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  • 1
    Electronic Resource
    Electronic Resource
    Decay Estimates for Solutions of Linear Elasticity for Anisotropic Media (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 15-31 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We analyse the time decay of solutions to the Cauchy problem for the linear hyperbolic system of elasticity for anisotropic media. As an example, we will consider media with hexagonal symmetry. First we derive decay estimates for special initial data using the method of stationary phase in several variables and degenerate phase function based on the Malgrange preparation theorem. Asymptotic expansions are given to prove the sharpness of the weaker time decay found for zinc and beryl than in the isotropic case. A method using Besov spaces leads to Lp-Lq-estimates.
    Additional Material: 4 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Multidimensional Oscillations for Non-linear Hyperbolic Mixed Problem: The Justified Non-linear Geometric Optics Method (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 217-233 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The mixed-Neumann problem for the non-linear wave equation □u-a(u)(∣∂tu)∣2-∣∇u∣2 = fε(z) is studied. The function fε(z) = ∑k∊Kfk(z,ε-1φk(z),ε), ε∊[0,1], K is finite, fk(z,θk,ε) are 2π-periodic with respect to θk. The existence of solution uε on a domain z = (t,x,y)∊[0,T]×∝+×∝d, d = 1 or 2, is proved when ε is sufficiently small; T does not depend on ε. By the non-linear geometric optics method the asymptotic (with respect to ε→0) solution ũ ε is constructed. The estimation for the rest ε2rε = uε-ũε is derived and the limit rε, ε→0, is studied.
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  • 3
    Electronic Resource
    Electronic Resource
    The Child-Langmuir Asymptotics of the Vlasov-Poisson Equation for Cylindrically or Spherically Symmetric Diodes Part 2: Analysis of the Reduced Problem and Determination of the Child-Langmuir Current (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 313-340 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper analyses the Child-Langmuir asymptotics of the Vlasov-Poisson problem in cylindrical or spherical symmetry. The problem was stated in the first part of this paper [2]. We recall that the Child-Langmuir asymptotics concerns the boundary value problem for the Vlasov-Poisson system in the situation where the thermal energy of the injected particles at the boundary is small compared with the external applied bias.In the first part, we derived the set of estimates which allow us to pass to the limit in the asymptotic problem. In the present part, we analyse the limit (or ‘reduced’) problem, which leads us to a characterization of the limit or ‘Child-Langmuir’ current which flows through the system.
    Additional Material: 8 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Lyapunov Stability of a Class of Operator Integro-differential Equations with Applications to Viscoelasticity (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 341-361 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Lyapunov stability is analysed for a class of integro-differential equations with unbounded operator coefficients. These equations arise in the study of non-conservative stability problems for viscoelastic thin-walled elements of structures. Some sufficient stability conditions are derived by using the direct Lyapunov method. These conditions are formulated for arbitrary kernels of the Volterra integral operator in terms of norms of the operator coefficients. Employing these conditions the supersonic flutter of a viscoelastic panel is studied and explicit expressions for the critical gas velocity are derived. Dependence of the critical flow velocity on the material characteristics and compressive load is analysed numerically.
    Additional Material: 5 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chemical Reactor Dynamics: Stability of Steady States (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 381-400 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The equations describing the dynamics and steady states of a tubular reactor are studied in the region where an arbitrary number of steady-state solutions exist. The stability of these solutions is examined and their persistence for increases in the parameter values is determined. The physical implications of these solutions are examined.
    Additional Material: 3 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Heteroclinic Solutions for a System of Strongly Coupled ODEs (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 451-461 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use the implicit function theorem to prove an existence of a heteroclinic orbit to a system of two non-linear second-order ODEs. The perturbation is carried out around infinite value of a ‘coupling parameter’. The form of the system which is considered in this paper is related to the system defining travelling wave solutions in a two temperature model of the laser sustained plasma.
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  • 7
    Electronic Resource
    Electronic Resource
    Semi-internal Stabilization for a Non-linear Bernoulli-Euler Equation (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 897-907 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a non-linear plate equation of Bernoulli-Euler type with a locally distributed damping term. Our main result asserts that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially. The method we use is a combination of multiplier techniques and of a compactness-uniqueness argument.
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  • 8
    Electronic Resource
    Electronic Resource
    Local Solutions of Semilinear Wave Equations in Hs+1 (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 145-170 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Cauchy problem for the wave equation with power type non-linearity ±∣u∣σ*u and data in Hs+1(∝n)×Hs(∝n) is considered, where 0〈s〈(n/2)-1 and n≥3. Under the growth restriction σ*≤4/(n-2-2s) in many cases the existence of a local solution with u(t)∊Hs+1(∝n) is shown which is unique in a closely related class.
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  • 9
    Electronic Resource
    Electronic Resource
    Measure-valued Solutions of the Euler Equations for Ideal Compressible Polytropic Fluids (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 235-252 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of global measure-valued solutions to the Euler equations describing the motion of an ideal compressible and heat conducting fluid is proved. The motion is considered in a bounded domain Ω⊂∝3 with impermeable boundary. The solution is a limit of an approximate solution obtained by adding the sixth-order elliptic operator in the equation of momentum.
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  • 10
    Electronic Resource
    Electronic Resource
    Hadamard's Finite Part (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1017-1052 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A systematic way of ascribing values to integrals which diverge at infinity is described. For integrals with algebraic or logarithmic behaviour it is akin to Hadamard's finite part for integrands which have singularities at finite points. The power of the method is illustrated by examples of particular integrals and the convolution of distributions which are beyond the range of standard theory. Both one-dimensional and multi-dimensional integrals are included. The theory also enables the definition of products of distributions which are considered normally to be too singular for multiplication.
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  • 11
    Electronic Resource
    Electronic Resource
    Critical Exponents for a System of Heat Equations Coupled in a Non-linear Boundary Condition (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1099-1120 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider a system of heat equations ut = Δu, vt = Δv in an unbounded domain Ω⊂∝N coupled through the Neumann boundary conditions uv = vp, vv = uq, where p〉0, q〉0, pq〉1 and ν is the exterior unit normal on ∂Ω. It is shown that for several types of domain there exists a critical exponent such that all of positive solutions blow up in a finite time in subcritical case (including the critical case) while there exist positive global solutions in the supercritical case if initial data are small.
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  • 12
    Electronic Resource
    Electronic Resource
    Periodic Solutions of Non-linear Anisotropic Partial Differential Equations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 363-374 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Periodic solutions of arbitrary period to semilinear partial differential equations of Zabusky or Boussinesq type are obtained. More generally, for a linear differential operator A(y,∂), the equation A(y,∂)u = (-1)∣γ∣∂γf(y,∂γu), y = (t,x)∊∝k×G is studied, where homogeneous boundary conditions on ∂G and periodicity conditions on t are imposed. The solutions are obtained by variational methods in anisotropic Sobolev spaces.
