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Year
  • 1
    ISSN: 1434-193X
    Keywords: 1β-Methylcarbapenems ; Palladium ; Ruthenium ; Catalysis ; Cyclizations ; Stereoselective hydrogenation ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: -An efficient diastereoselective multi-step synthesis of bicyclic 1β-methylcarbapenem antibiotic precursors has been developed, starting from the commercially available 4-acetoxyazetidin-2-one 4. Chiral ruthenium catalysts are used in the hydrogenation step to control the β-stereochemistry at the 1-position, and a π-allylpalladium ring-closure strategy is used to form the functionalized carbapenem skeleton.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1434-193X
    Keywords: Cyclocarbonylation ; Alkynes ; Catalysis ; Palladium ; Vinyl triflates ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: -o-Ethynylphenols react with vinyl triflates, in the presence of tetrakis(triphenylphosphane)palladium(0) and under carbon monoxide, to form 3-alkylidene-2-coumaranones in good yield.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1434-193X
    Keywords: Chirality ; Catalysis ; Amino acids ; Crown ethers ; Heterocyclic compounds ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The enantioselectivity exerted by a new series of chiral catalysts containing N,O-heterocycles of different sizes has been checked in the addition of diethylzinc to benzaldehyde, which was used as a model reaction. The catalysts were derived from natural amino acids, following a relatively simple procedure, and in several cases excellent ee values were obtained. The results were complementary since ee's ranged from 98% (R) to 94% (S) excesses of the final 1-phenylpropan-1-ol. Molecular mechanics calculations suggested that the production of the R alcohol may be explained by a mechanism similar to that described by Noyori, in which ZnEt2 interacts solely with the N-C-C-OH fragment, whereas the formation of the S enantiomer needed the direct participation of the lateral chain of the parent amino acid and the N,O-heterocycle.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1434-193X
    Keywords: Cerium(III) chloride heptahydrate ; Catalysis ; 1,3-Dicarbonyl compounds ; Enones ; Michael reactions ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: -Cerium(III) chloride heptahydrate in the presence of sodium iodide catalyses the Michael addition of 1,3-dicarbonyl compounds to α,β-unsaturated ketones and α,β-unsaturated aldehydes with extraordinary efficiency. The very mild conditions allow high chemoselectivity as shown by the absence of the typical side reactions, which can be observed in the conventional base-catalyzed processes. More interestingly, when at least one of the starting materials is liquid at room temperature, the reaction can also be performed without solvents. The CeCl3· 7 H2O/NaI catalyst system can be easily separated from the reaction mixture and it can be reused without an appreciable loss of activity. Advantages of the present procedure, which utilizes cheap and “friendly” reagents, over the previously reported ones, are discussed.
    Additional Material: 1 Ill.
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  • 5
    ISSN: 1434-193X
    Keywords: Hydroaminomethylation ; Rhodium ; Catalysis ; Carbonylation ; Heterofunctionalised allylic compounds ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: -Heterofunctionalised allylic ethers 1, silanes 5, and amines 9 are hydroformylated in the presence of primary or secondary amines 2 to form the corresponding γ-amino- and δ-amino-functionalised compounds. The rhodium(I)-catalysed reaction sequence proceeds by aldehyde formation and subsequent reductive amination to generate the corresponding functionalised secondary or tertiary amines. This selective one-pot hydroaminomethylation procedure establishes access to γ-amino- and δ-amino-functionalised ethers, amines or silanes with potential biological activity.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1999 (1999), S. 1767-1770 
    ISSN: 1434-193X
    Keywords: Baeyer-Villiger reaction ; Lactones ; Methyltrioxorhenium ; Catalysis ; Oxidations ; Cyclobutanones ; Ketones ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: γ-Butyrolactones were obtained in good yields and high regioselectivity by a Baeyer-Villiger oxidation with H2O2 catalysed by methyltrioxorhenium. The lactonization was chemoselective in the presence of double bonds, aromatic rings, and chlorine substituents. A trimethylsiloxy-substituted ketone was converted directly into a hydroxylated lactone in good yield and regioselectively.
    Additional Material: 1 Tab.
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  • 7
    ISSN: 1434-193X
    Keywords: Amino alcohols ; Polymers ; Enantioselective reagents ; Catalysis ; Merrifield resins ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Starting from simple amino acid esters and Merrifield resins, a small library of polymer-bound chiral-β-amino alcohols can be prepared. By reaction with LiALH4 the corresponding chiral reducing agents are obtained, having structural variations at both the α and β positions. All supported reagents are able to reduce acetophenone to 1-phenylethanol. Enantioselectivity is observed when the steric hindrance in the chiral fragment is increased. Best results are obtained for the supported derivative of α,α-diphenyl phenylalaninol.
    Additional Material: 2 Tab.
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  • 8
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1999 (1999), S. 2219-2230 
    ISSN: 1434-193X
    Keywords: Retrodisproportionation ; Arenes ; EPR spectroscopy ; Thermochemistry ; Coal liquefaction ; Catalysis ; Hydrogen transfer ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The transfer of hydrogen from excess 9,10-dihydroanthracene (DHA) to acceptors such as α-methylstyrene is catalyzed, i.e. occurs at temperatures in the range 200-260 °C instead of 280-320 °C, when hydrocarbons with weaker C-H bonds than DHA, e.g. 6H-benzo[cd]pyrene (4), 7H-dibenzo[a,kl]anthracene (5), 4-methyl-7H-benzo[de]naphthacene (6) or 8H-dibenzo[b,fg]pyrene (7), are added to the reaction mixture. The reactions are initiated by bimolecular H-atom transfer from 4-7 to the acceptor (retrodisproportionation) and proceed by nonchain radical mechanisms. This is supported by isotopic labelling and kinetic isotope effects, substituent and solvent effects, EPR spectroscopy of intermediate radicals, and by a comparison of the thermochemical and kinetic characteristics of these reactions.
    Additional Material: 7 Ill.
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  • 9
    ISSN: 1434-193X
    Keywords: Carbene complexes ; Catalysis ; Metallahexatrienes ; Vinyl cyclopentadienes ; Transmetallation ; Rhodium ; Tungsten ; Chromium ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We report on the first example of a transition metal-catalyzed cyclization reaction of a Fischer carbene complex. It comprises the generation of vinyl- and divinyl cyclopentadienes under exceedingly mild conditions at 20 °C by condensation of (1-amino-1,3-butadien-2-yl)carbene complexes (= cross-conjugated metallahexatrienes) (CO)5M=C(OEt)C(=CHNR2)CR1=CHR23 (M = Cr, W) with alkynes R3C≡CH 4 (R3 = Ph, cyclohex-1-enyl, isopropenyl, methoxymethyl, 1-trimethylsiloxycyclohex-1-yl) in the presence of catalytic amounts of [(COD)RhCl]2. The starting compounds 3 are accessible in high yields by addition of enamines (E)-R2NCH=CHR22 to (1-alkynyl)carbene complexes (CO)5M=C(OEt)C≡CR11 (M = Cr, W; R1 = Ph, cyclohex-1-enyl).
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1999 (1999), S. 1421-1426 
    ISSN: 1434-193X
    Keywords: Anhydrides ; Coupling reaction ; Enols ; Palladium ; Tin ; Catalysis ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: -A new three-step synthesis of diarylmaleic anhydrides 6, starting from 3-aryl-2-hydroxybut-2-enedioates 2, is reported.
    Additional Material: 1 Ill.
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  • 11
    ISSN: 1434-193X
    Keywords: Alkenes ; Epoxidation ; Manganese ; Porphyrins ; Catalysis ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of MnIII porphyrins progressively halogenated in the β-pyrrolic positions was employed to catalyse the epoxidation of cis-stilbene by iodosylbenzene, and to study the role of the electronic effects on the stereoselectivity of this process. A gradual improvement in the stereoselectivity on increasing the number of β-halogen atoms was observed. The role of steric effects upon the epoxidation was also investigated by placing ortho-substituents in the meso-phenyl rings, and it was found that steric effects are more important than electronic effects toward the stereoselectivity of this process. These results can be rationalised by proposing a competition between a nonstereoselective electrophilic pathway of addition and a stereospecific pathway of oxygen insertion, the former being disfavoured by electron-withdrawing substituents. Alternatively, the formation of an open intermediate between the MnV oxene and the substrate could be suggested, where the stereoselectivity ought to be determined by the competition between closure of the epoxide ring and rotation around the C-C bond. In this case, the enhanced stereoselectivity given by our polyhalogenated porphyrins might be attributed to an acceleration of the epoxide ring closure caused by the electron-withdrawing effect of the halogen substituents.
