Dynamical forcing of circular groups

In this paper we introduce and study the notion of dynamical forcing. Basically, we develop a toolkit of techniques to produce finitely presented groups which can only act on the circle with certain prescribed dynamical properties.

As an application, we show that the set consisting of rotation numbers which can be forced by finitely presented groups is an infinitely generated -module, containing countably infinitely many algebraically independent transcendental numbers. Here a rotation number is forced by a pair , where is a finitely presented group and is some element, if the set of rotation numbers of as varies over is precisely the set .

We show that the set of subsets of which are of the form

where varies over countable groups, are exactly the set of closed subsets which contain and are invariant under . Moreover, we show that every such subset can be approximated from above by for finitely presented .

As another application, we construct a finitely generated group which acts faithfully on the circle, but which does not admit any faithful action, thus answering in the negative a question of John Franks.

     

Promoting essential laminations

We show that a co-orientable taut foliation of a closed, orientable, algebraically atoroidal 3-manifold is either the weak stable foliation of an Anosov flow, or else there are a pair of very full genuine laminations transverse to the foliation.     

The admissibility of M11 over number fields

A group G is $\mathbb{Q}$-admissible if there exists a G-crossed product division algebra over $\mathbb{Q}$. The $\mathbb{Q}$-admissibility conjecture asserts that every group with metacyclic Sylow subgroups is $\mathbb{Q}$-admissible. We prove that the Mathieu group $M_{11}$ is $\mathbb{Q}$-admissible, in contrast to any other sporadic group.     

High-resolution STM imaging of novel poly(G)-poly(C) DNA molecules

High-resolution scanning tunneling microscopy (STM) imaging of single double-stranded poly(G)-poly(C) DNA molecules, made by a novel synthesis method, shows the molecules morphology. The STM images reveal a periodic structure of approximately 4 nm, seen as repeating "bulbs" along the molecules. These "bulbs" are associated with the molecule helix (the major grooves). "Nicks", two per 100 nm on the average, are observed along the DNA as well. The STM measurements were supported by a morphological statistics of the DNA molecule groove length and apparent height relative to the surface.     

A Characterization of the degree sequences of 2‐trees

A graph G is a 2‐tree if G = K₃, or G has a vertex v of degree 2, whose neighbors are adjacent, and G/ v is a 2‐ tree. A characterization of the degree sequences of 2‐trees is given. This characterization yields a linear‐time algorithm for recognizing and realizing degree sequences of 2‐trees. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:191‐209, 2008     

Synthesis of the 7-deaza and 5-aza-7-deaza purine analogs of the antiherpes agent 9-[(1,3-dihydroxy-2-propoxy)methyl]guanine (DHPG)

Synthesis of 2-amino-7-[(1,3-dihydroxy-2-propoxy)methyl]pyrrolo[2,3-d]pyrimidin-4-one (3) a 7-deaza purine analogue and 2-amino-8-[(1,3-dihydroxy-2-propoxy)methyl]imidazo[1,2-a]-s-triazin-4-one (4) a 5-aza-7-deaza purine analogue of DHPG (2) are reported.     

Immunofiltration as sample cleanup for the immunochemical detection of beta-agonists in urine

Despite the ban of the European Union on use of drugs to improve animal growth, occasionally beta-agonist drugs are still found in samples from cattle. Over time, the specified limits for the detection of these illegal drugs have been lowered. To improve the immunochemical screening of urine samples to detect lower levels of several beta-agonists, immunofiltration (IF) was applied for sample cleanup in combination with a beta-agonist-ELISA. In the applied IF format, free (non-immobilised) anti-salbutamol polyclonal antibodies were mixed with the urine sample in an ultra-filtration device (cut off 30 kDa) and the sample was removed by centrifugation. The antibody bound beta-agonists were freed from the antibodies by the addition of a mixture of methanol and 0.1 M acetic acid (1:1; v/v) and centrifugation. The filtrate, containing the free beta-agonists, was evaporated to dryness and the residue dissolved in buffer, an aliquot of which was analysed with the beta-agonist ELISA. Compared with the direct beta-agonist ELISA, this IF cleanup procedure resulted in a 30-times lower limit of detection (LOD) of 0.14 ng ml(-1) (salbutamol equivalents). The anti-salbutamol antibodies recognised several beta-agonists and the combination of IF with the beta-agonist ELISA was found suitable for the detection of at least ten beta-agonists in urine with comparable LODs.     

Discontinuum between a thiolate and a thiol ligand

The effect of H-bond donation to the thiolate ligand of (eta(5)-C(5)H(5))Fe(CO)(2)SR (1) to give H-bond adducts (1 small middle dotHX) and eventually protonation to give [(eta(5)-C(5)H(5))Fe(CO)(2)(HSR)](+) (1H(+)()) has been investigated experimentally and computationally. The electronic structures of 1(R = Me), several derivatives of 1(R = Me) small middle dotHX, and 1(R = Me)H(+)() have been investigated using DFT (density functional theory) computational methods. As previously suggested, these calculations indicate the HOMO of 1 is Fedpi-Sppi antibonding and largely sulfur in character. The calculations indicate the electronic structure of 1 is not altered markedly by H-bond donation to the S center, but protonation results in a reorganization of the electronic structure of 1H(+)() and a HOMO that is largely metal in character. The reduction of Fe-S distances upon protonation of 1(R = Ph) to give 1(R = Ph)H(+)() small middle dotBF(4)()(-)() (2.282(2) and 2.258(2) A, respectively), as determined by single-crystal X-ray crystallography, also indicates diminished Fedpi-Sppi antibonding. Using the carbonyl stretching frequencies as a gauge of the donor ability of the thiolate ligand, we conclude that H-bonding has a continuous effect on the donor properties of the thiolate ligand of 1 (i.e., is a function of the pK(a) of the H-bond donor). A discontinuous effect results when the pK(b) of 1 is reached and the complex is protonated. For our study of 1, the maximal effect of H-bonding is about 30% of protonation. Because the position of acid-base equilibrium depends on the relative basicities of the thiolate ligand and the conjugate base of the H-bond donor (and the relative heats of solvation of the acids and their conjugate bases), a true continuum of effects can be anticipated only for systems that are pK-matched in their given environments. Thus, when the conjugate base of the H-bond donor is a stronger base than the thiolate ligand (as in the present case), H-bond donation has a relatively small effect, but protonation triggers a large, discontinuous effect on the electronic structure of 1.     

The multiconfigurational spin tensor electron propagator method (MCSTEP): Comparison with extended Koopmans' theorem results

Summary We applied the multiconfigurational spin tensor electron propagator method (MCSTEP) for determining the lowest few (in energy) vertical ionization potentials (IPs) of HF, H₂O, NH₃, CH₄, N₂, CO, HNC, HCN, C₂H₂, H₂CO, and B₂H₆. We chose these molecules so that we could compare MCSTEP IPs with recently reported extended Koopmans' theorem (EKT) IPs on the same molecules. Using standard Dunning core-valence basis sets with relatively small complete active spaces, MCSTEP results are in very good to excellent agreement with experiment. These MCSTEP IPs are obtained using matrices no larger than 400 × 400. EKT matrices are even smaller; however, to obtain similar but generally slightly worse agreement with experiment, fairly large active spaces are required with EKT.