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  • 13
    Electronic Resource
    Electronic Resource
    Asymptotic Analysis of a Semiconductor Model Based on Fermi-Dirac Statistics (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 401-424 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The quasi-hydrodynamic carrier transport equations for semiconductors extended to Fermi-Dirac statistics are considered. It is shown that in the high injection case, these equations reduce to a drift-diffusion model with non-linear diffusion terms. The limiting procedure is proved rigorously and error estimates are shown. We compute numerically static voltage-current characteristics of a forward biased pn-junction diode and compare the curves with the corresponding characteristics obtained from the standard drift-diffusion model based on Boltzmann statistics. It turns out that there exists a so-called threshold voltage at which the behaviour of the characteristic changes. Under high injection conditions, the dependence of the current on the bias appears to be approximately polynomial. The characteristics are studied analytically for a unipolar device.
    Additional Material: 6 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Convergence of Velicity Blobs Method for the Euler Equation (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 463-479 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A particles numerical method for incompressible fluid, based on a Hamiltonian formalism due to Oseledets [8], was recently introduced and exploited by Buttke [1]. Here we investigate the convergence of the solutions of such a particles system to the solutions of the incompressible Euler equation, and point out some features of the Hamiltonian formalism.
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  • 15
    Electronic Resource
    Electronic Resource
    The Two-Dimensional Exterior Stokes Problem, Existence, Regularity and Decay Properties (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 507-528 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Stokes problem-Δu+∇p = f, div u = g in Ω, u∣∂Ω = h is investigated for two-dimensional exterior domains Ω. By means of potential theory, existence, uniqueness and regularity results for weak solutions are proved in weighted Sobolev spaces with weights proportional to ∣x∣δ as ∣x∣→∞. For f = 0,g = 0, explicit decay formulas are obtained for the solutions u and p. Finally, the results are compared with the theory of r-generalized solutions, i.e. ∇u∊Lr.
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  • 16
    Electronic Resource
    Electronic Resource
    Existence, Uniqueness and Mass Conservation for the Coagulation-Fragmentation Equation (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 571-591 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove global existence and uniqueness to the initial value problem for the coagulation-fragmentation equation for an unbounded coagulation kernel with possible linear growth at infinity and a fragmentation kernel from a very large class of unbounded functions. We show that the solutions satisfy the mass conservation law.
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  • 17
    Electronic Resource
    Electronic Resource
    A Green's Function Approach to Wave Propagation and Potential Flow around Obstacles in Infinite Cylindrical Channels (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 607-638 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study (a) acoustic waves generated by a time-harmonic force distribution and (b) the potential flow with prescribed velocity at infinity in an infinite cylinder Ω0 = Ω′×∝ with bounded cross-section Ω′⊂∝2 in the presence of m embedded obstacles B1,…,Bm. By using Green's function Gκ(x,y) of the Neumann problem for the reduced wave equation ΔU+κ2U = 0 in the unperturbed domain Ω0, both problems can be reduced to integral equations over the boundaries of the obstacles. The main properties of Gκ(x,y), which are required for this approach, are derived in the first part of this paper.
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  • 18
    Electronic Resource
    Electronic Resource
    Approximation of Neural Network Dynamics by Reaction-Diffusion Equations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 651-677 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The equations of the Hopfield network, without the constraint of symmetry, can have complex behaviours. Cottet borrowed techniques from particle methods to show that a class of such networks with symmetric, translation-invariant connection matrices may be approximated by a reaction-diffusion equation. This idea is extended to a wider class of network connections yielding a slightly more complex reaction-diffusion equation. It is also shown that the approximation holds rigorously only in certain spatial regions (even for Cottet's special case) but the small regions where it fails, namely within transition layers between regions of high and low activity, are not likely to be critical.
    Additional Material: 3 Ill.
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  • 19
    Electronic Resource
    Electronic Resource
    The Limiting Absorption Principle for Elastic Wave Propagation Problems in Perturbed Stratified Media ∝3 (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 187-215 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the self-adjoint operator governing the propagation of elastic waves in perturbed stratified media ∝3 with free boundary-interface conditions. In this paper we establish the limiting absorption principle for this self-adjoint operator in appropriate Hilbert space. The proof of the limiting absorption principle is based on the division theorem which is proved by means of eigenfunction expansions for the self-adjoint operator governing the propagation of elastic waves in unperturbed stratified media ∝3.
    Additional Material: 2 Ill.
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  • 20
    Electronic Resource
    Electronic Resource
    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670190401
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  • 21
    Electronic Resource
    Electronic Resource
    Resonance Phenomena in Local Perturbations of Parallel-plane Waveguides (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 773-823 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study initial and boundary value problems for the wave equation ∂2tu-Δu = fe-iωt with Dirichlet or Neumann boundary data in smooth domains Ω, which coincide with Ω0 = ∝2×(0,1) outside a sufficiently large sphere. The concept of a standing wave, introduced in [7], seems to be of special relevance. A standing wave of frequency ω is defined as a non-trivial solution U of the equation ΔU+ω2U = 0 in Ω, which satisfies on ∂Ω the prescribed boundary condition U = 0 or ∂U/∂n = 0, respectively, and a suitable condition at infinity. For instance, U(x) = sinπkx3 is a standing wave of frequency πk in the unperturbed domain Ω0 with Dirichlet boundary data. As shown in a series of joint papers with K. Morgenröther, u(x,t) is bounded as t→∞ if Ω does not admit standing waves of frequency ω. The main purpose of the present paper is the proof of the converse statement: If standing waves of frequency ω exist in Ω, then u(x,t) is unbounded as t→∞ for suitably chosen f∊C∞0(Ω). Thus the appearance of resonances is closely related to the presence of standing waves. The leading term of the asymptotic expansion of u(x,t) as t→∞ will be specified. In particular, it turns out that the resonance rate is either t or ln t. The rate t appears if and only if ω2 is an eigenvalue of the spatial operator, while the rate ln t can only occur if ω = πk. In the case of Neumann boundary data, U = 1 is a standing wave of frequency 0 for every local perturbation Ω of Ω0. The corresponding resonance has already been studied in [21].
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  • 22
    Electronic Resource
    Electronic Resource
    Asymptotic Behaviour of the Interface of Some non-linear Diffusion Problems (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 375-380 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper an asymptotic result concerning the interface for some problems connected with radially symmetric non-linear diffusion is presented.
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  • 23
    Electronic Resource
    Electronic Resource
    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670190501
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  • 24
    Electronic Resource
    Electronic Resource
    Volterra Integral Equation Models for Semiconductor Devices (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 425-450 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Van Roosbroeck's bipolar drift diffusion equations cover the qualitative behaviour of many semiconductor devices. The complexity of the model equations however prevents efficient implementations needed in circuit simulations. Under close-to-thermal-equilibrium biasing conditions (zero space charge assumption, low injection limit) the van Roosbroeck system can be replaced by a system of coupled non-linear Volterra integral equations of the second kind. Involving only the macroscopic quantities current, applied voltage and serial resistance this Volterra system can be handled with comparably little effort. Volterra integral equations models are formulated for a large class of semiconductor devices with abrupt pn-junctions. The model equations are made explicit for diodes, transistors and thyristors. A survey on various results concerning Volterra models describing the switching behaviour of pn-diodes is given. The integral equation model allows to recover all relevant properties of the voltage-current characteristics.
