Weak* Hypercyclicity and Supercyclicity of Shifts on ℓ∞

We study hypercyclicity and supercyclicity of weighted shifts on ℓ^∞, with respect to the weak * topology. We show that there exist bilateral shifts that are weak * hypercyclic but fail to be weak * sequentially hypercyclic. In the unilateral case, a shift T is weak * hypercyclic if and only if it is weak * sequentially hypercyclic, and this is equivalent to T being either norm, weak, or weak-sequentially hypercyclic on c₀ or ℓ^p (1 ≤ p < ∞). We also show that the set of weak * hypercyclic vectors of any unilateral or bilateral shift on ℓ^∞ is norm nowhere dense. Finally, we show that ℓ^∞ supports an isometry that is weak * sequentially supercyclic.     

Implications upon theory discrimination of an accurate measurement of the time rate of change of the gravitational “constant” G and other cosmological parameters

A substantial improvement in the accuracy of ˙ G tests (The dot denotes the time derivative.) would make it realistic to speak in terms of a measurement of ˙G , rather than merely a smaller upper bound on | ˙G|. We show that the accuracy Δ | ˙G/G|≈? 10^‐14 yr^‐1 may be sufficient, given the accuracy of other cosmological parameters, to observe effects predicted by higher dimensions theories and, hence, to discriminate among different models. The ˙G design goal for the SEE (Satellite Energy Exchange) mission is Δ (˙G/G) ≈? 10^‐14 yr^‐1.     

Semiclassical mechanics of rotons

The roton elementary excitations in superfluid liquid ⁴He have an unusual dispersion curve. The energy is an approximately quadratic function of (p - p₀), the difference between the magnitude of the momentum p and a characteristic value p₀. As a result, while for p > p₀ a roton has its (group) velocity parallel to its momentum, when p < p₀ the velocity and momentum are antiparallel. When p = p₀, the roton has non-zero momentum but zero velocity. These kinematic properties lead to unusual trajectories when rotons scatter or experience external forces. This paper examines this behaviour in the classical (ray optics) limit, where the roton wavelength is small compared with all other dimensions. Several experiments illustrate these effects. The examples are interesting in themselves, and also offer unconventional pedagogical possibilities.     

Interconversion of contact and separated ion pairs in silyl- and arylthio-substituted alkyllithium reagents

Ether-solvated contact and separated ion pairs (CIP and SIP) for two lithium reagents, tris(trimethylsilyl)methyllithium (1) and bis(3,5-bistrifluoromethylphenylthio)methyllithium (2), have been characterized and observed for the first time under conditions of slow exchange by NMR spectroscopy, and barriers to interconversion have been measured. A Saunders isotope perturbation experiment was used to support identification of the CIP and SIP species for 2.     

Lipid binding interactions of antimicrobial plant seed defence proteins: puroindoline-a and β-purothionin

The indolines and thionins are basic, amphiphilic and cysteine-rich proteins found in cereals; puroindoline-a (Pin-a) and β-purothionin (β-Pth) are members of these families in wheat (Triticum aestivum). Pin-a and β-Pth have been suggested to play a significant role in seed defence against microbial pathogens, making the interaction of these proteins with model bacterial membranes an area of potential interest. We have examined the binding of these proteins to lipid monolayers composed of 1,2-dipalmitoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (DPPG) using a combination of neutron reflectometry, Brewster angle microscopy, and infrared spectroscopy. Results showed that both Pin-a and β-Pth interact strongly with condensed phase DPPG monolayers, but the degree of penetration was different. β-Pth was shown to penetrate the lipid acyl chain region of the monolayer and remove lipids from the air/liquid interface during the adsorption process, suggesting this protein may be able to both form membrane spanning ion channels and remove membrane phospholipids in its lytic activity. Conversely, Pin-a was shown to interact mainly with the head-group region of the condensed phase DPPG monolayer and form a 33 ? thick layer below the lipid film. The differences between the interfacial structures formed by these two proteins may be related to the differing composition of the Pin-a and β-Pth hydrophobic regions.     

The effect of HMPA on the reactivity of epoxides,aziridines, and alkyl halides with organolithium reagents

A kinetic study of the effect of added HMPA cosolvent on the reaction of 2-lithio-1,3-dithiane (1), bis(phenylthio)methyllithium (2), and bis(3,5-bistrifluoromethylphenylthio)methyllithium (3) with methyloxirane (propylene oxide), N-tosyl-2-methylaziridine, and the several alkyl halides (BuCl, BuBr, BuI, allyl chloride) was carried out. Widely varied rate effects of HMPA on these SN2 substitutions were observed, ranging from >108 rate increases for 1 and butyl chloride to >103 rate decreases for 3 and methyloxirane. These reactions appear to go through separated ion pair intermediates, so a key effect is the ease of ion pair separation of the lithium reagent (3 > 2 > 1). Because 3 is already almost fully separated in THF, HMPA has no effect on the rate of halide substitution, but a large reduction is observed with the epoxide as substrate, a consequence of strong lithium assistance to the ring opening which is suppressed when excess HMPA is present. When ion pair separation is difficult (1), modest rate increases (104) are seen for epoxide opening, but very large increases are seen for aziridine (106) and alkyl halide reactions (108), for which lithium assistance is much less important. Reagent 2 shows more complicated behavior in reaction with the epoxide: 1-2 equiv of HMPA causes a small rate increase, while larger amounts cause a large rate decrease. Here the rate-accelerating effects of SIP formation are more nearly balanced with the rate-retarding effects of suppression of lithium catalysis.     

Dynamic covalent chemistry

Dynamic covalent chemistry relates to chemical reactions carried out reversibly under conditions of equilibrium control. The reversible nature of the reactions introduces the prospects of "error checking" and "proof-reading" into synthetic processes where dynamic covalent chemistry operates. Since the formation of products occurs under thermodynamic control, product distributions depend only on the relative stabilities of the final products. In kinetically controlled reactions, however, it is the free energy differences between the transition states leading to the products that determines their relative proportions. Supramolecular chemistry has had a huge impact on synthesis at two levels: one is noncovalent synthesis, or strict self-assembly, and the other is supramolecular assistance to molecular synthesis, also referred to as self-assembly followed by covalent modification. Noncovalent synthesis has given us access to finite supermolecules and infinite supramolecular arrays. Supramolecular assistance to covalent synthesis has been exploited in the construction of more-complex systems, such as interlocked molecular compounds (for example, catenanes and rotaxanes) as well as container molecules (molecular capsules). The appealing prospect of also synthesizing these types of compounds with complex molecular architectures using reversible covalent bond forming chemistry has led to the development of dynamic covalent chemistry. Historically, dynamic covalent chemistry has played a central role in the development of conformational analysis by opening up the possibility to be able to equilibrate configurational isomers, sometimes with base (for example, esters) and sometimes with acid (for example, acetals). These stereochemical "balancing acts" revealed another major advantage that dynamic covalent chemistry offers the chemist, which is not so easily accessible in the kinetically controlled regime: the ability to re-adjust the product distribution of a reaction, even once the initial products have been formed, by changing the reaction's environment (for example, concentration, temperature, presence or absence of a template). This highly transparent, yet tremendously subtle, characteristic of dynamic covalent chemistry has led to key discoveries in polymer chemistry. In this review, some recent examples where dynamic covalent chemistry has been demonstrated are shown to emphasise the basic concepts of this area of science.