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951.
We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response
equation respecting causality and power dissipation. The proposed Hamiltonian couples the given system to auxiliary fields,
in the universal form of a so-called canonical heat bath. After integrating out the heat bath the original dissipative evolution
is exactly reproduced. Furthermore, we show that the dynamics associated to a minimal Hamiltonian are essentially unique,
up to a natural class of isomorphisms. Using this formalism, we obtain closed form expressions for the energy density, energy
flux, momentum density, and stress tensor involving the auxiliary fields, from which we derive an approximate, “Brillouin-type,”
formula for the time averaged energy density and stress tensor associated to an almost mono-chromatic wave. 相似文献
952.
953.
Tomoaki Ono 《Proceedings of the American Mathematical Society》2000,128(2):353-360
Let be a tower of rings of characteristic . Suppose that is a finitely presented -module. We give necessary and sufficient conditions for the existence of -bases of over . Next, let be a polynomial ring where is a perfect field of characteristic , and let be a regular noetherian subring of containing such that . Suppose that is a free -module. Then, applying the above result to a tower of rings, we shall show that a polynomial of minimal degree in is a -basis of over .
954.
Ignacio Villanueva 《Proceedings of the American Mathematical Society》2000,128(3):793-801
Given a -linear operator from a product of spaces into a Banach space , our main result proves the equivalence between being completely continuous, having an -valued separately continuous extension to the product of the biduals and having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to being weakly compact, and that, for , being weakly compact implies the conditions above but the converse fails.
955.
956.
Derivations and Automorphisms of the Positive Part of the Two-parameter Quantum Group Ur,s(B3) 下载免费PDF全文
We compute the derivations of the positive part of the two-parameter quantum group U_(r,s)(B_3) and show that the Hochschild cohomology group of degree 1 of this algebra is a threedimensional vector space over the base field C. We also compute the groups of(Hopf) algebra automorphisms of the augmented two-parameter quantized enveloping algebra ?_(r,s)~(≥0)(B_3). 相似文献
957.
A matching in a graph is said to be extendable if there exists a perfect matching of containing . In 1989, it was shown that every connected planar graph with at least vertices has a matching of size three which is not extendable. In contrast, the study of extending certain matchings of size three or more has made progress in the past decade when the given graph is -connected planar triangulation or -connected plane graphs with few non-triangular faces.In this paper, we prove that if is a -connected plane graph of even order in which at most two faces are not triangular and is a matching of size four in which the edges lie pairwise distance at least three apart, then is extendable. A related result concerning perfect matching with proscribed edges is shown as well. 相似文献
958.
A way to extend operators in spaces of continuous functions to spaces of continuous set-valued functions is proposed. This extension is developed through the Steiner selections of the set-valued functions. Their properties and characteristics of the convergence of sequences of operators of this class are studied. In Part Ⅱ of this series some applications to approximation theory will be shown. 相似文献
959.
Rheological and fracture properties of optimally mixed flour doughs from three wheat cultivars which perform differently in cereal products were studied in uniaxial and biaxial extension. Doughs were also tested in small angle sinusoidal oscillation. In accordance with previously published results the linear region was found to be very small. The rheological properties at small deformations hardly depended on the cultivar. A higher water content of the dough resulted in a lower value for the storage modulus and a slightly higher value for tan . For both uniaxial and biaxial extension a more than proportional increase in stress was found with increasing strain, a phenomenon called strain hardening. In uniaxial extension (i) stresses at a certain strain were higher and (ii) the stress was less dependent on the strain rate than in biaxial extension. This indicates that in elongational flow orientational effects are of large importance for the mechanical properties of flour dough. This conclusion is consistent with published data on birefringence of stretched gluten. Fracture stress and strain increased with increasing deformation rate. The observed time-dependency of fracture properties can best be explained by inefficient transport of energy to the crack tip. Presumably, this is caused by energy dissipation due to inhomogeneous deformation because of friction between structural elements, e.g. between dispersed particles and the network. Differences in the rheological properties at large deformations between the cultivars were observed with respect to (i) stress, (ii) strain hardening, (iii) strain rate dependency of the stress, (iv) fracture properties and (v) the stress difference between uniaxial and biaxial extension. 相似文献
960.