Virial coefficients and equations of state for mixtures of hard discs,hard spheres and hard hyperspheres

The composition-independent virial coefficients of a d-dimensional binary mixture of (additive) hard hyperspheres following from a recent proposal for the equation of state of the mixture (Santos, A., Yuste, S. B., and López de Haro, M., 1999, Molec. Phys., 96, 1) are examined. Good agreement between theoretical estimates and available exact or numerical results is found for d = 2, 3, 4 and 5, except for mixtures whose components are very disparate in size. A slight modification that remedies this deficiency is introduced and the resummation of the associated virial series is carried out, leading to a new proposal for the equation of state. The case of binary hard sphere mixtures (d = 3) is analysed in some detail.     

A Popov-theory-based survey on digital control of infinite-dimensional systems with unboundedness

This paper represents a Popov-theory-based assessment of thecurrent status of the digital control of infinite–dimensionalsystems with certain unboundedness in control and/or observation,summarizing some results and indicating which, in the authors'opinion, would be the promising directions for future research.     

An adaptive control scheme for a continuous plant under Known output delay, unmodelled dynamics, and input saturation

This paper deals with robustness of adaptive control of continuoussystems subject to known output delay, input saturation, unmodelledlinear dynamics, and bounded disturbances. A simple gradient-typealgorithm with a relative deadzone is used. The relative deadzoneis built with an estimated contribution of the unmodelled dynamicsto the system output. The basic tool used for stability androbustness analysis is Gronwall's lemma.     

A Simple Model for the Variation of Permeability due to Partial Saturation in Dual Scale Porous Media

The main focus of this work is to model macroscopically the effects of partial saturation upon the permeability of dual scale fibrous media made of fiber bundles when a Newtonian viscous fluid impregnates it. A new phenomenological model is proposed to explain the discrepancies between experimental pressure results and analytical predictions based on Darcy's law. This model incorporates the essential features of relative permeability but without the necessity of measuring saturation of the liquid for its prediction. The model is very relevant for the small scale industrial systems where a liquid is forced to flow through a fibrous porous medium. It requires four parameters. Two of them are the two permeability values based on the two length scales. One length scale is of the order of magnitude of the individual fiber radius and corresponds to the permeability of the completely staurated medium, the other is of the order of magnitude of the distance between the fiber bundles and corresponds to the permeability of the partially saturated medium. The other two parameters are the lengths of the two partially saturated regions of the flow domain. The two lengths of the partially saturated region and the permeability of the fully saturated flow domain can be directly measured from the experiments. The excellent agreement between the model and the experimental results of inlet pressure profile with respect to time suggests that this model may be used to describe the variation of the permeability behind a moving front in such porous media for correct pressure prediction. It may also be used to characterize the fibrous medium by determining the two different permeabilities and the relative importance of the unsaturated portion of the flow domain for a given architecture.     

Cognitive level in problem segments and theory segments

Problems play an important role in mathematics instruction and are therefore frequently seen as central points of application for measures of instructional development. The research project “Quality of instruction and mathematical understanding in different cultures” examines the cognitive level of practice problems and theory problems in a three-lesson unit on the Introduction to Pythagorean theorem¹: Analogously to the TIMSS 1999 video study, a differentiation was made between the cognitive level of problem statement and the cognitive level of problem implementation. Additionally, the lesson time was also divided into practice and theory segments. The results show that teachers with a high proportion of connection activities in practice segments do not necessarily also spend a greater proportion of time on an analogous level for theory.     

Time integration of the non-linear Galerkin method

e-mail: bosco{at}mac.cie.uva.es, frutos@mac.cie.uva.es Numerical tests are presented that, for the Kuramoto-Sivashinskyand a reaction-diffusion equation, compare the non-linear Galerkinmethod with standard pseudospectral and pure spectral Galerkindiscretizations. The results show that, for these problems,the non-linear Galerkin method is not competitive with eitherpure spectral Galerkin or pseudospectral discretizations.     

Exponential stability for a contact problem in thermoelasticity

We consider the unilateral problem for the thermoelastic equationand we show that the solution decays exponentially to zero astime goes to infinity; that is, denoting by E(t) the first-orderenergy of the system, we show that positive constants C and exist which satisfy E(t)CE(0)e^–$$$.     

龙爪芦荟和库拉索芦荟中微量锗的测定与红外光谱区别

采用吸光光度法对龙爪芦荟和库拉索芦荟中的微量锗进行了测定,并探讨了两种芦荟的红外光谱的区别。结果表明,龙爪芦荟中含锗量在26.1～28.6μg·g-1,回收率为91.6%～97 5%。库拉索芦荟中含锗量在16.8～20.0μg·g-1,回收率为87.1%～94.5%。两种芦荟的FT IR光谱图在2100cm-1处有明显差异,由此可区别两种芦荟。