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  • Polymer and Materials Science  (6)
  • global convergence  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Globally Convergent Inexact Generalized Newton Method for First-Order Differentiable Optimization Problems (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 551-568 
    Details
    ISSN: 1573-2878
    Keywords: nonsmooth optimization ; inexact Newton methods ; generalized Newton methods ; global convergence ; superlinear rate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Motivated by the method of Martinez and Qi (Ref. 1), we propose in this paper a globally convergent inexact generalized Newton method to solve unconstrained optimization problems in which the objective functions have Lipschitz continuous gradient functions, but are not twice differentiable. This method is implementable, globally convergent, and produces monotonically decreasing function values. We prove that the method has locally superlinear convergence or even quadratic convergence rate under some mild conditions, which do not assume the convexity of the functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004605428858
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  • 2
    Electronic Resource
    Electronic Resource
    Scaled Optimal Path Trust-Region Algorithm (1999)
    Springer
    Journal of optimization theory and applications 102 (1999), S. 127-146 
    Details
    ISSN: 1573-2878
    Keywords: Trust-region methods ; unconstrained optimization ; Bunch–Parlett factorization ; optimal paths ; global convergence ; local convergence rates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Trust-region algorithms solve a trust-region subproblem at each iteration. Among the methods solving the subproblem, the optimal path algorithm obtains the solution to the subproblem in full-dimensional space by using the eigenvalues and eigenvectors of the system. Although the idea is attractive, the existing optimal path method seems impractical because, in addition to factorization, it requires either the calculation of the full eigensystem of a matrix or repeated factorizations of matrices at each iteration. In this paper, we propose a scaled optimal path trust-region algorithm. The algorithm finds a solution of the subproblem in full-dimensional space by just one Bunch–Parlett factorization for symmetric matrices at each iteration and by using the resulting unit lower triangular factor to scale the variables in the problem. A scaled optimal path can then be formed easily. The algorithm has good convergence properties under commonly used conditions. Computational results for small-scale and large-scale optimization problems are presented which show that the algorithm is robust and effective.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021846613163
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  • 3
    Electronic Resource
    Electronic Resource
    Projected quasi-Newton algorithm with trust region for constrained optimization (1990)
    Springer
    Journal of optimization theory and applications 67 (1990), S. 369-393 
    Details
    ISSN: 1573-2878
    Keywords: Two-sided projected Hessians ; trust regions ; differentiable penalty functions ; global convergence ; two-step Q-superlinear rate ; constrained optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Ref. 1, Nocedal and Overton proposed a two-sided projected Hessian updating technique for equality constrained optimization problems. Although local two-step Q-superlinear rate was proved, its global convergence is not assured. In this paper, we suggest a trust-region-type, two-sided, projected quasi-Newton method, which preserves the local two-step superlinear convergence of the original algorithm and also ensures global convergence. The subproblem that we propose is as simple as the one often used when solving unconstrained optimization problems by trust-region strategies and therefore is easy to implement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940481
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  • 4
    Electronic Resource
    Electronic Resource
    The flammability of polyacrylonitrile and its copolymers IV. The flame retardant mechanism of ammonium polyphosphate (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Fire and Materials 18 (1994), S. 307-312 
    Details
    ISSN: 0308-0501
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Ammonium polyphosphate is shown to be an effective flame retardant for homopolymeric and selected fibre-forming copolymers of acrylonitrile. Compared with other phosphates and phosphorus-containing species, it significantly increases both limiting oxygen index and char levels. The mechanism of retardancy is shown to be both physical and chemical in character. When heated to 300°C, the polyphosphate melts and converts to polyphosphoric acid which acts as a physical barrier to surface polymer oxidation and promotes nucleophilic oligomerization of pendant, adjacent nitrile groups. A reduction in the activation energy of this first stage of acrylic polymer degradation suggests that the favoured decomposition route gives rise via oligomerization to char-promoting precursors. Char analyses indicate an empirical formula of C30H13N7P2, which compares favourably with that of a proposed phosphorylated, polynuclear, aromatic heterocyclic structure.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fam.810180506
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  • 5
    Electronic Resource
    Electronic Resource
    Effect of Melting Behaviour on Upward Flame Spread of Thermoplastics (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Fire and Materials 21 (1997), S. 1-6 
    Details
    ISSN: 0308-0501
