Influence of the counterion size on swelling and collapse of polyelectrolyte gel

A theory that predicts the effect of the counterion size on the swelling and collapse of a weakly charged polyelectrolyte gel was developed. In addition to excluded-volume interactions between monomer units of the gel, the theory involves the counterion-monomer unit and counterion-counterion interactions in terms of the virial approximation. The character of interactions between different units in the system varies from repulsion to attraction depending on the type of solvent, counterion, and dielectric permittivity of the solvent. For solvents with a low permittivity, the effect of condensation of counterions resulting in the formation of ion pairs is taken into account.     

Thermal and dielectric behaviors of poly(vinylidene fluoride-trifluoroethylene) copolymers at the curie transition

The thermal and dielectric behaviors of poly(vinylidene fluoride-trifluoroethylene) copolymers near the ferroelectric-to-paraelectric phase transition are investigated for samples with 20, 25, 30, and 40 mol% trifluoroethylene (TrFE). The data suggest that the transition becomes continuous for a particular composition near 50 mol% TrFE. Experimental data are sensitive to thermal history (kinetics of crystallization, and kinetics and cycling over the structural transition). It is found that several anomalies are present at the structural change, and in particular the 30 mol% TrFE sample shows the most marked anomalies. These phenomena can be attributed to defects, but another possibility would be the existence of an intemediate supplementary phase. Both hypotheses are discussed.     

Elektrische Charakterisierung von Hochfrequenz-Niederdruck-Gasentladungen

In recent years there has emerged significant interest in low pressure radio frequency (rf) glow discharges which are used widely particulary in IC fabrication. Various parameters of the rf glow discharge have been found to be useful for its electrical characterization; however, there is no uniformity and agreement. Extensive experimental investigations on various discharge systems have shown, that the self-bias on the rf driven electrode, the complex conductivity and the breakdown characteristic are preferable parameters of rf discharges. Advantageously the self-bias and the complex conductivity should be presented in dependence on the pressure and the applied rf voltage. The discharge current cannot be measured quite accurately due to currents via leaky capacitors and the deviations from a sinusoidal form of the current due to nonlinearities.     

Euler configurations and quasi-polynomial systems

Consider the problem of three point vortices (also called Helmholtz’ vortices) on a plane, with arbitrarily given vorticities. The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria. This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an interaction proportional to r ^b, for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = −2 of this last statement is the well-known theorem due to Euler: in the Newtonian 3-body problem, for any choice of the 3 masses, there are 3 Euler configurations (also known as the 3 Euler points). These small upper bounds strengthen the belief of Kushnirenko and Khovanskii [18]: real varieties defined by simple systems should have a simple topology. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.     

Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc.     

Developing professional judgement with the aid of a ‘low-profile’ group support system

This paper reports positive results from an application of one type of group support system (GSS) to a training application. Reviews of the findings of other trials of GSS have been mixed, and inconclusive. We describe the results of a series of seven training sessions in a field-based application of group process support. The subjects were professionals working in various agencies concerned with the welfare of older people. A ‘low-profile’ type of group support system, based on wireless handsets, was used. This design enabled responses from each participant to be input and displayed anonymously. Each session was aimed at stimulating a dialogue focused on the reasons for differences of judgement, as displayed on a single projected feedback screen. Changes of individual judgements were recorded for subsequent analysis and comparison with already known ‘expert judgements’. Frequent changes of judgement were recorded. A significant proportion of these were related to an improvement, which could not be explained as simply the result of conforming behaviour. We propose that the mode of operation and design of a ‘low-profile’ GSS have the potential to create a learning environment by reducing personal anxieties while encouraging group-based learning with focussed conversation. We conclude that this type of GSS design is particularly suited to ‘selective’-type tasks in groups.     

On upper and lower D*-supercontinuous multifunctions

We define a multifunction F: X ⇝ Y to be upper (lower) D*-supercontinuous if F ⁺(V) (F ⁻(V)) is d*-open in X for every open set V of Y. We obtain some characterizations and several properties concerning upper (lower) D*-supercontinuous multifunctions.      

Error estimation,adaptivity and data transfer in enriched plasticity continua to analysis of shear band localization

In this paper, an adaptive FE analysis is presented based on error estimation, adaptive mesh refinement and data transfer for enriched plasticity continua in the modelling of strain localization. As the classical continuum models suffer from pathological mesh-dependence in the strain softening models, the governing equations are regularized by adding rotational degrees-of-freedom to the conventional degrees-of-freedom. Adaptive strategy using element elongation is applied to compute the distribution of required element size using the estimated error distribution. Once a new mesh is generated, state variables and history-dependent variables are mapped from the old finite element mesh to the new one. In order to transfer the history-dependent variables from the old to new mesh, the values of internal variables available at Gauss point are first projected at nodes of old mesh, then the values of the old nodes are transferred to the nodes of new mesh and finally, the values at Gauss points of new elements are determined with respect to nodal values of the new mesh. Finally, the efficiency of the proposed model and computational algorithms is demonstrated by several numerical examples.     

A dynamic scorecard for monitoring baseline performance with application to tracking a mortgage portfolio

A principled technique for monitoring the performance of a consumer credit scorecard through time is derived from Kalman filtering. Standard approaches sporadically compare certain characteristics of the new applicants with those predicted from the scorecard. The new approach systematically updates the scorecard combining new applicant information with the previous best estimate. The dynamically updated scorecard is tracked through time and compared to limits calculated by sequential simulation from the baseline scorecard. The observation equation of the Kalman filter is tailored to take the results of fitting local scorecards by logistic regression to batches of new clients that arrive in the current time interval. The states in the Kalman filter represent the true or underlying score for each attribute in the card: the parameters of the logistic regression. Their progress in time is modelled by a random walk and the filter provides the best estimate of the scores using past and present information. We illustrate the technique using a commercial mortgage portfolio and the results indicate significant emerging deficiencies in the baseline scorecard.     

Eigenvalue ratios of vibrating strings

Summary New results for the eigenvalue ratios of vibrating strings are presented partially in connection with previous results concerning Schr?dinger operators.