Free arrangements and rhombic tilings

Let Z be a centrally symmetric polygon with integer side lengths. We answer the following two questions:

1. When is the associated discriminantal hyperplane arrangementfree in the sense of Saito and Terao?
2. When areall of the tilings of Z by unit rhombicoherent in the sense of Billera and Sturmfels?

Surprisingly, the answers to these two questions are very similar. Furthermore, by means of an old result of MacMahon on plane partitions and some new results of Elnitsky on rhombic tilings, the answer to the first question helps to answer the second. These results then also give rise to some interesting geometric corollaries. Consideration of the discriminantal arrangements for some particular octagons leads to a previously announced counterexample to the conjecture by Saito [ER2] that the complexified complement of a real free arrangement is aK (π, 1) space.     

The electromagnetic interaction in chiral perturbation theory

We investigate electromagnetic effects in the framework of chiral perturbation theory. Using a completely independent method, we confirm Urech’s results for the divergences of the one-loop functional in the electromagnetic sector. We perform a one-loop analysis of allP _t2 (P=π, K, η) and theK _t3 form factors $f_ + ^{K^ + \pi ^o } (0),f_ + ^{K^o \pi ^ - } (0)$ , including a systematic treatment of theO(e ² p ²) contributions in the mesonic part. We illustrate our results by several numerical estimates.     

Determination of heavy metal concentration in feed and permeate streams of polymer enhanced ultrafiltration process

Polymer enhanced ultrafiltration (PEUF) is a newly developed method for the removal of heavy metals from aqueous solutions. This method was applied for the removal of mercury and cadmium with the presence of polyethyleneimine (PEI) as a water soluble polymer. After ultrafiltration experiments for metal–polymer mixtures, two separate streams, namely, retentate and permeate, former of which contains mainly metal–polymer complex and free polymer molecules while latter of which mainly contains free metal ions, were obtained. At the end of PEUF experiments, performance of operation was determined by concentration analyses which was achieved by atomic absorption spectroscopy (AAS) applied in a different way for permeate and retentate streams considering the effect of presence of polymer. For mercury analysis, cold vapor AAS was applied. It was observed that the presence of PEI did not affect the atomic absorption signal when 10% HCl was added to the sample solutions. For calcium and cadmium, flame AAS was used. It was observed that change in PEI concentration results in change in measured concentration of calcium and cadmium. Therefore, two new approaches were developed for accurate measurement of concentrations of calcium and cadmium. It was also observed that presence of other metals did not affect the accuracy of the measurement of a particular metal in the concentration range studied.     

Partial Quenching of Parametrical Tetragonality of a Chromium(III) Complex by Pressure Tuning

The ligand-field spectrum of [Cr(NH(3))(4)F(2)]AsF(6) has been pressure-tuned up to 100 kbar. The parametrical analysis shows that the absolute values of the two independent tetragonalities of the chromophoric ion both decrease with increasing isotropic pressure so that the molecular ion becomes more isotropic. Moreover, the Cr-N single bonds appear to be more compressible than the Cr-F bonds, for which it is parametrically clear that they have a partial multiple-bond character. While the spectrochemical parameter for F(-), Delta(F), increases with pressure, its two components Delta(sigma)(F) and Delta(pi)(F) decrease. It is confirmed that nephelauxetism increases with pressure.     

Microwave sputtering of conductors and insulators for optical emission and mass spectrometry

A microwave-powered slab-line cavity was used to excite a discharge in low pressure argon or neon and to demonstrate the sputtering of conducting and non-conducting samples by a microwave excited discharge. Both optical emission spectroscopy and mass spectrometry were used as detection systems. The dependence of the signals on gas pressure and net microwave power was investigated.     

Measurement/data-processing method to improve the ruggedness of membrane-based sensors: Application to amperometric oxygen sensor

This paper describes alternative measurement and data-processing approaches that can reduce effects of experimental variables on results obtained with a membrane-based sensor for oxygen. In the new approaches, the membrane-based sensor is first equilibrated with the sample solution, after which a polarizing voltage is applied and current vs. time data are recorded as the response decays toward a steady-state condition. Current vs. time data are then processed by a fixed-time option and an integration option designed to determine the charge corresponding to the total amount of oxygen inside the membrane when a polarizing voltage is applied. The current measured at a fixed time and the total charge varied linearly with oxygen concentration between 0.05 and 0.26 mmol l(-1). Pooled relative standard deviations (N = 35) for the measurement/data-processing step were near 0.4% for the new pre-equilibrium options compared to a value of 0.3% for the steady-state option. Dependencies of the pre-equilibrium options on membrane thickness and stirring rate in the most sensitive regions were at least two orders of magnitude smaller than for the steady-state option.     

Spectral transport model for turbulence

The spectrum of inhomogeneous turbulence is modeled by an approach that is not limited to regimes of large Reynolds numbers or small mean-flow strain rates. In its simplest form and applied to incompressible flow, the model depends on five phenomenological constants defining the strength of turbulence coupling to mean flow, turbulence transport in physical and wave-number space, and mixing of stress-tensor components. The implications for homogeneous isotropic turbulence are investigated in detail and found to correspond well to the conclusions from more fundamental theories. Under appropriate limiting conditions, a turbulent system described by the model will relax over time into a state of approximate spectral equilibrium permitting a reduction to a one-point model for the system that is substantially like the familiar K- model. This yields preliminary estimates of the present model's parameters and points to the way to improved modeling of flows beyond the applicability of the K- method.