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1.
ZDM – Mathematics Education - Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems... 相似文献
2.
This paper examines the behavior of a class of nonlinearly elastic rods under tension. These rods can suffer longitudinal extension, transverse contraction, shear, and flexure. The deformation is governed by an eighth order, quasilinear system of ordinary differential equations. A convergent perturbation process shows that there is a very rich collection of solutions that bifurcate from the trivial affine configuration. Global results are obtained for hyperelastic rods. These solutions describe instabilities of the shear and necking type and can exhibit hysteresis.
The research of the first author was supported by National Science Foundation Grant MPS 73-08587 A02. Some of the results reported here were obtained by the second author in his master's thesis. 相似文献
Résumé On considère le comportement d'une classe de poutres nonlinéairement élastiques en état de tension. Ces poutres peuvent souffrir une extension longitudinale, une contraction transversale, un cisaillement et une fiexion. La déformation est gouvernée par un système quasi-linéaire d'équations différentielles ordinaires du huitième ordre. Un procès convergeant de perturbations montre qu'il y a une collection très riche de solutions qui bifurquent de la configuration banale affine. Dans le cas hypérélastique on obtient des résultats globaux. On montre que ces solutions décrivent des instabilités du type de cisaillement et d'étranglement et peuvent exhiber une hystérésis.
The research of the first author was supported by National Science Foundation Grant MPS 73-08587 A02. Some of the results reported here were obtained by the second author in his master's thesis. 相似文献
3.
An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic
porous medium containing two immiscible fluids. The theory is based on the Berryman–Thigpen–Chin (BTC) model, in which capillary
pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently
low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the time domain.
These partial differential equations describe two independent modes of dilatational wave motion that are analogous to the
Biot fast and slow compressional waves in a single-fluid system. The equations can be solved analytically under a variety
of initial and boundary conditions. The stipulation of “low frequency” underlying the derivation of our equations in the time
domain is shown to require that the excitation frequency of wave motions be much smaller than a critical frequency. This frequency
is shown to be the inverse of an intrinsic time scale that depends on an effective kinematic shear viscosity of the interstitial
fluids and the intrinsic permeability of the porous medium. Numerical calculations indicate that the critical frequency in
both unconsolidated and consolidated materials containing water and a nonaqueous phase liquid ranges typically from kHz to
MHz. Thus engineering problems involving the dynamic response of an unsaturated porous medium to low excitation frequencies
(e.g., seismic wave stimulation) should be accurately modeled by our equations after suitable initial and boundary conditions
are imposed. 相似文献
4.
The kinetics of the noncatalyzed reaction between α, ω -dicarboxypoly-amide-11 and α, ω -dihydroxypolyoxyalkylenes is investigated by using the reactions of 11-dodecylamidoundecanoic acid with 1-dodecanol, 2-tridecanol, α-dodecyl-ω-hydroxypolyoxyethylene or α-dodecyl-ω;-hydroxypolyoxypropylene as models. Kinetic data fit a 3rd overall order (2 in acid and 1 in alcohol). Rate constants and activation parameters are determined and compared. 相似文献
5.
The effects of quasi-periodicity on the splitting of invariant manifolds are examined. We have found that some harmonics that could be expected to be dominant in some ranges of the perturbation parameter actually are nondominant. It is proved that, under reasonable conditions, this is due to the arithmetic properties of the frequencies. 相似文献
6.
Nera Cagnoli Paolo Ceccherelli Massimo Curini Maria Carla Marcotullio Ernest Wenkert 《合成通讯》2013,43(11):1261-1271
Copper oxide-catalyzed decomposition of 1-diazoacetyl-1-methyl-3-methylenecyclohexanes produces strained tricycles whose reduction or hydrolysis affords 6-bicyclo[3.2.1]octanones. 相似文献
7.
We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, assuming some restriction of the Generalized Continuum Hypothesis, there are many outer automorphisms. 相似文献
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10.
A Review of: “Aquatic Chemistry (An Introduction Emphasizing Chemical Equilibria in Natural Waters)”
Ernest Merian 《International journal of environmental analytical chemistry》2013,93(3-4):317-318
Abstract 2nd Edition, by Prof. Dr. Werner Stumm, Swiss Federal Institute of Technology, Zurich, and Prof. Dr. James J. Morgan, California Institute of Technology, Pasadena, 780 pages (including 97 tables, 167 figures, an appendix of 8 pages “Thermodynamic Properties of Common Chemical Species in Aquatic Systems”, an author index of 10 pages, and a subject index of 14 pages), stiff paper cover, format 234 ± 161 mm, ISBN 0-471-04831-3, John Wiley & Sons, New York (1981) 相似文献