    Additional Material: 4 Ill.
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  • 25
    Electronic Resource
    Electronic Resource
    Scattering by Rough Surfaces: the Dirichlet Problem for the Helmholtz Equation in a Non-locally Perturbed Half-plane (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 959-976 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.
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  • 26
    Electronic Resource
    Electronic Resource
    On Variational Models for Quasi-static Bingham Fluids (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 991-1015 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a quasi-static incompressible flow of Bingham type with constituent law\[ \begin{array}{ll} T = p\left| {\cal E}u\right| ⁁{p-2}{\cal E}u+\beta \frac{{\cal E}u}{\left| {\cal E}u\right| } & \text{if }{\cal E}u\neq 0, \\ \left| T\right| \leq \beta & \text{if }{\cal E}u = 0, \end{array} \] T = p∣Eu∣p-2Eu+β Eu ∣Eu∣ if Eu≠0,∣T∣≤β if Eu = 0, where p≥2 and β〉0. Here Eu denotes the strain velocity and T the corresponding stress. The problem admits a variational formulation in the sense that the velocity field u minimizes the energy I(u) = ∫Ω∣Eu∣p+β∣Eu∣dx in the space {v∊H1,p(Ω,∝n): div v = 0} subject to appropriate boundary conditions. We then show smoothness of u on the set {x∊Ω: Eu≠0}.
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  • 27
    Electronic Resource
    Electronic Resource
    Global Solutions to a Penrose-Fife Phase-field Model Under Flux Boundary Conditions for the Inverse Temperature (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1053-1072 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we study an initial-boundary value problem for a system of phase-field equations arising from the Penrose-Fife approach to model the kinetics of phase transitions. In contrast to other recent works in the field, the correct form of the boundary condition for the temperature field is assumed which leads to additional difficulties in the mathematical treatment. It is demonstrated that global existence of strong solutions can be shown under essentially the same assumptions on the data as in the previous papers where a simplified boundary condition for the heat exchange with the surrounding medium has been used.
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  • 28
    Electronic Resource
    Electronic Resource
    An Alternative Method for a Classical Problem in the Calculus of Variations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1091-1097 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A numerical technique for determining the solution of the brachistochrone problem is presented. The brachistochrone problem is first formulated as a non-linear optimal control problem. Using Chebyshev nodes, we construct the Mth degree polynomial interpolation to approximate the state and the control variables. Application of this method results in the transformation of differential and integral expressions into some non-linear algebraic equations to which Newton-type methods can be applied. Simulation studies demonstrate computational advantages relative to existing methods in the literature.
    Additional Material: 3 Tab.
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    On the Blow-up of the Solutions of a Quasilinear Wave Equation With a Semilinear Source Term (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1135-1140 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, following the ideas of Lax, we prove a blow-up result for a class of solutions of the equation φtt-φxx-φ2xφxx-φ3 = 0, corresponding, in certain cases, to the development of a singularity in the second derivatives of φ. These solutions solve locally (in time) the Cauchy problem for smooth initial data belonging to the uniformly local Sobolev spaces considered by Kato and by Majda.
    Additional Material: 1 Ill.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670191401
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    Homogenization of the Stokes Problem With Non-homogeneous Slip Boundary Conditions (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 857-881 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the Stokes system with non-homogeneous Fourier boundary conditions depending on a parameter, in a domain with periodic inclusions of the size of the period. Following the values of this parameter, we obtain at the limit a Darcy's law, a Brinkmann type equation or a Stokes type equation.We also present a physical model to which the results apply. This model describes the flow of an incompressible viscous fluid through a porous medium under the action of an exterior electric field.
    Additional Material: 1 Ill.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670191701
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    Time Decay of the Solutions of the Vlasov-Poisson System in the Plasma Physical Case (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1409-1413 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We introduce a new identity satisfied by solutions of the Vlasov-Poisson system. It has the property that all quantities which appear have a definite sign, and this allows us to prove new results on the time decay of the solutions in the plasma physical case.
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    Biquaternionic Integral Representations for Massive Dirac Spinors in a Magnetic Field and Generalized Biquaternionic Differentiability (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1415-1431 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Dirac equation with a vector potential is considered using a biquaternionic formalism and boundary integral representations for its solutions are obtained. In order to characterize these solutions by a property of local approximability by linearization the corresponding notion of biquaternionic differentiability and its generalization in the sense of Bers (adapted to the spatial case) are given.
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    Interaction of Elastic and Scalar Fields (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1445-1469 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The three-dimensional mathematical problems of the interaction of an elastic and some scalar fields are investigated. It is assumed that the elastic structure under consideration is a bounded homogeneous anisotropic body occupying domain Ω¯+⊂∝3 and the physical scalar field is defined in the exterior domain Ω- = ∝3\Ω+. These two fields satisfy the governing equations in the corresponding domains together with the transmission conditions on the interface ∂Ω+. The problems are studied by the potential method and the existence and uniqueness theorems are proved.
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    Graded Mesh Refinement and Error Estimates for Finite Element Solutions of Elliptic Boundary Value Problems in Non-smooth Domains (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 63-85 
    Details
    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 effective numerical treatment of elliptic boundary value problems when the solutions contain singularities. The paper deals first with the theory of problems of this type in the context of weighted Sobolev spaces and covers problems in domains with conical vertices and non-intersecting edges, as well as polyhedral domains with Lipschitz boundaries. Finite element schemes on graded meshes for second-order problems in polygonal/polyhedral domains are then proposed for problems with the above singularities. These schemes exhibit optimal convergence rates with decreasing mesh size. Finally, we describe numerical experiments which demonstrate the efficiency of our technique in terms of ‘actual’ errors for specific (finite) mesh sizes in addition to the asymptotic rates of convergence.
    Additional Material: 12 Ill.
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    Approach to Equilibrium for the Coagulation-Fragmentation Equation via a Lyapunov Functional (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 171-185 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that the non-linear coagulation-fragmentation equation with constant kernels has a unique equilibrium solution. This equilibrium solution is given explicitly in terms of the initial data and the kernels. Weak L1 convergence of time-dependent solutions to the unique equilibrium is demonstrated via an invariance principle employing a suitable lower semicontinuous Lyapunov functional.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670190301
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    Existence and Uniqueness of a Solution to the Cauchy Problem for the Damped Boussinesq Equation (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 639-649 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for discontinuous initial perturbations this solution is infinitely differentiable with respect to time t and space co-ordinates for t〉0 on a bounded time interval.