    Additional Material: 1 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1-24 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the large time asymptotics of solutions u(x, t) of the wave equation with time-harmonic force density f(x)e-iωt, ω≥0, in the semi-strip Ω= (0, ∞)×(0, 1) for a given f∊C∞0(Ω). We assume that u satisfies the initial condition u=(∂/∂t)u=0 for t=0 and the boundary conditions u=0 for x2=0 and x2=1, and (∂/∂x1)u=αu for x1=0, with given α, -π≤α〈∞. Let Dα be the self-adjoint realization of -Δ in Ω with this boundary condition. For -π≤α〈0, Dα has eigenvalues λj=π2j2-α2, j=1, 2, … For j≥2 these eigenvalues are embedded in the continuous spectrum of Dα, σc(Dα)=[π2, ∞]. For α≥0, Dα has no eigenvalues. We consider the asymptotic behaviour of u(x, t), t→∞, as a function of α. In the case α=0 resonances of order √t at ω=πj, j=1, 2, …, were found in References 5 and 10. We prove that for α=-π there is a resonance of order t2 for ω=0 and resonances of order t for every ω〉0 (note that 0 is an eigenvalue of D-π). Moreover, for -π〈α〈0 there are resonances of order t at ω=√λj. The resonance frequencies are continuous functions of α for -π〈α〈0 and tend to πj, j=1, 2, … as α goes to zero.On the contrary in the case α〉0 there are no real resonances in the sense that the solution remains bounded in time as t→∞. Actually in this case, the limit amplitude principle is valid for all frequencies ω≥0. This rather striking behaviour of the resonances is explained in terms of the extension of the resolvent R(κ)=(Dα-κ2)-1 as a meromorphic function of κ into an appropriate Riemann surface. We find that as α crosses zero the real poles of R(κ) associated with the eigenvalues remain real, but go into a second sheet of the Riemann surface. This behaviour under perturbation is rather different from the case of complex resonances which has been extensively studied in the theory of many-body Schrödinger operators where the (real) eigenvalues embedded in the continuous spectrum turn under a small perturbation into complex poles of the meromorphic extension of the resolvent, as a function of the spectral parameter κ2. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 117-128 
    ISSN: 0170-4214
    Keywords: third-grade fluid ; existence ; uniqueness ; classical solution ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The global existence and uniqueness of classical solution of steady motions of a third-grade fluid provided assumptions on positivness of μ (coefficient of viscosity) and α1, γ (material coefficients) is proved. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 227-249 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Integral equations associated with the basic boundary value problems for the Laplace and Stokes equations are considered. The integral operators for these integral equations are interpreted as the pseudodifferential operators, and their principal symbols are calculated. The symbols are obtained in terms of the principal curvatures and the coefficients of the first quadratic form of the boundary. As a consequence, the initial approximation is suggested for the iterative methods solving the integral equations. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 327-359 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The boundary integral equation method is used to prove the convergence of the Drude-Born-Fedorov equations with variable coefficients, possibly non-smooth, to Maxwell's equations as chirality admittance tends to zero. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 565-588 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: New explicit stability conditions are derived for a linear integro-differential equation with periodic operator coefficients. The equation under consideration describes oscillations of thin-walled viscoelastic structural members driven by periodic loads. To develop stability conditions two approaches are combined. The first is based on the direct Lyapunov method of constructing stability functionals. It allows stability conditions to be derived for unbounded operator coefficients, but fails to correctly predict the critical loads for high-frequency excitations. The other approach is based on transforming the equation under consideration in such a way that an appropriate ‘differential’ part of the new equation would possess some reserve of stability. Stability conditions for the transformed equation are obtained by using a technique of integral estimates. This method provides acceptable estimates of the critical forces for periodic loads, but can be applied to equations with bounded coefficients only. Combining these two approaches, we derive explicit stability conditions which are close to the Floquet criterion when the integral term vanishes. These conditions are applied to the stability problem for a viscoelastic bar compressed by periodic forces. The effect of material and structural parameters on the critical load is studied numerically. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 5 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 653-664 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In order to maintain spectrally accurate solutions, the grids on which a non-linear physical problem is to be solved must also be obtained by spectrally accurate techniques. The purpose of this paper is to describe a pseudospectral computational method of solving integro-differential systems with quadratic performance index. The proposed method is based on the idea of relating grid points to the structure of orthogonal interpolating polynomials. The optimal control and the trajectory are approximated by the m th degree interpolating polynomial. This interpolating polynomial is spectrally constructed using Legendre-Gauss-Lobatto grid points as the collocation points, and Lagrange polynomials as trial functions. The integrals involved in the formulation of the problem are calculated by Gauss-Lobatto integration rule, thereby reducing the problem to a mathematical programming one to which existing well-developed algorithms may be applied. The method is easy to implement and yields very accurate results. An illustrative example is included to confirm the convergence of the pseudospectral Legendre method, and a comparison is made with an existing result in the literature. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 2 Tab.
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 701-718 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article establishes the existence of a trapped-mode solution to a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls; the forces of gravity and surface tension are operative. A trapped mode corresponds to an eigenvalue of the composition of an inverse differential operator and a Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by extending previous results dealing with the case when surface tension is absent. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 501-517 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper an initial-boundary-value problem in one-space dimension is studied for the Broadwell model extended to a gas mixture undergoing bimolecular reactions. Techniques of semigroup of bounded positive operators in a suitable Banach space are used to prove existence and uniqueness of the solution on bounded time intervals whose length depends on the initial data. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 685-700 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the present work, the problem of electromagnetic wave propagation in three-dimensional stratified media is studied. The method of decoupling the electric and magnetic fields is implemented, and the spectral approach is adopted, componentwise, to the vector equation involving the electric field. Operational calculus of self-adjoint, positive operators in suitable Hilbert spaces is used to solve the corresponding initial value problems. The spectral families of these operators for the cases of the whole space and of a finite layer are constructed. A discussion on the applicability of the obtained results to physical problems is also included. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 757-780 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove under the assumption of small initial data the global existence of a classical solution to the equations in viscoelasticity, associated with a free damping boundary condition. We also show that if we choose the initial data large enough, blow up will occur in finite time. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 797-821 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the thermoelastic plate system,utt-γΔutt+Δ2u+αΔθ=0,θt-κΔθ-αΔut=0 and we make a comparison between the models in which γ=0 and γ〉0. We conclude that in the first case the plate system is of a parabolic type, while when γ〉0 the corresponding system has a hyperbolic behaviour. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 23
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 883-894 
    ISSN: 0170-4214
    Keywords: solitary wave ; stability ; long wave-short wave resonance equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper concerns the orbital stability for solitary waves of the Long Wave-Short Wave resonance equations. Since the abstract results of Grillakis et al. [7, 8] cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 24
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1049-1066 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider particle transport in a three-dimensional convex region V, bounded by the regular surface ∂V. We assume that particles are specularly reflected by ∂V and that a source q is assigned on ∂V; more general non-homogeneous boundary conditions are also discussed. The problem is non-linear because the boundary condition is not homogeneous. We prove existence of a unique strict solution and by using the theory of semigroups we derive the explicit expression of such a solution in terms of the boundary source q. In the appendix, we indicate how some properties of affine operators can be used to derive the solution. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1085-1105 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A phase-field model based on the Coleman-Gurtin heat flux law is considered. The resulting system of non-linear parabolic equations, associated with a set of initial and Neumann boundary conditions, is studied. Existence, uniqueness, and regularity results are proved. An asymptotic analysis is also carried out, in the case where the coefficient of the interfacial energy term tends to 0. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 26
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1115-1148 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We apply the Child-Langmuir asymptotics of the Vlasov-Poisson system to the case of a bipolar diode, i.e. a vacuum diode where two species of particles of opposite electric charge are flowing. This leads to a simplified model which, if at least one of the two injected currents is not too large, has a unique solution. Moreover, in that case, the currents flowing inside the diode are limited by the so-called bipolar Child-Langmuir currents. In the case of large currents, other solutions may appear, and the formation of virtual electrodes may occur inside the diode. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
    Additional Material: 3 Ill.
