Evaluation,Pitfalls and Recommendations for the “Water Layer Test” for Solid Contact Ion‐selective Electrodes

The “water layer test” is a crucial validation step of solid‐contact ion‐selective electrodes. It can confirm or contest the claim that the tested electrode is indeed a genuine solid contact electrode without an aqueous film between the ion‐selective membrane and its solid contact. Information about the presence of a water layer is essential for the interpretation of drifts in the electrode potentials commonly experienced with solid contact electrodes. Since its publication, the water layer test has been ubiquitously used, but without a standardized protocol the interpretation (or misinterpretation) of the test results led to uncertainties in the conclusions. Through both experiments and simulations based on theoretical models we have investigated the experimental parameters that can influence the results of the water layer test. We propose guidelines to minimize the possibility of misinterpretation of the results of the water layer test by considering the key factors that affect the shape of transients recorded during the water layer test. Most importantly, we emphasize the importance of allowing sufficient time for conditioning the tested electrode before the water layer test and providing adequate time for equilibration during the experiment. Using a thin ion‐selective membrane and thin solid‐contact layer for the tests is also recommended.     

Brownian motion on a homogeneous random fractal

Summary We introduce a simple random fractal based on the Sierpinski gasket and construct a Brownian motion upon the fractal. The properties of the process on the Sierpinski gasket are modified by the random environment. A sample path construction of the process via time truncation is used, which is a direct construction of the process on the fractal from the associated Dirichlet forms. We obtain estimates on the resolvent and transition density for the process and hence a value for the spectral dimension which satisfiesd _s=2d _f/d_w. A branching process in a random environment can be used to deduce some of the sample path properties of the process.     

Transition density estimates for Brownian motion on affine nested fractals

A class of affine nested fractals is introduced which have different scale factors for different similitudes but still have the symmetry assumptions of nested fractals. For these fractals estimates on the transition density for the Brownian motion are obtained using the associated Dirichlet form. An upper bound for the diagonal can be found using a Nash-type inequality, then probabilistic techniques are used to obtain the off-diagonal bound. The approach differs from previous treatments as it uses only the Dirichlet form and no estimates on the resolvent. The bounds obtained are expressed in terms of an intrinsic metric on the fractal.     

A stochastic partial differential equation model for the pricing of mortgage-backed securities

We develop a dynamic structural model for the wealth of individual mortgagors in a mortgage pool. We model the process of default and prepayment and, by taking a limit as the pool size goes to infinity, derive a stochastic partial differential equation (SPDE) which can be used to describe the evolution of the loss process from the pool. We prove existence and uniqueness of solutions to this SPDE and show how our model is able to capture, in a flexible way, the prices of credit risky tranches of mortgage-backed securities under different market conditions.     

Reversed-phase liquid chromatography of immunoglobulin G molecules and their fragments with the diphenyl column

A diphenyl column was able to resolve two closely related monoclonal IgG2 molecules, while a C8 column failed to separate these IgGs under identical chromatographic conditions. The diphenyl column also showed a better separation of a mixture of two light and two heavy chains than the C8 column. The influence of amino acid side chains from protein sequences in binding to the diphenyl and C8 stationary phases was studied by using a set of synthetic peptides with the sequence GXXLLLKK, where X represents substitution with all of the 20 amino acids. Peptides containing aromatic amino acids showed a greater binding on the diphenyl column than on the C8 column. This increase in retention was attributed to pi-pi interactions between the aromatic amino acid side chains and the diphenyl ligand. Based on the retention of peptides on the diphenyl column, new retention coefficients were assigned for the separation of proteins. A good correlation was observed between the sum of retention coefficients (SigmaRc) for IgGs and their retention time on the diphenyl column. On-column hydrogen-deuterium exchange showed that the diphenyl column had a larger surface of interaction with protein than the C8 column. pi-pi interactions and the large contact surface resulted in improved resolution of IgGs and their fragments on the diphenyl column.     

Poissonian Behavior of Ising Spin Systems in an External Field

We apply the Stein–Chen method for Poisson approximation to spin-half Ising-type models in positive external field which satisfy the FKG inequality. In particular, we show that, provided the density of minus spins is low and can be expanded as a convergent power series in the activity (fugacity) variable, the distribution of minus spins is approximately Poisson. The error of the approximation is inversely proportional to the number of lattice sites (we obtain upper and lower bounds on the total variation distance between the exact distribution and its Poisson approximation). We illustrate these results by application to specific models, including the mean-field and nearest neighbor ferromagnetic Ising models.     

Growth arrest-specific gene 6 expression in proliferating rabbit vascular smooth muscle cells in vitro and in vivo

Proliferation and migration of vascular smooth muscle cells (VSMCs) are involved in the processes of atherosclerosis and restenosis. The protein product of the growth arrest-specific gene 6 (Gas-6) has recently been identified as a ligand for the Axl/Rse/Mer tyrosine kinase receptor family, which may be involved in proliferation and migration of VSMCs. Here we show that Gas-6 gene expression is increased in proliferating VSMCs in tissue culture (2.5-fold increase by Northern blot) and following neointimal proliferation in a rabbit balloon-injury model (3-fold increase by Western blot). Neither platelet-derived growth factor (PDGF) nor thrombin stimulate the expression of Gas-6 in cultured VSMCs despite the ability of the PDGF, but not thrombin, to stimulate proliferation in growth-arrested cells. These data suggest a role for the Gas-6 regulatory system in VSMC proliferation, which may be a target for therapeutic interventions in the atherosclerotic process and restenosis after angioplasty.     

The determination of selenium by atomic absorption spectrophotometry

The problems involved in the determination of selenium by atomic absorption spectrophotometry are discussed. A practical method is described for which the sensitivity is approximately 1 p.p.m. Such concentrations can be determined in organic samples, but with mineral samples the preliminary treatment renders the procedure unsuitable for concentrations lower than 50 p.p.m. in a sulphide ore.