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51.
Rajesh H. Somani Igors Sics Benjamin S. Hsiao 《Journal of polymer science. Part A, Polymer chemistry》2006,44(24):3553-3570
Combined in situ rheo-SAXS (small-angle X-ray scattering) and -WAXD (wide-angle X-ray diffraction) studies using couette flow geometry were carried out to probe thermal stabilty of shear-induced oriented precursor structure in isotactic polypropylene (iPP) at around its normal melting point (162 °C). Although SAXS results corroborated the emerging consensus about the formation of “long-living” metastable mesomorphic precursor structures in sheared iPP melts, these are the first quantitative measures of the limiting temperature at which no oriented structures survive. At the applied shear, rate = 60 s−1 and duration ts = 5 s, the oriented iPP structures survived a temperature of 185 °C for 1 h after shear, while no stable structures were detected at and above 195 °C. Following Keller's concepts of chain orientation in flow, it is proposed that the chains with highly oriented high molecular weight fraction are primarily responsible for their stability at high temperatures. Furthermore, the effects of flow condition, specifically the shear temperature, on the distributions of oriented and unoriented crystals were determined from rheo-WAXD results. As expected, at a constant flow intensity (i.e., rate = 30 s−1 and duration, ts = 5 s), the oriented crystal fraction decreased with the increase in temperature above 155 °C, below which the oriented fraction decreased with the decrease in temperature. As a result, a crystallinty “phase” diagram, i.e., temperature versus crystal fraction ratio, exhibited a peculiar “hourglass” shape, similar to that found in many two-phase polymer–polymer blends. This can be explained by the competition between the oriented and unoriented crystals in the available crystallizable species. Below the shear temperature (155 °C), the unoriented crystals crystallized so rapidly that they overwhelmed the crystallization of the oriented crystals, thus depleting a major portion of the crystallizable species and increasing their contribution in the final total crystalline phase. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3553–3570, 2006 相似文献
52.
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54.
A trajectory-following method for unconstrained optimization 总被引:2,自引:0,他引:2
A trajectory-following method with interesting properties is considered for solving unconstrained nonlinear programming problems. The trajectory is defined by a special system of ordinary differential equations. This system uses only the gradient of the objective function. Numerical examples are given.The work of the second author was supported by the DFG Schwerpunkt Anwendungs-bezogene Optimierung and Steuerung. 相似文献
55.
Benjamin A. Lotto 《Integral Equations and Operator Theory》1990,13(2):216-230
For a given functionb in the unit ball ofH
and an arbitraryH
functionm, the question of whenm is a multiplier of the de Branges space
(that is, when
is invariant under multiplication bym) is examined. Some necessary and sufficient conditions thatm be a multiplier of
are found and it is shown that there are no nonconstant inner multipliers of
whenb is a nonconstant extreme point of the unit ball ofH
. A new proof is given of the known fact that
is invariant under multiplication byz whenb is not an extreme point of the unit ball ofH
. Finally, we give a new proof of the known fact that an inner functionm is a multiplier of
forb(z)=(1+z)/2 if and only ifm belongs to the range of
.Some of the work in this paper originally appeared in the author's doctoral disseratation written at the University of California at Berkeley under the supervision of Donald Sarason. 相似文献
56.
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58.
The spin content of the proton is investigated by studying the flavor singlet axial structure of the nucleon in a non-topological chiral soliton model. In order to construct a nucleon state we used the generator coordinate projection method as well as a coherent state for the meson wave function. Using a standard set of parameters we found the value g A 0 ? 0.44 for the flavor singlet axial vector coupling constant. This result is not far from that of a typical valence quark model. 相似文献
59.
Kochocki JA Allison WW Alner GJ Ambats I Ayres DS Balka LJ Barr GD Barrett WL Benjamin D Border P Brooks CB Cobb JH Cockerill DJ Coover K Courant H Dahlin B DasGupta U Dawson JW Edwards VW Fields TH Kirby-Gallagher LM Garcia-Garcia C Giles RH Goodman MC Heller K Heppelman S Hill N Hoftiezer JH Jankowski DJ Johns K Joyce T Kafka T Litchfield PJ Lopez FV Lowe M Mann WA Marshak ML May EN McMaster L Milburn RH Miller W Napier A Oliver WP Pearce GF Perkins DH Peterson EA Price LE Roback D Rosen DB 《Physical review D: Particles and fields》1990,42(9):2967-2973
60.
Kurt Schütte 《Archive for Mathematical Logic》1988,27(1):85-99
Summary This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger [3]. The generalized systemT(V) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V) is provable in a formal system of second order arithmetic with the axiom schema of
2
1
-comprehension in a similar way, as it is proved in [6] for the weaker notation systemT(V). 相似文献