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The effect of melting behaviour on upward flame spread of thermoplastic materials when subjected to small ignition sources and considered to suffer no external flux was studied using large-scale tests. For moderate fire conditions the cone calorimeter was utilized, with the sample set in a vertical orientation to study the melting behaviour of the specimens. Under these conditions the results indicate that the melting behaviour significantly affects upward flame spread behaviour. A pool of the melt which formed at the base of the vertically oriented sample tested creates a pool fire which then controls the fire growth and flame spread. In contrast, it was found that some thermoplastic materials which have higher glass transition temperatures or undergo a special pyrolysis process such as depolymerization, intumescing or charring do not experience significant melting behaviour when exposed to the same thermal insult. As a result, they behave very differently in terms of upward flame spread. The study also indicates that the melting behaviour of thermoplastic materials is an important characteristic in fires which should be taken into account in the development of modelling, in particular for upward flame spread models. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    In situ studies of epitaxial silicon growth by gas source molecular beam epitaxy (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Advanced Materials for Optics and Electronics 7 (1997), S. 215-224 
    Details
    ISSN: 1057-9257
    Keywords: silicon ; epitaxy ; kinetics ; dynamics ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: The value of in situ monitoring to study growth dynamics and surface reaction kinetics in a gas source molecular beam epitaxy process is illustrated with reference to the growth of Si films on Si(001) substrates using a beam of disilane (Si2H6). By using a combination of reflection high-energy electron diffraction (RHEED) and reflection anisotropy spectroscopy (RAS), we show first how morphological (long-range order) and local electronic structure effects can be separated in the evaluation of growth dynamics. This involves the measurement of step density changes by RHEED concomitantly with the variation in domain coverage on the Si(001) (2×1)+(1×2) reconstructed surface by RAS. This approach is then extended to investigate the kinetics of hydrogen desorption, which is the rate-limiting step in Si growth from Si2H6. It is shown that over a significant temperature range, zeroth-order kinetics are obeyed and this is explained on the basis of a step-mediated desorption process. Finally we show how this influences the growth rate on substrates of differing degrees of vicinality. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Matrix-size interactions in epoxy-glass fibers composites in relation to mechanical relaxations and effects of thermal aging (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 55 (1995), S. 1771-1777 
    Details
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A study was carried out to examine the effect of removing the size from the surface of glass fibers in order to determine its role with respect to thermoxidative aging. Dynamic mechanical relaxation data have revealed that mechanical losses were always greater than the calculated upper bound values. The effects of removing the size from the surface glass fibers for epoxy matrix composites were found to be completely different when a fluoroligomer was used to modify the resin. Contrary to the case of the conventional epoxy resin, the characteristics of the composites containing fluoroligomer-modified resin were found to be insensitive to the removal of the size from the glass fibers surface. The presence of the size on the surface of the fibers provides an interlayer that degrades through the formation of more lightly crosslinked products than the matrix, thereby providing a large increase in dynamic mechanical losses after thermal aging. © 1995 John Wiley & Sons, Inc.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/app.1995.070551307
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  • 8
    Electronic Resource
    Electronic Resource
    Mechanisms of carbon dioxide laser stereolithography in epoxy-based materials (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 62 (1996), S. 491-500 
    Details
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: We present in this article the use of infrared laser radiation to achieve localized curing in thermosensitive epoxy resin compounds. In stereolithography, the objective is to cure a localized region in a material by precisely confining the laser energy to the area that is to be cured. Industry already uses ultraviolet laser radiation at 352 nm to fabricate three-dimensional structures. Via infrared laser curing, we demonstrate the viability of a completely thermal localized curing process. In our experiment, we have focused the beam from a carbon dioxide (CO2) laser onto a sample composed of epoxy resin, diethylene triamine, and silica powder. Such resins typically cure, or solidify, when heated to moderately high temperatures, and our results show that we can confine the heating of the material, and, therefore, its curing in all three dimensions. We present a physical and a chemical model to describe the process and measure the curing rate as a function of temperature. In order to model the flow of heat in our sample as a result of infrared laser irradiation, we solved the time-dependent heat equation in cylindrical coordinates using the Crank-Nicholson finite-difference method. The results allow us to predict the curing behavior of the sample as a function of laser irradiation conditions, and we find good agreement with our preliminary experimental observations. © 1996 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Optical activity based on macromolecular asymmetryPart XXVI of Haloaldehyde Polymers; Part XXV : E.G. Brame, A. M. Raevsky, G. K. Semin, G. D. Jaycox, and O. Vogl, Polymer Bulletin 10(11/12), 521 (1983) (1985)
    New York : Wiley-Blackwell
    Die Makromolekulare Chemie 13 (1985), S. 1-12 
    Details
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Optically active isotactic polychloral was prepared in which the optical activity comes exclusively from molecular asymmetry (i.e., helical conformation). Molecular asymmetry requires a high conformational energy barrier for the polymer backbone, and an asymmetric initiator to induce a predominance of one helical screw-sense. Polychloral meets the criteria. Asymmetric initiators used to obtain optically active polychloral include tetramethyl ammonium (+)- or (-)-0-acetylmandelate, tetramethylammonium (+)- or (-)-0-methylmandelate, the lithiumalkoxides of methyl (+)- or (-)-mandelate, lithium cholesten-3β-oxide, lithium cholestan-3β-oxide, and lithium (+)- or (-)-2-octanoxide. Using the above initiators at 0.5 mol %, a maximum specific rotation of [α] D25 = 5000 was obtained for polychloral. Errors in specific rotation were typically ±7%.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/macp.1985.020131985102
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