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We prove that a bounded operator on a Banach lattice, satisfying a growth condition, is regular. Also, we prove that the generator of a C
0-semigroup on such a lattice for which such an operator exists is bounded. 相似文献
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The dynamics of non-linear oscillators comprising of a single-degree-of-freedom system and beams with elastic two-sided amplitude constraints subject to harmonic loads is analyzed. The beams are clamped at one end, and constrained against unilateral contact sites near the other end. The structures are modelled by a Bernoulli-type beam supported by springs using the finite element method. Rayleigh damping is assumed. Symmetric and elastic double-impact motions, both harmonic and sub-harmonic, are studied by way of a Poincaré mapping that relates the states at subsequent impacts. Stability and bifurcation analyses are performed for these motions, and domains of instability are delineated. Impact work rate, which is the rate of energy dissipation to the impacting surfaces, is evaluated and discussed. In addition, an experiment conducted by Moon and Shaw on the vibration of a cantilevered beam with one-sided amplitude constraining stop is modelled. Bifurcation observed in the experiment could be captured. 相似文献
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Herbert Henning 《ZDM》2003,35(4):172-176
The author discusses at some examples exemplarily, how the pedagogy of mathematics education in the GDR from curricular and educational/psychological knowledge from the time before 1945 has developed scientifically. 相似文献
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Henning Knutsen 《International Journal of Theoretical Physics》1986,25(7):741-754
A class of McVittie's new nonquadratic solutions is investigated in some detail with regard to its physical properties. It is found that decreasing pressure and density are not compatible with center regularity for these perfect fluid spheres. It is further seen that for gaseous spheres (i.e., the density drops to zero at the outer boundary of the sphere together with the pressurep) oscillatory motions arenot possible. For these gaseous models the pressure and the density are both positive inside the outer surface, and their respective gradients are negative. For the outer gaseous shells models are constructed where for a certain time interval the pressure is increasing for contracting models. Without any restriction with respect to time, for these shell models it found that the density is increasing for contracting models, and the adiabatic speed of sound is less than the speed of light. It is also found that the trace of the energy-momentum tensor is positive, the total mass is negative, and for collapsing shells the rate of change of circumference as measured by an observer riding on the shell is an increasing function of time. However, all these models have the strange geometric feature that the physical radius is a decreasing function of comoving radial coordinate. 相似文献