Damped Boussinesq Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 805-812 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
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    On a Non-symmetric Problem in Electrochemical Machining (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 841-854 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a free boundary value problem arising from a non-symmetric problem of electrochemical machining (ECM). After a conformal mapping of the unknown domain the problem is transformed to a non-smooth non-linear Riemann-Hilbert problem for holomorphic functions in the complex unit disk. A special technique allows to remove the singularities in the boundary condition. Utilizing existence results for smooth non-orientable Riemann-Hilbert problems, existence and uniqueness of a solution are shown. Finally, we propose an iterative method of Newton type for the effective numerical computation of the free boundary of the anode and present some test results. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    The Impedance Boundary Value Problem for the Helmholtz Equation in a Half-Plane (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 813-840 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5]. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the Finiteness of the Number of Determining Elements for von Karman Evolution Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 855-865 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the existence of a wide collection of finite sets of functionals that completely determine the long-time behaviour of strong solutions to the von Karman evolution equations. This collection contains finite sets of determining modes, nodes and local volume averages. The approach presented relies on the concept of a completeness defect for a set of linear functionals and it involves some ideas from abstract approximation theory. Our method is general enough and also can be applied to other non-linear partial differential equations which are of second order in time. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On a Boundary Value Problem of the Biharmonic Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 867-883 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we study a system of biharmonic equations coupled by the boundary conditions. These boundary conditions contain some combinations of the values, div, curl, and grad. Applications in mathematical physics are possible and the investigations will be done with the help of hypercomplex methods. It is also the aim of the paper to demonstrate the application of Clifford analytic methods to the solution of boundary value problems. The results on a special boundary value problem for the biharmonic equation will be used for the investigation of some first-order systems of partial differential equations. We study a theoretical problem connected with the ∂¯-problem and the solution of a Beltrami system by using a fixed-point iteration. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the Dirichlet Problem for the Two-dimensional Biharmonic Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 885-890 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Modified fundamental solutions are used to show that the system of boundary integral equations in a direct method for the interior Dirichlet problem for the two-dimensional biharmonic equation has at most one solution on any smooth closed boundary contour. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Singular Transmission Problem: Alfvenic Resonance in Plasmas (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 891-903 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The non-homogeneous magnetohydrodynamics equation is studied, with emphasis on the singularities due to Alfvén resonance. It is shown that for any arbitrary function defined on the singular set, there exists a unique solution of the problem coinciding with this function. Then the values on the singular set which correspond to the correct physical solution are determined proving that this is unique except for a discrete set of geometrical configurations. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On a Class of Overdetermined Eigenvalue Problems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 905-914 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we present some new results of symmetry for inhomogeneous Dirichlet eigenvalue problems overdetermined by a condition involving the gradient of the first eigenfunction on the boundary. One specificity of the problem studied is the dependence of the equation and the boundary condition on the distance to the origin. The method of investigation is based on the use of continuous Steiner symmetrization together with some domain derivative tools. An application is given to the study of an overdetermined eigenvalue problem for a wedge-like membrane. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Linear Thermoelastic Plate Equation with Dirichlet Boundary Condition (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 915-932 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the initial-boundary value problem for a linear thermoelastic plate equation and we prove that the energy associated to the system decays exponentially to zero as time goes to infinity. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Threshold Result for a Non-local Parabolic Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 933-943 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we consider the Cauchy problem:(ECP)ut-Δu+p(x)u=u(x,t)∫∝3u2(y,t)/∣x-y∣dy; x∊∝3, t〉0,u(x, 0)=u0(x)≥0 x∊∝3, (0.2)The stationary problem for (ECP) is the famous Choquard-Pekar problem, and it has a unique positive solution ū(x) as long as p(x) is radial, continuous in ∝3, p(x)≥ā〉0, and lim∣x∣→∞p(x)=p¯〉0. In this paper, we prove that if the initial data 0≤u0(x)≤(≢)ū(x), then the corresponding solution u(x, t) exists globally and it tends to the zero steady-state solution as t→∞, if u0(x)≥(≢)ū(x), then the solution u(x,t) blows up in finite time. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 84
