The synthesis and mesogenic properties of side chain polymethacrylates with terminal branched groups

The synthesis is described of six polymethacrylates attached through oxytetramethylene and oxyhexamethylene spacers to an azobenzene moiety consisting of branched terminal iso -butoxy, iso -amyloxy and n -amyloxy groups. The monomers show a nematic mesophase while their polymers show an additional higher order smectic C phase. The effects of the terminal branched alkoxy group and the spacers on mesomorphic properties are discussed. The phase characteristics, thermal stabilities and molecular masses of the polymers were investigated by DSC, XRD, TGA and GPC. The polymers were also characterized by UV-vis, IR and NMR spectroscopy.     

Exploiting and controlling gel-to-crystal transitions in multicomponent supramolecular gels

Multicomponent supramolecular gels provide opportunities to form materials that are not accessible when using the single components alone. Different scenarios are possible when mixing multiple components, from complete co-assembly (mixing of the components within the self-assembled structures formed) to complete self-sorting such that each structure contains only one of the components. Most examples of multicomponent gels that currently exist form stable gels. Here, we show that this can be used to control the mechanical properties of the gels, but what is probably most exciting is that we show that we can use a magnetic field to control the shape of the crystals. The gelling component aligns in a magnetic field and so results in anisotropic crystals being formed.

Multicomponent supramolecular gels provide opportunities to form materials that are not accessible when using the single components alone.     

Group homomorphisms inducing isomorphisms in cohomology

In this article, we call a ring R right generalized semiregular if for any a ∈ R there exist two left ideals P, L of R such that lr(a) = P⊕ L, where P ? Ra and Ra ∩ L is small in R. The class of generalized semiregular rings contains all semiregular rings and all AP-injective rings. Some properties of these rings are studied and some results about semiregular rings and AP-injective rings are extended. In addition, we call a ring R semi-π-regular if for any a ∈ R there exist a positive integer n and e ² = e ∈ a ⁿ R such that (1 ? e)a ⁿ  ∈ J(R), the Jacobson radical of R. It is shown that a ring R is semi-π-regular if and only if R/J(R) is π-regular and idempotents can be lifted modulo J(R).     

Okounkov bodies and toric degenerations

Let $\varDelta $ be the Okounkov body of a divisor $D$ on a projective variety $X$ . We describe a geometric criterion for $\varDelta $ to be a lattice polytope, and show that in this situation $X$ admits a flat degeneration to the corresponding toric variety. This degeneration is functorial in an appropriate sense.     

Role of Context in Risk-Based Reasoning

In this article we report the influence of contextual factors on mathematics and science teachers' reasoning in risk-based decision-making. We examine previous research that presents judgments of risk as being subjectively influenced by contextual factors and other research that explores the role of context in mathematical problem-solving. Our own approach has been to develop carefully designed software tools that support the user to empathize with a hypothetical person, Deborah, who suffers from a medical condition. The tools were used by a group of teachers who were asked to help Deborah decide whether to have an operation that could cure the condition but which carries particular risks. In order to make this decision, the teachers were required to model the risks of the operation and also the lifestyle decisions that Deborah might make. We trace the teachers' efforts to coordinate judgments of likelihood and impact. The data emphasize the sensitivity of reasoning to matters of context; we set out in detail the various ways in which the process was affected by context.     

Arc Spaces and Equivariant Cohomology

We present a new geometric interpretation of equivariant cohomology in which one replaces a smooth, complex G-variety X by its associated arc space J _∞ X, with its induced G-action. This not only allows us to obtain geometric classes in equivariant cohomology of arbitrarily high degree, but also provides more flexibility for equivariantly deforming classes and geometrically interpreting multiplication in the equivariant cohomology ring. Under appropriate hypotheses, we obtain explicit bijections between $ \mathbb{Z} $ -bases for the equivariant cohomology rings of smooth varieties related by an equivariant, proper birational map. We also show that self-intersection classes can be represented as classes of contact loci, under certain restrictions on singularities of subvarieties. We give several applications. Motivated by the relation between self-intersection and contact loci, we define higher-order equivariant multiplicities, generalizing the equivariant multiplicities of Brion and Rossmann; these are shown to be local singularity invariants, and computed in some cases. We also present geometric $ \mathbb{Z} $ -bases for the equivariant cohomology rings of a smooth toric variety (with respect to the dense torus) and a partial flag variety (with respect to the general linear group).     

Dynamic spin-polarized resonant tunneling in magnetic tunnel junctions

Precisely engineered tunnel junctions exhibit a long sought effect that occurs when the energy of the electron is comparable to the potential energy of the tunneling barrier. The resistance of metal-insulator-metal tunnel junctions oscillates with an applied voltage when electrons that tunnel directly into the barrier's conduction band interfere upon reflection at the classical turning points: the insulator-metal interface and the dynamic point where the incident electron energy equals the potential barrier inside the insulator. A model of tunneling between free electron bands using the exact solution of the Schr?dinger equation for a trapezoidal tunnel barrier qualitatively agrees with experiment.     

Urea-Urease Reaction in Controlling Properties of Supramolecular Hydrogels: Pros and Cons

Supramolecular hydrogels are useful in many areas such as cell culturing, catalysis, sensing, tissue engineering, drug delivery, environmental remediation and optoelectronics. The gels need specific properties for each application. The properties arise from a fibrous network that forms the matrix. A common method to prepare hydrogels is to use a pH change. Most methods result in a sudden pH jump and often lead to gels that are hard to reproduce and control. The urease-urea reaction can be used to control hydrogel properties by a uniform and controlled pH increase as well as to set up pH cycles. The reaction involves hydrolysis of urea by urease and production of ammonia which increases the pH. The rate of ammonia production can be controlled which can be used to prepare gels with differing properties. Herein, we show how the urease-urea reaction can be used for the construction of next generation functional materials.     

A mild and efficient synthesis of 4-quinolones and quinolone heterocycles

The cycloacylation of aniline derivatives to 4-quinolones in the presence of Eaton's reagent is described. This high-yielding methodology is applicable to a wide variety of functionalized anilines and requires milder conditions than those traditionally employed. This cyclization protocol is used to prepare a host of heterocycles and bis-quinolones and is characterized by relatively low reaction temperature and ease of product isolation.