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  • 40
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    Relationship Between the Albedo and Scattering Operators for the Boltzmann Equation with Semi-transparent Boundary Conditions (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1-13 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The albedo and scattering operators are central objects in the time-dependent transport theory. Their mutual relationship has recently been established by Arianfar and Emamirad for the case of transparent boundaries. In this paper, we extend the result to general boundary conditions. To allow for this extension, the scattering theory for a transport-like equation is generalized to include partially reflecting boundary conditions. The existence of the wave and scattering operators is directly inferred from the properties of the evolution operators that are determined, in turn, by the physics of collisions within and at the boundaries of the scattering domain.
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    On the Growth of the Vorticity Support for an Incompressible Non-viscous Fluid in a Two-dimensional Exterior Domain (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 53-62 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the time evolution of the support of a positive vorticity for a non-viscous incompressible fluid evolving in ∝2-D, where D is a compact domain with smooth boundary. We bound its growth. In the same time we prove also that a fluid particle initially close to the origin cannot go fast away.
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    The Global Attractors for the Periodic Initial Value Problem For a Coupled Non-linear Wave Equation (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 131-144 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of global attractors of the periodic initial value problem for a coupled non-linear wave equation is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of uniform a priori estimates for time.
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    On Large Solutions for the Quasistatic Problem in Non-linear Viscoelasticity with the Constitutive Equations of Bodner-Partom (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 933-942 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work proves global in time existence of large solutions for a quasistatic problem in non-linear viscoelasticity in the three-dimensional case. The basic idea is to apply the energy method for local in time solutions.
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    On Integral Representations and Boundary Properties of Spinor Fields (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 977-989 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new approach to the boundary value problem for the classic Dirac equation is proposed. This approach is based on a recent version of the metaharmonic quaternionic analysis developed in [14-16]. In particular, the following problem is studied: when and how a given function on a surface can be extended to a time-harmonic spinor field.
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    Erratum (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 253-253 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
    Type of Medium: Electronic Resource
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  • 46
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    Sufficient Conditions for Converging Drift-Diffusion Discrete Systems. Application to The Finite Element Method (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 33-51 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we generalize the abstract results of Mock and Marcowich [13, 12] for convergence of discrete Van Roosbroeck systems [12, 13, 17], to the case when the solutions are typically in W1,4-ε and not in H2. These conditions are verified on finite element discretizations. Error estimates are derived when the solution is unique. Due to the singularity at the flat angles, these estimates in the H1 norm are only O(h1/2). The techniques that are presented are broad and may be applied to other type of discretizations.
    Additional Material: 1 Ill.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670190101
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  • 48
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670190201
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    The Approximation of the Optimal Control of Vibrations - A Geometrical Approach (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 87-129 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we employ concepts from Banach space geometry in order to examine the problem of approximating the optimal distributed control of vibrating media whose motion is governed by a wave equation with a 2n-order self-adjoint and positive-definite linear differential operator. We show that this geometrical approach, arrived at via duality theory, provides the exact framework in which the approximation problem must be placed in order to get the correct convergence results, for it is here that the necessary and sufficient conditions for the approximate norm or time minimal control can be fully developed. Using the theory of Asplund, we are also able to improve the traditional weak* convergence results for the more difficult case of L∞ controls. Finally, we consider certain numerical examples which help illustrate our theoretical results.
    Additional Material: 2 Ill.
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  • 50
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    The Asymptotic Behaviour and Blow-up Properties of Solutions of a Non-local Burgers' Equation (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 737-759 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we continue the work of [1] and obtain a complete picture of asymptotic behavior and blow-up properties of solutions of a non-local Burgers' equation.
    Additional Material: 6 Tab.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670191001
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    The Child-Langmuir Asymptotics of the Vlasov-Poisson Equation for Cylindrically or Spherically Symmetric Diodes Part 1: Statement of the Problem and Basic Estimates (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 287-312 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Child-Langmuir asymptotics of the Vlasov-Poisson system provides a model for vacuum diodes which operate under large biases. In these conditions the energy of the injected particles at the cathode is very small compared with the applied external bias. From the mathematical view point, this leads to an interesting and non-standard asymptotic problem for the Vlasov-Poisson equation, which has already been investigated in the one-dimensional Cartesian case, in [7]. The purpose of this paper is to extend the analysis to the cylindrically or spherically symmetric case. Surprisingly, the behaviour of the solutions of the model is somehow different than in the Cartesian case. This feature had not been noticed by the physicists before. Furthermore, the mathematical analysis is much more involved than in [7] because of the geometrical effects, and the techniques that are used are quite different. They mainly rely on the use of supersolutions in the spirit of [18, 19]. This work is divided in two parts. In this first part, we state the problem and establish the basic estimates which are needed for the asymptotic analysis.
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    Some Generalized Problems for Polyharmonic Functions (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 883-896 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the first section of this paper, some non-local boundary value problem for the polyharmonic equation in the plane is considered. This problem consists in determining solution of the polyharmonic equation satisfying some special non-local-type boundary condition on two curves. The existence theorem is proved. In the second section, an example for the case of the biharmonic equation is considered. In the third section, some non-local, non-linear problem of Riquier type is examined. The Riquier-type problem consists in determining the polyharmonic function in the plane whose value together with its successive Laplacians are prescribed on the boundary. The existence theorem is proved and an example for the case of the biharmonic equation is considered.
    Additional Material: 1 Ill.
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    Fourier-Finite-element Approximation of Elliptic Interface Problems in Axisymmetric Domains (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 909-931 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper deals with the Fourier-finite-element method (FFEM), which combines the approximate Fourier method with the finite-element method, and its application to Poisson-like equations -p̂Δ3û = f̂ in three-dimensional axisymmetric domains Ω^. Here, p^ is a piecewise constant coefficient having a jump at some axisymmetric interface. Special emphasis is given to estimates of the Fourier-finite-element error in the Sobolev space H1(Ω^), if the interface is smooth or if it meets the boundary of Ω^ at some edge. In general, the solution û contains a singularity at the interface, which is described by a tensor product representation and treated numerically by appropriate mesh grading in the meridian plane of Ω^. The rate of convergence of the combined approximation in H1(Ω^) is proved to be O(h+N-1) (h, N: the parameters of the finite-element- and Fourier-approximation, with h→0, N→∞). The theoretical results are confirmed by numerical experiments.
    Additional Material: 5 Ill.
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    Asymptotic Analysis of Abstract Linear Kinetic Equations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 481-505 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we provide a theory of the asymptotic expansion for an abstract kinetic equation. We show that the modified Chapman-Enskog procedure, introduced in [19], gives the error of order of ε2, uniformly in time, on the second level of approximation and in particular that the zeroth moment of the solution (the spatial density of particles) can be approximated by the solution of the diffusion-type equation with the same accuracy. The theory is applied to several types of kinetic equations with the Fokker-Planck collision operator.