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    The Incompressible Limit and the Initial Layer of the Compressible Euler Equation in ∝n+ (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 945-958 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the incompressible limit of the compressible Euler equation in the half-space ∝n+. It is proved that the solutions of the non-dimensionalized compressible Euler equation converge to the solution of the incompressible Euler equation when the Mach number tends to zero. If the initial data v∞0 do not satisfy the condition ‘∇⋅v∞0=0’, then the initial layer will appear. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 85
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    Stability Analysis of Navier-Stokes Flows in Annuli (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 959-978 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the linearized stability of planer flows of incompressible, viscous fluid in two-dimensional annular domains. A certain family of steady, explicit solutions which have spiral streamlines are considered. The Navier-Stokes equations are linearized at these solutions and we show analytically or numerically that these solutions are stable to perturbation of steady states, whatever the Reynolds number or the aspect ratio of the annuli may be. Hopf bifurcations from them are also examined numerically. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Homogenization of a spectral problem for a pile foundation structure (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 979-988 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The subject of this paper is the study of free oscillations of a composite material consisting of an elastic medium and a large number of elastic piles periodically immersed in a part of the medium. The ends of piles lying on the boundary of the medium are clamped to a force-free rigid plate. Such a partially composite structure arises in pile foundation mechanics. Assuming that the period of pile structure tends to zero, we obtain the macroscopic equations for free oscillations by homogenization method and prove the corresponding convergence result. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 87
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    Rawlins' problem for half-plane diffraction: its generalized eigenfunctions with real wave numbers (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 989-1014 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with a famous diffraction problem for a single half-plane Σ: x〉0, y=0 as an obstacle and for some time-harmonic plane incident wave field. Rawlins in 1975 was the first to solve the mixed (Dirichlet/Neumann) boundary value problem for the scalar Helmholtz equation. He also was the first to solve the equivalent pair of coupled Wiener-Hopf equations explicitly by factoring their discontinuous 2×2 Fourier matrix symbol in 1980. Although for real wave numbers k the usual factorization procedure fails it will serve as the basis: Following the lines given by Ali Mehmeti in his habilitation thesis [1] for the (Dirichlet/Dirichlet) boundary value problem we combine the idea of integral path deforming along the branch cuts of the characteristic square root √(ξ2-k2) given in Meister's book [13] with the modern Wiener-Hopf method solution derived by Speck [24] explicitly in a H1+ε, ε≥0, Sobolev space setting. The symmetry of the intermediate spaces Hs, H-s, ∣s∣〈1 2, which is due to generalized factorization, plays a key role in deforming the Fourier integral paths in order to get Laplace transform representations of the generalized eigenfunctions of the problem. As a remarkable fact 0〈ε〈¼ must hold here. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 88
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    Spectral theory for the wave equation in two adjacent wedges (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1015-1044 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Consider the two adjacent rectangular wedges K1, K2 with common edge in the upper halfspace of ∝3 and the operator A (=-Laplacian multiplied by different constant coefficients a1, a2 in K1, K2, respectively) acting on a subspace of ∏2j=1L2(Kj). This subspace should consist of those sufficiently regular functions u=(u1,u2) satisfying the homogeneous Dirichlet boundary condition on the bottom of the upper halfspace. Moreover, the coincidence of u1 and u2 along the interface of the two wedges is prescribed as well as a transmission condition relating their first one-sided derivatives. We interpret the corresponding wave equation with A defining its spatial part as a simple model for wave propagation in two adjacent media with different material constants. In this paper it is shown (by Friedrichs' extension) that A is selfadjoint in a suitable Hilbert space. Applying the Fourier (-sine) transformations we reduce our problem with singularities along the z-axis to a non-singular Klein-Gordon equation in one space dimension with potential step. The resolvent, the limiting absorption principle and expansion in generalized eigenfunctions of A are derived (by Plancherel theory) from the corresponding results concerning the latter equation in one space dimension. An application of the spectral theorem for unbounded selfadjoint operators on Hilbert spaces yields the solution of the time dependent problem with prescribed initial data. The paper is concluded by a discussion of the relation between the physical geometry of the problem and its spectral properties. