An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

The notion of motion: covariational reasoning and the limit concept

This paper investigates outcomes of building students’ intuitive understanding of a limit as a function's predicted value by examining introductory calculus students’ conceptions of limit both before and after instruction. Students’ responses suggest that while this approach is successful at reducing the common limit equals function value misconception of a limit, new misconceptions emerged in students’ responses. Analysis of students’ reasoning indicates a lack of covariational reasoning that coordinates changes in both x and y may be at the root of the emerging limit reached near x = c misconception. These results suggest that although dynamic interpretations of limit may be intuitive for many students, care must be taken to foster a dynamic conception that is both useful at the introductory calculus level and is in line with the formal notion of limit learned in advanced mathematics. In light of the findings, suggestions for adapting the pedagogical approach used in this study are provided.     

Proof of gridlock in a polymer model

It has been suggested that some lattice models of polymers, especially ones that incorporate more realistic excluded volume interactions extending to further neighbors, may be subject to gridlock. A model is defined to have the property of gridlock if it cannot melt at any temperature unless a density decrease is allowed. Classical theories of polymer melting are incompatible with the property of gridlock. This paper proves rigorously that a two-dimensional square-lattice model of polymer chains that have nearest-neighbor excluded volume interactions (called the X1S model) has the gridlock property. The proof uses elementary concepts from graph theory. Also, different interpretations of the X1S model are given in terms of real polymers. This leads to a discussion of a number of different classes of melting depending upon whether the intramolecular rotameric energies and the attractive intermolecular energies are antagonistic to or supportive of the melting transition.     

A general strategy for creating "inactive-conformation" abl inhibitors

Kinase inhibitors that bind to the ATP cleft can be broadly classified into two groups: those that bind exclusively to the ATP site with the kinase assuming a conformation otherwise conducive to phosphotransfer (type I), and those that exploit a hydrophobic site immediately adjacent to the ATP pocket made accessible by a conformational rearrangement of the activation loop (type II). To date, all type II inhibitors were discovered by using structure-activity-guided optimization strategies. Here, we describe a general pharmacophore model of type II inhibition that enables a rational "hybrid-design" approach whereby a 3-trifluoromethylbenzamide functionality is appended to four distinct type I scaffolds in order to convert them into their corresponding type II counterparts. We demonstrate that the designed compounds function as type II inhibitors by using biochemical and cellular kinase assays and by cocrystallography with Abl.     

On the protonated state of amidinium-like diaromatic derivatives: X-ray and UV studies

We present the crystal structures of the chloride salts of the mono-guanidinium 1 (–CH₂CH₂– linker) and the bis-isouronium 2 (–O– linker) that have been resolved by us indicating that these compounds are diprotonated in the solid state as informed by the counterions positions. To determine the pK _a values of these compounds as well as those of their analogues 3 (mono-2-aminoimidazolinium with a –CH₂CH₂– linker) and 4 (mono-guanidinium with a –O– linker), the corresponding UV–Vis titrations were carried out. Thus, in aqueous solution compounds 1, 3 and 4 were present as mono-cationic species while derivative 2 was a bis-cation.     

Analytical performance characteristics of thin and thick film amperometric microcells

The analytical performance of amperometric microcells with different electrode geometries is compared for enzyme activity measurements. The microcells were fabricated with thin film photolithography or thick film screen-printing in four different designs. The cells made with the thin film process used flexible substrate with microelectrode array or a circular, disk-shaped working electrode. The screen-printed working electrodes had semicircle or disk shape on ceramic chips. Putrescine oxidase (PUO) activity measurement was used as a model. The determination of PUO activity is important in the clinical diagnosis of premature rupture of the amniotic membrane. An electropolymerized m-phenylenediamine size-exclusion layer was used to eliminate common interferences. The size exclusion layer revealed also to be advantageous in protecting the electrodes from fouling by putrescine (enzyme substrate). The electrode fouling of bare electrodes was insignificant for screen-printed electrodes, but very severe for electroplated platinum working electrodes. The microelectrode array electrodes demonstrated smaller RSD and higher normalized sensitivities for hydrogen peroxide and PUO activity. All the other electrodes were demonstrating comparable analytical performances.     

Onsager,ice, biomembranes,dimer models and the F-model

Personal recollections give a sampling of some of Onsager's later interests in ice and biomembranes. The author's involvement in these topics led to modeling a particular biomembrane phase transition using dimer models. Recent work is described for a particularly rich dimer model which is isomorphic to the F-model in three kinds of fields (direct, staggered, and quarter). New results for the full three-dimensional phase diagram show (1) how the anomalous OK multicritical point is destroyed by a direct field, and (2) how a new line of critical points must be added to the phase diagram in direct and staggered fields obtained previously by Baxter, due to diverging susceptibilities in the quarter field.