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  • 27
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1107-1113 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the Cauchy problem for the equation∂u/∂t + u ∂u/∂x + u/x = 0 for x 〉 0, t ≥ 0, with u(x, 0) = u0-(x) for x 〈 x0, u(x, 0) = u0+(x) for x 〉 x0, u0-(x0) 〉 u0+(x0). Following the ideas of Majda, 1984 and Lax, 1973, we construct, for smooth u0- and u0+, a global shock front weak solution u(x, t) = u-(x, t) for x 〈 φ(t), u(x, t) = u+(x, t) for x 〉 φ(t), where u- and u+ are the strong solutions corresponding (respectively) to u0- and u0+ and the curve t → φ(t) is defined by dφ/dt (t) = 1/2[u-(φ(t), t) + u+(φ(t), t)], t ≥ 0 and φ(0) = x0.© 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 28
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1195-1206 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A variational approach to a non-linear non-local identification problem related to the non-linear transport equation is studied. Introducing a similarity transformation, the problem is formulated as an identification problem for a non-linear differential equation of second order with an additional non-local condition. For the solution of the forward problem stability in H1-norm with respect to the identification parameter is obtained. Using this result the existence of a solution to the identification problem is proved. Some results of computational experiments are given. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 29
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1233-1267 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the plate equation in a polygonal domain with free edges. Its resolution by boundary integral equations is considered with double layer potentials whose variational formulation was given in Reference 25. We approximate its solution (u, (∂u/∂n)) by the Galerkin method with approximated spaces made of piecewise polynomials of order 2 and 1 for, respectively, u and (∂u/∂n). A prewavelet basis of these subspaces is built and equivalences between some Sobolev norms and discrete ones are established in the spirit of References 14, 16, 30 and 31. Further, a compression procedure is presented which reduces the number of nonzero entries of the stiffness matrix from O(N2) to O(N log N), where N is the size of this matrix. We finally show that the compressed stiffness matrices have a condition number uniformly bounded with respect to N and that the compressed Galerkin scheme converges with the same rate than the Galerkin one. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 30
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1287-1296 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The relativistic Vlasov-Maxwell-Fokker-Planck system is used in modelling distribution of charged particles in plasma. It consists of a transport equation coupled with the Maxwell system. The diffusion term in the equation models the collisions among particles, whereas the viscosity term signifies the dynamical frictional forces between the particles and the background reservoir. In the case of one space variable and two momentum variables, we prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 31
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1415-1439 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider reactive mixtures of dilute polyatomic gases in full vibrational non-equilibrium. The governing equations are derived from the kinetic theory and possesses an entropy. We recast this system of conservation laws into a symmetric conservative form by using entropic variables. Following a formalism developed by the authors in a previous paper, the system is then rewritten into a normal form, that is, in the form of a quasilinear symmetric hyperbolic-parabolic system. Using a result of Vol'pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 32
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1479-1494 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Approximate solutions of the non-linear Boltzmann equation, which have the structure of the linear combination of three global Maxwellians with arbitrary hydrodynamical parameters, are considered. Some sufficient conditions which allow the error between the left- and the right-hand sides of the equation tend to zero, and which are calculated either in the mixed metric or in the pure integral metric, are obtained. The class of the distributions, which minimized this error for the arbitrary Knudsen number, is found. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 33
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1519-1542 
    ISSN: 0170-4214
    Keywords: non-hyperbolic systems ; two-phase flows ; dispersion terms ; symmetrization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers a system of partial differential equations of convection dispersion type, modelling a stratified two-phase fluid flow. Local existence in time is proved for a sufficiently smooth initial data, given in the set of physically admissible states. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1559-1569 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study the motion of an elastic conducting wire in a magnetic field. The motion of the conductor induces a current in the wire (Faraday's law) which, in turn produces a force on the wire. We consider the linear equation obtained by linearizing the resulting equations of motion about an equilibrium solution. This is a hyperbolic partial differential equation with a non-local term. We prove existence and uniqueness of a weak solution of an initial-boundary value problem for this equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 35
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1637-1654 
    ISSN: 0170-4214
    Keywords: generalized Stokes equations ; incompressible flow ; least-squares ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity-stress-pressure formulation) in six equations and six unknowns together with Riemann-Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H1 product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L2-norm and in the H1-norm. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 36
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1619-1635 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the two-parameter non-linear Sturm-Liouville problems. By using the variational method on general level sets, the variational eigenvalues are obtained. The purpose of this paper is to study the properties of these variational eigenvalues with respect to the parameter of general level sets. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 37
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 187-226 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the limit behaviour of solution of Poisson's equation in a class of thin two-dimensional domains, both simply connected or single-hollowed, as its thickness becomes very small. The method is based on a transformation of the original problem into another posed on a fixed domain, obtention of a priori estimates and convergence results when thickness parameter tends to zero. As an important application of abstract results we obtain the limit expressions for functions appearing in elastic beam theories as torsion and warping functions. In this way, we provide a mathematical justification and a correct definition of torsion, warping and Timoshenko functions and constants that should be used in the open and closed thin-walled elastic beam theories. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 38
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 269-279 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The generalized Möbius function and Möbius inversion formula are applied to a multiplicative semigroup. A general mathematical method based on this Möbius inversion is presented to solve inversion problems of expansions with unequally weighted terms. By this method, all the inverse lattice problems in physics can be solved concisely. The solutions of four inverse lattice problems: the Fibonacci structure, the square lattice structure, the bcc and the hcp lattice structures are given. These are difficult to be solved by other methods. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 39
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 361-374 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use the eigenfunction expansion of Green's function of Dirichlet problems to obtain sampling theorems. The analytic properties of the sampled integral transforms as well as the uniform convergence of the sampling series are proved without any restrictions on the integral transforms. We obtain a one- and multi-dimensional versions of sampling theorems. In both cases the sampling series are written in terms of Lagrange-type interpolation expansions. Some examples and the truncation error as well as the stability of the obtained sampling expansions are discussed at the end of the paper. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 40
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 393-416 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a dynamical von Kármán system in the presence of thermal effects. Our model includes the possibility of a rotational inertia term in the system. We show that the total energy of the solution of such system decays exponentially as t→+∞. The decay rates we obtain are uniform on bounded sets of the energy space. The main ingredients of our method of proof are suitable properties of a decoupled system, the energy method and the compactness of the nonlinear map associated to the von Kármán system. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 41
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 479-488 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This short article discusses the spectrum of the Neumann Laplacian in the infinite domain Ω⊂∝n, n ≥2 created by inserting a compact obstacle P into the uniform cylinder Ω0 =(-∞, ∞)×Ω′. The main result is the existence of at least one embedded eigenvalue when P is an (n -2)-dimensional surface whose unit normal is parallel to Ω′ at each point of P . The special case when P is symmetric about {0}×Ω′ is also treated. It is shown that there is at least one symmetric eigenvector and, when P is sufficiently long, at least one antisymmetric eigenvector. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 42
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 551-564 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the existence of solutions to the three-dimensional elastoplastic problem with Hencky's law and Neumann boundary conditions by elliptic regularization and the penalty method, both for the case of a smooth boundary and of an interior two dimensional crack. It is shown, in particular, that the variational solution satisfies all boundary conditions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 43
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 251-268 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The propagation of Hölder regularity of the solutions to the 3D Euler equations is discussed. Our method is a special semi-linearization of the vorticity equation combined with the classical Schauder interior estimates. © 1998 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 44
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 433-461 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the solution of Maxwell equations in the modelling of the scattering of a time-harmonic electromagnetic wave by an obstacle located in a two-layered medium. The use of the Silver-Müller radiation condition in each layer is shown to provide a well-posed scattering problem. The analysis is based on the study of the Green tensor, which allows to relate the radiation condition to an integral representation formula. The analyticity properties of the scattering problem with respect to the frequency are then investigated. This gives rise to a limiting absorption principle and furnishes a characterization of the resonances. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 45
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 489-499 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We apply our recently developed distributional technique [2, 3] to study time-domain asymptotics. This enables us to present a rigorous mathematical discussion and extensions of the results given by Chapman [1] and subsequent workers in this field. The present analysis is facilitated by defining functions which are distributionally small at infinity. We find that one of the advantages of using this technique is that multidimensional extensions can be derived very easily. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 46