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    Connections between Size Functions and Critical Points (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 555-569 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A mathematical approach to the concept of shape of a submanifold M of a Euclidean space had previously been given by means of ‘measuring functions’ (e.g. diameter or volume) and of the derived ‘size functions’. This paper relates the study and the computation of any such size function to the structure of critical points of the associated measuring function.
    Additional Material: 3 Ill.
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    The Riesz-Clifford Functional Calculus for Non-Commuting Operators and Quantum Field Theory (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 593-605 
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    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on Clifford analysis. Applications to the quantum field theory are described.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670190801
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    Scattering Frequencies and a Class of Perturbed Systems of Elastic Waves (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 699-716 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the system of elastic waves in three dimensions under the presence of an impurity of the medium which we represent by a real-valued function q(x) (or q(x,t)). The medium is assumed to be isotropic and occupies the whole space Ω = ∝3. We study the location of the scattering frequencies associated with such phenomenon. We conclude that there is a large region on the complex plane which is free of scattering frequencies. In the remaining region they are discrete provided that q satisfies suitable assumptions concerning its behaviour at infinity.
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    The Validity of Generalized Ginzburg-Landau Equations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 717-736 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider parabolic systems defined on cylindrical domains close to the threshold of instability, in which the Fourier modes with positive growth rates are concentrated at a non-zero critical wave number. In particular, we consider systems for which a so-called Ginzburg-Landau equation can be derived. Due to the presence of continuous spectrum, classical bifurcation theory is not available to describe bifurcating solutions. Thus, we consider a modified system with artificial spectral gap, which possesses an infinite-dimensional centre manifold. The amplitude equation on this manifold is called a generalized Ginzburg-Landau equation. From previous work [18] it is known that the Fourier modes are exponentially concentrated at integer multiples of the critical wave number. Hence, the error made by this modification is exponentially small in powers of the bifurcation parameter. The approximations obtained via the generalized Ginzburg-Landau equation are valid on a much longer time scale than those obtained by using the classical Ginzburg-Landau equation as an amplitude equation.
    Additional Material: 2 Ill.
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    Exact Solutions of Discrete Kinetic Models and Stationary Problems for the Plane Broadwell Model (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 825-845 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A review of exact solutions of discrete velocity models is given. Different methods of constructing the solutions are discussed. New methods are proposed for the stationary Broadwell model, and new class of solutions is obtained. Two-dimensional flows in channel are studied on the basis of exact solutions and analogy with the Carleman model. Explicit example of non-unique solution to a boundary value problem is given. Exact hydrodynamic equations are derived for the stationary Broadwell model. A role of the Navier-Stokes approximation is discussed in detail by comparison with these exact equations.
    Additional Material: 2 Ill.
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  • 62
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    Weak Solutions of a Semilinear Hyperbolic System on a Nondecreasing Domain (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1303-1316 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The initial-boundary value problem in non-cylindrical domain for a semilinear hyperbolic system is investigated. A weak solution is constructed by the method of semidiscretization in time variable combining with variational calculus, when the time sections of domain has non-decreasing property.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670191601
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670191101
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  • 65
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    On the Initial-boundary-value Problem for the Extensible Beam with Attached Load (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 943-957 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: When one end of an extensible beam whose ends are a fixed distance apart, is hinged while to other end a load is attached, the mathematical model describing the vibrations of the beam contains a non-linearity both in the partial differential equation as well as in the dynamical boundary condition. We introduce weak damping and consider the resulting boundary-value problem within the framework of the theories of B-evolutions and fractional powers of a closed pair of operators. This approach enables us to construct a unique weak solution which exhibits exponential decay by employing Faedo-Galerkin approximations.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670191201
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  • 67
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    On the Low-frequency Asymptotic Expansion for some Second-order Elliptic Systems in a Two-dimensional Exterior Domain (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1073-1090 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We derive the low-frequency asymptotic expansion of the exterior boundary value problems in two dimensions for second-order elliptic system concerning the theory of elastostatics. As an application of our result, the rate of the local energy decay of solutions of the initial boundary value problem for the corresponding dynamical system is discussed.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670191301
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    Properties of Positive Solutions for Non-local Reaction-Diffusion Problems (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1141-1156 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we investigate the properties of positive solutions for three non-local reaction-diffusion problems. The conditions on the existence and non-existence of global positive solutions are given. Moreover, we prove that the blow-up set is the whole region when the non-linearity occurs in the equation.
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    Existence of Global Weak Solutions for Coupled Thermoelasticity under Non-Linear Boundary Conditions (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1265-1277 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of global weak solutions for coupled thermoelasticity with non-linear contact boundary conditions corresponding to the friction problem is considered. The time-continuous Galerkin method and a priori estimates obtained with Gronwall's inequality in connection with embedding theorems are applied to accomplish a straightforward generalization of one of the results proved by Martins and Oden 9.
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    Finite Time Blow-up for a Non-linear Parabolic Equation with a Gradient Term and Applications (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1317-1333 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give new finite time blow-up results for the non-linear parabolic equations ut-Δu = up and ut-Δu+μ∣∇u∣q = up. We first establish an a priori bound in Lp+1 for the positive non-decreasing global solutions. As a consequence, we prove in particular that for the second equation on ∝N, with q = 2p/(p+1) and small μ〉0, blow-up can occur for any N≥1, p〉1, (N-2)p〈N+2 and without energy restriction on the initial data. Incidentally, we present a simple model in population dynamics involving this equation.
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    A Variational Problem Related to Self-trapping of an Electromagnetic Field (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1397-1407 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
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    Riemann Problems for 5×5 Systems of Fully Non-linear Equations Related to Hypoplasticity (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1433-1444 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The equations of motion for two-dimensional deformations of an incompressible elastoplastic material involve five equations, two equations expressing conservation of momentum, and three constitutive laws, which we take in the rate form, i.e. relating the stress rate to the strain rate. In hypoplasticity, the constitutive laws are homogeneous of degree one in the stress and strain rates. This property has the consequence that although the equations are not in conservation form, there is nonetheless a natural way to characterize planar shock waves. The Riemann problem is the initial value problem for plane waves, in which the initial data for stress and velocity consist of two constant vectors separated by a single discontinuity. The main result is that, under appropriate assumptions, the Riemann problem has a scale invariant piecewise constant solution. The issue of uniqueness is left unresolved. Indeed, we give an example satisfying the conditions for existence, for which there are many solutions. Using asymptotics, we show how solutions of the Riemann problem are approximated by smooth solutions of a system regularized by the addition of viscous terms that preserve the property of scale invariance.
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    Galerkin Approximation of Weak Solutions of the Drift Diffusion Model for Semiconductors Coupled with Maxwell's Equations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1471-1488 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove global existence of weak solutions of the drift diffusion model for semiconductors coupled with Maxwell's equations for the electromagnetic field by using a Galerkin method. The recombinations term for the density of electrons and holes may depend on the densities, the gradient of the densities and the electromagnetic field.
