Solution and X-ray structure of triethylsilylmethyl-substituted tropylium cation

The beta-silyl tropylium cation 9 has been successfully generated in the presence of the noncoordinating counterion tetrakis(pentafluorophenyl)borate in benzene and toluene. The (13)C and (29)Si NMR spectra of 9 demonstrate that the beta-silicon substituent interacts strongly with the aromatic pi-system of the cation by hyperconjugation. The crystal structure of 9 shows structural effects consistent with this interaction. [structure--see text]     

Surjectivity for Hamiltonian loop group spaces

Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,), and assume that the moment map :XL ^* is proper. We consider the function ||²:X, and use a version of Morse theory to show that the inclusion map j:^-1(0)X induces a surjection j ^*:H _G ^*(X)H _G ^*(^-1(0)), in analogy with Kirwans surjectivity theorem in the finite-dimensional case. We also prove a version of this surjectivity theorem for quasi-Hamiltonian G-spaces.     

Admissible control and observation operators for Volterra integral equations

The admissibility of observation operators and control operators for linear Volterra systems is studied by means of the theory of composition operators on Hardy spaces.Under certain assumptions it is shown to be equivalent to admissibility for the classical Cauchy problem. A duality between control and observation operators is also established,extending known results for the Cauchy problem,which is a special case.     

A biophysical model of an inner hair cell

Whole-cell patch-clamp recordings on isolated inner hair cells (IHCs) of guinea pig cochleae have revealed the presence of voltage-gated potassium channels. A biophysical model of an IHC is presented that indicates activation of slow voltage-gated potassium channels may lead to receptor potentials whose dc component decreases during the stimulus, and membrane potential hyperpolarizes when the stimulus is turned off. Both the decreasing dc and the hyperpolarization are, respectively, consistent with rapid adaptation and suppression of spontaneous rate in the auditory nerve. Receptor potentials recorded in vivo do not show these features, and when a nonspecific leak is included in the model to simulate microelectrode impalement, the model's receptor potentials become similar to those in vivo. The nonspecific leak creates an electrical shunt that masks slow channel activity and allows the cell to depolarize. Both the decreasing dc and the hyperpolarization are sensitive to the resting potential. Because the reported resting potentials in vivo and in vitro differ greatly, the model is used to investigate homeostatic mechanisms responsible for the resting potential. It is found that the voltage-gated potassium channels have the greatest influence on the resting potential, but that the standing transducer current may be sufficient to eliminate the decreasing dc and after-stimulus hyperpolarization.     

Structure and function of enzymes adsorbed onto single-walled carbon nanotubes

We have examined the structure and function of two enzymes, alpha-chymotrypsin (CT) and soybean peroxidase (SBP), adsorbed onto single-walled carbon nanotubes (SWNTs). SBP retained up to 30% of its native activity upon adsorption, while the adsorbed CT retained only 1% of its native activity. Analysis of the secondary structure of the proteins via FT-IR spectroscopy revealed that both enzymes undergo structural changes upon adsorption, with substantial secondary structural perturbation observed for CT. Consistent with these results, AFM images of the adsorbed enzymes indicated that SBP retains its native three-dimensional shape while CT appears to unfold on the SWNT surface. This study represents the first in depth investigation of protein structure and function on carbon nanotubes, which is critical in designing optimal carbon nanotube-protein conjugates.     

Self-assembly of chiral DNA nanotubes

A system of DNA "tiles" that is designed to assemble to form two-dimensional arrays is observed to form narrow ribbons several micrometers in length. The uniform width of the ribbons and lack of frayed edges lead us to propose that they are arrays that have curled and closed on themselves to form tubes. This proposal is confirmed by the observation of tubes with helical order.     

Are there phase transitions in information space?

The interplay between two basic quantities--quantum communication and information--is investigated. Quantum communication is an important resource for quantum states shared by two parties and is directly related to entanglement. Recently, the amount of local information that can be drawn from a state has been shown to be closely related to the nonlocal properties of the state. Here we consider both formation and extraction processes, and analyze informational resources as a function of quantum communication. The resulting diagrams in information space allow us to observe phaselike transitions when correlations become classical.     

Neutrinos of energy approximately 10(16) eV from gamma-ray bursts in pulsar wind bubbles

The supranova model for gamma-ray bursts (GRBs) is becoming increasingly more popular. In this scenario the GRB occurs weeks to years after a supernova explosion, and is located inside a pulsar wind bubble (PWB). Protons accelerated in the internal shocks that emit the GRB may interact with the external PWB photons producing pions which decay into approximately 10(16) eV neutrinos. A km(2) neutrino detector would observe several events per year correlated with the GRBs.