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Global existence for degenerate parabolic equations with a non-local forcing (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1069-1087 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We establish local existence and comparison for a model problem which incorporates the effects of non-linear diffusion, convection and reaction. The reaction term to be considered contains a non-local dependence, and we show that local solutions can be obtained via monotone limits of solutions to appropriately regularized problems. Utilizing this construction, it is further shown that, under conditions of either ‘weak reaction’ or ‘sufficiently small’ initial mass, solutions exist for all time. Finally, we provide an alternative analysis of global existence and investigate blow up in finite time for the case of power law diffusion and convection. These results show the extent to which the assumption of weak reaction may be relaxed and still obtain global existence. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 90
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    Travelling waves in plasma sustained by a laser beam (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1089-1109 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: By means of the Conley connection index theory we prove existence of travelling wave solutions to a system of equations in a two temperature model of laser maintained plasma. These solutions describe locally the motion of plasma boundaries. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Multidimensional characteristic Galerkin methods for hyperbolic systems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1111-1125 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider characteristic Galerkin methods for the solution of hyperbolic systems of partial differential equations of first order. A new recipe for the construction of approximate evolution operators is given in order to derive consistent methods. With the help of semigroup theory we derive error estimates for classes of characteristic Galerkin methods. The theory is applied to the wave equation and also to the Euler equations of gas dynamics. In the latter case one can show that Fey's genuinely multidimensional method can be reinterpreted as a characteristic Galerkin method. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Stress L∞-estimates and the uniqueness problem for the quasistatic equations to the model of Bodner-Partom (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1127-1134 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper proves the uniqueness result for global in time large solutions of quasistatic equations to an inelastic model of material behavior of metals, provided that an a priori L∞-estimation for the Cauchy stress tensor holds. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Influence of the nature of modifier in the enzymatic activity of chemical modified semipurified lipase from Candida rugosa (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 252-260 
    Details
    ISSN: 0006-3592
    Keywords: lipase ; chemical modification ; stability ; esterification ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Semipurified lipase of Candida rugosa (CRSL) was subjected to chemical modification, and the activities of the modified lipase, in hydrolysis and esterification reactions, were examined. The esterification reactions were carried out in the absence and presence of isooctane. When the enzyme was modified with polyethylene glycol (PEG), two methodologies were studied. The activation of PEG with p-NO2-phenylchloroformate gives better biocatalysts than those obtained with cyanuric chloride-PEG. The chemical modification with PEG increases the stability of pure lipases in isooctane at 50°C (extreme conditions). The chemically modified enzymes are useful for biotransformations in organic solvents. In addition the nitration of tyrosines with tetranitromethane was also studied. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 252-260, 1997.
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    Effect of hypoosmotic stress on hybridoma cell growth and antibody production (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 565-570 
    Details
    ISSN: 0006-3592
    Keywords: hybridoma ; hypoosmotic stress ; specific antibody productivity ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: To investigate the response of hybridoma cells to hypoosmotic stress, S3H5/γ2bA2 and DB9G8 hybridomas were cultivated in the hypoosmolar medium [Dulbecco's modified Eagle's medium (DMEM) supplemented with 10% serum] resulting from sodium chloride subtraction. Both hybridomas showed similar responses to hypoosmotic stress in regard to cell growth and antibody production. The cell growth and antibody production at 276 mOsm/kg were comparable to those at 329 mOsm/kg (standard DMEM). Both cells grew well at 219 mOsm/kg, though their growth and antibody production were slightly decreased. When the osmolality was further decreased to 168 mOsm/kg, the cell growth did not occur. When subjected to hyperosmotic stress, both cells displayed significantly enhanced specific antibody productivity (qAb). However, the cells subjected to hypoosmotic stress did not display enhanced qAb. Taken together, both hyperosmotic and hypoosmotic stresses depressed the growth of S3H5/γ2bA2 and DB9G8 hybridomas. However, their response to hypoosmotic stress in regard to qAb was different from that to hyperosmotic stress. © 1997 John Wiley & Sons, Inc. Biotechnol Biong 55: 565-570, 1997.