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    Well-posedness of the Hydrodynamic Model for Semiconductors (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1489-1507 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper concerns the well-posedness of the hydrodynamic model for semiconductor devices, a quasi-linear elliptic-parbolic-hyperbolic system. Boundary conditions for elliptic and parabolic equations are Dirichlet conditions while boundary conditions for the hyperbolic equations are assumed to be well-posed in L2 sense. Maximally strictly dissipative boundary conditions for the hyperbolic equations satisfy the assumption of well-posedness in L2 sense. The well-posedness of the model under the boundary conditions is demonstrated.
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    Masthead (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670191801
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    Masthead (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 60 (1996) 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240600201
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  • 78
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    Masthead (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 61 (1996) 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240610201
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    Masthead (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996) 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630501
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    T-Cell lymphoma cell lines (HUT102 and HUT78) established at the National Cancer Institute: History and importance to understanding the biology, clinical features, and therapy of cutaneous T-cell lymphomas (CTCL) and adult T-cell leukemia-lymphomas (ATLL) (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 12-23 
    Details
    ISSN: 0730-2312
    Keywords: CTCL ; Sezary ; HTLV-I ; HIV ; IL-2 ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Efforts at the National Cancer Institute to generate continuous in vitro cultures from patients with mycosis fungoides and the Sezary syndrome, neoplasms with a mature T-helper phenotype, led to the establishment of two cell lines, HUT78 and HUT102. Further characterization of these cell lines led to the identification of the first human retrovirus, HTLV-1, in the HUT102 cells, and the clinical description of the syndrome of HTLV-1 associated acute T-cell leukemia/lymphoma; the serum antibody test to screen for this virus was developed from the serum of the patient from whom the cell line was derived. The HUT78 cell line was pivotal in the identification and characterization of the HIV retrovirus in that a subclone, H9, proved to be permissive for replication of HIV in vitro. Propagation of HIV in vitro in H9 cells allowed for the development of immunological reagents to screen blood supplies for the presence of the virus. Further biologic and molecular studies of these lines have led not only to a better understanding of the underlying diseases but also to the development of rational therapeutic approaches. © 1996 Wiley-Liss, Inc.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/jcb.240630503
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    Biology of colorectal and gastric cancer cell lines (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 131-141 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Cell lines established from the human colorectal and gastric cancers may provide very useful tools to the study of the disease and to develop and test new therapeutic approaches, and a large bank of well-characterized cell lines should reflect the diversity of tumor phenotypes and provide adequate models for the study of tumor heterogeneity. Colorectal lines are relatively easy to establish, while gastric cancer cell lines remain extremely difficult to propagate in long-term culture, and the number of cell lines is very limited. In this paper, we describe the up-to-date results of the characteristics of our nine colorectal cancer cell lines and four gastric cancer cell lines. Based on culture, xenograft, and ultrastructural morphologies, these cell lines could be subtyped into well-differentiated, moderately differentiated, poorly differentiated, and mucinous carcinomas. Basic properties concerning expression and secretion of antigens, neuroendocrine features, receptor binding of various gastrointestinal hormones and neurotransmitters, cytogenetic studies, gene amplification and expression, and chemosensitivity profiles are described. In particular, a greater number of receptors for hormones and neurotransmitters are expressed on human colorectal cancer cell lines compared to gastric cancer cell lines, raising the possibility that castrointestinal hormones may have a greater autocrine effect on colon cancer cell growth. Despite major differences in the biology of colorectal cancer and gastric cancer as indicated by clinical studies, the multiple properties that we examined reveals marked similarities between the colorectal and gastric cancer cell lines. However, in vitro chemosensitivity patterns to cytotoxic drugs are very different in colorectal and gastric cell lines. Some of these observations may be due to the relatively low expression of the multidrug-resistance-associated (MDR1) gene in gastric cancer cell lines. In addition, colorectal cancer cell lines express receptors for peptide hormones more frequently. © 1996 Wiley-Liss, Inc.
    Additional Material: 4 Tab.
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    URL: http://dx.doi.org/10.1002/jcb.240630508
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    Dipyridamole mediated enhanced antiproliferative activity of 10-ethyl-10-deazaaminopterin (10-EDAM) against human lung cancer cell lines (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 165-172 
    Details
    ISSN: 0730-2312
    Keywords: 10-EDAM ; dipyridamole ; methotrexate ; lung cancer ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: 10-ethyl-10-deazaaminopterin (10-EDAM) is a rationally designed derivative of the antifolate, methotrexate (MTX). In a number of tumor models these design features have resulted in an improved spectrum of antiproliferative activity as compared with the parent compound. Using an MTT growth assay, we compared in vitro antiproliferative activity of 10-EDAM with MTX in eight lung cancer cell lines. Growth was inhibited in all lines tested by clinically achievable concentrations of 10-EDAM (0.1-1,000 nM). 10-EDAM was more cytotoxic than MTX at the same concentrations in all eight lung cancer cell lines. In an effort to enhance the antiproliferative effect, we evaluated the addition of dipyridamole (DPM), an inhibitor of nucleoside transport, to 10-EDAM (0.1-10 μm). DPM decreased the concentration of 10-EDAM required to cause 50% growth inhibition (IC50) in all eight cell lines tested. This supperssion was statistically significant by 2-sided sign test (P = .0078). By contrast, the IC50 of MTX was decreased in only two of the eight cell lines when DPM was added (0.1-10 μM). In defined thymidine depleted media, cell kill by the combination of 10-EDAM and DPM was no greater than 10-EDAM alone, consistent with the possibility that DPM exerts some of its effect by inhibition of extrinsic nucleoside salvage. In consideration of the published activity of 10-EDAM in lung cancer and the modest clinical toxicity of DPM based biochemical modulation, we conclude the current in vitro data provide justification for clinical evaluation of this combination in patients with lung cancer. © 1996 Wiley-Liss, Inc.This article is a US Government work and, as such, is in the public domain in the United States of America.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/jcb.240630512
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    MYC family DNA amplification in 126 tumor cell lines from patients with small cell lung cancer (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 210-217 
    Details
    ISSN: 0730-2312
    Keywords: Lung neoplasms ; oncogenes ; drug therapy ; mortality ; pathology ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: We identified 126 tumor cell lines established from patients with small cell cancer at the NCI-Navy Medical Oncology Branch from 1977 through 1992. Extensive clinical information was available on 96 patients from whom these cell lines were established. These patients comprised approximately one fourth of the 407 patients treated on prospective therapeutic clinical trials during the same time period. The proportion of tumor cell lines established from previously untreated patients with both limited and extensive stage small cell lung cancer increased during the 16 years of the study (P = 0.008). MYC family DNA amplification was present in 16 of 44 (36%) tumor cell lines established from previously treated patients compared to 7 of 52 (11%) of tumor cell lines established from untreated patients (P = 0.009). MYC DNA amplification in tumor cell lines established from patients previously treated with chemotherapy continued to be associated with shortened survival (P = 0.001). The initiation of a policy to obtain tumor tissue for the purpose of selecting chemotherapeutic agents given to individual patients was associated with an increase in the proportion of patients from whom tumor cell lines could be established for both extensive and limited stage patients (P = 0.001 and 0.05, respectively). © 1996 Wiley-Liss, Inc.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/jcb.240630516