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 519-549 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with a specific finite element strategy for solving elliptic boundary value problems in domains with corners and edges. First, the anisotropic singular behaviour of the solution is described. Then the finite element method with anisotropic, graded meshes and piecewise linear shape functions is investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates for functions from anisotropically weighted spaces are derived. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 47
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 605-617 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a general method of analysis for investigating the whirl stability of a rotor-bearing system whose appendage is flexibly attached to the spinning shaft. Sufficient conditions of asymptotic stability involving system different parameters are derived based on Liapunov's theory. An inclusive analysis of the effect of the combined flexibilities of the elastic attachment of the appendage to the shaft and the two end bearings coupled with the other various parameters of the system on the dynamic stability is presented. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 48
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 665-684 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the steady compressible Navier-Stokes equations near the equilibrium state v = 0, ρ = ρ0 (v the velocity, ρ the density) corresponding to a large potential force. We introduce a method of decomposition for such equations: the velocity field v is split into a non-homogeneous incompressible part u (div (ρ0u) = (0) and a compressible (irrotational) part ∇φ. In such a way, the original complicated mixed elliptic-hyperbolic system is split into several ‘standard’ equations: a Stokes-type system for u, a Poisson-type equation for φ and a transport equation for the perturbation of the density σ = ρ - ρ0. For ρ0 = const. (zero potential forces), the method coincides with the decomposition of Novotny and Padula [21]. To underline the advantages of the present approach, we give, as an example, a ‘simple’ proof of the existence of isothermal flows in bounded domains with no-slip boundary conditions. The approach is applicable, with some modifications, to more complicated geometries and to more complicated boundary conditions as we will show in forthcoming papers. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 49
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 619-651 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider acoustic scattering from an obstacle inside an inhomogeneous structure. We prove in the paper that if the outside inhomogeneity is known then the obstacle and possible inside inhomogeneity are uniquely determined by the fixed energy far field data. The proof is based on new mapping properties of layer potentials in spaces that specify one point. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 939-967 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The linear problem for the velocity potential around a slightly curved thin finite wing is considered under the Joukowskii-Kutta hypothesis. The exponents of possible singularities of solutions at angular points on wing's trailing edge are expressed in terms of eigenvalues of mixed boundary value problems for the Beltrami-Laplace operator on the hemisphere and the semicircle. These singularities have a structure such that the circulation function turns out to be continuous in interior angular points of the trailing edge. In the case of trapezoidal shape of the wing ends there occur square-root singularities of the velocity field at the trailing edge endpoints and the same singularities, of course, are extended along the lateral sides of the wake behind the wing. It is proved that for any angular point on the trailing edge the exponents of all above-mentioned singularities form a countable set in the upper complex half-plane with the only accumulation point at infinity. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 985-1014 
    ISSN: 0170-4214
    Keywords: Vlasov-Poisson-Fokker-Planck ; long-time behaviour ; fundamental solutions ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the long-time behaviour of solutions of the Vlasov-Poisson-Fokker-Planck equation for initial data small enough and satisfying some suitable integrability conditions. Our analysis relies on the study of the linearized problems with bounded potentials decaying fast enough for large times. We obtain global bounds in time for the fundamental solutions of such problems and their derivatives. This allows to get sharp bounds for the decay of the difference between the solutions of the Vlasov-Poisson-Fokker-Planck equation and the solution of the free equation with the same initial data. Thanks to these bounds, we get an explicit form for the second term in the asymptotic expansion of the solutions for large times. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1067-1084 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An initial-value problem modelling coagulation and fragmentation processes is studied. The results of earlier papers are extended to models where either one or both of the rates of coagulation and fragmentation depend on time. An abstract integral equation, involving the solution operator to the linear fragmentation part, is investigated via the contraction mapping principle. A unique global, non-negative, mass-conserving solution to this abstract equation is shown to exist. The latter solution is used to generate a global, non-negative, mass-conserving solution to the original non-autonomous coagulation and multiple-fragmentation equation. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1185-1194 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove the global existence and study decay property of the solutions to the initial boundary value problem for the quasi-linear wave equation with a dissipative term without the smallness of the initial data. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1207-1226 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Reaction random-walk systems are hyperbolic models to describe spatial motion (in one dimension) with finite speed and reactions of particles. Here we present two approaches which relate reaction random-walk equations with reaction diffusion equations. First, we consider the case of high particle speeds (parabolic limit). This leads to a singular perturbation analysis of a semilinear damped wave equation. A initial layer estimate is given. Secondly, we consider the case of a transcritical bifurcation. We use techniques similar to that of the Ginzburg-Landau method to find a modulation equation for the amplitude of the first unstable mode. It turns out that the modulation equation is Fisher's equation, hence near the bifurcation point travelling wave solutions are obtained. The approximation result and the corresponding estimate is given in terms of the bifurcation parameter. Both results are based on an a priori estimate for classical solutions which follows from explicit representations of the solution of the linear telegraph equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1365-1377 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the article the problem of regulation of the cardiovascular system is investigated from the point of view of control process theory. This problem was reduced to finding the optimal control in the sense of speed in a bilinear system. In the first part of the article the possibility of applying Saburov's method for the solution to bilinear control problems is considered. The second part of the article is devoted to the application of this method to a concrete problem from practical medicine. The method has allowed the complete synthesis of an optimal control to be carried out  -  the sliding mode takes place and it was investigated completely. The results obtained are interesting from the point of view of control process theory, and testify to the high efficiency of the method. The final results allow concrete recommendations about the regulation of the cardiovascular system. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1399-1413 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The steady-state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot be expected for physical reasons. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1343-1363 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider an elastic plate with the non-deformed shape ΩΣ := Ω \ Σ, where Ω is a domain bounded by a smooth closed curve Γ and Σ ⊂ Ω is a curve with the end points {γ1, γ2}. If the force g is given on the part ΓN of Γ, the displacement u is fixed on ΓD := Γ \ ΓN and the body force f is given in Ω, then the displacement vector u(x) = (u1(x), u2(x)) has unbounded derivatives (stress singularities) near γk, k = 1, 2   u(x) = ∑2k, l=1 Kl(γk)r1/2kSCkl(θk) + uR(x)     near γk.Here (rk, θk) denote local curvilinear polar co-ordinates near γk, k = 1, 2, SCkl (θk) are smooth functions defined on [-π, π] and uR(x) ∊ {H2(near γk)}2. The constants Kl(γk),   l = 1, 2, which are called the stress intensity factors at γk (abbr. SIFs), are important parameters in fracture mechanics. We notice that the stress intensity factors Kl(γk) (l = 1, 2;  k = 1, 2) are functionals Kl(γk) = Kl(γk; L, Ω, Σ) depending on the load L, the shape of the plate Ω and the shape of the crack Σ. We say that the crack Σ is safe, if Kl(γk; Ω)2 + K2(γk; Ω)2 〈 RẼ. By a small change of Ω the shape Σ can change to a dangerous one, i.e. we have K1(γk; Ω)2 + K2(γk; Ω)2 ≥ RẼ. Therefore it is important to know how Kl(γk) depends on the shape of Ω.For this reason, we calculate the Gâteaux derivative of Kl(γk) under a class of domain perturbations which includes the approximation of domains by polygonal domains and the Hadamard's parametrization Γ(τ) := {x + τφ(x)n(x);  x ∊ Γ}, where φ is a function on Γ and n is the outward unit normal on Γ. The calculations are quite delicate because of the occurrence of additional stress singularities at the collision points {γ3, γ4} = ΓD ∩ ΓN.The result is derived by the combination of the weight function method and the Generalized J-integral technique (abbr. GJ-integral technique). The GJ-integrals have been proposed by the first author in order to express the variation of energy (energy release rate) by extension of a crack in a 3D-elastic body. This paper begins with the weak solution of the crack problem, the weight function representation of SIF's, GJ-integral technique and finish with the shape sensitivity analysis of SIF's. GJ-integral Jω(u; X) is the sum of the P-integral (line integral) Pω(u, X) and the R-integral (area integral) Rω(u, X). With the help of the GJ-integral technique we derive an R-integral expression for the shape derivative of the potential energy which is valid for all displacement fields u ∊ H1. Using the property that the GJ-integral vanishes for all regular fields u ∊ H2 we convert the R-integral expression for the shape derivative to a P-integral expression. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1543-1558 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that a stochastic system of N interacting particles in a slab approximates, in the Boltzmann-Grad limit, a one-dimensional Boltzmann equation with diffusive boundary conditions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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  • 59