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    Production of recombinant bacterial endoglucanase as a co-product with ethanol during fermentation using derivatives of Escherichia coli KO11 (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 547-555 
    Details
    ISSN: 0006-3592
    Keywords: ethanol ; cellulose ; hemicellulose ; endoglucanase ; cellulase ; lignocellulose ; biomass ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This study demonstrates a new approach to reduce the amount of fungal cellulase required for the conversion of cellulose into ethanol. Escherichia coli KO11, a biocatalyst developed for the fermentation of hemicellulose syrups, was used to produce recombinant endoglucanase as a co-product with ethanol. Seven different bacterial genes were expressed from plasmids in KO11. All produced cell-associated endoglucanase activity. KO11(pLOI1620) containing Erwinia chrysanthemi celZ (EGZ) produced the highest activity, 3,200 IU endoglucanase/L fermentation broth (assayed at pH 5.2 and 35°C). Recombinant EGZ was solubilized from harvested cells by treatment with dilute sodium dodecyl sulfate (12.5 mg/ml, 10 min, 50°C) and tested in fermentation experiments with commercial fungal cellulase (5 filter paper units/g cellulose) and purified cellulose (100 g/L). Using Klebsiella oxytoca P2 as the biocatalyst, fermentations supplemented with EGZ as a detergent-lysate of KO11(pLOI1620) produced 14%-24% more ethanol than control fermentations supplemented with a detergent-lysate of KO11(pUC18). These results demonstrate that recombinant bacterial endoglucanase can function with fungal cellulase to increase ethanol yield during the simultaneous saccharification and fermentation of cellulose. © 1997 Wiley & Sons, Inc. Biotechnol Bioeng 55: 547-555, 1997.
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    Engineering mRNA stability in E. coli by the addition of synthetic hairpins using a 5′ cassette system (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 577-580 
    Details
    ISSN: 0006-3592
    Keywords: mRNA stability ; hairpins ; gene expression control ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An expression system has been developed for the introduction of DNA cassettes into the region between the transcription and translation start sites of a gene of interest. This cassette system was used to engineer mRNA stability through the introduction of hairpins at the 5′ end. A synthetic DNA cassette was designed so that the resulting mRNA hairpin would be positioned one nucleotide from the 5′ mRNA end. The hairpin-containing mRNA exhibited a half-life 3 times that of the mRNA with no hairpin, resulting in increases in both mRNA and protein levels. These results indicate that it is possible to engineer mRNA stability as an additional means of controlling gene expression. © 1997 John Wiley & Sons Inc. Biotechnol Bioeng 55: 557-580, 1997
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    Application of membrane-based preferential transport to whole broth processing (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 581-591 
    Details
    ISSN: 0006-3592
    Keywords: adsorptive membranes ; oscillatory flow ; integrated processes ; in situ product recovery ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Preferential transport in adsorptive membranes can be used to selectively remove biochemicals directly from fermentation broths. During preferential transport, an adsorbing solute is selectively transported across the membrane while nonadsorbing solutes and cells are retained by the membrane. This technique was used to separate lysozyme directly from a feed containing lysozyme, myoglobin, and yeast cells. We found that because the oscillatory flows used in preferential transport involve strokes that are close to symmetric, they are very efficient in alleviating cake formation due to cell deposition on the membrane surface. Theoretical results suggest that, by optimizing process variables, preferential transport can lead to a continuous concentrated stream of the adsorbing protein. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 581-591, 1997.