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    Bombesin receptor structure and expression in human lung carcinoma cell lines (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 237-246 
    Details
    ISSN: 0730-2312
    Keywords: bombesin receptor ; gastrin releasing peptide receptor ; neuromedin B receptor ; bombesin ; autocrine growth ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Mammalian bombesin-like peptides gastrin-releasing peptide (GRP) and neuromedin B (NMB) are regulatory neuropeptides involved in numerous physiologic processes, and have been implicated as autocrine and/or paracrine growth factors in human lung carcinoma. Three structurally and pharmacologically distinct bombesin receptor subtypes have been isolated and characterized: the gastrin releasing peptide receptor (GRP-R), the neuromedin B receptor (NMB-R), and bombesin receptor subtype-3 (BRS-3). The three receptors are structurally related, sharing about 50% amino acid identity. They are members of the G-protein coupled receptor superfamily with a seven predicted transmembrane segment topology charcteristic of receptors in this family. The signal transduction pathway for GRP-R and NMB-R involves coupling to a pertussis-toxin insensitive G-protien, activation of phospholipase C (PLC), generation of inositol trisphosphate (IP3), release of intracellular calcium, and activation of protein kinase C. While all three bombesin receptors are activated by bombesin agonists, GRP-R, and NMB-R, and BRS-3 have very different affinities for the mammalian bombesin-like peptides GRP and NMB, as well as bombesin receptor antagonists. The three bombesin receptor subtypes are expressed in an overlapping subset of human lung carcinoma cell lines. Any therapeutic strategy based on modulation of bombesin growth responses in human lung carcinoma cell lines. Any therapeutic strategy based on moducation of bombesin growth reponses in human lung carcinoma would be well served to take into account the pharmacologic heterogeneity of the relevant receptors. © 1996 Wiley-Liss, Inc.This article is a US Government work and, as such, is in the public domain in the United States of America.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/jcb.240630519
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    Expression in human lung cancer cell lines of genes of prohormone processing and the neuroendocine phenotype (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 257-268 
    Details
    ISSN: 0730-2312
    Keywords: small cell cancer ; non-small cell lung cancer ; peptidylglycin α-amidating monooxygenase ; lung tumor cell lines ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Lung tumor cells and cell lines, principally the histologically classified small cell lung cancer, are characterized by the expression of neuroendocrine (NE) features including AADC (aromatic amico acid decarboxylase, previously called DOPA decarboxylase) and the production of many peptide harmones. The general mechanisms by which most aspects of the NE phenotype affect the clinical behavior of lung tumor cells are unknown, but it is well recognized that peptide hormones can have systemic effects (paraneoplastic syndromes) and several have been shown to be autocrine growth factors for cancer cells, In order to determine the relationship between expression of different aspects of the NE phenotype in lung cancer cell lines, we have compared expression of a gene required for biosynthesis of some active peptide hormones (PAM, peptidyglycine α-amidating monooxygenase) to the gene for AADC in 32 lung cancer cell lines. Expression of these genes was quantified by both steady state Northern blot analysis and radiochemical enzymatic activity measurement. To ensure a range of expression of NE markers, non-small cell lung cancer (NSCLC) cell lines were chosen to include several which had previously been shown to express NE markers, and several small cell lung cancer (SCLC) cell lines with previous low level of AADC were included. PAM enzyme activity and Northern blot analysis showed a two to three log variation in level of expression in both the small cell and non-small cell lines. A smaller range was found for AADC expression. Using the highly sensitive PAM enzyme assays, all cell lines were found to express detectable PAM. PAM activities were secreted into the growth medium of all cell lines.There was so simple correlation apparent betwenn AADC and PAM gene expression in the lung cancer cell lines. However, calssic small cell lines demonstrated high levels of expression of both PAM and AADC genes, as did the carcinoid subset of the NSCLC lines. NSCLC lines expressed levels of PAM mRNA and enzyme activities equivalent to those of SCLC, but had infrequent expression of AADC (principlly only carcinoid NSCLC expressed AADC). These data demonstrate that separate aspects of the NE phenotype can be diffrentially expresses in lung cancer histological sub-type. Expression of PAM enzymes in all sub-tupe of lung cancer suggests that peptide prohormone activitioin may be common mechanism for autocrine growth stimulation even in non-NE NSCLC cell lines, or may reflect maintenance in cell lines of a common pathway of lung tumor promotion. © 1996 Wiley-Liss, Inc.This article is a US Government work and, as such, is in the public domain in the United States of America.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630521
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    Masthead (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996) 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630301
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    Regulation of nuclear oncogenes expressed in lung cancer cell lines (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 218-227 
    Details
    ISSN: 0730-2312
    Keywords: lung cancer ; cell lines ; nuclear oncogenes ; myc genes ; c-jun ; c-fos ; transcription factors ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Lung cancer is a major cause of mortality in the United States and accounts for the majority of all cancer deaths in both men and women. It is hoped that through broadening our understanding of the mechanisms involved in transformation of bronchial epithelial cells we will be able to improve methods of diagnosis and treatment of this disease, with the ultimate goal of reducing on lung cancer mortality. A knowledge of the molecular mechanisms involved in processes such as cell division and differentiation is paramount to this task, because it is known that aberrant responses to growth factors or cytokines found in the normal celluar milieu can lead to abnormal cell growth and/or transformation. Signals initiated at the cell membrane by tumor promoters, growth factors, or cytokines are transduced from the cell membrane to the nucleus and are, in part, mediated centrally by transcription factors encoded by nuclear protooncogenes. The transcription factor myc, jun, and fos have been characterized in both normal and transformed lung epithelial cells through detailed studies using cell lines. In this manuscript, we review what is known about the expression and regulation of these nuclear protooncogenes in normal and malignant epithelial cells of the lung, and their role in the development of lung cancer. © 1996 Wiley-Liss, Inc.This article is a US Government work and, as such, is in the public domain in the United States of America.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630517
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  • 88
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    GRP receptors are present in non small cell lung cancer cells (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 247-256 
    Details
    ISSN: 0730-2312