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1571-1591 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The asymptotic behaviour of solutions of certain semilinear elliptic Dirichlet boundary value problems defined on a semi-infinite cylinder is investigated by means of energy arguments and maximum principles. Various hypotheses are made on the form of the semilinear term, and in some cases it is found that the rate of decay of solutions is faster than the optimal decay rate for harmonic functions. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1655-1679 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper the problem of collision analysis for a mobile robot operating in a planar environment with moving objects (obstacles) is addressed. The pattern of motion of the potential obstacles cannot be predicted; only a bound on their maximum velocity is available. Based on this information, at its current position the robot constructs the Hazard Region that corresponds to the path it contemplates. If the Hazard Region contains at least one obstacle, then there is a potential for this obstacle to collide with the robot (in which case perhaps another path should be planned). We first derive the solution for Hazard Region for two standard path primitives, a straight line segment and a circular arc segment; the solution is exact, except for one special case (for which the approximation error is estimated). This result is then applied to a more complex case when the path presents a combination of those primitives. Such are, for example, the optimal (shortest) paths with constrained curvature (known as Dubins paths [3]), which connect two points, each with a prescribed direction of motion. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1681-1704 
    ISSN: 0170-4214
    Keywords: stratified medium ; acoustic waves ; self-adjoint operators ; spectrum ; limiting absorption principle ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the acoustic propagator A=-∇·c2∇ in the strip Ω={(x, z)∊∝2∣0〈z〈H} with finite width H〉0. The celerity c depends for large ∣x∣ only on the variable z and describes the stratification of Ω: it is assumed to be in L∞(Ω), bounded from below by cmin〉0, such that there exists M〉0 with c(x, z)=c1(z) if x〈 -M and c(x, z)=c2(z) if x〉M. We look at the propagator A as a ‘perturbation’ of the free propagators Aj in Ω associated to the velocities cj, j=1, 2, and implement a ‘perturbative’ method, adapting ideas of Majda and Vainberg. The spectrum of A is defined in section 2, a limiting absorption principle is proved in section 3 outside of a countable set Γ(A). The points of Γ(A) can only accumulate at the left of the thresholds of the free propagators. The needed material about Aj, j=1, 2, and some technical estimates for A are given in Appendix. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 62
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 25-42 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Considered is the rotation of a robot arm or rod in a horizontal plane about an axis through the arm's fixed end and driven by a motor whose torque is controlled. The model was derived and investigated computationally by Sakawa and co-authors in [7] for the case that the arm is described as a homogeneous Euler beam. The resulting equation of motion is a partial differential equation of the type of a wave equation which is linear with respect to the state, if the control is fixed, and non-linear with respect to the control.Considered is the problem of steering the beam, within a given time interval, from the position of rest for the angle zero into the position of rest under a certain given angle.At first we show that, for every L2-control, there is exactly one (weak) solution of the initial boundary value problem which describes the vibrating system without the end condition.Then we show that the problem of controllability is equivalent to a non-linear moment problem. This, however, is not exactly solvable. Therefore, an iteration method is developed which leads to an approximate solution of sufficient accuracy in two steps. This method is numerically implemented and demonstrated by an example. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 63
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 59-91 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A time-dependent Ginzburg-Landau-type model of a superconducting-normal-superconducting junction is presented. The existence and the uniqueness of the solutions are proved. When the data of the model are symmetric of some kinds, the solutions turns out to be symmetric of some kinds. In this symmetric case, an approximate model with the small thickness of the normal material in the middle of the junction as coefficients of a differential system is established for the sake of numerical computations. And also the existence and the uniqueness of the solution to this approximate model are set up. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 64
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 165-185 
    ISSN: 0170-4214
    Keywords: boundary integral equations ; boundary finite element ; free edge polygonal plate ; hypersingular kernels ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the problem of a polygonal plate with free edges. It is a boundary value problem for the biharmonic operator on a polygon with Neumann boundary conditions. Its resolution is studied via boundary integral equations. A variational formulation of the boundary problem obtained by a double-layer potential is given. Finally, we implement the method and give numerical results. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 65
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 129-163 
    ISSN: 0170-4214
    Keywords: wavelets on closed surfaces ; Dirichlet's and Neumann's problem ; scaling function ; scale discrete wavelets ; integral formulas ; exact fully discrete wavelet transform ; band-limited harmonic wavelets ; Runge-Walsh approximation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Wavelets on closed surfaces in Euclidean space ∝3 are introduced starting from a scale discrete wavelet transform for potentials harmonic down to a spherical boundary. Essential tools for approximation are integration formulas relating an integral over the sphere to suitable linear combinations of function values (resp. normal derivatives) on the closed surface under consideration. A scale discrete version of multiresolution is described for potential functions harmonic outside the closed surface and regular at infinity. Furthermore, an exact fully discrete wavelet approximation is developed in case of band-limited wavelets. Finally, the role of wavelets is discussed in three problems, namely (i) the representation of a function on a closed surface from discretely given data, (ii) the (discrete) solution of the exterior Dirichlet problem, and (iii) the (discrete) solution of the exterior Neumann problem. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 66
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 417-432 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We state a 1D model with quasi-stationary gas flows approximation for a carbon reactivity test in the production of silicon. The mathematical problem we formulate is a non-linear boundary value problem for a third-order ordinary differential equation with non-linear boundary conditions, which are non-local in time. We prove existence and uniqueness of a classical solution and provide a numerical example. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 281-325 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a bending model for a shallow arch, namely the type of curved rod where the curvature is of the order of the diameter of the cross section. The model is deduced in a rigorous mathematical way from classical tridimensional linear elasticity theory via asymptotic techniques, by taking the limit on a suitable re-scaled formulation of that problem as the diameter of the cross section tends to zero. This model is valid for general cases of applied forces and material, and it allows us to calculate displacements, axial stresses, bending moments and shear forces. The equations present a more general form than in the classical Bernoulli-Navier bending theory for straight slender rods, so that flexures and extensions are proved to be coupled in the most general case. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 68
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 375-392 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system using the technique of sub and supersolutions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 69
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 589-603 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the paper we study the problem of control by means of a heat source g for a thermoelastic system of equationsutt - ρ∇·p(θ, ∇u) - νΔut + DΔ2 u = f, cv(θ, ∇u)θt - κΔθ - ρθ[pθ (θ, ∇u)·∇ut] - ν∣∇ut∣2 = g, in a two-dimensional domain, where both viscosity ν and rigidity D are positive. Such a system has been considered in our former papers, and existence of solutions as well as uniqueness have been obtained. Here we prove the continuity and differentiability of solutions under somewhat stronger assumptions. An example of a control problem and necessary optimality conditions are presented. The system has an interpretation as a plate reinforced with shape memory alloy (SMA) wire mesh. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 719-731 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations can be obtained by the AKNS class. The technique developed relies on the construction of the wave functions which are solutions of the associated AKNS system; that is, a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Bäcklund transformations (BTs) are employed to generate two new solutions from the old. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 781-795 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the boundary value problem for a semilinear equation□u(t, x)-μu(t, x)+aum(t, x)=0, μ〉0, a∊ℜ in the interior domain. We find a time global classical solution with exponential decay property by using singular hyperbolic equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 895-906 
    ISSN: 0170-4214
    Keywords: geometrical inverse problems ; crack detection ; identifiability ; stability ; Lipschitz stability ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with the detection of emergent plane cracks, by using boundary measurements. An identifiability result (uniqueness of the solution) is first proved. Then, we look at the stability of this solution with respect to the measurement. A weak stability result is proved, as well as a Lipshitz stability result for straight cracks, by using domain-derivative techniques. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1467-1477 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, the existence, both locally and globally in time, the uniqueness of solutions and the non-existence of global solutions to the initial boundary value problem of a generalized Modification of the Improved Boussinesq equation utt-uxx-uxxtt=σ(u)xx are studied and a few examples are discussed. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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    Mathematical Methods in the Applied Sciences 21 (1998), S. 1593-1617 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study the following problem:ut-Δu=-f(u) in Ω×(0, T)≡QT,∂u ∂n=g(u) on ∂Ω×(0, T)≡ST,u(x, 0)=u0(x) in Ω, where Ω⊂∝N is a smooth bounded domain, f and g are smooth functions which are positive when the argument is positive, and u0(x)〉0 satisfies some smooth and compatibility conditions to guarantee the classical solution u(x, t) exists. We first obtain some existence and non-existence results for the corresponding elliptic problems. Then, we establish certain conditions for a finite time blow-up and global boundedness of the solutions of the time-dependent problem. Further, we analyse systems with same kind of boundary conditions and find some blow-up results. In the last section, we study the corresponding elliptic problems in one-dimensional domain. Our main method is the comparison principle and the construction of special forms of upper-lower solutions using related equations. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 75
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    Springer
    Reaction kinetics and catalysis letters 65 (1998), S. 75-81 
    ISSN: 1588-2837
    Keywords: Catalysis ; polypeptides ; p-nitrophenyl acetate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The hydrolysis kinetics ofp-nitrophenyl acetate by basic polypeptides with a variety of amino acid residues were analyzed. The results suggest that the tertiary structure of microenvironment brought about by random coil assembly is more important as a binding site than the number of basic residues (catalytic sites).
