Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

Differentiation between intra-axial metastatic tumor progression and radiation injury following fractionated radiation therapy or stereotactic radiosurgery using MR spectroscopy, perfusion MR imaging or volume progression modeling

Objective

To determine the accuracy of magnetic resonance spectroscopy (MRS), perfusion MR imaging (MRP), or volume modeling in distinguishing tumor progression from radiation injury following radiotherapy for brain metastasis.

Methods

Twenty-six patients with 33 intra-axial metastatic lesions who underwent MRS (n=41) with or without MRP (n=32) after cranial irradiation were retrospectively studied. The final diagnosis was based on histopathology (n=4) or magnetic resonance imaging (MRI) follow-up with clinical correlation (n=29). Cho/Cr (choline/creatinine), Cho/NAA (choline/N-acetylaspartate), Cho/nCho (choline/contralateral normal brain choline) ratios were retrospectively calculated for the multi-voxel MRS. Relative cerebral blood volume (rCBV), relative peak height (rPH) and percentage of signal-intensity recovery (PSR) were also retrospectively derived for the MRPs. Tumor volumes were determined using manual segmentation method and analyzed using different volume progression modeling. Different ratios or models were tested and plotted on the receiver operating characteristic curve (ROC), with their performances quantified as area under the ROC curve (AUC). MRI follow-up time was calculated from the date of initial radiotherapy until the last MRI or the last MRI before surgical diagnosis.

Results

Median MRI follow-up was 16 months (range: 2-33). Thirty percent of lesions (n=10) were determined to be radiation injury; 70% (n=23) were determined to be tumor progression. For the MRS, Cho/nCho had the best performance (AUC of 0.612), and Cho/nCho >1.2 had 33% sensitivity and 100% specificity in predicting tumor progression. For the MRP, rCBV had the best performance (AUC of 0.802), and rCBV >2 had 56% sensitivity and 100% specificity. The best volume model was percent increase (AUC of 0.891); 65% tumor volume increase had 100% sensitivity and 80% specificity.

Conclusion

Cho/nCho of MRS, rCBV of MRP, and percent increase of MRI volume modeling provide the best discrimination of intra-axial metastatic tumor progression from radiation injury for their respective modalities. Cho/nCho and rCBV appear to have high specificities but low sensitivities. In contrast, percent volume increase of 65% can be a highly sensitive and moderately specific predictor for tumor progression after radiotherapy. Future incorporation of 65% volume increase as a pretest selection criterion may compensate for the low sensitivities of MRS and MRP.     

A chemical test of the principle of critical point universality: the solubility of nickel (II) oxide in isobutyric acid + water near the consolute point

A mixture of isobutyric acid + water has an upper consolute point at 38.8 mass?% isobutyric acid and temperature near 26?°C. Nickel (II) oxide dissolves in this mixture by reacting with the acid to produce water and nickel isobutyrate. The solubility of nickel (II) oxide in isobutyric acid + water has been measured as a function of temperature at compositions, 25, 38.8, and 60 mass?% isobutyric acid. For values of the temperature, T, which were at least 2 K in excess of the liquid-liquid phase transition temperature, the measured values of the solubility, s, lie on a straight line when plotted in van't Hoff form with ln?s versus 1∕T. The slope, (?ln?s∕?(1∕T)), of the line is negative indicating that the dissolution reaction is endothermic. When the temperature was within 2 K of the phase transition temperature, however, (?ln?s∕?(1∕T)) diverged toward negative infinity. The principle of critical point universality predicts that when excess solid nickel (II) oxide is in dissolution equilibrium with liquid isobutyric acid + water, (?ln?s∕?(1∕T)) should diverge upon approaching the consolute point along the critical isopleth at 38.8 mass?% isobutyric acid. As determined by the sign of the enthalpy of solution, the sign of this divergence is expected to be negative. Not only do our experiments confirm these predictions, but they also show that identical behavior can be observed at both 25 and 60 mass?% isobustyric acid, compositions which lie substantially to either side of the critical composition.     

Reactions of diethylmagnesium - ethyllithium solutions with pyridine

In contrast to the reactions of pyridine with diethylmagnesium or ethyllithium alone, which lead only to 1,2-addition, reactions with diethylmagnesium-ethyllithium solutions lead to significant amounts of 1,4-addition; magnesium ate species are proposed to be responsible.     

Perfluorocyclobutane aromatic ether polymers

Novel polymers containing alternating perfluorocyclobutane and aromatic ether subunits are prepared from aryl poly(trifluorovinyl ether) monomers via the thermal [2π + 2π] dimerization of the trifluorovinyl ether functionality. A model study is described, which probes the nature of the perfluorocyclobutane rings formed during the polymerization reaction. The bifunctional monomer 4,4′-bis(trifluorovinyloxy) biphenyl and the trifunctional monomer 1,1,1-tris(4-trifluorovinyloxyphenyl)ethane are prepared and polymerized to provide thermoplastic and thermoset polymers, respectively. Characterization of the mechanical and dielectric properties of these new polymers is presented. © 1993 John Wiley & Sons, Inc.     

ℤ n Baxter model: Symmetries and the Belavin parametrization

The _n Baxter model is an exactly solvable lattice model in the special case of the Belavin parametrization. For this parametrization we calculate the partition function,, in an antiferromagnetic region and the order parameter in a ferromagnetic region. We find that the order parameter is expressible in terms of a modular function of leveln which forn = 2 is the Onsager-Yang-Baxter result. In addition we determine the symmetry group of the finite lattice partition function for the general _n Baxter model.     

MODELING CLIMATE CHANGE AND THE EFFECT ON THE NORWEGIAN SALMON FARMING INDUSTRY

Abstract Global warming is expected to affect the ecosystem in the Northeast Atlantic, and substantial changes will also affect the aquaculture industry. Farming of salmon and trout is the biggest aquaculture industry in Norway, with an export value of about 3 billion US dollars in 2007. The objective of the paper is to analyze the potential economic effect a general increase in sea temperature can have on the Norwegian salmon aquaculture industry. The assessment of the economic impact of global warming is made possible by estimating a growth function, which explicitly includes sea water temperature. The analysis compares the economic effect of a climate change on fish farming plants in the south and the north of Norway. The scenarios are based on a model with monthly seasonal variation in temperature.     

Algorithms for the computation of polynomial relationships for the hard hexagon model

We calculate the polynomial relationships P(, z) = 0 and P(, κ) = 0 in both the ordered and disordered regimes for the hard hexagon model. We start with Baxter's exact solution which gives the physical quantities κ, , and z parametrically as a function of a variable τ and exploit the modular properties of Baxter's solution. Using elementary Riemann surface theory, the computation can be reduced to algorithms involving only linear algebra. These algorithms are implemented using a computer algebra system. The method will be applicable to other exactly solvable models in which cusp expansions can be computed.