    Keywords: GRP receptor ; cytosolic calcium ; growth ; arachidonic acid ; protien kinase C ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Previously, GRP receptors wer charachterized in sasmll cell lung cancer cells and here non-small cell lung cancer (NSCLC) cells were investigated: (125I-Tyr4) bombesin (BN) or 125I-GRP bound with high affinity to NCI-H720 (lung carcioid) and NCI-H1299 (large cell carcinoma) cells. Binding was specific, time dependent, and saturable. Specific (125I-Tyr4) BN binding to NCI-H1299 cells was inhibited with high affinity by GRP, BN, GRP14-27, (D-Phe6)BN6-13methyl ester, moderate affinity by NMB, and low affinity by NMB, and low, and low affinity by GRP1-16. BN (10nM) transiently elevated cytosolic calcium in a dose dependent manner. BN caused translocation of protein kinase C from the cytosol to the membrane and the translocation caused by BN was reversed by (D-Phe6)BN6-13 methylester. BN stimulated arachidonic acid release and the increase caused by BN was reversed by (D-Phe6)BN6-13 methylester. Using a clonogenic assay, BN stimulated the growth of NCI-H720 cells, and ythe number of colonies was reduced using (D-Phe6)BN6-13 methylester. These data suggest that GRP receptors that are present in lung carcinoid and NSCLC cells may regulate proliferation. © 1996 Wiley-Liss, Inc.This article is a US Government work and, as such, is in the public domain in the United States of America.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630520
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    Transferrin dependence of Ga(NO3)3 inhibition of growth in human-derived small cell lung cancer cells (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 276-287 
    Details
    ISSN: 0730-2312
    Keywords: Ga nitrate ; transferrin ; transferrin receptors ; small cell lung cancer ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: The effect of a combination of anti-transferrin receptor (TFR) antibody, 42/6, and Ga(No3)3 on cell growth was examined in small cell lung cancer (SCLC) cell lines: classic, NCl-H209, NCl-H345, NCl-H510; and variant, NCl-H82 and NCl-N417. The role of TFR and transferrin(TF) in Ga(No3)3 cellular uptake was also tested. Exogenous TF did not enhance the cytotoxicity of Ga. At 〉 3 μg/mL, Ga(No3)3 inhibited growth in all cell lines in TF-supplemented or deficient media. At 〈 3 μg/mL, Ga stimulated growth for all cells but this effect was eliminated by TF or 42/6. Classic SCLC lines required 3-4-fold less exogenous gallium than variant lines to reduce cell number by 50%. The mean Ga uptake (ng/106 cells) in H345 and H209 cell lines was 4-5-fold compared to H82 and N417 uptake (P 〈 0.001). 42/6 reduced exogenous TF-stimulated growth. Antibody plus Ga(No3)3 caused a slight further cell number decline in all cell lines in TF-supplemented or deficient media. These results suggest that the addition of 42/6 antibody treatment would not increase the effectiveness of Ga(No3)3 in patients. Both exogenous and endogenous TF and TFR play an important role in Ga uptake in these cells. © 1996 Wiley-Liss, Inc.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630523
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    Strategy and planning for chemopreventive drug development: Clinical development plans II (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 54-71 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: This is the second publication of Clinical Development Plans from the National Cancer Institute, Division of Cancer Prevention and Control, Chemoprevention Branch and Agent Development Committee. The Clinical Development Plans summarize the status of promising chemopreventive agents regarding evidence for safety and chemopreventive efficacy in preclinical and clinical studies. They also contain the strategy for further development of these drugs, addressing pharmacodynamics, drug effect measurements, intermediate biomarkers for monitoring efficacy, toxicity, supply and formulation, regulatory approval, and proposed clinical trials. Sixteen new Clinical Development Plans are presented here: curcumin, dehydroepiandrosterone, folic acid, genistein, indole-3-carbinol, perillyl alcohol, phenethyl isothiocyanate, 9-cis-retinoic acid, 13-cis-retinoic acid, l-selenomethionine and 1,4-phenylenebis(methylene)selenocyanate, sulindac sulfone, tea, ursodiol, vitamin A, and (+)-vorozole. The objective of publishing these plans is to stimulate interest and thinking among the scientific community on the prospects for developing these and future generations of chemopreventive drugs. © 1997 Wiley-Liss, Inc.
    Additional Material: 1 Tab.
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    URL: http://dx.doi.org/10.1002/jcb.240630705
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    Clinical development plan: Folic acid (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 100-113 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630708
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  • 92
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    Masthead (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 60 (1996) 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240600101
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  • 93
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    Masthead (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 60 (1996) 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240600401
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    Involvement of signal transduction pathways in lung cancer biology (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 228-236 
    Details
    ISSN: 0730-2312
    Keywords: transduction ; biological signals ; oncogenesis ; lung cancer ; bombesin ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Pathways involved in the transduction of biological signals within cells overlap with those involved in oncogenesis. Previous studies have identified a number of discrete disturbances of some elements of these pathways in human lung cancer cells, by virtue of the overexpression or the mutation of certain key molecules. The sequence of biochemical events triggered by a mitogenic stimulus such as the exposure to bombesin-like peptides are being unravelled. The opportunity exists to identify additional changes involving regulatory proteins which may contribute to the regulation of these systems and which may function as suppressors of the malignant phenotype. Furthermore, the understanding of these pathways may identify targets for the pharmacological regulation of tumor cell response to mitogens which may be usable in the clinic. © 1996 Wiley-Liss, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630518
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    Monoclonal antibody αIR-3 inhibits non-small cell lung cancer growth in vitro and in vivo (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. 269-275 
    Details
    ISSN: 0730-2312
    Keywords: IGF-I ; non-small cell lung cancer ; monoclonal antibodies ; growth ; receptors ; Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: The ability of monoclonal antibody (mAb) αI̊-3 to interact with non-small cell lung cancer (NSCLC) cells was investigated. MAb αI̊-3 inhibited specific binding of 125I-IGF-I and 125I-αI̊-3 to a panel of 8 NSCLC cell lines with high affinity (IC50 = 200 and 50 ng/ml, respectively). 125I-αI̊-3 bound with high affinity (Kd = 40 ng/ml) to a single class of sites (Bmax = 8,000/cell) using NCI-H838 cells. 125I-αI̊-3 was internalized when exposed to NCI-H838 or H1299 cells at 37°C but not 4°C. αI̊-3 immunoprecipitated major 90 and 130 kD proteins. IGF-I stimulated and αI̊-3 inhibited the clonal growth of NCI-H1299 cells. αI̊-3 slowed the growth of NCI-H157 and H838 xenografts in nude mice. In a biodistribution study 125I-αI̊-3 was preferentially localized to the tumor as opposed to other organs. These data suggest that IGF-I may be a regulatory agent in NSCLC. © 1996 Wiley-Liss, Inc.This article is a US Government work and, as such, is in the public domain in the United States of America.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630522
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    Foreword: Prospects for chemoprevention in cohorts with cancer risk makers (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. i 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630602
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  • 97
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    Masthead (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 62 (1996) 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240620201
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    Masthead (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 62 (1996) 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240620401
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    Masthead (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996) 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630601
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    Editor' note (1996)
    New York, N.Y. : Wiley-Blackwell
    Journal of Cellular Biochemistry 63 (1996), S. i 
    Details
    ISSN: 0730-2312
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcb.240630603
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