Spectroscopic Investigations of Polymer Nanocomposites

The addition of an inorganic component to polymers leads to improvements in various physical and mechanical properties. Various examples on filled elastomeric networks will show that a mechanical characterization can be nicely combined with a spectroscopic investigation for a better understanding of the properties of the composite materials.     

Discrete Sturm comparison theorems on finite and infinite intervals

The Sturm comparison theorem for second-order Sturm–Liouville difference equations on infinite intervals is established and discussed.     

Transition from zero-dimensional to one-dimensional behavior in InAs and CdSe nanorods

Tunneling and optical spectroscopy performed on InAs nanorods 7–25 nm long, reveal a clear dependence of the band gap on length. This (zero-dimension like) behavior is different from that of CdSe rods, where the band gap is nearly independent of length, a signature of quasi-one-dimensionality. The transition between these two regimes is governed by the ratio between the Bohr radius and the nanorods length. The gaps measured by tunneling spectroscopy are larger than the optical gaps by a factor that depends on the tunneling configuration. This is attributed to a combination of the Coulomb interaction and the voltage division between the two tunnel junctions in the STM experiment. However, the tunneling gaps were found to reduce in dense aggregates of rods.     

Minimal area problems for functions with integral representation

We study the minimization problem for the Dirichlet integral in some standard classes of analytic functions. In particular, we solve the minimal areaa ₂-problem for convex functions and for typically real functions. The latter gives a new solution to the minimal areaa ₂-problem for the classS of normalized univalent functions in the unit disc. Supported by NSF grant DMS-0412908.     

Theoretical Considerations Regarding the Optimization of Cardiac Assistance by lntraaortic Balloon Pumping

A lumped parameter model representing the effects of cardiac assistance by intraaortic balloon pumping was developed. The model permits closed-form calculations of important hemodynamic events in the system. The equations derived from the model were used to determine pumping parameters for optimum assistance. The model indicates that, in the ideal case, optimization of assistance requires instantaneous inflation of the balloon to maximum volume at end systole and instantaneous complete deflation at end diastole. Since an impulse flow rate is not realizable in practice, the model was used to investigate the effects of finite inflation/deflation periods. In general, it was found that fast inflation/deflation rates give higher benefits than slow rates. The optimal time to begin inflation is end systole. Timing of deflation was shown to involve a tradeoff between lower end diastolic pressure (achieved with early deflation) and increase of mean diastolic pressure and cardiac output (achieved with late deflation). The model's predictions were validated using a nonlinear distributed parameter digital computer model previously described. The lumped model results should make possible a quantitative as well as a simple approach to automatic control of in-series cardiac assistance.     

Mass spectrometric studies on a β-ketosulfone

The fragmentation of the β-ketosulfone-γ-methylsulfonyl-γ-benzoylbutyronitrile under electron bombardment follows a number of different pathways: formation of the benzoyl ion (Major path); remova of acrylonitrile; liberation of the methylsulfonyl radical or of methylsulfonic acid; and finally elimination of a methylenecyano radical. The fragments observed can be explained by these five degradation paths. The reactions are compared with the photochemical cleavage of this β-ketosulfone in benzene solution.     

Quality control of wastewater treatment: A new approach

This paper presents a new approach to quality control of wastewater treatment. The first part formulates basic principles of statistical process control (SPC) and Taguchi Method. Then it is shown that the classical SPC technique used in industry, cannot be to applied to wastewater treatment plants without adaptation and that the Taguchi Method is inapplicable in this case. This is followed by an example from literature, which demonstrates the problems of applying the SPC method to wastewater treatment. The third part of the paper presents a case study where the performance of a greywater treatment plant is examined. The performance is analyzed by means of cross-correlation between input and output parameters. A new approach to SPC of wastewater treatment, either “Dynamic SPC” or “linear regression SPC”, is presented, and a permeability coefficient is developed (the ratio of the output and input energies). Both are proposed as monitoring tools for wastewater treatment systems.     

A generalized Schwarz lemma at the boundary

Let be an analytic function mapping the unit disc to itself. We generalize a boundary version of Schwarz's lemma proven by D. Burns and S. Krantz and provide sufficient conditions on the local behavior of near a finite set of boundary points that requires to be a finite Blaschke product. Afterwards, we supply several counterexamples to illustrate that these conditions may also be necessary.