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    In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae: II. Mathematical model (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 592-608 
    Details
    ISSN: 0006-3592
    Keywords: Saccharomyces cerevisiae ; metabolic modeling ; sensitivity analysis ; glycolysis ; compartmentation ; transient response ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model of glycolysis in Saccharomyces cerevisiae is presented. The model is based on rate equations for the individual reactions and aims to predict changes in the levels of intra- and extracellular metabolites after a glucose pulse, as described in part I of this study. Kinetic analysis focuses on a time scale of seconds, thereby neglecting biosynthesis of new enzymes. The model structure and experimental observations are related to the aerobic growth of the yeast. The model is based on material balance equations of the key metabolites in the extracellular environment, the cytoplasm and the mitochondria, and includes mechanistically based, experimentally matched rate equations for the individual enzymes. The model includes removal of metabolites from glycolysis and TCC for biosynthesis, and also compartmentation and translocation of adenine nucleotides. The model was verified by in vivo diagnosis of intracellular enzymes, which includes the decomposition of the network of reactions to reduce the number of parameters to be estimated simultaneously. Additionally, sensitivity analysis guarantees that only those parameters are estimated that contribute to systems trajectory with reasonable sensitivity. The model predictions and experimental observations agree reasonably well for most of the metabolites, except for pyruvate and adenine nucleotides. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 592-608, 1997.
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    A novel membrane reactor design for controlled studies of interacting populations (simulation of the interaction between microorganism and plant suspension cultures) (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 609-615 
    Details
    ISSN: 0006-3592
    Keywords: interacting populations ; membrane reactor ; induced metabolic changes ; elicitation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The design of a reactor in which two interacting cell populations (microorganisms and plants) could grow under controlled conditions was considered. In this reactor, the cell populations are separated by a membrane which permits semi-in vivo study of induced interaction-specific changes in metabolism. In this paper, the interaction of suspension culture of Nicotiana tabacum (tobacco) and the Oomycete, Phytophthora nicotiana was simulated. The results of the computer simulation show the induced metabolic changes as a consequence of the biological interaction. The paper introduces a novel approach in the strategy for the study of interacting population in suspension cultures. This type of system has potential applications in studies of the regulation of secondary metabolism and for the production of high values pharmaceuticals. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 609-615, 1997.
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    Application of fluid mechanic and kinetic models to characterize mammalian cell detachment in a radial-flow chamber (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 55 (1997), S. 616-629 
    Details
    ISSN: 0006-3592
    Keywords: cell adhesion ; radial-flow chamber ; hydrodynamic shear ; detachment kinetics ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The strength of adhesion and dynamics of detachment of murine 3T3 fibroblasts from self-assembled monolayers were measured in a radial-flow chamber (RFC) by applying models for fluid mechanics, adhesion strength probability distributions, and detachment kinetics. Four models for predicting fluid mechanics in a RFC were compared to evaluate the accuracy of each model and the significance of inlet effects. Analysis of these models indicated an outer region at large radial positions consistent with creeping flow, an intermediate region influenced by inertial dampening, and an inner region dominated by entrance effects from the axially-oriented inlet. In accompanying experiments patterns of the fraction of cells resisting detachment were constructed for individual surfaces as a function of the applied shear stress and evaluated by comparison with integrals of both a normal and a log-normal distribution function. The two functions were equally appropriate, yielding similar estimates of the mean strength of adhesion. Further, varying the Reynolds number in the inlet, Red, between 630 and 1480 (corresponding to volumetric flow rates between 0.9 and 2.1 mL/s) did not affect the mean strength of adhesion. For these same experiments, analysis of the dynamics of detachment revealed three temporal phases: 1) rapid detachment of cells at the onset of flow, consistent with a first-order homogeneous kinetic model; 2) time-dependent rate of detachment during the first 30 sec. of exposure to hydrodynamic shear, consistent with the first-order heterogeneous kinetic model proposed by Dickinson and Cooper (1995); and 3) negligible detachment, indicative of pseudo-steady state after 60 sec. of flow. Our results provide rigorous guidelines for the measurement of adhesive interactions between mammalian cells and prospective biomaterial surfaces using a RFC. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 616-629, 1997.
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