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    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 155-157 
    ISSN: 1434-1948
    Keywords: Bite angle ; Catalysis ; P ligands ; Palladium ; Cross-coupling ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The effect of the natural bite angle (βn) of diphosphane ligands on catalyst selectivity and activity in the palladium-catalyzed cross-coupling of sec-butyl magnesium chloride with bromobenzene was investigated. The calculated natural bite angles range from 78° for dppe (1,2-bisdiphenylphosphanoethane) to 110° for Xantphos. The natural bite angle of diphosphane ligands has a large effect on catalyst selectivity and activity. Both rate and selectivity of the cross-coupling reaction increase with increasing bite angle and reach a maximum value with DPEphos (βn = 102.7° ). Larger bite angles of the diphosphane ligands result in a decreased selectivity and activity.
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    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 1269-1281 
    ISSN: 1434-1948
    Keywords: Oxidation ; Catalysis ; Phthalocyanine ; Iron ; Anthracene ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Iron(III) tetrasulfophthalocyanine (FePcS) was shown to catalyze the oxidation of polycyclic aromatic hydrocarbons by H2O2. Benzo[a]pyrene and anthracene were converted to the corresponding quinones while biphenyl-2,2′-dicarboxylic acid was the main product of phenanthrene oxidation. The mechanism of the anthracene oxidation by H2O2 in the presence of FePcS or by KHSO5 with iron(III) meso-tetrakis(3,5-disulfonatomesityl)porphyrin (FeTMPS) (see Figure 1 for catalyst structures) has been investigated in details by using kinetic isotope effects (KIEs) and 18O labeling studies. KIEs measured on the substrate consumption in the competitive oxidation of [H10]anthracene and [D10]anthracene by FePcS/H2O2 and FeTMPS/KHSO5 were essentially the same, 0.75 ± 0.02 and 0.76 ± 0.06, respectively. These inverse KIEs on the first oxidation step can be explained by the sp2-to-sp3 hybridization change during the addition of an electrophilic oxoiron complex to the sp2 carbon center of anthracene to form a σ adduct (this inverse KIE being enhanced by stronger stacking interactions between the perdeuterated substrate with the macrocyclic catalyst). Although the first oxidation step seems to be the same, different distribution of the oxidation products of anthracene and very different 18O incorporation into anthrone and anthraquinone in catalytic oxidations performed in the presence of H218O suggested that different active species should be responsible for anthracene oxidation in both catalytic systems. All the results obtained are compatible with an involvement of TMPSFeV=O (or TMPS+FeIV=O), having two redox equivalents above the iron(III) state of the metalloporphyrin precursor, while PcSFeIV=O (one redox equivalent above FeIII state of FePcS) was proposed to be the active species in the metallophthalocyanine-based system.
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  • 78
    ISSN: 1434-193X
    Keywords: Heck reaction ; Cross coupling ; Palladium ; Catalysis ; 6π-Electrocyclization ; Cyclohexa-1,3-dienes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 1,6-Disubstituted (E, Z, E)-1,3,5-hexatrienes (4 and 5) were prepared by vicinal twofold Heck coupling reactions from 1,2-dibromocyclopentene (1), 1,2-dibromocyclohexene (2), 1,2-diiodocyclopentene (8), 1,2-diiodocyclohexene (9), 1-bromo-2-trifluoromethanesulfonyloxycyclohex-1-ene (11), or 1-chloro-2-nonafluorobutanesulfonyloxycyclohex-1-ene (19) with alkenes 3, e. g. methyl, tert-butyl, menthyl, 8-phenylmenthyl acrylate, styrene, and alkenylsilanes, respectively, in moderate to mostly good and very good yields (20-92 %). The coupling of alkenylsilanes 3f-k could only be achieved with the 1,2-diiodocycloalkenes 8 and 9, respectively. The corresponding hexatrienes 5 with two different substituents in the 1- and 6-positions were prepared by a sequence of two coupling reactions with different alkenes from 1-chloro-2-nonafluorobutanesulfonyloxycyclo-hex-1-ene (19) or by Wittig-Horner-Emmons olefination of 2-bromocyclohexene-1-carbaldehyde (24) and subsequent Heck reaction of the resulting (E,Z)-bromodienes 25. Several of the hexatrienes (4aa, ee, 5aa, ee, al, am, el) readily underwent a 6π-electrocyclization upon heating in an inert atmosphere to give the 5- or 6-ring-annelated cis-5,6-disubstituted cyclohexadienes 26, 27 (50-95 %). Starting from 5am 2,3-disubstituted tetrahydronaphthalene 28am was formed under oxidative conditions (air) in the reaction and in the work-up procedure. The bissilyl-substituted derivatives 4ff, jj, 5ff did not cyclize under thermal conditions, apparently due to the steric demand of the two silyl substituents which would have to end up cis with respect to each other in the cyclohexadiene products.
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    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 1835-1846 
    ISSN: 1434-1948
    Keywords: Clusters ; Catalysis ; Carboxylato complexes ; Hydrogenations ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A strategy of using functionalized clusters as ligands for cationic metal centers facilitates the construction of designed transition metal cluster assemblies. Examples of cluster metal carboxylates with conventional as well as novel structures are given and an application of these large molecular species to the generation of heterogeneous hydrogenation catalysts with unusual activities and selectivities is described.
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  • 80
    ISSN: 1434-1948
    Keywords: Arene complexes ; Catalysis ; Diazadiene complexes ; Iron ; Metal vapour ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Two different routes to novel [(diene)(η6-2,6-dimethylpyridine)Fe] complexes are reported, both of which utilize metal vapour reactions. The presence of two small substituents on the 2,6-position of pyridine is essential for the η6-coordination of the heterocycle. Investigations on the reactivity and stability of the [(diene)(η6-arene)Fe] complexes are presented, including those of the benzene, phosphinine, and pyridine derivatives. These investigations give some hints to the relevant factors for determining the interaction between an iron atom and a π-coordinated neutral arene ligand, and their modification by a nitrogen or a phosphorus atom. Selective substitution of the 1,5-cyclooctadiene (COD) ligand of [(COD)(η6-arene)Fe] complexes by some 1,4-diaza-1,3-diene (DAD) derivatives is possible in the case of the benzene or phosphinine arene ligands, and [(DAD)(η6-arene)Fe] complexes are formed, but all DAD derivatives tested so far cause the complete disintegration of [(COD)(η6-2,6-dimethylpyridine)Fe]. [(DAD)(η6-arene)Fe] complexes exhibit a catalytic potential, which was evaluated by experiments on the catalytic cyclodimerization of 1,3-butadiene in the presence of [(Et2AlOEt)2] as a co-catalyst. This reaction yields up to 92% of 1,5-cyclooctadiene, and an almost quantitative butadiene conversion is possible in the presence of less than 0.1% of the catalyst. Structural investigations on [(N,N′-bis(cyclohexyl)ethylenediimine)(η6-toluene)Fe] 5a reveal some details of the Fe-DAD interaction. An effective electron back-donation from occupied iron d-orbitals into the π*-LUMO of the DAD is indicated.
