Computing the Fredholm index of Toeplitz operators with continuous symbols

We show how to compute the Fredholm index of a Toeplitz operator with a continuous symbol constructed from any subnormal operator with compact self-commutator. We also show that the essential spectral pictures of such Toeplitz operators can be prescribed arbitrarily.

     

Dynamics and stability of a new class of periodic solutions of the optical parametric oscillator

The stability and dynamics of a new class of periodic solutions is investigated when a degenerate optical parametric oscillator system is forced by an external pumping field with a periodic spatial profile modeled by Jacobi elliptic functions. Both sinusoidal behavior as well as localized hyperbolic (front and pulse) behavior can be considered in this model. The stability and bifurcation behaviors of these transverse electromagnetic structures are studied numerically. The periodic solutions are shown to be stabilized by the nonlinear parametric interaction between the pump and signal fields interacting with the cavity diffraction, attenuation, and periodic external pumping. Specifically, sinusoidal solutions result in robust and stable configurations while well-separated and more localized field structures often undergo bifurcation to new steady-state solutions having the same period as the external forcing. Extensive numerical simulations and studies of the solutions are provided.     

Characterization of the interactions between synthetic nematic LCs and model cell membranes

Differential scanning calorimetry (DSC) was used to characterize interactions of synthetic LCs, 4-pentyl-4'-cyanobiphenyl (5CB) and TL205 (a mixture of cyclohexane-fluorinated biphenyls and fluorinated terphenyls) with simple mimics of cell membranes. The investigation was motivated by reports that living cells can be placed into contact with TL205 without apparent toxicity, whereas contact of cells with 5CB leads to cell death. The tendency was examined for 5CB and TL205 to spontaneously partition into and influence the organization for model cell membranes composed of phospholipids. Upon contact of an aqueous dispersion of DPPC liposomes with neat LC for 4 h, 5CB partitioned into the liposomes at a weight ratio of 5:1 DPPC:5CB, whereas TL205 partitioned at a ratio of 310:1 DPPC:TL205. DSC endotherms indicated that the 5CB spontaneously partitioned into the liposomes was far more perturbing than TL205. DSC endotherms of DPPC bilayers containing the same concentration of either 5CB or TL205 also revealed 5CB to be more perturbing than TL205. The effect of up to 7.8 wt % of TL205 was small, resulting in a shift in the melting transition from 41.4°C to 40.1°C and a minor change in peak width, indicating only minor effects on the organization of the bilayer. These effects are similar to those caused by cholesterol in DPPC bilayers. In contrast, 5CB shifted the DPPC melting transition from 41.4°C to ∼36°C and increased the width of the transition peak by a factor of ten, indicating a destabilization of the ordered phase in the bilayer and a disruption of the cooperative nature of the gel-to-LC transition of the phospholipid bilayer. Taken together, the results demonstrate that 5CB and TL205 differ significantly in their interactions with model cell membranes, which suggests one possible origin of their different toxicities toward cells.     

An M/M/1 retrial queue with unreliable server

We analyze an unreliable M/M/1 retrial queue with infinite-capacity orbit and normal queue. Retrial customers do not rejoin the normal queue but repeatedly attempt to access the server at i.i.d. intervals until it is found functioning and idle. We provide stability conditions as well as several stochastic decomposability results.     

Probing the C?H⋅⋅⋅π Weak Hydrogen Bond in Anesthetic Binding: The Sevoflurane–Benzene Cluster

Cooperativity between weak hydrogen bonds can be revealed in molecular clusters isolated in the gas phase. Here we examine the structure, internal dynamics, and origin of the weak intermolecular forces between sevoflurane and a benzene molecule, using multi‐isotopic broadband rotational spectra. This heterodimer is held together by a primary C H⋅⋅⋅π hydrogen bond, assisted by multiple weak C H⋅⋅⋅F interactions. The multiple nonbonding forces hinder the internal rotation of benzene around the isopropyl C H bond in sevoflurane, producing detectable quantum tunneling effects in the rotational spectrum.     

Evaluation of Baylis–Hillman Routes to 3-(Aminomethyl)coumarin Derivatives

The relative merits of two different Baylis–Hillman approaches toward the preparation of coumarin derivatives, containing peptide-like side chains, have been explored. In one approach, use of methyl acrylate as the activated alkene requires a protecting group strategy, an approach that is not necessary when using tert-butyl acrylate.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

Mesostructure from Hydration Gradients in Demosponge Biosilica

Organisms of the phylum Porifera, that is, sponges, utilize enzymatic hydrolysis to concatenate bioavailable inorganic silicon to produce lightweight, strong, and often flexible skeletal elements called spicules. In their optical transparency, these remarkable biomaterials resemble fused silica, despite having been formed under ambient marine biological conditions. Although previous studies have elucidated the chemical mechanisms of spicule formation and revealed the extensive hydration of these glasses, their precise composition and local and medium‐range structures had not been determined. We have employed a combination of compositional analysis, ¹H and ²⁹Si solid‐state nuclear magnetic resonance spectroscopy, and synchrotron X‐ray total scattering to characterize spicule‐derived silica produced by the demosponge Tethya aurantia. These studies indicate that the materials are highly hydrated, but in an inhomogeneous manner. The spicule‐derived silica is, on average, perfectly dense for the given extent of hydration and regions of fully condensed and unstrained Si?O networks persist throughout each monolithic spicule. To accommodate chemical strain and defects, the extensive hydration is concentrated in distinct regions that give rise to mesostructural features. The chemistry responsible for producing spicule silica resembles hydrolytic sol‐gel processing, which offers exceptional control over the precise local atomic arrangement of materials. However, the specific processing involved in forming the sponge spicule silica further results in regions of fully condensed silica coexisting with regions of incomplete condensation. This mesostructure suggests a mechanism for atomistic defect tolerance and strain relief that may account for the unusual mechanical properties of the biogenic spicules.