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  • 81
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    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 275-281 
    ISSN: 1434-1948
    Keywords: Molybdenum ; Peroxo complexes ; Hydrogen bonds ; Catalysis ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The ring-opening reaction of epoxycyclohexane with 2-[3(5)-pyrazolyl]pyridine results in the formation of racemic trans-2-[3-(2-pyridyl)-1-pyrazolyl]cyclohexanol (1). Kinetic resolution with lipase B from candida antarctica gives the (1S,2S) enantiomer of 1, the solid-state structure of which was determined by X-ray crystallography, as an enantiomerically pure tridentate ligand. Investigation by NMR spectroscopy of the corresponding oxodiperoxomolybdenum complex 2, where 1 acts as a bidentate chelate, proves the formation of a weak intramolecular MoVI(O2)····HO-C bridge in CHCl3 solution. This H bonding is broken by solvents such as acetone, THF or DMF, which are capable of forming hydrogen bonds to alcohols. Intermolecular hydrogen bonds between the OH groups and molybdenum peroxo moieties are also found in the solid-state structure of 2, leading to a helical arrangement of the peroxo complexes.
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  • 82
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    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 1163-1168 
    ISSN: 1434-1948
    Keywords: Chelates ; P,N ligands ; Phosphaferrocene ; Catalysis ; Heterocycles ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The new pyridyl-substituted phosphaferrocene ligands 3 and 6 are prepared by addition of lithiated pyridine or α-picoline to 2-formyl-3,4-dimethylphosphaferrocene (1). The ligands 3 and 6 react with [Cp*RuCl]4 in THF to give the P,N-chelate complexes [Cp*RuCl·3] (9) and [Cp*RuCl·6] (10) with high diastereoselectivity. Addition of monodentate ligands like CO or PPh3 to the complexes leads by displacement of the Ru-bound pyridyl group to the respective carbonyl or phosphane complexes with monodentate P-coordinated phospha-ferrocene ligands. Reaction of the ligand 6 with [(C3H5)PdCl]2 and NH4PF6 gives the seven-membered chelate complex [(C3H5)Pd·6]PF6 (13) which was characterized by X-ray diffraction. The ligands 3 and 6 were tested in the palladium-catalyzed asymmetric alkylation of 1,3-diphenylallyl acetate.
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  • 83
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    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 1673-1675 
    ISSN: 1434-1948
    Keywords: Ruthenium ; Copper ; Oxidations ; Catalysis ; Alcohols ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The oxidation of allylic and benzylic alcohols to aldehydes can be carried out at room temperature with molecular oxygen, in the presence of the bifunctional ruthenium-copper system (nPr4N)(RuO4)-CuCl acting as the catalyst.
    Additional Material: 1 Tab.
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  • 84
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    Liebigs Annalen 1998 (1998), S. 1867-1872 
    ISSN: 1434-193X
    Keywords: Catalysis ; Metal ion catalysis ; Kinetics ; 3-Acetyl-2,5-dimethylfuran ; 2-Acetylselenophene ; Enolisation reaction ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Rate constants for the enolisation reactions of title compounds have been measured by their rates of halogenation at 25 °C in water, in several buffers, in dilute hydrochloric acid, in dilute sodium hydroxide, and in the presence of some metal ion salts. The results have been compared with those previously obtained from the corresponding reactions of acetophenone and a number of other acetyl heterocycles. Electronegativity of the heteroatoms and the “π-excessive” nature of the heterocyclic rings appear to be the main factors determining the relative reactivities in the acid-catalysed reactions. Brønsted β values and isotope effects, kH/kD, point to a more symmetrical transition state for the investigated acetyl heterocycles than that for acetophenone in the general base-catalysed reaction. Metal-activating factors (MAF), i.e. the catalytic constant for metal-ion (Cu2+, Zn2+, and Ni2+) catalysis, kM, relative to that for proton catalysis, kH, are discussed as an empirical measure of the “hard or soft” character of the carbonyl groups in acyl heterocycles.
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  • 85
    ISSN: 1434-1948
    Keywords: Vanadium ; Amidinate ; Ethene Polymerization ; Catalysis ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new type of amidinate ancillary ligand has been prepared, which incorporates a pendant tertiary amine functionality. The crystal structure of a vanadium(III) derivative, [SiMe3NC(Ph)NCH2CH2NMe2]VCl2(THF) (1), shows that the ligand can adopt a facial geometry, with an unusual distortion of the amidinate nitrogen bearing the pendant functionality. With AlEt2Cl cocatalyst the compound 1 produces a single-site catalytic system for the polymerization of ethene.
    Additional Material: 1 Ill.
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  • 86
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    Berichte der deutschen chemischen Gesellschaft 1998 (1998), S. 729-731 
    ISSN: 1434-1948
    Keywords: Catalysis ; Oligomerization ; Organometallics ; Oligopeptides ; Ruthenium complexes ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Consecutive addition of one-equivalent portions of glycine ethyl ester to [(p-cymene)Ru(GGGOMe-H+)Cl] leads to considerable amounts of (tetra- to nonapeptide)ruthenium complexes in a one-pot reaction, in which the (p-cymene)RuCl fragment acts as a catalyst. The analogous reaction with alanine methyl ester affords AGGG and AAGGG complexes as the main products. The course of these metal-catalyzed peptide oligomerizations has been followed by mass spectrometry. The synthesis and characterization of the pentapeptide complex [(C6Me6)Ru(GGGGGOMe-H+)] is reported.
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  • 87
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    Communications in Numerical Methods in Engineering 14 (1998), S. 229-240 
    ISSN: 1069-8299
    Keywords: filling of thin section ; finite element method ; surface tension ; interface element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An interface element to model the pressure discontinuity due to surface tension when applied to the filling of a thin section cavity is presented. The equations used to form the element matrix for the interface element are the line integral form of the continuity and momentum equations. During the development of the finite element model, the pressure difference across the free surface due to surface tension is treated as an additional traction and is applied to all element sides which form the free surface. Simple numerical examples are then presented to illustrate the technique on the filling of a rectangular thin section cavity. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
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  • 88
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    Communications in Numerical Methods in Engineering 14 (1998), S. 253-269 
    ISSN: 1069-8299
    Keywords: potential flow ; optimization approach ; sensitivity analysis ; adjoint variable method ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Potential flow problems around immersed bodies have been treated by an optimization approach. When the stream function is used as the field variable, the boundary values may not be known a priori and may be taken as the decision parameters to minimize integral objective functionals. The circulation integrals around the immersed bodies or the Kutta condition at the trailing edges of the bodies may be used to construct the objective function of optimization. The sensitivity analysis needed for the minimization process is performed by the adjoint variable method, while the numerical solutions of the primary (flow) and adjoint equations have been obtained by the finite element method. Having checked the present method with exact solutions and the classical superposition method, several flow problems involving one or more immersed bodies with or without circulation are investigated numerically. © 1998 John Wiley & Sons, Ltd.
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  • 89
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    Communications in Numerical Methods in Engineering 14 (1998), S. 289-304 
    ISSN: 1069-8299
    Keywords: stress intensity factors (SIF) ; finite element method (FEM) ; reciprocal work contour integral (RWCI) ; path-independent integrals (PII) ; displacement correlation technique (DCT) ; quarter-point displacement technique (QPDT) ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for improving the approximations of stress intensity factors computed from path-independent integrals is developed. The method uses Richardson's extrapolation. Numerical results are given to show the efficiency and the stability of the present method. © 1998 John Wiley & Sons, Ltd.
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  • 90
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    Communications in Numerical Methods in Engineering 14 (1998), S. 321-333 
    ISSN: 1069-8299
    Keywords: eigenvalue analysis ; sensitivity evaluation ; large-scale systems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a general rank-1 matrix formula which allows for proper rearrangement of individual terms in multiproduct forms involving vectors and matrices. A far-reaching application of the new matrix formula to eigenvalue sensitivity evaluation is presented in the paper. Such an application reduces the sensitivity expressions to elegant, very fast and recursive forms with substantial savings in computer resources. The formula is applicable to rank-1 matrices of special structures which may constitute derivatives of the system state matrix, which is widely used in control system applications, with respect to various parameters of interest. In such cases, the use of the rank-1 formula yields exact non-approximate solutions which are identical to those obtained by other conventional formulas. The applicability of the rank-1 formula is believed to cover a wide variety of practical engineering systems pertaining to control and stability. © 1998 John Wiley & Sons, Ltd.
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  • 91
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    Communications in Numerical Methods in Engineering 14 (1998), S. 719-730 
    ISSN: 1069-8299
    Keywords: phase-change problems ; conduction-advection equation ; upwind weight function ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for solving transient multidimensional phase-change problems considering advective effects is presented. This temperature-based formulation includes the definition of a phase-change function able to deal with classical isothermal and non-isothermal phase-change cases. Moreover, a new upwind weight function is defined in order to avoid numerical oscillations in problems with dominant advective effects. Further, some important aspects related to its numerical implementation are also addressed. The ability of this methodology is illustrated, firstly, in the solution of a one-dimensional test example. Finally, the numerical simulation of a direct-chill continuous casting process is performed. © 1998 John Wiley & Sons, Ltd.
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  • 92
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    Communications in Numerical Methods in Engineering 14 (1998), S. 763-772 
    ISSN: 1069-8299
    Keywords: coupled vibrations ; Timoshenko beam ; boundary integral equation method ; symbolic computation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Symbolic computer algebra systems relieve one from the tedious task of different mathematical operations which are essential to obtain solutions. Due to their highly advanced features they have come to be used widely in computational mechanics. This paper describes an application of the modern computer algebra system Mathematica to the derivation of fundamental solutions necessary for the application of the boundary integral equation method. The problem treated is an asymmetric cross-section Timoshenko beam in free vibration. For this problem, the derivation of fundamental solutions involves lengthy mathematical operations which are very tedious if performed explicitly by hand. Therefore, using Mathematica we derive the fundamental solutions and generate the influence matrices from which the natural frequencies can be found. © 1998 John Wiley & Sons, Ltd.
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  • 93
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    Communications in Numerical Methods in Engineering 14 (1998), S. 751-761 
    ISSN: 1069-8299
    Keywords: acoustic ; electromagnetic ; integral equations ; scattering ; time domain ; radar cross-section ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Analysis of high frequency scattering using pulsed illumination generates surface fields which are small over most of the scatterer most of the time. A reformulation of the usual integral equation time domain approach which exploits this is presented. It is shown that cost scaling can be reduced, with costs reduced by an order of magnitude for the examples presented, with negligible accuracy loss. © 1998 John Wiley & Sons, Ltd.
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  • 94
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    Communications in Numerical Methods in Engineering 14 (1998), S. 797-808 
    ISSN: 1069-8299
    Keywords: mesh equidistribution ; area preserving map ; singular BVP ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an adaptive mesh method is employed to solve a class of singular boundary value problems. The approach is based on an area-preserving map and some mesh shape control in two-dimensional space. Two benchmark problems, which both involve singularities in physical domains, are tested. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
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  • 95
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    Communications in Numerical Methods in Engineering 14 (1998), S. 195-208 
    ISSN: 1069-8299
    Keywords: differential quadrature method ; elastic torsion ; numerical solution ; Poisson equation ; Laplace equation ; geometric mapping ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing equation of an elastic prismatic shaft is the two-dimensional Poisson equation defined on the cross-sectional area of the shaft. In this paper, the differential quadrature method (DQM) is employed to solve the Poisson equation on some non-rectangular domains. Singularities, which may appear in the expression of stress components or boundary conditions at a degenerated point of the grid, are removed by means of the Taylor expansion. The results of three examples are compared with the exact solutions. It is shown that accurate results can be achieved by the DQM. In addition, three geometric transformations are conducted in the third example so that the effect of mapping on the convergence and accuracy of results is investigated. It is found that rapid convergence can be fulfilled if the degenerated point of the mesh falls on a Dirichlet boundary. The approach addressed in the paper can be extended to other potential problems governed by either the Poisson equation or the Laplace equation. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
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  • 96
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    Communications in Numerical Methods in Engineering 14 (1998), S. 209-218 
    ISSN: 1069-8299
    Keywords: three-dimensional convection-diffusion equation ; fourth-order compact scheme ; iterative methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present an explicit fourth-order compact finite difference scheme for approximating the three-dimensional convection-diffusion equation with variable coefficients. This 19-point formula is defined on a uniform cubic grid. We compare the advantages and implementation costs of the new scheme with the standard 7-point scheme in the context of basic iterative methods. Numerical examples are used to verify the fourth-order convergence rate of the scheme and to show that the Gauss-Seidel iterative method converges for large values of the convection coefficients. Some algebraic properties of the coefficient matrices arising from different discretization schemes are compared. We also comment on the potential use of the fourth-order compact scheme with multilevel iterative methods. © 1998 John Wiley & Sons, Ltd.
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  • 97
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    Communications in Numerical Methods in Engineering 14 (1998), S. 241-251 
    ISSN: 1069-8299
    Keywords: finite elements ; pollutant ; saturated porous medium ; semi-implicit method ; velocity correction ; mass transfer ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A practical problem of pollutant migration has been studied for different concentration differences and mass diffusivities using the finite element method. The results indicate that the pollutant takes years to travel 10 m into the water-saturated soil when the mass diffusivity and concentration differences are less. © 1998 John Wiley & Sons, Ltd.
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  • 98
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    Communications in Numerical Methods in Engineering 14 (1998), S. 277-285 
    ISSN: 1069-8299
    Keywords: numerical simulation ; steel ; quenching ; finite volume method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: On the basis of the control volume method the algorithm and computer program for prediction of the hardness distribution in quenched steel specimens with complex geometries have been developed. The algorithm and computer program are designed to solve 2D situation problems such as the quenching of complex cylinders, cones, spheres, etc. The computer program consists of three parts: automatic computation of domain and grid generation, computation of cooling curve in grid-points, and computation of hardness in grid-points. The mathematical model has been tested experimentally. The test showed that the model describes the hardness distribution in a quenched steel specimen of a complex form, with quite satisfactory accuracy. © 1998 John Wiley & Sons, Ltd.
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  • 99
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    Communications in Numerical Methods in Engineering 14 (1998), S. 271-275 
    ISSN: 1069-8299
    Keywords: basis transformation ; interpolations ; finite elements ; thin plates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The 9 df thin plate element of Mohr and Mohr uses cubic interpolation to obtain values of w at the third points of the element sides, in turn interpolating from these and the vertex values within the element. Recently this element has been modified and successfully applied to ‘potential’ problems. Subsequently it was found that the interpolations of the element of Bazeley et al. (1965, 1968) gave identical results for potential problems. In the present paper it is shown that this is because the interpolations of the two elements are exactly equivalent. © 1998 John Wiley & Sons, Ltd.
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  • 100
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    Communications in Numerical Methods in Engineering 14 (1998), S. 313-319 
    ISSN: 1069-8299
    Keywords: fluid mechanics ; vortex dynamics ; viscous flow ; Navier-Stokes equation ; vortex methods ; splitting procedure ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical scheme has been obtained rigorously from the initial-boundary value problem for the Navier-Stokes (NS) equations in the context of the vortex method. The technique is based on a transformation of the NS equation into a parabolic equation which has an exact solution. The numerical scheme is derived by expanding the exact solution in Taylor series in powers of a small time interval. Numerical implementation is developed with use of vortex particles to represent the vortex flow domain. The method is used to solve practical engineering problems. The technique can also incorporate turbulence modelling. © 1998 John Wiley & Sons, Ltd.
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